(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 521026, 10668] NotebookOptionsPosition[ 480745, 9447] NotebookOutlinePosition[ 487665, 9635] CellTagsIndexPosition[ 485901, 9591] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["SALVADOR 2.3 User Manual", "Title", CellChangeTimes->{ 3.399232205864999*^9, {3.405797510944893*^9, 3.405797512255454*^9}, { 3.416254366136771*^9, 3.41625436648273*^9}, {3.4298822639996967`*^9, 3.4298822651246395`*^9}}, FontSize->16], Cell["\<\ Qi Zheng Department of Epidemiology and Biostatistics School of Rural Public Health Texas A&M Health Science Center College Station, Texas 77843 qzheng@srph.tamhsc.edu September 10, 2008\ \>", "Text", CellChangeTimes->{{3.405797523332537*^9, 3.405797527237715*^9}, { 3.410363332368301*^9, 3.410363341213464*^9}, {3.410539780628064*^9, 3.41053978935591*^9}, {3.416322655178401*^9, 3.416322657974399*^9}, { 3.4298799671617565`*^9, 3.4298799730367193`*^9}, {3.4299730186654577`*^9, 3.4299730191966534`*^9}}], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell[TextData[{ "SALVADOR is a package intended as a tool for estimating mutation rates \ using data generated under the Luria-Delbruck experimental protocol (Luria \ and Delbruck 1941). The package was originally designed for use in mutation \ research, but later it also appears to be a useful tool for educational \ purposes. For the most part, this manual adheres to the notation and \ terminology used in the review article by Zheng (1999), where numerous \ important references can be found. The focus of SALVADOR is on maximum \ likelihood estimators derived under the Lea-Coulson formulation (Lea and \ Coulson 1949). This formulation has been extensively studied; among major \ contributions are those made by Koch (1982), Mandelbrot (1974), Crump and \ Hoel (1974), Stewart et al. (1990) and Ma et al. (1992). SALVADOR also \ contains estimators derived under the Haldane formulation and the Bartlett \ formulation. The Haldane formulation was explained in Sarkar (1991), and \ later was more thoroughly examined by Zheng (2007). The Bartlett formulation \ was proposed in Bartlett's discussion of the Armitage (1952) paper and was \ further elaborated in Bartlett's textbook on stochastic processes (Bartlett \ 1978). The algorithms implemented in SALVADOR for the Bartlett formulation \ are those due to Zheng (2008). New to the current version (v2.3) is a maximum \ likelihood estimator that accounts for plating efficiency under the \ Lea-Coulson formulation (Zheng 2008a). Some of the methods contained in \ SALVADOR appear outmoded, but they are of historical interest and some are \ employed by SALVADOR to generate excellent initial estimates for the maximum \ likelihood estimators. Methods for simulating experimental data are provided \ mainly for educational purposes. For reasons of computational efficiency, \ SALVADOR was written in a mixture of the ", StyleBox["Mathematica", FontSlant->"Italic"], " and the C language. Consequently, two programs must be install from \ within ", StyleBox["Mathematica ", FontSlant->"Italic"], "." }], "Text", CellChangeTimes->{{3.410363352730536*^9, 3.410363595772013*^9}, { 3.410363646560019*^9, 3.410363675967919*^9}, {3.41036372085113*^9, 3.410363725212797*^9}, {3.410363782985035*^9, 3.410363849715348*^9}, { 3.410364045986123*^9, 3.410364049553675*^9}, 3.410536746661158*^9, { 3.416337133322323*^9, 3.416337215922466*^9}, {3.4298802757066574`*^9, 3.4298803208782434`*^9}, {3.429880697012458*^9, 3.429880842390109*^9}, { 3.4298809072765813`*^9, 3.429880909932661*^9}, {3.429881166526087*^9, 3.4298811800721817`*^9}, {3.429881223132201*^9, 3.4298812825662775`*^9}, 3.429881369811252*^9, {3.429881406965454*^9, 3.4298814160431147`*^9}, { 3.429881607502061*^9, 3.429881610345666*^9}, {3.4298818671762652`*^9, 3.4298818927218323`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SetDirectory", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.405798017059188*^9, 3.405798021378516*^9}, { 3.405871805622244*^9, 3.40587181443196*^9}, {3.416253424503328*^9, 3.416253424816045*^9}, {3.4165898750653305`*^9, 3.416589878859921*^9}, { 3.430062155552023*^9, 3.43006216446367*^9}, {3.4300709953528357`*^9, 3.430071004915826*^9}}], Cell[BoxData["\<\"c:\\\\sal2-3\"\>"], "Output", CellChangeTimes->{ 3.40579802250899*^9, 3.405871820052871*^9, 3.405874616833936*^9, 3.409343829124299*^9, 3.409862315921209*^9, 3.409863387726748*^9, 3.410018717158975*^9, 3.410019376888017*^9, 3.410031004217604*^9, 3.410032300398233*^9, 3.410033662995713*^9, 3.410101494328547*^9, 3.410183881963634*^9, 3.410362740889692*^9, 3.410538046978613*^9, 3.410538823281233*^9, 3.410546255263446*^9, 3.410547076505561*^9, 3.416253434714555*^9, 3.416322812185342*^9, 3.416331575945501*^9, 3.416589906577611*^9, 3.429879058880141*^9, 3.429882922898247*^9, 3.4298902310186396`*^9, 3.429898422549802*^9, 3.429971122819233*^9, 3.429972549606863*^9, 3.4300543335325336`*^9, 3.4300611411094418`*^9, 3.4300632570599213`*^9, 3.4300644879446664`*^9, {3.4300653238968353`*^9, 3.430062190964774*^9}, 3.430071014119422*^9, 3.430071780346151*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Install", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.405798013281692*^9, 3.405798028804156*^9}, { 3.409862306528163*^9, 3.409862307957002*^9}, {3.410027553053443*^9, 3.41002755536248*^9}, {3.416253427139977*^9, 3.41625342751659*^9}}], Cell[BoxData[ RowBox[{"LinkObject", "[", RowBox[{"\<\"\\\".\\\\salvadorV2-3.sal\\\"\"\>", ",", "7", ",", "7"}], "]"}]], "Output", CellChangeTimes->{ 3.399232301367369*^9, 3.399297556223308*^9, 3.405798030178005*^9, 3.405871821272653*^9, 3.405874618043231*^9, 3.409343830297271*^9, 3.409862317082008*^9, 3.40986338888865*^9, 3.41001871831872*^9, 3.410019377999052*^9, 3.410031005409903*^9, 3.410032301508906*^9, 3.410033664111904*^9, 3.410101495527618*^9, 3.410183883080314*^9, 3.4103627420754*^9, 3.410538048176384*^9, 3.410538824400959*^9, 3.410546256431774*^9, 3.410547077659508*^9, 3.416253435879298*^9, 3.416322814156272*^9, 3.416331577558866*^9, 3.41658990668692*^9, 3.429879058989517*^9, 3.429882923147983*^9, 3.4298902311279306`*^9, 3.429898422659148*^9, 3.4299711230852947`*^9, 3.4299725497318497`*^9, 3.4300543338453417`*^9, 3.4300611412188206`*^9, 3.4300632571849008`*^9, 3.4300644880696573`*^9, {3.4300653240218663`*^9, 3.430062192110913*^9}, 3.4300710142131767`*^9, 3.430071780455531*^9}] }, Open ]], Cell[BoxData[ RowBox[{"<<", "salvadorV2-3.m"}]], "Input", CellChangeTimes->{ 3.399232178216777*^9, {3.405798005228347*^9, 3.40579801031762*^9}, { 3.410027557629625*^9, 3.410027559847376*^9}, {3.416253430123234*^9, 3.416253430438548*^9}}], Cell["\<\ (To avoid distraction by a plethora of warning messages against use of \ similar variable names, e.g., var1 and var2, we suppress such warning \ messages.)\ \>", "Text", CellChangeTimes->{{3.429881907549198*^9, 3.429881930751135*^9}, 3.429882008434657*^9}], Cell["Off[General::spell1]", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Simulation", "Section", FontSize->16], Cell[TextData[{ "To simulate under the Lea-Coulson formulation one needs to specify five \ basic parameters: 1) a mutation rate (per cell per unit time) \[Mu]; 2) a \ cellular birth rate for nonmutants ", Cell[BoxData[ FormBox[ SubscriptBox["\[Beta]", "1"], TraditionalForm]]], "; 3) a cellular birth rate for mutants ", Cell[BoxData[ FormBox[ SubscriptBox["\[Beta]", "2"], TraditionalForm]]], "; 4) an initial population size ", Cell[BoxData[ FormBox[ SubscriptBox["N", "0"], TraditionalForm]]], "; and 5) a final population size ", Cell[BoxData[ FormBox[ SubscriptBox["N", "T"], TraditionalForm]]], ". It is strongly recommended that, before running a simulation, you check \ the parameters of interest by computing the mean and variance of the number \ of mutants, for unrealistic parameters can lead to very time-consuming \ computational tasks and useless results. We now use the following five \ parameters to simulate a fluctuation experiment ." }], "Text", CellChangeTimes->{{3.410364190902192*^9, 3.410364235690321*^9}, { 3.429898002336316*^9, 3.429898035529029*^9}, 3.4298987397392883`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"mu", "=", RowBox[{"10", "^", RowBox[{"-", "8"}]}]}], ";", RowBox[{"b1", "=", "1.2"}], ";", RowBox[{"b2", "=", "1.1"}], ";", RowBox[{"N0", "=", "100"}], ";", RowBox[{"Nt", "=", RowBox[{"2.4", "*", RowBox[{"10", "^", "8"}]}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "MeanOfMutants"}]], "Input"], Cell[BoxData[ StyleBox["\<\"MeanOfMutants[\!\(\[Mu],\[Beta]\_1,\[Beta]\_2,N\_0,N\_T\)] \ \\ncomputes the mean number of mutants on each sister culture.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.43007178072117*^9}, CellTags->"Info3430053780-3362690"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MeanOfMutants", "[", RowBox[{"mu", ",", "b1", ",", "b2", ",", "N0", ",", "Nt"}], "]"}]], "Input"], Cell[BoxData["16.94451339681247`"], "Output", CellChangeTimes->{ 3.399232303345956*^9, 3.399297557748075*^9, 3.405871822395906*^9, 3.409343831914213*^9, 3.409862318191285*^9, 3.409863390817729*^9, 3.410018719703243*^9, 3.410019379406386*^9, 3.410031006947399*^9, 3.410032302827264*^9, 3.410033665789814*^9, 3.410101496897676*^9, 3.410183885331463*^9, 3.410362743458442*^9, 3.410538049474999*^9, 3.410538826224216*^9, 3.410546257785439*^9, 3.410547078981628*^9, 3.416253437156895*^9, 3.416589906968001*^9, 3.429879059286396*^9, 3.429882923819148*^9, 3.4298902315182557`*^9, 3.429898422955948*^9, 3.429971123711323*^9, 3.4299725500286922`*^9, 3.4300543344553175`*^9, 3.430061141531333*^9, 3.430063257466104*^9, 3.4300644883508873`*^9, { 3.4300653243188157`*^9, 3.430062193996168*^9}, 3.430071014478815*^9, 3.4300717807524214`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "VarOfMutants"}]], "Input"], Cell[BoxData[ StyleBox["\<\"VarOfMutants[\!\(\[Mu],\[Beta]\_1,\[Beta]\_2,N\_0,N\_T\)]\\\ ncomputes the variance of the number of mutants on each sister culture.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071780846176*^9}, CellTags->"Info3430053780-4056072"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"VarOfMutants", "[", RowBox[{"mu", ",", "b1", ",", "b2", ",", "N0", ",", "Nt"}], "]"}]], "Input"], Cell[BoxData["995576.0796417681`"], "Output", CellChangeTimes->{ 3.399232304243326*^9, 3.39929755859924*^9, 3.405871823449933*^9, 3.409343832876936*^9, 3.409862319267665*^9, 3.40986339165923*^9, 3.410018720539308*^9, 3.410019380265963*^9, 3.410031007427085*^9, 3.4100323039027*^9, 3.410033666412907*^9, 3.410101497401928*^9, 3.410183886816*^9, 3.410362744169578*^9, 3.410538049981277*^9, 3.410538827138502*^9, 3.410546258967604*^9, 3.410547079828649*^9, 3.416253437981498*^9, 3.4165899071085415`*^9, 3.429879059442648*^9, 3.4298829239752336`*^9, 3.4298902317368374`*^9, 3.429898423112158*^9, 3.4299711238678293`*^9, 3.429972550184925*^9, 3.430054334627362*^9, 3.4300611416875887`*^9, 3.430063257622328*^9, 3.430064488507127*^9, { 3.4300653244751043`*^9, 3.430062195525118*^9}, 3.4300710146194477`*^9, 3.430071780877428*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "simuMutants"}]], "Input"], Cell[BoxData[ StyleBox["\<\"simuMutants[\!\(\[Mu],\[Beta]\_1,\[Beta]\_2, \ N\_0,N\_T\)]\\nsimulates the number of mutants in a sister culture. Note \!\(\ \[Mu]\) is the\\nmutation rate per cell per unit time; \!\(\[Beta]\_1\) is \ growth rate for\\nnonmutants; \!\(\[Beta]\_2\) is growth rate of mutants; \ \!\(N\_0\) is the initial\\npopulation size; \!\(N\_T\) is the population \ size prior to plating.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717809868083`*^9}, CellTags->"Info3430053780-3497384"] }, Open ]], Cell["\<\ Now we simulate the numbers of mutants in 20 sister cultures.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"simuMutants", "[", RowBox[{"mu", ",", "b1", ",", "b2", ",", "N0", ",", "Nt"}], "]"}], ",", RowBox[{"{", "20", "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "2", ",", "4", ",", "2", ",", "26", ",", "22", ",", "1", ",", "1", ",", "44", ",", "11", ",", "31", ",", "0", ",", "0", ",", "5", ",", "1", ",", "1", ",", "4", ",", "6", ",", "1", ",", "4", ",", "33"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232305709512*^9, 3.39929755967305*^9, 3.405871824651859*^9, 3.409343834828107*^9, 3.409862320270008*^9, 3.409863392868279*^9, 3.410018721652458*^9, 3.410019381239064*^9, 3.410031008449014*^9, 3.41003230481289*^9, 3.410033667328831*^9, 3.410101498270182*^9, 3.410183888076085*^9, 3.410362745151322*^9, 3.410538050970609*^9, 3.410538828100631*^9, 3.410546260096943*^9, 3.410547081054429*^9, 3.416253439210638*^9, 3.4165899072490816`*^9, 3.429879059583275*^9, 3.4298829242874036`*^9, 3.4298902319554195`*^9, 3.4298984232839885`*^9, 3.4299711241808434`*^9, 3.4299725503411584`*^9, 3.4300543349558105`*^9, 3.430061141843845*^9, 3.430063257778552*^9, 3.4300644886633654`*^9, { 3.4300653246313934`*^9, 3.430062197277224*^9}, 3.4300710147600794`*^9, 3.4300717810180597`*^9}] }, Open ]], Cell["\<\ The above simulation is based on a continuous-time formulation, under which \ the Luria-Delbruck distribution was derived. There is an obvious \ discrete-time counterpart, which was well explained by Angerer (2001).\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "simuAngerer"}]], "Input"], Cell[BoxData[ StyleBox["\<\"simuAngerer[\!\(\[Mu]\), d] simulates the first d \ cellular\\ndivisions using a discrete-time mutation model. Each division of a \ nonmutant\\ncell can give rise to a mutant daughter cell with probability \ \!\(\[Mu]\).\\nThe evolution of the mutation process can be viewed by setting \ ShowGrowth->True,\\nand the initial population size can be set to n0 by \ setting InitialSize->n0.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717811274405`*^9}, CellTags->"Info3430053781-8974776"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"simuAngerer", "[", RowBox[{"0.3", ",", "12", ",", RowBox[{"ShowGrowth", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.41053976315957*^9, 3.410539763713222*^9}}], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "1", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["div=", 1, " wild=", 2, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717811586924`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "1"}], SequenceForm["div=", 2, " wild=", 2, " mutant=", 1], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717811586924`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "3", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "2"}], SequenceForm["div=", 3, " wild=", 2, " mutant=", 2], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717811743183`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "4", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "3", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "2"}], SequenceForm["div=", 4, " wild=", 3, " mutant=", 2], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717811899443`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "5", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "4", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "2"}], SequenceForm["div=", 5, " wild=", 4, " mutant=", 2], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717811899443`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "6", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "5", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "2"}], SequenceForm["div=", 6, " wild=", 5, " mutant=", 2], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717812055693`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "7", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "5", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "3"}], SequenceForm["div=", 7, " wild=", 5, " mutant=", 3], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717812055693`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "8", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "6", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "3"}], SequenceForm["div=", 8, " wild=", 6, " mutant=", 3], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717812211957`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "9", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "6", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "4"}], SequenceForm["div=", 9, " wild=", 6, " mutant=", 4], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.4300717812211957`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "10", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "7", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "4"}], SequenceForm["div=", 10, " wild=", 7, " mutant=", 4], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.430071781236821*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "11", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "8", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "4"}], SequenceForm["div=", 11, " wild=", 8, " mutant=", 4], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.430071781236821*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"div=\"\>", "\[InvisibleSpace]", "12", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "9", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "4"}], SequenceForm["div=", 12, " wild=", 9, " mutant=", 4], Editable->False]], "Print", CellChangeTimes->{ 3.399232307257645*^9, 3.399297560702918*^9, 3.405871826063666*^9, 3.409343836015797*^9, 3.40986232165567*^9, 3.409863394288138*^9, 3.410018722787947*^9, 3.410019382202825*^9, 3.410031009600103*^9, 3.41003230587128*^9, 3.410033668573537*^9, 3.410101499230413*^9, 3.410183889269774*^9, 3.410362746361691*^9, 3.410538052181982*^9, 3.41053882923978*^9, 3.410539764704491*^9, 3.410546260994688*^9, 3.410547082100136*^9, 3.416253440360629*^9, 3.416589907389622*^9, 3.4298790597239017`*^9, 3.429882924521531*^9, 3.429890232205228*^9, 3.4298984234245777`*^9, 3.429971124337351*^9, 3.429972550497391*^9, 3.430054335112214*^9, 3.430061142000101*^9, 3.4300632579347763`*^9, 3.430064488819605*^9, {3.4300653247876825`*^9, 3.430062198244115*^9}, 3.430071014900712*^9, 3.430071781252447*^9}] }, Open ]], Cell[BoxData["4"], "Output", CellChangeTimes->{ 3.399232308800831*^9, 3.399297562125371*^9, 3.405871827955982*^9, 3.409343837463877*^9, 3.409862323076594*^9, 3.409863395696216*^9, 3.410018724155647*^9, 3.410019383620696*^9, 3.410031010966123*^9, 3.410032307216252*^9, 3.410033670019734*^9, 3.410101500766691*^9, 3.410183890735622*^9, 3.410362747874082*^9, 3.410538053702795*^9, 3.41053883066987*^9, 3.410539764953649*^9, 3.410546262458985*^9, 3.410547083452815*^9, 3.416253441820479*^9, 3.4165899074989314`*^9, 3.4298790598332777`*^9, 3.4298829249741774`*^9, 3.429890232392584*^9, 3.4298984235495453`*^9, 3.429971124462556*^9, 3.4299725506223774`*^9, 3.4300543354406624`*^9, 3.430061142140731*^9, 3.4300632580597553`*^9, 3.4300644889445963`*^9, {3.4300653249127135`*^9, 3.430062199507126*^9}, 3.430071014994467*^9, 3.430071781252447*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Important Distributions", "Section", FontSize->16], Cell[TextData[{ "SALVADOR can compute the probability mass functions (p.m.f.) of commonly \ used distributions in fluctuation analysis: the Poisson distribution, the LD \ or Luria-Delbruck distribution, the M or Mandelbrot (1974) distribution, and \ the convolution of a Poisson and an LD distribution. The last distribution \ was popularized in fluctuation analysis by Cairns et al. (1988). Using \ pmf2cdf, you can transform a list of p.m.f. to a list of c.d.f. (cumulative \ distribution function). As a demonstration we first compute ", Cell[BoxData[ FormBox[ SubscriptBox["p", "1"], TraditionalForm]]], ", ..., ", Cell[BoxData[ FormBox[ SubscriptBox["p", "10"], TraditionalForm]]], " of a Poisson distribution having mean 10.5." }], "Text", CellChangeTimes->{{3.41036428177619*^9, 3.410364287594364*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfPoisson"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfPoisson[\!\(\[Lambda]\),k] returns a list of \ probabilities\\n\!\({p\_0,p\_1,...,p\_k}\) according to a Poisson(\!\(\ \[Lambda]\)) distribution.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071781361828*^9}, CellTags->"Info3430053781-3895988"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfPoisson", "[", RowBox[{"10.5", ",", "10"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.000027536449349747158`", ",", "0.000289132718172345`", ",", "0.0015179467704048118`", ",", "0.0053128136964168465`", ",", "0.013946135953094211`", ",", "0.02928688550149784`", ",", "0.05125204962762128`", ",", "0.07687807444143194`", ",", "0.10090247270437894`", ",", "0.1177195514884426`", ",", "0.1236055290628648`"}], "}"}]], "Output", CellChangeTimes->{ 3.39923230969356*^9, 3.399297562975132*^9, 3.40587182880989*^9, 3.409343838401014*^9, 3.409862324033239*^9, 3.409863396637605*^9, 3.410018725173783*^9, 3.410019384513457*^9, 3.410031011946999*^9, 3.410032308155405*^9, 3.410033670888264*^9, 3.410101501699226*^9, 3.4101838916879*^9, 3.410362750374117*^9, 3.410538054728688*^9, 3.41053883169454*^9, 3.410546263484814*^9, 3.41054708491639*^9, 3.416253442787386*^9, 3.4165899076550875`*^9, 3.42987905998953*^9, 3.4298829252239137`*^9, 3.429890234672082*^9, 3.429898424346216*^9, 3.4299711251198854`*^9, 3.4299725517628784`*^9, 3.4300543371611066`*^9, 3.4300611423126125`*^9, 3.4300632582316017`*^9, 3.430064489116459*^9, { 3.430065325194034*^9, 3.430062200346078*^9}, 3.4300710151350985`*^9, 3.430071781408705*^9}] }, Open ]], Cell["\<\ Now we plot the c.d.f. of a Luria-Delbruck distribution, so its upper tail \ behavior can be more easily examined.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfLD"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfLD[\!\(m,\[Phi],k\)] returns a list of \ probabilities\\n\!\({p\_0,p\_1,..., p\_k}\) according to a Luria-Delbr\!\(\ \[UDoubleDot]\)uck\\ndistribution, LD(m,\!\(\[Phi]\)). Note pmfLD[m,k] is the \ same as pmfLD[m,1,k].\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.43007178150246*^9}, CellTags->"Info3430053781-6282249"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"LDprob", "=", RowBox[{"pmfLD", "[", RowBox[{"5.7", ",", "150"}], "]"}]}], ";", " ", RowBox[{"LDprob", "[", RowBox[{"[", RowBox[{"Range", "[", "10", "]"}], "]"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.003345965457471272`", ",", "0.009536001553793125`", ",", "0.016767469398752913`", ",", "0.02355789717184977`", ",", "0.02910035040826871`", ",", "0.03312787122784504`", ",", "0.03569563178469149`", ",", "0.03701109059727024`", ",", "0.037328993778887536`", ",", "0.036895826091020184`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232310579658*^9, 3.399297564038233*^9, 3.405871829746768*^9, 3.409343839265052*^9, 3.409862325106963*^9, 3.409863397597759*^9, 3.41001872616843*^9, 3.410019385614202*^9, 3.410031012808038*^9, 3.410032309079971*^9, 3.410033671747795*^9, 3.410101502641669*^9, 3.410183892692687*^9, 3.410362751482916*^9, 3.4105380557792*^9, 3.410538832576893*^9, 3.410546264471648*^9, 3.410547085988495*^9, 3.416253443852822*^9, 3.416589907780012*^9, 3.4298790601145315`*^9, 3.4298829254424324`*^9, 3.4298902348125987`*^9, 3.4298984245805316`*^9, 3.429971125276393*^9, 3.429972552028475*^9, 3.430054337380072*^9, 3.4300611424532433`*^9, 3.4300632583878255`*^9, 3.4300644893664412`*^9, { 3.430065325475354*^9, 3.430062201180979*^9}, 3.430071015260105*^9, 3.4300717815180855`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"LDcdf", "=", RowBox[{"pmf2cdf", "[", "LDprob", "]"}]}], ";", " ", RowBox[{"LDcdf", "[", RowBox[{"[", RowBox[{"Range", "[", "10", "]"}], "]"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.003345965457471272`", ",", "0.012881967011264397`", ",", "0.02964943641001731`", ",", "0.05320733358186708`", ",", "0.08230768399013579`", ",", "0.11543555521798082`", ",", "0.1511311870026723`", ",", "0.18814227759994254`", ",", "0.22547127137883008`", ",", "0.26236709746985026`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232310838694*^9, 3.399297564262749*^9, 3.405871829997291*^9, 3.409343839527732*^9, 3.409862325349054*^9, 3.409863397736794*^9, 3.410018726465545*^9, 3.410019385837465*^9, 3.410031012943566*^9, 3.41003230930553*^9, 3.410033672002133*^9, 3.410101502895598*^9, 3.410183892952693*^9, 3.410362751736344*^9, 3.410538056035247*^9, 3.410538832828077*^9, 3.410546264701258*^9, 3.410547086218745*^9, 3.416253444101372*^9, 3.4165899077956276`*^9, 3.4298790601301565`*^9, 3.429882925520475*^9, 3.429890234828212*^9, 3.4298984246273947`*^9, 3.429971125307694*^9, 3.4299725520753446`*^9, 3.430054337458274*^9, 3.4300611424688687`*^9, 3.430063258434693*^9, 3.430064489413313*^9, { 3.4300653255378695`*^9, 3.430062201408105*^9}, 3.430071015275731*^9, 3.4300717815337114`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Range", "[", RowBox[{"0", ",", "150"}], "]"}], ",", "LDcdf"}], "}"}], "]"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.399232213251354*^9, 3.39923221391871*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw1zQlYzHkcx/Hp2JUOR5diejSVJJIti9LxQZdJxzQdM50zE0vHk0pLEZtm UW2KtIQebLUp5OgR2XXliJKzWyG1KV2U2ya7++zv+3+e//N/3s/nef2/PNla n1WKHA5n37/vf196ROoN27+uiXL8v147ntSbI2qXZrDm4I5Lz1hU8CHWKnCL dWv7Yn+c9SRs3TBSa6BZwVobdSMJDpY7L7HWwxZ5rZuT6DprLu6WFz1Q07nN 2hD6i6Vch/Y61kbgJd8JOVz7gLUJFHa/nGIzpZ61KbT93OUfPBpZmyH0de8O g6hm1uaQ9u3asz+6lfUc9Mxf/T5H0MZ6LqpPr98/ceoT1vNQ4DRWc7L6Kevv 8MKTV2Q7p4O1FaatTN0i7KW2RkVCaL5f3nPW83HOalviqF0n6++h6hmerNxM vQDXLOsFpqu7WC/Exd6SR1pD1IugH5lovD76L9Y26AowKxropLZFTJrOBnWf btaLMaDrFSv5g9oO77lK7hHcF6ztoT4+W/1QIrUD0gNz5dH3qR0xXj2ryYbX wxpIX2ikHx7DOgWorpvZaX+e9iV4eNj3qd4o7UuQW/s+2M6+l+1LcbPCqLFv I+uUpZj6NFEmraB9GYxNzGxaBmhfhuIw88ly3ku2O2G7y9u03ULWKU6wv/bh J0s57c7YWxgTse007c4YrHy1r7KNdhec6/RN7VfuY7sL4u0SFR3msOa4omgb P+uugHZX3Ou6HFXxI+1u0L/M6ZiQR7sbQhMkgcOVtC/Hy+Sgg/EttC9HnoDb Uvyedj66z1c/PqLVz3Y++tc/mR5vyZrjjnuZ44bN+bS741l8wubH4bSvQOlX vddZybSvwJN3H+V+ubR7YAr/xF7b47R7oDOPf2F5Fe2eeGXUdWVnE+2eePSi 8P6kftq90K5xP6p9jHYvNDUc2Ppp8gDbvXFRrLMu1oQ1vDHXwZi3fAHrFG9Y N5S9zXBlfdUb0zO0euxE5AUw2dyfvmoNeQG8N82eoJZIXoANbpf51jvIC/Cu dO+1rl/J+0Ajm3+MV0TeBzcOYnD4DHkf2K9OshJfIe+DL89HO4LqyAtRvPuN 8VgLeSGi8+OHlnWTF6J8lPN13jB5ISwL2zpvj5L3xduaLx8nqAwy74u4ZSMJ 32qxTvHFQZN4abkB66u+OHWroUDHjDXHD7vqfD9ZWZH3w54oCyUNO/J+qDXd 41DsTN4P9YUZagpe5P3hZXekbLqIvD9y8lM9lKXk/ZG9N/Xz6Qjy/hjmfT4+ M558ACzF+UsjN5IPwFuD0+kbU8kHgDu4YFFgBvkAwF1hRDWHvAgxuuVuWfvJ i5D26szF7iPkRZjcpHVZs4S8CIK/o8p0T5EXo/XS/vaRCvJi6J7Yll1ykbwY fUENo4uukxejozHL8/ca8oFY41RVMHSffCD2ZExS120iH4h6sWsOt518IHyF bVZKneSDID4f+by2h3wQqqZZpyUMkg+C64GtKgpvyAdh6jPu4riP5INhkVT6 +uYX8sF4UK0y8lVxiPlgfHhUzjFUYX01GDfj1JpNNVhzQlDWXW6mo8kaIdgk eFTQr0s+BNoLVw4cm0Y+BEkOScVCQ/KhqExOin5hQj4UN2JkDeGzyIeitUVh bZ0F+VD0n7e4bWhFPgxn1376QbqAfBicQ3rvZtmSD0PCG4NNpQ7kw2D+8y+9 Z5aSlyC2eVpmiQtrQwm+OdXevJNP/5MgQmhqK/NkLZEgw7nKwNSH/i/Bzrmq fa1+rI9IcGGGttIWMd2TQDm8pkYzhHWHBPJ1qvl5ErovRbFSXcPElXRfiok+ 1nWJq+m+FJeCzzTXR9J9KWa0cvm8GLovheK4O+ukcXRfiqLoowW5CXRfirMZ fKM/N9B9KY7lTrRr3Ej3ZQixnbWwazPdlyE2q0LUnUL3ZajSftjVJqf7Mngp lerf2k73ZZBfybQ5mk73ZfD4bSwlOZPuy9CpfGO2a/aQ4z8VC+8y "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0., 150.}, {0., 0.9549899916457003}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{ 3.399232311976149*^9, 3.399297564591388*^9, 3.405871830314011*^9, 3.40934383984543*^9, 3.409862325662285*^9, 3.409863398031067*^9, 3.410018726807645*^9, 3.41001938614806*^9, 3.410031013217242*^9, 3.410032309630367*^9, 3.410033672320351*^9, 3.410101503225365*^9, 3.410183893301229*^9, 3.410362752070287*^9, 3.410538056338916*^9, 3.410538833164837*^9, 3.410546265035803*^9, 3.410547086538819*^9, 3.416253444415098*^9, 3.416589907811243*^9, 3.4298790601770325`*^9, 3.4298829257546024`*^9, 3.429890234859438*^9, 3.4298984246742573`*^9, 3.429971125526804*^9, 3.429972552137838*^9, 3.43005433769288*^9, 3.43006114250012*^9, 3.4300632584971824`*^9, 3.430064489475808*^9, { 3.430065325600385*^9, 3.430062201655696*^9}, 3.430071015291357*^9, 3.4300717815649633`*^9}] }, Open ]], Cell["\<\ Now we compare an approximate form and the exact form of an M distribution.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfM"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfM[m,r,k] returns a list of \ probabilities\\n\!\({p\_0,p\_1,...,p\_k}\) according to an \!\(M(m,r,1)\) \ distribution;\\npmfM[m,\!\(r,\[Phi]\),n] returns the same list according to \ an\\n\!\(M(m,r,\[Phi])\) distribution. Note m is the mean number of \ mutations,\\n\!\(r=\[Beta]\_1/\[Beta]\_2\) is the ratio of nonmutant growth \ rate to mutant\\ngrowth rate, and \!\(\[Phi]=1-N\_0/N\_T\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717816899695`*^9}, CellTags->"Info3430053781-9194219"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfM", "[", RowBox[{"10.5", ",", "0.8", ",", "10"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.000027536449349747158`", ",", "0.00012850343029882007`", ",", "0.00034573541961349213`", ",", "0.0007047470220843672`", ",", "0.001209956176818187`", ",", "0.0018478624868760109`", ",", "0.002593033991680133`", ",", "0.0034141644273363568`", ",", "0.0042789138833278706`", ",", "0.005157198619975631`", ",", "0.006023079521618202`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232313064543*^9, 3.399297565737155*^9, 3.405871831107172*^9, 3.409343840667844*^9, 3.409862326467132*^9, 3.409863399118937*^9, 3.41001872786356*^9, 3.410019387098971*^9, 3.410031014299471*^9, 3.410032310713523*^9, 3.410033673159637*^9, 3.410101504320483*^9, 3.410183894477027*^9, 3.410362753031824*^9, 3.410538057312128*^9, 3.41053883424659*^9, 3.410546266001924*^9, 3.410547087336341*^9, 3.416253445619139*^9, 3.4165899081079397`*^9, 3.429879060442661*^9, 3.429882925957513*^9, 3.429890235031181*^9, 3.4298984249398146`*^9, 3.4299711257615643`*^9, 3.429972552356564*^9, 3.4300543379118457`*^9, 3.430061142656376*^9, 3.430063258762763*^9, 3.430064489741415*^9, { 3.4300653258504477`*^9, 3.430062202583528*^9}, 3.430071015431989*^9, 3.4300717817680984`*^9}] }, Open ]], Cell["\<\ If we assume \[Phi]=1, we can also use an algorithm devised by Koch (1982) \ (based on an algorithm of Lea and Coulson (1949)) to compute the p.m.f. of an \ M distribution.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfMKoch"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfMKoch[m,r,k] computes \!\({p\_0,p\_1,...,p\_k}\)\\nfor an \ \!\(M(m,r,1)\) distribution, using Koch's algorithm. Note that r is \ the\\nreciprocal of Koch's original parameter b (called \!\(\[Rho]\) in \ SALVADOR v.1).\\n(This function is not recommended for large k.)\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717819087305`*^9}, CellTags->"Info3430053781-6469246"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfMKoch", "[", RowBox[{"10.5", ",", "0.8", ",", "10"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.000027536449349747158`", ",", "0.00012850343029882007`", ",", "0.000345735419613492`", ",", "0.0007047470220843671`", ",", "0.0012099561768181867`", ",", "0.0018478624868760109`", ",", "0.0025930339916801328`", ",", "0.0034141644273363563`", ",", "0.00427891388332787`", ",", "0.00515719861997563`", ",", "0.006023079521618202`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232314042741*^9, 3.399297566624569*^9, 3.405871832253313*^9, 3.409343841570603*^9, 3.409862327338074*^9, 3.409863400261231*^9, 3.410018729033787*^9, 3.410019388077027*^9, 3.410031015349665*^9, 3.410032311903121*^9, 3.410033674308056*^9, 3.410101505353708*^9, 3.410183895685955*^9, 3.41036275420257*^9, 3.410538058218622*^9, 3.41053883513769*^9, 3.410546266877118*^9, 3.410547088509342*^9, 3.416253446483871*^9, 3.416589908326558*^9, 3.4298790606614137`*^9, 3.4298829262072487`*^9, 3.4298902351873107`*^9, 3.4298984251585083`*^9, 3.4299711260119753`*^9, 3.42997255257529*^9, 3.4300543380995307`*^9, 3.430061142812632*^9, 3.4300632590439663`*^9, 3.430064489975773*^9, { 3.4300653260692525`*^9, 3.430062203654688*^9}, 3.4300710156194987`*^9, 3.4300717819712343`*^9}] }, Open ]], Cell["\<\ To use the exact form of the M distribution, the parameter \[Phi]<1 must be \ specified.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfM", "[", RowBox[{"10.5", ",", "0.8", ",", "0.9999", ",", "10"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.000027536449349747158`", ",", "0.00012851628179849647`", ",", "0.00034579998601629806`", ",", "0.0007049322303118315`", ",", "0.0012103555467003165`", ",", "0.001848583177486612`", ",", "0.002594184692586304`", ",", "0.0034158449832227705`", ",", "0.004281207952509995`", ",", "0.005160169530586169`", ",", "0.006026768867509346`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232314314586*^9, 3.399297567007968*^9, 3.405871832504739*^9, 3.409343841860543*^9, 3.409862327634074*^9, 3.409863400504857*^9, 3.410018729179706*^9, 3.410019388340601*^9, 3.410031015590833*^9, 3.410032312144713*^9, 3.41003367455483*^9, 3.410101505619182*^9, 3.410183895961039*^9, 3.410362754477141*^9, 3.410538058509663*^9, 3.410538835405216*^9, 3.410546267159746*^9, 3.410547088754355*^9, 3.416253446877429*^9, 3.4165899083577895`*^9, 3.429879060708289*^9, 3.429882926254074*^9, 3.429890235202924*^9, 3.4298984251897507`*^9, 3.429971126043277*^9, 3.42997255262216*^9, 3.430054338115171*^9, 3.4300611428282576`*^9, 3.4300632590908337`*^9, 3.430064490007021*^9, { 3.430065326116139*^9, 3.430062203866096*^9}, 3.43007101565075*^9, 3.4300717820024853`*^9}] }, Open ]], Cell["\<\ Finally let us take a look at the convolution of a Poisson distribution and \ an LD distribution .\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfCairns"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfCairns[\!\(m,\[Phi],\[Lambda],k\)] returns a list \ of\\nprobabilities \!\({p\_0,...,p\_k}\) according to the convolution of\\nan \ LD(\!\(m,\[Phi]\)) distribution and a Poisson(\!\(\[Lambda]\)) \ distribution.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071782127492*^9}, CellTags->"Info3430053782-2659468"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfCairns", "[", RowBox[{"2.5", ",", "1", ",", "8.5", ",", "10"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.00001670170079024566`", ",", "0.00016284158270489518`", ",", "0.0008008117576822997`", ",", "0.0026513515064390237`", ",", "0.006657036789692023`", ",", "0.013540891094019241`", ",", "0.023283755824621593`", ",", "0.034883438214832446`", ",", "0.046594311140815386`", ",", "0.05652302198442521`", ",", "0.06324871361500846`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232315452832*^9, 3.399297568222632*^9, 3.405871833440701*^9, 3.409343842811601*^9, 3.409862328539956*^9, 3.409863401632343*^9, 3.410018730176829*^9, 3.410019389558412*^9, 3.410031016896*^9, 3.410032313080717*^9, 3.410033675497527*^9, 3.41010150681263*^9, 3.410183897278855*^9, 3.410362755509445*^9, 3.41053805966915*^9, 3.410538836626285*^9, 3.410546268373362*^9, 3.41054708968721*^9, 3.416253448075485*^9, 3.4165899085451765`*^9, 3.429879060927042*^9, 3.4298829264413767`*^9, 3.4298902353590536`*^9, 3.4298984253928237`*^9, 3.429971126278037*^9, 3.4299725527940164`*^9, 3.430054338271575*^9, 3.4300611429688883`*^9, 3.4300632593251696`*^9, 3.4300644902101316`*^9, { 3.430065326288057*^9, 3.430062205044249*^9}, 3.4300710158382597`*^9, 3.4300717821899953`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Point Estimation of Mutation Rates", "Section", FontSize->16], Cell[TextData[{ "Under the Lea-Coulson formulation attention is focused on the mean number \ of mutations m, from which the mutation rate ", Cell[BoxData[ FormBox[ SubscriptBox["\[Mu]", "\[Beta]"], TraditionalForm]]], " can be easily obtained. The recommended estimation method is the maximum \ likelihood method. We use the experimental data of Demerec (1945) to \ illustrate the capabilities of SALVADOR. The following are the known \ experimental parameters of Demerec's experiment." }], "Text", CellChangeTimes->{{3.410364320329896*^9, 3.41036436667893*^9}, { 3.410364399752039*^9, 3.410364416912841*^9}, {3.4300553345554204`*^9, 3.4300554539667406`*^9}, {3.4300555515071516`*^9, 3.4300555596328797`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"N0", "=", "90"}], ";", RowBox[{"Nt", "=", RowBox[{"1.9", "*", RowBox[{"10", "^", "8"}]}]}], ";", RowBox[{"phi", "=", RowBox[{"1", "-", RowBox[{"N0", "/", "Nt"}]}]}], ";"}]], "Input"], Cell["\<\ The experimental data of Demerec's (1945) experiment are given below.\ \>", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"demerec", "=", RowBox[{"{", RowBox[{ "33", ",", "18", ",", " ", "839", ",", "47", ",", "13", ",", "126", ",", "48", ",", "80", ",", "9", ",", "71", ",", "196", ",", "66", ",", "28", ",", "17", ",", "27", ",", "37", ",", "126", ",", "33", ",", "12", ",", "44", ",", "28", ",", "67", ",", "730", ",", "168", ",", "44", ",", "50", ",", "583", ",", "23", ",", "17", ",", "24"}], "}"}]}], ";"}]], "Input"], Cell["\<\ We can fit an LD(m,1) distribution to the data by calling newtonLD, which \ uses the Newton-Raphson methods to compute the maximum likelihood estimate \ (m.l.e.) of m.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "newtonLD"}]], "Input"], Cell[BoxData[ StyleBox["\<\"newtonLD[data,opts] uses the Newton-Raphson method to \ compute\\nmle of m for the LD model.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717823306274`*^9}, CellTags->"Info3430053782-1486419"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonLD", "[", "demerec", "]"}]], "Input"], Cell[BoxData["10.843826994529076`"], "Output", CellChangeTimes->{ 3.39923231691911*^9, 3.399297569553423*^9, 3.405871834510698*^9, 3.40934384422193*^9, 3.409862329730053*^9, 3.409863402683819*^9, 3.410018731256008*^9, 3.410019390598696*^9, 3.41003101816883*^9, 3.410032314325374*^9, 3.410033676537845*^9, 3.410101507881639*^9, 3.410183898513138*^9, 3.410362757239552*^9, 3.410538060717168*^9, 3.410538837998729*^9, 3.4105462694136*^9, 3.410547090714965*^9, 3.416253449311617*^9, 3.416589908841873*^9, 3.429879061223921*^9, 3.4298829269096317`*^9, 3.429890235608862*^9, 3.4298984256740017`*^9, 3.429971126716257*^9, 3.429972553043989*^9, 3.430054338693866*^9, 3.4300611432970257`*^9, 3.430063259606373*^9, 3.4300644904288664`*^9, { 3.4300653265224905`*^9, 3.430062206244229*^9}, 3.430071016103898*^9, 3.4300717824556336`*^9}] }, Open ]], Cell["\<\ Sometimes it is necessary to choose an initial guess, to set convergence \ criteria or to specify the maximum number of iterations. Thus it is helpful \ to familiarize yourself with the options of newtonLD.\ \>", "Text"], Cell[CellGroupData[{ Cell["Options[newtonLD]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"Phi", "\[Rule]", "1"}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"MaxIterations", "\[Rule]", "50"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232317178209*^9, 3.399297569811509*^9, 3.405871834878533*^9, 3.409343844491752*^9, 3.409862330024227*^9, 3.409863402977122*^9, 3.410018731537765*^9, 3.410019390863121*^9, 3.410031018428682*^9, 3.410032314586894*^9, 3.410033676829054*^9, 3.410101508142647*^9, 3.410183898803731*^9, 3.410362757510431*^9, 3.410538061093553*^9, 3.410538838139055*^9, 3.410546269674589*^9, 3.410547090994985*^9, 3.416253449571749*^9, 3.416589908873104*^9, 3.4298790612551713`*^9, 3.42988292692524*^9, 3.4298902356244745`*^9, 3.4298984257052436`*^9, 3.429971126731908*^9, 3.4299725530596123`*^9, 3.430054338709506*^9, 3.4300611433439026`*^9, 3.430063259621995*^9, 3.4300644904444904`*^9, { 3.4300653265381193`*^9, 3.430062206366589*^9}, 3.43007101613515*^9, 3.430071782502511*^9}] }, Open ]], Cell["\<\ For example, we can choose two distinct starting points and see how the two \ converge to the same m.l.e. Note that if InitialM is set to a negative \ number, SALVADOR uses its own rules to determine an initial guess (Zheng \ 2005).\ \>", "Text", CellChangeTimes->{{3.43005573794573*^9, 3.430055790575445*^9}}], Cell[CellGroupData[{ Cell["newtonLD[demerec,InitialM->3,ShowIterations->True]", "Input"], Cell[CellGroupData[{ Cell[BoxData["3"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.430071782533763*^9}], Cell[BoxData["5.9410741308071096`"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.4300717825493884`*^9}], Cell[BoxData["9.34988232782199`"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.43007178258064*^9}], Cell[BoxData["10.733970006389027`"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.4300717826118917`*^9}], Cell[BoxData["10.843274363697045`"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.430071782643143*^9}], Cell[BoxData["10.843826980617358`"], "Print", CellChangeTimes->{ 3.399232317492092*^9, 3.399297569957298*^9, 3.405871835206182*^9, 3.409343844797641*^9, 3.40986233025387*^9, 3.40986340321734*^9, 3.410018731675268*^9, 3.410019391238995*^9, 3.410031018735382*^9, 3.410032314972062*^9, 3.410033677066246*^9, 3.410101508525164*^9, 3.410183899213937*^9, 3.410362758232793*^9, 3.410538061481018*^9, 3.410538838373695*^9, 3.410546269816688*^9, 3.410547091372444*^9, 3.41625344995427*^9, 3.4165899089043355`*^9, 3.429879061286422*^9, 3.42988292692524*^9, 3.4298902356400876`*^9, 3.429898425767728*^9, 3.4299711267475586`*^9, 3.4299725530596123`*^9, 3.4300543387251463`*^9, 3.4300611433751535`*^9, 3.4300632596376176`*^9, 3.4300644904601145`*^9, { 3.430065326553748*^9, 3.430062206485265*^9}, 3.4300710161976533`*^9, 3.4300717826743946`*^9}] }, Open ]], Cell[BoxData["10.843826994529072`"], "Output", CellChangeTimes->{ 3.399232317700066*^9, 3.399297570251483*^9, 3.40587183529296*^9, 3.409343845009318*^9, 3.409862330576684*^9, 3.409863403521109*^9, 3.41001873197241*^9, 3.410019391302513*^9, 3.410031018950489*^9, 3.410032315032794*^9, 3.410033677380114*^9, 3.410101508589772*^9, 3.410183899275325*^9, 3.410362758410657*^9, 3.410538061546135*^9, 3.410538838669265*^9, 3.410546270210871*^9, 3.410547091452671*^9, 3.416253450015262*^9, 3.4165899090917225`*^9, 3.4298790614739237`*^9, 3.4298829270344996`*^9, 3.4298902357337656`*^9, 3.4298984259083166`*^9, 3.4299711268414626`*^9, 3.429972553168976*^9, 3.430054338818989*^9, 3.4300611436095376`*^9, 3.4300632597469745`*^9, 3.430064490553858*^9, { 3.4300653266475215`*^9, 3.430062206787047*^9}, 3.4300710163695374`*^9, 3.4300717827056465`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["newtonLD[demerec,InitialM->15,ShowIterations->True]", "Input"], Cell[CellGroupData[{ Cell[BoxData["15"], "Print", CellChangeTimes->{ 3.399232317881449*^9, 3.399297570415925*^9, 3.40587183531567*^9, 3.409343845176803*^9, 3.409862330818549*^9, 3.409863403770946*^9, 3.410018732212105*^9, 3.410019391321008*^9, 3.410031019117039*^9, 3.410032315056144*^9, 3.410033677628852*^9, 3.410101508613881*^9, 3.410183899443664*^9, 3.410362758816577*^9, 3.410538061597877*^9, 3.410538838846003*^9, 3.410546270243113*^9, 3.410547091477457*^9, 3.41625345003486*^9, 3.416589909122954*^9, 3.4298790615051746`*^9, 3.4298829270344996`*^9, 3.4298902357493787`*^9, 3.429898425923938*^9, 3.429971126857113*^9, 3.429972553168976*^9, 3.430054338834629*^9, 3.4300611436564145`*^9, 3.4300632597469745`*^9, 3.430064490569482*^9, { 3.4300653266631503`*^9, 3.430062207029596*^9}, 3.4300710164164143`*^9, 3.430071782736898*^9}], Cell[BoxData["10.171664609935716`"], "Print", CellChangeTimes->{ 3.399232317881449*^9, 3.399297570415925*^9, 3.40587183531567*^9, 3.409343845176803*^9, 3.409862330818549*^9, 3.409863403770946*^9, 3.410018732212105*^9, 3.410019391321008*^9, 3.410031019117039*^9, 3.410032315056144*^9, 3.410033677628852*^9, 3.410101508613881*^9, 3.410183899443664*^9, 3.410362758816577*^9, 3.410538061597877*^9, 3.410538838846003*^9, 3.410546270243113*^9, 3.410547091477457*^9, 3.41625345003486*^9, 3.416589909122954*^9, 3.4298790615051746`*^9, 3.4298829270344996`*^9, 3.4298902357493787`*^9, 3.429898425923938*^9, 3.429971126857113*^9, 3.429972553168976*^9, 3.430054338834629*^9, 3.4300611436564145`*^9, 3.4300632597469745`*^9, 3.430064490569482*^9, { 3.4300653266631503`*^9, 3.430062207029596*^9}, 3.4300710164164143`*^9, 3.430071782752524*^9}], Cell[BoxData["10.822551997688214`"], "Print", CellChangeTimes->{ 3.399232317881449*^9, 3.399297570415925*^9, 3.40587183531567*^9, 3.409343845176803*^9, 3.409862330818549*^9, 3.409863403770946*^9, 3.410018732212105*^9, 3.410019391321008*^9, 3.410031019117039*^9, 3.410032315056144*^9, 3.410033677628852*^9, 3.410101508613881*^9, 3.410183899443664*^9, 3.410362758816577*^9, 3.410538061597877*^9, 3.410538838846003*^9, 3.410546270243113*^9, 3.410547091477457*^9, 3.41625345003486*^9, 3.416589909122954*^9, 3.4298790615051746`*^9, 3.4298829270344996`*^9, 3.4298902357493787`*^9, 3.429898425923938*^9, 3.429971126857113*^9, 3.429972553168976*^9, 3.430054338834629*^9, 3.4300611436564145`*^9, 3.4300632597469745`*^9, 3.430064490569482*^9, { 3.4300653266631503`*^9, 3.430062207029596*^9}, 3.4300710164164143`*^9, 3.4300717827837753`*^9}], Cell[BoxData["10.843806356058554`"], "Print", CellChangeTimes->{ 3.399232317881449*^9, 3.399297570415925*^9, 3.40587183531567*^9, 3.409343845176803*^9, 3.409862330818549*^9, 3.409863403770946*^9, 3.410018732212105*^9, 3.410019391321008*^9, 3.410031019117039*^9, 3.410032315056144*^9, 3.410033677628852*^9, 3.410101508613881*^9, 3.410183899443664*^9, 3.410362758816577*^9, 3.410538061597877*^9, 3.410538838846003*^9, 3.410546270243113*^9, 3.410547091477457*^9, 3.41625345003486*^9, 3.416589909122954*^9, 3.4298790615051746`*^9, 3.4298829270344996`*^9, 3.4298902357493787`*^9, 3.429898425923938*^9, 3.429971126857113*^9, 3.429972553168976*^9, 3.430054338834629*^9, 3.4300611436564145`*^9, 3.4300632597469745`*^9, 3.430064490569482*^9, { 3.4300653266631503`*^9, 3.430062207029596*^9}, 3.4300710164164143`*^9, 3.430071782815027*^9}], Cell[BoxData["10.843826994509673`"], "Print", CellChangeTimes->{ 3.399232317881449*^9, 3.399297570415925*^9, 3.40587183531567*^9, 3.409343845176803*^9, 3.409862330818549*^9, 3.409863403770946*^9, 3.410018732212105*^9, 3.410019391321008*^9, 3.410031019117039*^9, 3.410032315056144*^9, 3.410033677628852*^9, 3.410101508613881*^9, 3.410183899443664*^9, 3.410362758816577*^9, 3.410538061597877*^9, 3.410538838846003*^9, 3.410546270243113*^9, 3.410547091477457*^9, 3.41625345003486*^9, 3.416589909122954*^9, 3.4298790615051746`*^9, 3.4298829270344996`*^9, 3.4298902357493787`*^9, 3.429898425923938*^9, 3.429971126857113*^9, 3.429972553168976*^9, 3.430054338834629*^9, 3.4300611436564145`*^9, 3.4300632597469745`*^9, 3.430064490569482*^9, { 3.4300653266631503`*^9, 3.430062207029596*^9}, 3.4300710164164143`*^9, 3.430071782846279*^9}] }, Open ]], Cell[BoxData["10.843826994529072`"], "Output", CellChangeTimes->{ 3.399232318127705*^9, 3.399297570688497*^9, 3.40587183555703*^9, 3.409343845468939*^9, 3.409862330871048*^9, 3.409863403826103*^9, 3.410018732264413*^9, 3.410019391593798*^9, 3.410031019388868*^9, 3.410032315415881*^9, 3.410033677683508*^9, 3.410101508893825*^9, 3.410183899724345*^9, 3.410362759111138*^9, 3.410538061875001*^9, 3.410538839115388*^9, 3.410546270489724*^9, 3.41054709176092*^9, 3.416253450319747*^9, 3.416589909216647*^9, 3.4298790616458015`*^9, 3.4298829271281505`*^9, 3.4298902358274436`*^9, 3.4298984260020423`*^9, 3.4299711269353666`*^9, 3.4299725532627153`*^9, 3.4300543389128313`*^9, 3.4300611438439217`*^9, 3.4300632598407087`*^9, 3.430064490647601*^9, { 3.430065326741295*^9, 3.430062207089383*^9}, 3.430071016557047*^9, 3.43007178287753*^9}] }, Open ]], Cell["\<\ If you believe that mutants grow at a rate different from that for \ nonmutants, you may try to fit a M(m,r) model to your data. Note that r in \ the current version of SALVADOR is the reciprocal of \[Rho] in SALVADOR 1.0.\ \>", "Text", CellChangeTimes->{{3.410364496028041*^9, 3.410364534227688*^9}}], Cell[CellGroupData[{ Cell["?newtonM", "Input"], Cell[BoxData[ StyleBox["\<\"newtonM[data,opts] uses the Newton-Raphson method to \ compute\\nMLEs of m and r for the M(m,r) model.\"\>", "MSG"]], "Print", \ "PrintUsage", CellChangeTimes->{3.430071783002537*^9}, CellTags->"Info3430053782-9484289"] }, Open ]], Cell[CellGroupData[{ Cell["newtonM[demerec]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"9.852618286896067`", ",", "0.8938070840172461`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232319585132*^9, 3.399297571967154*^9, 3.405871837180585*^9, 3.409343846870007*^9, 3.409862332214394*^9, 3.409863404973293*^9, 3.41001873386554*^9, 3.410019392888859*^9, 3.410031020615055*^9, 3.410033678920467*^9, 3.410101510408273*^9, 3.410183900951936*^9, 3.410362760534872*^9, 3.410538063910148*^9, 3.410538840415315*^9, 3.410546272125849*^9, 3.410547093063752*^9, 3.416253451937619*^9, 3.4165899095601907`*^9, 3.4298790620208063`*^9, 3.429882927846142*^9, 3.4298902361865425`*^9, 3.4298984263613253`*^9, 3.429971127530093*^9, 3.429972553606428*^9, 3.430054339569728*^9, 3.430061144265813*^9, 3.4300632601844015`*^9, 3.430064490991327*^9, {3.4300653271007595`*^9, 3.430062208414343*^9}, 3.430071016947692*^9, 3.4300717832525496`*^9}] }, Open ]], Cell["Options of newtonM are similar to those of newtonLD.", "Text"], Cell[CellGroupData[{ Cell["Options[newtonM]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"MaxIterations", "\[Rule]", "50"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialR", "\[Rule]", RowBox[{"-", "1"}]}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232319815631*^9, 3.399297572198922*^9, 3.405871837409356*^9, 3.409343847112037*^9, 3.409862332433233*^9, 3.409863405207097*^9, 3.410018734099629*^9, 3.41001939311646*^9, 3.410031020846426*^9, 3.410033679261098*^9, 3.410101510639794*^9, 3.410183901209475*^9, 3.410362760778024*^9, 3.410538064156804*^9, 3.410538840644757*^9, 3.410546272374882*^9, 3.410547093291351*^9, 3.416253452161305*^9, 3.4165899095601907`*^9, 3.4298790620364313`*^9, 3.4298829278617496`*^9, 3.4298902362021556`*^9, 3.4298984263769464`*^9, 3.4299711275770454`*^9, 3.4299725536220512`*^9, 3.430054339601009*^9, 3.4300611443283153`*^9, 3.4300632602000237`*^9, 3.430064491006951*^9, {3.4300653271163883`*^9, 3.430062208707633*^9}, 3.430071016978943*^9, 3.430071783283801*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Interval Estimation of Mutation Rates", "Section"], Cell["\<\ SALVADOR relies on large-sample theory to construct confidence intervals \ (CIs). For the equal growth model under the Lea-Coulson formulation, the \ function for constructing a CI for m is LRIntervalLD.\ \>", "Text", CellChangeTimes->{{3.410536797469111*^9, 3.410536806759656*^9}, 3.430062645205379*^9}], Cell[CellGroupData[{ Cell["?LRIntervalLD", "Input"], Cell[BoxData[ StyleBox["\<\"LRIntervalLD[X,opts] uses data X to construct\\na likelihood \ ratio based confidence interval for m that has asymptotic\\nconfidence \ coefficient \!\(1-\[Alpha]\); \!\(\[Alpha]\) is specified by\\nAlpha->\!\(\ \[Alpha]\). Data are assumed to be generated by an\\nLD(m,\!\(\[Phi]\)) \ distribution; \!\(\[Phi]\) is specified by Phi->\!\(\[Phi]\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300717834088078`*^9}, CellTags->"Info3430053783-6762549"] }, Open ]], Cell["\<\ A 95% asymptotic confidence interval for m is obtained by the command\ \>", "Text"], Cell[CellGroupData[{ Cell["LRIntervalLD[demerec]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"8.650538086656958`", ",", "13.194764931218941`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232321268986*^9, 3.39929757365577*^9, 3.405871838776215*^9, 3.409343848545546*^9, 3.409862333748019*^9, 3.409863406505529*^9, 3.410018735490942*^9, 3.410019394496681*^9, 3.41003102226942*^9, 3.410033680692584*^9, 3.410101511851956*^9, 3.410183902786888*^9, 3.410362762014967*^9, 3.410538066205362*^9, 3.410538842032711*^9, 3.410546273807628*^9, 3.410547094591664*^9, 3.416253453520549*^9, 3.416589909934965*^9, 3.429879062427061*^9, 3.429882928423656*^9, 3.4298902365768676`*^9, 3.42989842675185*^9, 3.429971128062217*^9, 3.42997255399701*^9, 3.4300543401015015`*^9, 3.430061144781458*^9, 3.4300632606062064`*^9, 3.4300644913819246`*^9, {3.4300653275071115`*^9, 3.43006220986622*^9}, 3.43007101740084*^9, 3.430071783674446*^9}] }, Open ]], Cell["\<\ And a 90% confidence interval would be constructed by using the Alpha option. \ Note that if a (1-\[Alpha])100% CI is desired, then the options Alpha should \ be set to \[Alpha], not \[Alpha]/2.\ \>", "Text"], Cell[CellGroupData[{ Cell["LRIntervalLD[demerec,Alpha->0.1]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"8.991839033899883`", ",", "12.806736879987557`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232321927535*^9, 3.399297574199868*^9, 3.40587183942801*^9, 3.409343849106399*^9, 3.409862334412704*^9, 3.409863407170294*^9, 3.410018736144443*^9, 3.410019395045477*^9, 3.410031022813678*^9, 3.410033681251451*^9, 3.410101512507343*^9, 3.410183903353291*^9, 3.410362762678615*^9, 3.410538066793187*^9, 3.410538842585595*^9, 3.41054627446504*^9, 3.410547095143697*^9, 3.416253454082089*^9, 3.4165899101848145`*^9, 3.429879062645814*^9, 3.429882928689*^9, 3.4298902368266754`*^9, 3.429898427001786*^9, 3.4299711282969775`*^9, 3.4299725542469835`*^9, 3.4300543403204675`*^9, 3.4300611450314674`*^9, 3.4300632608249197`*^9, 3.4300644916319065`*^9, {3.4300653277571735`*^9, 3.43006221048347*^9}, 3.430071017666478*^9, 3.4300717839244585`*^9}] }, Open ]], Cell["In addition to Alpha, there are a few other options.", "Text"], Cell[CellGroupData[{ Cell["Options[LRIntervalLD]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Alpha", "\[Rule]", "0.05`"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}], ",", RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"MaxIterations", "\[Rule]", "50"}], ",", RowBox[{"Phi", "\[Rule]", "1.`"}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialLowerM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialUpperM", "\[Rule]", RowBox[{"-", "1"}]}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232322167807*^9, 3.399297574439078*^9, 3.405871839668869*^9, 3.409343849345463*^9, 3.40986233465465*^9, 3.409863407417742*^9, 3.410018736387407*^9, 3.410019395286185*^9, 3.410031023054364*^9, 3.410033681504019*^9, 3.410101512751059*^9, 3.410183903633465*^9, 3.410362762934463*^9, 3.410538067045635*^9, 3.410538842833056*^9, 3.410546274712462*^9, 3.410547095390343*^9, 3.416253454327999*^9, 3.41658991020043*^9, 3.429879062661439*^9, 3.429882928689*^9, 3.429890236842289*^9, 3.4298984270174074`*^9, 3.4299711282969775`*^9, 3.4299725542626066`*^9, 3.4300543403361077`*^9, 3.430061145047093*^9, 3.4300632608405423`*^9, 3.4300644916475306`*^9, {3.4300653277728024`*^9, 3.43006221059289*^9}, 3.430071017682104*^9, 3.4300717839400845`*^9}] }, Open ]], Cell["\<\ InitialM sets an initial guess for computing the maximum likelihood estimate \ of m, which is needed for computing a CI for m. The two options, \ InitialLowerM and initialUpperM, are starting points for computing the lower \ and upper boundary points of the desired CI for m. When these options are \ set to a negative number, SALVADOR adopts its own algorithms as described in \ Zheng (2004) to determine starting values. For example, if we choose 3 as \ an initial guess for the lower boundary point, and 16 as an initial guess for \ the upper boundary point, the iteration process will proceed as follows.\ \>", "Text", CellChangeTimes->{{3.41036466656472*^9, 3.41036468642401*^9}}], Cell[CellGroupData[{ Cell["\<\ LRIntervalLD[demerec,InitialLowerM->3,InitialUpperM->16,ShowIterations->True]\ \ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for lower limit ...\"\>"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784049465*^9}], Cell[BoxData["3"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784049465*^9}], Cell[BoxData["5.699422221344833`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784065091*^9}], Cell[BoxData["7.603623983988987`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784080717*^9}], Cell[BoxData["8.454611596733116`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784096343*^9}], Cell[BoxData["8.641442320849832`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784096343*^9}], Cell[BoxData["8.650516918615997`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.4300717841119685`*^9}], Cell[BoxData["8.650538086541877`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.4300717841275945`*^9}], Cell[BoxData["\<\"Iterating for upper limit ...\"\>"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.4300717841275945`*^9}], Cell[BoxData["16"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.43007178414322*^9}], Cell[BoxData["13.871854805032035`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.43007178414322*^9}], Cell[BoxData["13.263291837867612`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784158846*^9}], Cell[BoxData["13.195648858629793`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784174472*^9}], Cell[BoxData["13.194765082626425`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784190098*^9}], Cell[BoxData["13.194764931218943`"], "Print", CellChangeTimes->{ 3.399232322540342*^9, 3.399297574862865*^9, 3.405871840073162*^9, 3.409343849723025*^9, 3.409862335073821*^9, 3.409863407890188*^9, 3.410018736766769*^9, 3.410019395710483*^9, 3.410031023509349*^9, 3.41003368190117*^9, 3.41010151312029*^9, 3.410183904124537*^9, 3.410362763386128*^9, 3.410538067508025*^9, 3.4105388432477*^9, 3.410546275135781*^9, 3.410547095779203*^9, 3.416253454769324*^9, 3.4165899102941236`*^9, 3.429879062770816*^9, 3.4298829288138685`*^9, 3.429890237217001*^9, 3.4298984271267543`*^9, 3.4299711284065323`*^9, 3.429972554356346*^9, 3.4300543404455905`*^9, 3.430061145156472*^9, 3.430063260949899*^9, 3.430064491756898*^9, {3.430065327882205*^9, 3.430062210871339*^9}, 3.430071017791485*^9, 3.430071784190098*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"8.650538086656962`", ",", "13.194764931218943`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232322890394*^9, 3.399297575234795*^9, 3.405871840462796*^9, 3.409343850185453*^9, 3.409862335446411*^9, 3.409863408171613*^9, 3.410018737283294*^9, 3.410019396003927*^9, 3.410031023788232*^9, 3.410033682422885*^9, 3.410101513660178*^9, 3.410183904388608*^9, 3.410362763668546*^9, 3.410538067876025*^9, 3.410538843560006*^9, 3.410546275426875*^9, 3.410547096196182*^9, 3.416253455051898*^9, 3.4165899110749035`*^9, 3.4298790629426928`*^9, 3.4298829299845057`*^9, 3.4298902373262916`*^9, 3.429898427876562*^9, 3.4299711285786905`*^9, 3.429972554528203*^9, 3.4300543406019945`*^9, 3.430061145312728*^9, 3.4300632620903344`*^9, 3.4300644919131365`*^9, {3.4300653280384936`*^9, 3.430062211317592*^9}, 3.4300710179477425`*^9, 3.4300717842057233`*^9}] }, Open ]], Cell["\<\ You can also construct a Wald type CI for m by first computing expected \ Fisher information as suggested by Zheng (2002).\ \>", "Text"], Cell[CellGroupData[{ Cell["?fisherInfoLD", "Input"], Cell[BoxData[ StyleBox["\<\"fisherInfoLD[m,\!\(\[Phi]\),k] computes the \ Fisher\\ninformation for m according to an LD(m,\!\(\[Phi]\)) distribution; \ it retains\\nk terms in the series \!\(I(m)=\[Sum] f\^2\%j/p\_j\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071784315104*^9}, CellTags->"Info3430053784-9086444"] }, Open ]], Cell[CellGroupData[{ Cell["mhat=newtonLD[demerec]", "Input"], Cell[BoxData["10.843826994529076`"], "Output", CellChangeTimes->{ 3.399232323849735*^9, 3.399297576160225*^9, 3.405871841572234*^9, 3.409343851225335*^9, 3.409862336499098*^9, 3.409863409055256*^9, 3.410018738147128*^9, 3.410019397067075*^9, 3.410031024788667*^9, 3.410033683285186*^9, 3.410101514809892*^9, 3.410183905363923*^9, 3.41036276468677*^9, 3.410538068890651*^9, 3.410538844503508*^9, 3.410546276585036*^9, 3.410547097158705*^9, 3.4162534560712*^9, 3.4165899113247533`*^9, 3.4298790631770706`*^9, 3.4298829302498503`*^9, 3.4298902394184337`*^9, 3.4298984281577406`*^9, 3.4299711288291016`*^9, 3.4299725547469287`*^9, 3.430054340852241*^9, 3.4300611455783634`*^9, 3.4300632623715377`*^9, 3.4300644921474953`*^9, {3.4300653282729273`*^9, 3.430062212126784*^9}, 3.4300710181508784`*^9, 3.430071784408859*^9}] }, Open ]], Cell[CellGroupData[{ Cell["info=fisherInfoLD[mhat,50000]", "Input"], Cell[BoxData["0.02535709414926187`"], "Output", CellChangeTimes->{ 3.399232358104571*^9, 3.399297609334756*^9, 3.405871874814932*^9, 3.409343885294663*^9, 3.409862373009469*^9, 3.409863442375641*^9, 3.410018771305459*^9, 3.410019430313568*^9, 3.41003105805203*^9, 3.410033716978143*^9, 3.410101548028256*^9, 3.410183939037002*^9, 3.410362797966417*^9, 3.410538102147215*^9, 3.41053887775969*^9, 3.410546309941888*^9, 3.410547130489429*^9, 3.416253491074185*^9, 3.4165899364658694`*^9, 3.429879088255517*^9, 3.429882956175569*^9, 3.4298902648051715`*^9, 3.4298984548540297`*^9, 3.4299711539641256`*^9, 3.429972579869195*^9, 3.4300543662366104`*^9, 3.430061172391893*^9, 3.4300632875236015`*^9, 3.4300645172707267`*^9, {3.430065353904323*^9, 3.430062246543002*^9}, 3.4300710432771645`*^9, 3.430071809707029*^9}] }, Open ]], Cell[CellGroupData[{ Cell["{mhat-1.96 Sqrt[1/(30 info)], mhat+1.96 Sqrt[1/(30 info)]}", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"8.596606419965056`", ",", "13.091047569093096`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232358322626*^9, 3.399297609548265*^9, 3.405871875029057*^9, 3.409343885432904*^9, 3.409862373204035*^9, 3.40986344260324*^9, 3.410018771527041*^9, 3.410019430530117*^9, 3.410031058273658*^9, 3.410033717035039*^9, 3.410101548247529*^9, 3.410183939288208*^9, 3.410362798212434*^9, 3.410538102470319*^9, 3.410538877976455*^9, 3.410546310157947*^9, 3.410547130705603*^9, 3.416253491307943*^9, 3.416589936481485*^9, 3.429879088271142*^9, 3.4298829590787497`*^9, 3.4298902648207846`*^9, 3.4298984555725956`*^9, 3.429971153995427*^9, 3.429972579900442*^9, 3.4300543662522507`*^9, 3.4300611724231443`*^9, 3.4300632875548463`*^9, 3.4300645172863503`*^9, {3.430065353935581*^9, 3.430062246689355*^9}, 3.4300710432927904`*^9, 3.4300718097382803`*^9}] }, Open ]], Cell["\<\ This Wald type CI for m is very similar to the likelihood ratio based CI we \ just found.\ \>", "Text"], Cell["\<\ When fitting a differential growth model to data, use the function \ profileIntervalM to construct a profile likelihood based CI for m, and use \ the function profileIntervalR to construct a CI for r.\ \>", "Text"], Cell[CellGroupData[{ Cell["?profileIntervalM", "Input"], Cell[BoxData[ StyleBox["\<\"profileIntervalM[data,opt] computes profile likelihood\\nbased \ confidence intervals for m under the M(m,r) model.\"\>", "MSG"]], "Print", \ "PrintUsage", CellChangeTimes->{3.430071809832035*^9}, CellTags->"Info3430053809-3357107"] }, Open ]], Cell[CellGroupData[{ Cell["profileIntervalM[demerec]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"6.983065123318325`", ",", "13.007332373951023`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232360461298*^9, 3.399297611751164*^9, 3.40587187721397*^9, 3.409343887256277*^9, 3.409862375150535*^9, 3.409863444561341*^9, 3.41001877375874*^9, 3.410019432624399*^9, 3.41003106018937*^9, 3.410033719428469*^9, 3.410101550532914*^9, 3.410183941423554*^9, 3.410362800486085*^9, 3.410538104560686*^9, 3.410538880116054*^9, 3.410546312408689*^9, 3.410547132846253*^9, 3.416253493206198*^9, 3.416589937231034*^9, 3.4298790890367765`*^9, 3.4298829604054728`*^9, 3.429890265554596*^9, 3.4298984580563345`*^9, 3.4299711547623115`*^9, 3.42997258065036*^9, 3.43005436700299*^9, 3.430061173235675*^9, 3.430063288320344*^9, 3.430064518051922*^9, {3.4300653547170258`*^9, 3.4300622484972258`*^9}, 3.4300710440428286`*^9, 3.4300718104883184`*^9}] }, Open ]], Cell["\<\ To get a Wald type CI for m, we have to compute the expected Fisher \ information matrix approximately. Since we know little about the converging \ speed of computing this information matrix, it is strongly recommended that \ a Wald type CI be corroborated by a likelihood ratio based CI.\ \>", "Text"], Cell[CellGroupData[{ Cell["?fisherInfoMatrix", "Input"], Cell[BoxData[ StyleBox["\<\"fisherInfoMatrix[m,r,n] computes the expected \ Fisher\\ninformation matrix for the M(m,r) model, using n terms.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718105820737`*^9}, CellTags->"Info3430053810-4078900"] }, Open ]], Cell[CellGroupData[{ Cell["{mhatm,rhatm}=newtonM[demerec]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"9.852618286896067`", ",", "0.8938070840172461`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232361791917*^9, 3.399297613174106*^9, 3.405871878544838*^9, 3.409343888485902*^9, 3.409862376220842*^9, 3.409863445913676*^9, 3.410018775092967*^9, 3.410019433954523*^9, 3.410031061700178*^9, 3.410033720533588*^9, 3.410101551879912*^9, 3.410183942843689*^9, 3.410362802189798*^9, 3.410538106204546*^9, 3.410538881448959*^9, 3.410546313750805*^9, 3.410547134269364*^9, 3.416253494738637*^9, 3.4165899375745773`*^9, 3.4298790893805313`*^9, 3.4298829610610294`*^9, 3.4298902658824687`*^9, 3.4298984634143376`*^9, 3.4299711551066265`*^9, 3.429972581009696*^9, 3.430054367331438*^9, 3.430061173595064*^9, 3.430063288679659*^9, 3.430064518411271*^9, {3.430065355076491*^9, 3.430062249827401*^9}, 3.4300710443709707`*^9, 3.4300718108164606`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["infoMat=fisherInfoMatrix[mhatm,rhatm,5000]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.026539225837420653`", ",", RowBox[{"-", "0.25943587031378323`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.25943587031378323`"}], ",", "5.0613587187416105`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232362505306*^9, 3.399297613884005*^9, 3.405871879254695*^9, 3.409343889188412*^9, 3.409862376942782*^9, 3.409863446645902*^9, 3.410018775819264*^9, 3.410019434667072*^9, 3.41003106241932*^9, 3.410033721148488*^9, 3.410101552581447*^9, 3.410183943606381*^9, 3.410362802787615*^9, 3.410538106806352*^9, 3.410538882179905*^9, 3.410546314450177*^9, 3.410547135000251*^9, 3.4162534954556*^9, 3.4165899378556576`*^9, 3.429879089661785*^9, 3.4298829613419824`*^9, 3.4298902661635027`*^9, 3.4298984644297023`*^9, 3.42997115540399*^9, 3.4299725813065386`*^9, 3.4300543676129656`*^9, 3.4300611738919506`*^9, 3.430063288976485*^9, 3.430064518708125*^9, {3.43006535537344*^9, 3.430062250493878*^9}, 3.430071044652235*^9, 3.430071811097725*^9}] }, Open ]], Cell[CellGroupData[{ Cell["{{var11,var12},{var21,var22}}=Inverse[infoMat]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"75.52286098136481`", ",", "3.8711619262897594`"}], "}"}], ",", RowBox[{"{", RowBox[{"3.8711619262897594`", ",", "0.3960039931670547`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232362776068*^9, 3.399297614152333*^9, 3.40587187952092*^9, 3.409343889455808*^9, 3.40986237721083*^9, 3.409863446921076*^9, 3.410018776089239*^9, 3.410019434933368*^9, 3.410031062687256*^9, 3.41003372128867*^9, 3.410101552852609*^9, 3.410183943925007*^9, 3.410362803067036*^9, 3.410538107090303*^9, 3.410538882446752*^9, 3.410546314722507*^9, 3.410547135267814*^9, 3.416253495722999*^9, 3.4165899378712735`*^9, 3.42987908967741*^9, 3.4298829613575907`*^9, 3.4298902661791153`*^9, 3.4298984644921865`*^9, 3.4299711554196405`*^9, 3.429972581322162*^9, 3.4300543676129656`*^9, 3.430061173907576*^9, 3.4300632889921074`*^9, 3.430064518708125*^9, {3.4300653553890686`*^9, 3.430062250739813*^9}, 3.430071044667861*^9, 3.430071811113351*^9}] }, Open ]], Cell[CellGroupData[{ Cell["{mhatm-1.96 Sqrt[var11/30],mhatm+1.96 Sqrt[var11/30]}", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"6.7428025220100345`", ",", "12.9624340517821`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232363048112*^9, 3.399297614422286*^9, 3.405871879790111*^9, 3.40934388972854*^9, 3.409862377480988*^9, 3.409863447187553*^9, 3.410018776360596*^9, 3.410019435204365*^9, 3.410031062957587*^9, 3.410033721309381*^9, 3.41010155312406*^9, 3.4101839442422*^9, 3.410362803210897*^9, 3.410538107377088*^9, 3.410538882717324*^9, 3.410546314993063*^9, 3.41054713552844*^9, 3.416253495993558*^9, 3.416589937886889*^9, 3.429879089693035*^9, 3.4298829613575907`*^9, 3.4298902661791153`*^9, 3.429898465585656*^9, 3.4299711554352913`*^9, 3.4299725813377857`*^9, 3.430054367628606*^9, 3.4300611739232016`*^9, 3.4300632889921074`*^9, 3.430064518723749*^9, {3.4300653554046974`*^9, 3.430062250869414*^9}, 3.430071044683487*^9, 3.430071811128977*^9}] }, Open ]], Cell["\<\ Again the above Wald type CI is similar to the likelihood ratio based CI we \ just found.\ \>", "Text"], Cell["To get a 99% CI for M, set Alpha to 0.01, not 0.005.", "Text"], Cell[CellGroupData[{ Cell["profileIntervalM[demerec,Alpha->0.01]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"6.158961230587406`", ",", "14.043751024099272`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.399232364433902*^9, 3.399297615802983*^9, 3.405871881187293*^9, 3.40934389112413*^9, 3.409862378880124*^9, 3.409863448477171*^9, 3.410018777753127*^9, 3.410019436596366*^9, 3.410031064357334*^9, 3.410033722485096*^9, 3.410101554513201*^9, 3.410183945579819*^9, 3.410362804549836*^9, 3.410538108671699*^9, 3.410538884125695*^9, 3.410546316435091*^9, 3.410547136826132*^9, 3.416253497386848*^9, 3.4165899385115128`*^9, 3.429879090318043*^9, 3.4298829619975395`*^9, 3.4298902668036356`*^9, 3.4298984677257338`*^9, 3.4299711560613194`*^9, 3.4299725819627175`*^9, 3.4300543682385817`*^9, 3.4300611745482254`*^9, 3.4300632896326256`*^9, 3.4300645193487053`*^9, {3.4300653560454826`*^9, 3.430062252257866*^9}, 3.4300710452928925`*^9, 3.430071811754009*^9}] }, Open ]], Cell["\<\ To see if the differential growth model is necessary, we can construct a 95% \ CI for r.\ \>", "Text"], Cell[CellGroupData[{ Cell["profileIntervalR[demerec]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"0.6910073899881164`", ",", "1.1268801153166565`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232365724315*^9, 3.399297617082224*^9, 3.405871882471846*^9, 3.409343892418216*^9, 3.409862380219476*^9, 3.409863449778692*^9, 3.410018779043208*^9, 3.410019437891494*^9, 3.410031065688727*^9, 3.410033723910771*^9, 3.410101555811582*^9, 3.41018394688569*^9, 3.41036280587696*^9, 3.410538109976774*^9, 3.410538885446193*^9, 3.410546317735404*^9, 3.410547138137411*^9, 3.4162534986954*^9, 3.416589939136137*^9, 3.4298790909430513`*^9, 3.429882962637488*^9, 3.429890267428156*^9, 3.4298984684442997`*^9, 3.4299711566873474`*^9, 3.4299725825876493`*^9, 3.4300543688641977`*^9, 3.430061175188875*^9, 3.4300632902575216`*^9, 3.4300645199736614`*^9, {3.4300653567018967`*^9, 3.430062253542029*^9}, 3.430071045917925*^9, 3.4300718123790407`*^9}] }, Open ]], Cell["\<\ Because unity is contained in the above CI, the equal growth model appears \ sufficient. \ \>", "Text"], Cell["\<\ Sometimes it is necessary for the user to supply initial guesses when \ constructing a likelihood based CI.\ \>", "Text"], Cell[CellGroupData[{ Cell["Options[profileIntervalM]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Alpha", "\[Rule]", "0.05`"}], ",", RowBox[{"MaxIterations", "\[Rule]", "50"}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialR", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialLowerM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialUpperM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}], ",", RowBox[{"InitialLowerR", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialUpperR", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"ShowIterations", "\[Rule]", "False"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232365891189*^9, 3.399297617250601*^9, 3.405871882641202*^9, 3.409343892583417*^9, 3.409862380387348*^9, 3.409863449952092*^9, 3.410018779210715*^9, 3.410019438057371*^9, 3.410031065851901*^9, 3.410033724322804*^9, 3.410101555984509*^9, 3.410183947051764*^9, 3.410362806965061*^9, 3.410538110143347*^9, 3.410538885744901*^9, 3.410546317904489*^9, 3.410547138306813*^9, 3.41625349898751*^9, 3.416589939167368*^9, 3.4298790909743013`*^9, 3.429882962653096*^9, 3.4298902674437685`*^9, 3.4298984684755416`*^9, 3.429971156718649*^9, 3.429972582618896*^9, 3.430054368879838*^9, 3.430061175204501*^9, 3.4300632902887664`*^9, 3.4300645200049095`*^9, {3.4300653567175255`*^9, 3.43006225369492*^9}, 3.4300710459491763`*^9, 3.4300718124102926`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ profileIntervalR[demerec,InitialLowerR->0.5,InitialUpperR->1.5,ShowIterations-\ >True]\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for lower limit ...\"\>"], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071812660305*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"8.799956037182808`", ",", "0.5`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071812675931*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"2.2051609933372154`", ",", "0.3931600123903666`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718127071824`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"4.200254804916163`", ",", "0.6105082612451991`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071812738434*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"5.769529674213736`", ",", "0.5678451456136873`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718127696857`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"7.232244823015946`", ",", "0.6582003543178906`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071812800937*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"7.69206649240923`", ",", "0.687875554387641`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718128321886`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"7.732348888513267`", ",", "0.6909779394274912`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718128634405`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"7.732677433440342`", ",", "0.691007387417192`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071812894692*^9}], Cell[BoxData["\<\"Iterating for upper limit ...\"\>"], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718129259434`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"10.905280536609327`", ",", "1.5`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718129571953`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"13.335417373602379`", ",", "1.33786788711747`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718129884467`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"12.310028005062637`", ",", "1.16336295462329`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071813019698*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"11.946647814278784`", ",", "1.128951204366485`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.43007181305095*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"11.928254901550764`", ",", "1.1268873480338755`"}], "}"}]], "Print",\ CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.4300718130822015`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"11.92818509661708`", ",", "1.126880115407674`"}], "}"}]], "Print", CellChangeTimes->{ 3.399232366385951*^9, 3.399297617771918*^9, 3.405871883148169*^9, 3.409343893093406*^9, 3.409862380907045*^9, 3.409863450462224*^9, 3.410018779736944*^9, 3.410019438570118*^9, 3.410031066357002*^9, 3.410033724820696*^9, 3.410101556508882*^9, 3.410183947576954*^9, 3.410362807651414*^9, 3.410538110642368*^9, 3.410538886263824*^9, 3.41054631841717*^9, 3.410547138823832*^9, 3.416253499514089*^9, 3.4165899394172177`*^9, 3.429879091224305*^9, 3.4298829629028325`*^9, 3.4298902676779633`*^9, 3.4298984687567196`*^9, 3.429971156953409*^9, 3.429972582868869*^9, 3.430054369130084*^9, 3.4300611754545107`*^9, 3.430063290538725*^9, 3.4300645202548914`*^9, {3.4300653569832163`*^9, 3.43006225419167*^9}, 3.430071046199189*^9, 3.430071813113453*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"0.6910073899881204`", ",", "1.1268801153166557`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232367964672*^9, 3.399297619445545*^9, 3.405871884706015*^9, 3.409343894660625*^9, 3.409862382481226*^9, 3.409863452036138*^9, 3.410018781312545*^9, 3.410019440127731*^9, 3.410031067928737*^9, 3.410033726408398*^9, 3.410101558082824*^9, 3.41018394915389*^9, 3.410362809243113*^9, 3.410538112238891*^9, 3.410538887857429*^9, 3.410546319986791*^9, 3.410547140384871*^9, 3.416253501082579*^9, 3.4165899399013014`*^9, 3.429879091708686*^9, 3.429882963386696*^9, 3.429890268161967*^9, 3.4298984708655543`*^9, 3.4299711574385815`*^9, 3.4299725833375683`*^9, 3.430054369599296*^9, 3.430061175938904*^9, 3.430063291038642*^9, 3.430064520739232*^9, {3.4300653574677124`*^9, 3.430062255781707*^9}, 3.430071046683589*^9, 3.430071813144705*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Functions for extremely large observations", "Section"], Cell[TextData[{ "Occasionally, the user may encounter data having extremely large \ observations. This type of data may force SALVADOR to process numbers of \ exceedingly small magnitudes. As a typical C compiler cannot manipulate \ numbers of magnitudes smaller than ", Cell[BoxData[ FormBox[ SuperscriptBox["10", RowBox[{"-", "302"}]], TraditionalForm]]], ", underflow may occur. For example, if m=800, ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "0"], "=", SuperscriptBox["e", RowBox[{"-", "800"}]]}], TraditionalForm]]], " will be treated as zero, if a function written in C is involved in its \ computation. This can invalidate all the subsequent computations. However, \ the ", StyleBox["Mathematica", FontSlant->"Italic"], " language can manipulate numbers much smaller (the user is referred to the \ ", StyleBox["Mathematica", FontSlant->"Italic"], " system variable $MinNumber). For this reason, SALVADOR offers several \ functions whose names end with the numeral 0. Such a \"zero function\" uses \ the same algorithm as its counterpart does, but is implemented solely in the \ ", StyleBox["Mathematica", FontSlant->"Italic"], " language. For instance, newtonLD0 is a counterpart of newtonLD." }], "Text", CellChangeTimes->{{3.410364754759853*^9, 3.410364760323283*^9}, { 3.410364798780703*^9, 3.410364842313648*^9}, {3.410364877885287*^9, 3.410364879086103*^9}, {3.410364911857158*^9, 3.410365040133819*^9}, { 3.41036507894445*^9, 3.410365121520573*^9}, {3.410365151748369*^9, 3.41036532573173*^9}, {3.410365359352049*^9, 3.410365365020302*^9}, { 3.410365398422759*^9, 3.410365765238345*^9}, {3.410365986774751*^9, 3.410366018143178*^9}, {3.410370316374341*^9, 3.41037033887877*^9}, 3.410370378162593*^9, {3.410536901238131*^9, 3.410536916979412*^9}, { 3.4300643225500607`*^9, 3.430064379217946*^9}, {3.430064709725927*^9, 3.4300647143818493`*^9}, {3.430064748410703*^9, 3.430064752785395*^9}, { 3.4300647840331955`*^9, 3.4300647930794334`*^9}, {3.4300649510214386`*^9, 3.4300649566304183`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfLD0", "[", RowBox[{"5.7", ",", "15"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.003345965457471272`", ",", "0.009536001553793125`", ",", "0.016767469398752913`", ",", "0.02355789717184977`", ",", "0.02910035040826871`", ",", "0.03312787122784504`", ",", "0.03569563178469149`", ",", "0.03701109059727024`", ",", "0.037328993778887536`", ",", "0.036895826091020184`", ",", "0.03592532325303746`", ",", "0.03459129797471508`", ",", "0.03302908373591559`", ",", "0.03134060991570227`", ",", "0.029600473900395097`", ",", "0.027861747015718277`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232368136779*^9, 3.399297619621661*^9, 3.405871884884643*^9, 3.409343894834008*^9, 3.409862382781656*^9, 3.409863452217797*^9, 3.410018781620496*^9, 3.410019440298791*^9, 3.410031068104409*^9, 3.410033726590104*^9, 3.410101558254613*^9, 3.410183949331289*^9, 3.410362809294677*^9, 3.41053811228323*^9, 3.410538888041657*^9, 3.410546320167228*^9, 3.410547140568127*^9, 3.416253501264096*^9, 3.416589939916917*^9, 3.4298790917399364`*^9, 3.429882963417913*^9, 3.42989026817758*^9, 3.429898470896796*^9, 3.4299711574542317`*^9, 3.4299725833531914`*^9, 3.430054369614937*^9, 3.43006117595453*^9, 3.430063291038642*^9, 3.430064396232373*^9, 3.430064520754856*^9, { 3.430065357483341*^9, 3.430062255940847*^9}, 3.430071046699215*^9, 3.430071813160331*^9}] }, Open ]], Cell[CellGroupData[{ Cell["newtonLD0[demerec,InitialM->3,ShowIterations->True]", "Input"], Cell[CellGroupData[{ Cell[BoxData["3"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.4300718131759567`*^9}], Cell[BoxData["5.9410741308071096`"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.4300718214263787`*^9}], Cell[BoxData["9.34988232782198`"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.4300718297393045`*^9}], Cell[BoxData["10.733970006389026`"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.430071837989727*^9}], Cell[BoxData["10.843274363697043`"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.4300718462245235`*^9}], Cell[BoxData["10.843826980617358`"], "Print", CellChangeTimes->{ 3.399232368177652*^9, 3.399297619776007*^9, 3.405871884911909*^9, 3.409343894986933*^9, 3.409862382803456*^9, 3.409863452377587*^9, 3.410018781646809*^9, 3.410019440326188*^9, 3.410031068258273*^9, 3.410033726745964*^9, 3.41010155840699*^9, 3.410183949485818*^9, 3.410362809332563*^9, 3.410538112511202*^9, 3.410538888198174*^9, 3.410546320320524*^9, 3.410547140599153*^9, 3.416253501292746*^9, 3.4165899399481483`*^9, 3.429879091755562*^9, 3.42988296344913*^9, 3.42989026817758*^9, 3.4298984709280386`*^9, 3.4299711574698825`*^9, 3.4299725833688145`*^9, 3.430054369630577*^9, 3.4300611759857807`*^9, 3.430063291054264*^9, 3.4300643962636213`*^9, 3.43006452077048*^9, { 3.43006535749897*^9, 3.430062255979084*^9}, 3.430071046714841*^9, 3.43007185445932*^9}] }, Open ]], Cell[BoxData["10.84382699452907`"], "Output", CellChangeTimes->{ 3.39923246311916*^9, 3.399297707378074*^9, 3.405871979744605*^9, 3.409343983458116*^9, 3.409862471065617*^9, 3.409863540353244*^9, 3.410018869959085*^9, 3.410019528124131*^9, 3.410031156824621*^9, 3.41003381478441*^9, 3.41010164645681*^9, 3.410184038786436*^9, 3.41036289956058*^9, 3.410538205438839*^9, 3.410538976439201*^9, 3.410546412556973*^9, 3.410547228842544*^9, 3.4162535974181*^9, 3.416589989918068*^9, 3.429879141193694*^9, 3.429883013271462*^9, 3.429890317873759*^9, 3.429898520726124*^9, 3.429971207379965*^9, 3.429972633129025*^9, 3.4300544193826895`*^9, 3.4300612260033264`*^9, 3.4300633420614*^9, 3.430064446213229*^9, 3.4300645705950975`*^9, { 3.4300654088555355`*^9, 3.43006234741473*^9}, 3.430071096467388*^9, 3.4300718627097425`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Methods of Historical Interest", "Section", FontSize->16], Cell["\<\ The maximum likelihood method is widely regarded as the method of choice for \ estimating mutation rates; see, for example, the simulation studies of \ Rosche and Foster (2000). However, there are several methods of great \ historical interest; these relatively simple methods are still popular and \ some are actually adopted by SALVADOR to yield initial guesses for the \ maximum likelihood estimators. \ \>", "Text", CellChangeTimes->{{3.410537144408561*^9, 3.410537227018729*^9}, { 3.410537280691774*^9, 3.410537303837592*^9}}], Cell[TextData[{ "Note that the ", Cell[BoxData[ FormBox[ SubscriptBox["P", "0"], TraditionalForm]]], " method is not always applicable." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "MethodOfP0"}]], "Input"], Cell[BoxData[ StyleBox["\<\"MethodOfP0[data] estimates m, the expected number of \ mutations,\\nusing the \!\(P\_0\) method.\"\>", "MSG"]], "Print", \ "PrintUsage", CellChangeTimes->{3.4300718628347487`*^9}, CellTags->"Info3430053862-6070048"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MethodOfP0", "[", "demerec", "]"}]], "Input"], Cell[BoxData["\<\"The \\!\\(P\\_0 \\) method is not applicable to this \ case.\"\>"], "Print", CellChangeTimes->{ 3.399232685726302*^9, 3.399297926706528*^9, 3.405872200110365*^9, 3.409344212843763*^9, 3.409862708239738*^9, 3.409863771064247*^9, 3.41001908816021*^9, 3.410019749196106*^9, 3.410031378879992*^9, 3.410034036639298*^9, 3.410101866385312*^9, 3.410184259978283*^9, 3.410363133135685*^9, 3.410538434971237*^9, 3.410539197767194*^9, 3.410546636580043*^9, 3.410547450187409*^9, 3.41625383064318*^9, 3.416590111450649*^9, 3.42987926233587*^9, 3.429883134487073*^9, 3.429890438958801*^9, 3.4298986417054195`*^9, 3.4299713287980957`*^9, 3.429972755146998*^9, 3.4300545404021225`*^9, 3.4300613474139214`*^9, 3.430063463561201*^9, 3.430064570782584*^9, {3.4300654090274534`*^9, 3.43006234949198*^9}, 3.430071096623646*^9, 3.430071862881626*^9}] }, Open ]], Cell["\<\ Note that Luria and Delbruck's method of the mean has several variants, one \ of which was suggested by Armitage.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "MethodOfMeans"}]], "Input"], Cell[BoxData[ StyleBox["\<\"MethodOfMeans[data,opts] iteratively solves for m\\nthe \ equation \!\( m log(\[Beta] n m)=X\&_ \), where \!\(\[Beta]\) is \ a\\ncorrection factor, where \!\(X\&_\) is the sample mean, and where n is \ sample size.\\nThe correction suggested by Armitage corresponds to \ \!\(\[Beta]=3.46\)\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071862975381*^9}, CellTags->"Info3430053862-5530159"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "MethodOfMeans", "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Correction", "\[Rule]", "1"}], ",", RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}], ",", RowBox[{"MaxIterations", "\[Rule]", "20"}], ",", RowBox[{"InitialM", "\[Rule]", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232686515669*^9, 3.399297927484084*^9, 3.405872200974712*^9, 3.409344213670068*^9, 3.409862709254381*^9, 3.409863772034247*^9, 3.410019089002853*^9, 3.410019749915324*^9, 3.410031379673708*^9, 3.41003403764536*^9, 3.410101867251266*^9, 3.41018426076629*^9, 3.410363133909171*^9, 3.410538435754112*^9, 3.410539198659283*^9, 3.410546637361045*^9, 3.410547451052542*^9, 3.416253831649311*^9, 3.416590111606824*^9, 3.4298792624608717`*^9, 3.4298831346587667`*^9, 3.429890439099378*^9, 3.429898641861724*^9, 3.429971328970253*^9, 3.4299727553032312`*^9, 3.430054540527109*^9, 3.430061347945182*^9, 3.430063463701812*^9, 3.430064570938823*^9, {3.430065409152485*^9, 3.430062351211024*^9}, 3.430071096764278*^9, 3.430071863006633*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MethodOfMeans", "[", RowBox[{"demerec", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630222583`*^9}], Cell[BoxData["120.16666666666667`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630378847`*^9}], Cell[BoxData["26.147767717284403`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630378847`*^9}], Cell[BoxData["19.084388969180942`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630535097`*^9}], Cell[BoxData["18.941011339673526`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630535097`*^9}], Cell[BoxData["18.940937803789318`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630691357`*^9}], Cell[BoxData["18.940937803769877`"], "Print", CellChangeTimes->{ 3.399232686721163*^9, 3.399297927684841*^9, 3.405872201214505*^9, 3.409344213796538*^9, 3.409862709476687*^9, 3.409863772188228*^9, 3.410019089246241*^9, 3.410019750125267*^9, 3.410031379884092*^9, 3.410034037861149*^9, 3.410101867492414*^9, 3.410184260982335*^9, 3.410363134112569*^9, 3.410538435965083*^9, 3.410539198904153*^9, 3.410546637484163*^9, 3.410547451295582*^9, 3.416253831772659*^9, 3.4165901116224413`*^9, 3.4298792624764967`*^9, 3.429883134674375*^9, 3.429890439114998*^9, 3.4298986418773537`*^9, 3.429971328970253*^9, 3.4299727553188543`*^9, 3.430054540527109*^9, 3.4300613479764323`*^9, 3.430063463717435*^9, 3.430064570954447*^9, {3.4300654091681137`*^9, 3.430062351316244*^9}, 3.430071096779904*^9, 3.4300718630691357`*^9}] }, Open ]], Cell[BoxData["18.940937803769877`"], "Output", CellChangeTimes->{ 3.39923268749865*^9, 3.399297928375633*^9, 3.405872202071573*^9, 3.409344214601384*^9, 3.409862710271242*^9, 3.409863772377284*^9, 3.410019090105917*^9, 3.410019750821348*^9, 3.410031380660907*^9, 3.410034038648779*^9, 3.410101868346836*^9, 3.410184261787706*^9, 3.410363134887341*^9, 3.410538436746419*^9, 3.410539199783621*^9, 3.410546638278207*^9, 3.410547452160203*^9, 3.416253832554643*^9, 3.4165901116849113`*^9, 3.4298792625389977`*^9, 3.4298831347524176`*^9, 3.4298904391774764`*^9, 3.4298986419398756`*^9, 3.4299713290485067`*^9, 3.4299727553813477`*^9, 3.430054540589603*^9, 3.430061347992058*^9, 3.4300634637955523`*^9, 3.4300645710169425`*^9, {3.430065409215*^9, 3.430062351759064*^9}, 3.430071096842407*^9, 3.4300718630847616`*^9}] }, Open ]], Cell["\<\ To adopt Armitage's (1952) correction, chose \[Beta]=3.46.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MethodOfMeans", "[", RowBox[{"demerec", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}], ",", RowBox[{"Correction", "\[Rule]", "3.46"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631003876`*^9}], Cell[BoxData["120.14296724470137`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631003876`*^9}], Cell[BoxData["23.034501227344553`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631003876`*^9}], Cell[BoxData["16.307136085258612`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631160135`*^9}], Cell[BoxData["16.1773010142091`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631316395`*^9}], Cell[BoxData["16.17723950973725`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631316395`*^9}], Cell[BoxData["16.177239509723375`"], "Print", CellChangeTimes->{ 3.399232687744837*^9, 3.399297928598014*^9, 3.405872202306599*^9, 3.4093442148337*^9, 3.409862710507266*^9, 3.409863772600382*^9, 3.410019090336602*^9, 3.410019751155663*^9, 3.410031380907101*^9, 3.410034038894913*^9, 3.410101868583467*^9, 3.410184262043618*^9, 3.410363135139862*^9, 3.41053843702251*^9, 3.410539200113102*^9, 3.41054663850599*^9, 3.410547452393289*^9, 3.416253832777542*^9, 3.416590111700529*^9, 3.4298792625389977`*^9, 3.4298831347680264`*^9, 3.429890439193096*^9, 3.4298986419555063`*^9, 3.4299713290641575`*^9, 3.4299727553969707`*^9, 3.430054540589603*^9, 3.430061348007683*^9, 3.4300634638111753`*^9, 3.430064571032566*^9, {3.430065409215*^9, 3.430062351954316*^9}, 3.430071096842407*^9, 3.4300718631472645`*^9}] }, Open ]], Cell[BoxData["16.177239509723375`"], "Output", CellChangeTimes->{ 3.399232688423277*^9, 3.399297929332203*^9, 3.405872203064156*^9, 3.409344215592496*^9, 3.409862711257696*^9, 3.409863773233348*^9, 3.41001909109826*^9, 3.410019751839186*^9, 3.41003138159264*^9, 3.410034039588345*^9, 3.410101869326989*^9, 3.410184262745711*^9, 3.410363135821914*^9, 3.410538437713479*^9, 3.410539200805628*^9, 3.410546639237093*^9, 3.410547453135276*^9, 3.416253833518004*^9, 3.4165901117786164`*^9, 3.429879262585873*^9, 3.4298831348460684`*^9, 3.4298904392711945`*^9, 3.429898642033658*^9, 3.4299713291424108`*^9, 3.429972755475087*^9, 3.4300545406208496`*^9, 3.4300613480858097`*^9, 3.4300634638736687`*^9, 3.4300645711106863`*^9, {3.430065409261887*^9, 3.430062352487777*^9}, 3.43007109690491*^9, 3.4300718631472645`*^9}] }, Open ]], Cell["\<\ Replace the sample mean by the sample median in Luria and Delbruck's method \ of the mean gives Drake's (1991) estimator.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "drakeMedian"}]], "Input"], Cell[BoxData[ StyleBox["\<\"drakeMedian[data,opts] iteratively solve the equation\\nm \ log(m)=\!\(\[Xi]\&^\_0.5\), where \!\(\[Xi]\&^\_0.5\) is the sample median \ and\\nwhere m is the expected number of mutations per culture.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718632410192`*^9}, CellTags->"Info3430053863-2140964"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "drakeMedian", "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"InitialM", "\[Rule]", "1"}], ",", RowBox[{"MaxIterations", "\[Rule]", "20"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399232689358997*^9, 3.399297930245861*^9, 3.40587220393608*^9, 3.409344216536382*^9, 3.409862712197938*^9, 3.40986377411322*^9, 3.410019091982103*^9, 3.410019752738144*^9, 3.410031382506519*^9, 3.410034040522952*^9, 3.410101870242486*^9, 3.410184263679846*^9, 3.410363136742599*^9, 3.410538438637024*^9, 3.410539201783923*^9, 3.410546640120764*^9, 3.410547454041616*^9, 3.416253834445925*^9, 3.4165901119035563`*^9, 3.4298792627108746`*^9, 3.4298831350021534`*^9, 3.429890439411772*^9, 3.4298986421743317`*^9, 3.429971329283267*^9, 3.429972755615697*^9, 3.430054540745837*^9, 3.4300613482420626`*^9, 3.4300634640299025`*^9, 3.4300645712513013`*^9, {3.430065409386918*^9, 3.430062353299306*^9}, 3.4300710970455427`*^9, 3.430071863272271*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"drakeMedian", "[", RowBox[{"demerec", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863287897*^9}], Cell[BoxData["45.`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863287897*^9}], Cell[BoxData["18.515966159349116`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863303523*^9}], Cell[BoxData["15.953512321607496`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863303523*^9}], Cell[BoxData["15.904142530713985`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863319149*^9}], Cell[BoxData["15.904122228772625`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.430071863319149*^9}], Cell[BoxData["15.904122228769184`"], "Print", CellChangeTimes->{ 3.399232689541954*^9, 3.399297930426709*^9, 3.405872204116873*^9, 3.409344216733509*^9, 3.409862712391412*^9, 3.409863774301012*^9, 3.410019092163959*^9, 3.410019752921488*^9, 3.410031382687595*^9, 3.410034040717958*^9, 3.410101870425009*^9, 3.410184263868922*^9, 3.41036313692422*^9, 3.410538438822697*^9, 3.410539201968875*^9, 3.410546640306557*^9, 3.410547454225277*^9, 3.41625383462714*^9, 3.4165901119191737`*^9, 3.4298792627108746`*^9, 3.429883135017762*^9, 3.4298904394273915`*^9, 3.429898642189962*^9, 3.429971329298918*^9, 3.4299727556313205`*^9, 3.430054540745837*^9, 3.4300613482576876`*^9, 3.4300634640455265`*^9, 3.430064571266925*^9, {3.430065409402547*^9, 3.430062353465502*^9}, 3.4300710970455427`*^9, 3.4300718633347745`*^9}] }, Open ]], Cell[BoxData["15.904122228769184`"], "Output", CellChangeTimes->{ 3.399232690296378*^9, 3.399297931178197*^9, 3.405872204808018*^9, 3.409344217504753*^9, 3.409862713151101*^9, 3.409863775066636*^9, 3.410019092841166*^9, 3.410019753593454*^9, 3.410031383366073*^9, 3.410034041470877*^9, 3.410101871101544*^9, 3.410184264554369*^9, 3.410363137669639*^9, 3.410538439576049*^9, 3.410539202650046*^9, 3.410546640982008*^9, 3.410547454910813*^9, 3.416253835381441*^9, 3.4165901119816437`*^9, 3.4298792627577505`*^9, 3.429883135095804*^9, 3.42989043948987*^9, 3.429898642268114*^9, 3.4299713293771715`*^9, 3.429972755709437*^9, 3.4300545407927074`*^9, 3.4300613483358145`*^9, 3.43006346410802*^9, 3.430064571345044*^9, {3.4300654094338045`*^9, 3.430062354149017*^9}, 3.4300710971080456`*^9, 3.4300718633504004`*^9}] }, Open ]], Cell["\<\ This is different from the method of the median proposed by Lea and Coulson \ (1949).\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "MethodOfMedians"}]], "Input"], Cell[BoxData[ StyleBox["\<\"MethodOfMedians[data,opts] iteratively solve for m Lea\\nand \ Coulson's equation \!\(\[Xi]\&^\_0.5/m\)-log(m)-1.24=0,\\nwhere \ \!\(\[Xi]\&^\_0.5\) is the sample median. When the sample \ median\\n\!\(\[Xi]\&^\_0.5\)=0, it estimate m by \!\(e\^-1.24\) which may not \ be a\\nreliable estimate.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071863444155*^9}, CellTags->"Info3430053863-2297694"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MethodOfMedians", "[", RowBox[{"demerec", ",", " ", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718634754066`*^9}], Cell[BoxData["20.08928571428569`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718634754066`*^9}], Cell[BoxData["12.230344129718443`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718634910326`*^9}], Cell[BoxData["11.853138984844577`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718634910326`*^9}], Cell[BoxData["11.851891779187563`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718635066586`*^9}], Cell[BoxData["11.851891765263124`"], "Print", CellChangeTimes->{ 3.399232691188273*^9, 3.39929793214178*^9, 3.405872205735891*^9, 3.409344218413229*^9, 3.409862714123065*^9, 3.40986377597014*^9, 3.410019093877812*^9, 3.410019754546759*^9, 3.410031384324253*^9, 3.41003404253103*^9, 3.410101872072111*^9, 3.41018426554362*^9, 3.410363138668659*^9, 3.410538440586233*^9, 3.410539203612101*^9, 3.41054664195369*^9, 3.410547455883299*^9, 3.416253836275219*^9, 3.416590112137819*^9, 3.429879262882752*^9, 3.4298831352518897`*^9, 3.4298904396460676`*^9, 3.429898642424418*^9, 3.4299713295180273`*^9, 3.4299727558656697`*^9, 3.430054540902071*^9, 3.4300613484764423`*^9, 3.430063464264254*^9, 3.4300645714856596`*^9, {3.430065409574465*^9, 3.430062354958636*^9}, 3.4300710972330523`*^9, 3.4300718635066586`*^9}] }, Open ]], Cell[BoxData["11.851891765263124`"], "Output", CellChangeTimes->{ 3.399232691777998*^9, 3.399297932724332*^9, 3.405872206321537*^9, 3.409344219023896*^9, 3.409862714731062*^9, 3.409863776573291*^9, 3.410019094444066*^9, 3.410019755140308*^9, 3.410031384910963*^9, 3.410034043103479*^9, 3.410101872660418*^9, 3.410184266137136*^9, 3.410363139266725*^9, 3.410538441147536*^9, 3.410539204207032*^9, 3.410546642544632*^9, 3.410547456481454*^9, 3.416253836878066*^9, 3.4165901121846714`*^9, 3.4298792629140024`*^9, 3.4298831353143234`*^9, 3.4298904397085466`*^9, 3.4298986424869394`*^9, 3.4299713295806303`*^9, 3.429972755928163*^9, 3.430054540933318*^9, 3.4300613485545683`*^9, 3.430063464326748*^9, 3.4300645715481553`*^9, {3.430065409605723*^9, 3.430062355508573*^9}, 3.4300710972799296`*^9, 3.430071863522284*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"med", "=", RowBox[{"Median", "[", "demerec", "]"}]}]], "Input"], Cell[BoxData["44"], "Output", CellChangeTimes->{ 3.399232692082133*^9, 3.399297933015213*^9, 3.405872206610787*^9, 3.409344219327663*^9, 3.409862715032999*^9, 3.409863776785702*^9, 3.410019094650355*^9, 3.410019755344595*^9, 3.41003138519868*^9, 3.410034043323415*^9, 3.410101872963596*^9, 3.410184266351943*^9, 3.410363139558182*^9, 3.410538441380174*^9, 3.410539204414061*^9, 3.410546642836171*^9, 3.410547456687022*^9, 3.416253837169428*^9, 3.416590112200289*^9, 3.4298792629296274`*^9, 3.42988313534554*^9, 3.4298904397085466`*^9, 3.42989864250257*^9, 3.429971329596281*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.4300613485545683`*^9, 3.430063464326748*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355709609*^9}, 3.430071097295555*^9, 3.430071863522284*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MethodOfMedians", "[", RowBox[{"med", ",", " ", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.43007186353791*^9}], Cell[BoxData["20.08928571428569`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.43007186353791*^9}], Cell[BoxData["12.230344129718443`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.4300718635535355`*^9}], Cell[BoxData["11.853138984844577`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.4300718635535355`*^9}], Cell[BoxData["11.851891779187563`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.4300718635691614`*^9}], Cell[BoxData["11.851891765263124`"], "Print", CellChangeTimes->{ 3.399232692195127*^9, 3.399297933201397*^9, 3.405872206719706*^9, 3.409344219437319*^9, 3.409862715142279*^9, 3.409863776899119*^9, 3.410019094758392*^9, 3.410019755454711*^9, 3.410031385308249*^9, 3.410034043432908*^9, 3.410101873164435*^9, 3.410184266461032*^9, 3.410363139763552*^9, 3.410538441571052*^9, 3.410539204523769*^9, 3.410546642945051*^9, 3.410547456795136*^9, 3.416253837277743*^9, 3.416590112215906*^9, 3.4298792629296274`*^9, 3.429883135361149*^9, 3.429890439724166*^9, 3.42989864250257*^9, 3.429971329611932*^9, 3.4299727559437866`*^9, 3.430054540948941*^9, 3.430061348570194*^9, 3.430063464342371*^9, 3.430064571563779*^9, {3.4300654096213517`*^9, 3.430062355893444*^9}, 3.430071097311181*^9, 3.4300718635691614`*^9}] }, Open ]], Cell[BoxData["11.851891765263124`"], "Output", CellChangeTimes->{ 3.399232692813518*^9, 3.399297933744604*^9, 3.405872207327944*^9, 3.409344220058923*^9, 3.40986271576292*^9, 3.40986377752935*^9, 3.410019095372627*^9, 3.410019756062987*^9, 3.410031385937347*^9, 3.410034044057553*^9, 3.410101873710776*^9, 3.410184267077449*^9, 3.410363140309083*^9, 3.410538442111437*^9, 3.410539205137385*^9, 3.410546643549517*^9, 3.410547457404235*^9, 3.416253837888494*^9, 3.4165901122627587`*^9, 3.429879262960878*^9, 3.429883135423583*^9, 3.429890439786645*^9, 3.429898642580722*^9, 3.429971329674535*^9, 3.429972756021903*^9, 3.430054540980188*^9, 3.430061348632695*^9, 3.4300634644048643`*^9, 3.430064571626275*^9, {3.43006540965261*^9, 3.43006235640761*^9}, 3.4300710973580585`*^9, 3.4300718635847874`*^9}] }, Open ]], Cell["\<\ Lea and Coulson (1949) also proposed a method that bears some resemblance to \ the maximum likelihood method.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "semiMLE"}]], "Input"], Cell[BoxData[ StyleBox["\<\"semiMLE[data,\!\(m\_0:=1\)] computes an estimate\\nof m by \ solving \!\(\[Sum]Y\_i=0\), where \!\(Y\_i\) are the\\nLea-Coulson transforms \ of the original data. Note that\\n\!\(m\_0\) is a starting value used to \ solve the equation.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071863678542*^9}, CellTags->"Info3430053863-1206427"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"semiMLE", "[", "demerec", "]"}]], "Input"], Cell[BoxData["11.553643621646884`"], "Output", CellChangeTimes->{ 3.39923269366035*^9, 3.399297934750138*^9, 3.405872208296542*^9, 3.409344221082648*^9, 3.409862716631006*^9, 3.40986377849929*^9, 3.410019096403902*^9, 3.410019756847288*^9, 3.410031386920712*^9, 3.410034044934054*^9, 3.410101874709415*^9, 3.410184267976948*^9, 3.410363141335194*^9, 3.410538442856463*^9, 3.410539206000866*^9, 3.410546644399483*^9, 3.410547458254668*^9, 3.416253838753609*^9, 3.416590112418934*^9, 3.4298792630858793`*^9, 3.4298831356264935`*^9, 3.4298904399428415`*^9, 3.429898642737026*^9, 3.429971329909295*^9, 3.429972756178136*^9, 3.430054541167669*^9, 3.430061348788948*^9, 3.430063464561098*^9, 3.4300645717981377`*^9, {3.430065409777641*^9, 3.430062357267611*^9}, 3.4300710974830647`*^9, 3.4300718637097936`*^9}] }, Open ]], Cell["\<\ It is noteworthy that Jones at al. (1994) proposed a method based on the \ median that does not require an initial guess.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "jonesMedian"}]], "Input"], Cell[BoxData[ StyleBox["\<\"jonesMedian[data] estimates m by the method of the median\\nof \ Jones et al. (1994).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718638191743`*^9}, CellTags->"Info3430053863-9079730"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ jonesMedian[demerec]\ \>", "Input"], Cell[BoxData["10.43365243358806`"], "Output", CellChangeTimes->{ 3.399232694543736*^9, 3.399297935642574*^9, 3.40587220908881*^9, 3.409344222018252*^9, 3.409862717452889*^9, 3.40986377937689*^9, 3.410019097396601*^9, 3.410019757713458*^9, 3.410031387712334*^9, 3.410034045825461*^9, 3.410101875508716*^9, 3.410184268953136*^9, 3.410363142218256*^9, 3.410538443798382*^9, 3.410539206754617*^9, 3.410546645287302*^9, 3.410547459038518*^9, 3.416253839577818*^9, 3.416590112559491*^9, 3.429879263226506*^9, 3.4298831357825785`*^9, 3.429890440099039*^9, 3.42989864289333*^9, 3.4299713300501513`*^9, 3.4299727563187456`*^9, 3.4300545413082795`*^9, 3.430061348945201*^9, 3.4300634647173324`*^9, 3.430064571938753*^9, {3.430065409902672*^9, 3.430062358123743*^9}, 3.4300710976236973`*^9, 3.4300718638504257`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Haldane's Formulation", "Section"], Cell[TextData[{ "Under Haldane's formulation cell growth is synchronous. If a cell \ population is initiated by a single nonmutant cell, then the total number of \ cells (the sum of all mutants and all nonmutants) in the g-th generation is \ ", Cell[BoxData[ FormBox[ SuperscriptBox["2", RowBox[{"g", " "}]], TraditionalForm]]], ". Each division of a nonmutant cell can give rise to a mutant daughter cell \ with probability \[Mu]. The total number of mutants in the g-th generation is \ said to obey an Haldane distribution denoted by H(\[Mu],g). Relevant \ algorithms for the Haldane formulation are discussed in Zheng (2007). \n\nTo \ help visualize the Haldane formulation, the user can invoke simuHaldane to \ simulate the mutational process under Haldane's formulation.The function \ simuHaldane assumes that there is just one wild-type cell at the beginning, \ that is, ", Cell[BoxData[ FormBox[ SubscriptBox["N", "0"], TraditionalForm]]], "=1." }], "Text", CellChangeTimes->{{3.410537541400225*^9, 3.410537611205444*^9}, 3.4300563474678974`*^9, 3.430064992190415*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "simuHaldane"}]], "Input"], Cell[BoxData[ StyleBox["\<\"simuHaldane[g, \!\(\[Mu]\)] simulates Haldane's model\\nfor g \ generations. The evolution of the mutation process can be viewed by \ setting\\nShowGrowth->True.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718639598064`*^9}, CellTags->"Info3430053863-2784273"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"simuHaldane", "[", RowBox[{"8", ",", "0.02", ",", RowBox[{"ShowGrowth", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.410031624003177*^9, 3.410031627770921*^9}}], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "1", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["gen=", 1, " wild=", 2, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718639910583`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "4", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["gen=", 2, " wild=", 4, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718639910583`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "3", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "8", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["gen=", 3, " wild=", 8, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718639910583`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "4", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "16", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["gen=", 4, " wild=", 16, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718640066843`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "5", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "32", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "0"}], SequenceForm["gen=", 5, " wild=", 32, " mutant=", 0], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718640066843`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "6", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "63", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "1"}], SequenceForm["gen=", 6, " wild=", 63, " mutant=", 1], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718640223093`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "7", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "126", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "2"}], SequenceForm["gen=", 7, " wild=", 126, " mutant=", 2], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718640223093`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"gen=\"\>", "\[InvisibleSpace]", "8", "\[InvisibleSpace]", "\<\" wild=\"\>", "\[InvisibleSpace]", "250", "\[InvisibleSpace]", "\<\" mutant=\"\>", "\[InvisibleSpace]", "6"}], SequenceForm["gen=", 8, " wild=", 250, " mutant=", 6], Editable->False]], "Print", CellChangeTimes->{ 3.410031628889232*^9, 3.410034046767663*^9, 3.410101876562597*^9, 3.410184269986265*^9, 3.410363143242764*^9, 3.410538444876497*^9, 3.410539207693601*^9, 3.410546646090811*^9, 3.410547459837474*^9, 3.416253840404967*^9, 3.4165901127000484`*^9, 3.429879263351508*^9, 3.4298831359386635`*^9, 3.4298904401771374`*^9, 3.4298986429714823`*^9, 3.429971330159706*^9, 3.4299727564281087`*^9, 3.4300545413707733`*^9, 3.430061349085829*^9, 3.4300634648735666`*^9, 3.4300645720949917`*^9, { 3.4300654100277033`*^9, 3.43006235902801*^9}, 3.430071097748704*^9, 3.4300718640379353`*^9}] }, Open ]], Cell[BoxData["6"], "Output", CellChangeTimes->{ 3.399232696700847*^9, 3.399297937747968*^9, 3.405872211278355*^9, 3.405874735922783*^9, 3.409344224142182*^9, 3.409862718552389*^9, 3.409863780405021*^9, 3.41001909827427*^9, 3.410019758721516*^9, 3.410031388749941*^9, 3.410031629103754*^9, 3.410034047660239*^9, 3.410101877453516*^9, 3.410184270887502*^9, 3.410363144108613*^9, 3.410538445767844*^9, 3.410539208584304*^9, 3.41054664696743*^9, 3.410547460757441*^9, 3.416253841303552*^9, 3.4165901127781363`*^9, 3.4298792633983836`*^9, 3.4298831360323143`*^9, 3.4298904402552357`*^9, 3.4298986430652647`*^9, 3.42997133023796*^9, 3.429972756506225*^9, 3.4300545414176435`*^9, 3.4300613491795807`*^9, 3.4300634649516835`*^9, 3.430064572188735*^9, {3.4300654100902185`*^9, 3.430062359851731*^9}, 3.430071097811207*^9, 3.4300718640379353`*^9}] }, Open ]], Cell["\<\ Now we simulate a fluctuation experiment by assuming \[Mu]=0.002 and g=8.\ \>", "Text", CellChangeTimes->{{3.410537372489647*^9, 3.410537412351356*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"datHal0", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"simuHaldane", "[", RowBox[{"8", ",", "0.005"}], "]"}], ",", RowBox[{"{", "75", "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.409862918773656*^9, 3.409862922885614*^9}, { 3.410031641123515*^9, 3.410031646138677*^9}, {3.410031814500148*^9, 3.410031817319471*^9}, {3.410539883212001*^9, 3.410539884106094*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "0", ",", "9", ",", "68", ",", "8", ",", "1", ",", "0", ",", "2", ",", "0", ",", "4", ",", "1", ",", "8", ",", "2", ",", "0", ",", "1", ",", "0", ",", "1", ",", "4", ",", "1", ",", "1", ",", "0", ",", "2", ",", "2", ",", "0", ",", "1", ",", "1", ",", "2", ",", "5", ",", "3", ",", "64", ",", "3", ",", "8", ",", "2", ",", "1", ",", "1", ",", "0", ",", "11", ",", "1", ",", "0", ",", "2", ",", "0", ",", "1", ",", "2", ",", "3", ",", "1", ",", "0", ",", "0", ",", "8", ",", "1", ",", "2", ",", "2", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "2", ",", "2", ",", "8", ",", "2", ",", "4", ",", "0", ",", "0", ",", "9", ",", "0", ",", "5", ",", "11", ",", "7", ",", "2", ",", "1", ",", "0", ",", "8", ",", "1", ",", "8"}], "}"}]], "Output", CellChangeTimes->{ 3.399232697068845*^9, 3.399297938023876*^9, 3.4058722115565*^9, 3.405874736292134*^9, 3.409344224517916*^9, 3.409862718662213*^9, 3.409862924247738*^9, 3.409863781415165*^9, 3.410019099374858*^9, 3.410019759585291*^9, 3.410031389695385*^9, 3.410031647868006*^9, 3.410031820112169*^9, 3.410034048584191*^9, 3.410101878558298*^9, 3.410184271847179*^9, 3.410363145216501*^9, 3.410538446196105*^9, 3.410539209005561*^9, 3.410539885454233*^9, 3.410546647390575*^9, 3.410547461189391*^9, 3.416253841730682*^9, 3.416590112856224*^9, 3.4298792634765096`*^9, 3.4298831361103573`*^9, 3.429890440348954*^9, 3.4298986431434164`*^9, 3.429971330316213*^9, 3.429972756599965*^9, 3.43005454149576*^9, 3.430061349257707*^9, 3.430063465045424*^9, 3.4300645722668543`*^9, {3.430065410168363*^9, 3.43006236024961*^9}, 3.4300710978893356`*^9, 3.430071864116064*^9}] }, Open ]], Cell[TextData[{ "Note that simuHaldane assumes ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["N", "0"], "=", "1."}], TraditionalForm]]], " However, this is not an obstacle. For example, if ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["N", "0"], " ", "=", "3"}], TraditionalForm]]], " is the desired initial number of nonmutant cells, we can process the above \ data as follows." }], "Text", CellChangeTimes->{{3.410031672536807*^9, 3.410031810058326*^9}, { 3.410537469863996*^9, 3.410537485133712*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"datHal", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Plus", "@@", "#"}], ")"}], "&"}], "/@", " ", RowBox[{"Partition", "[", RowBox[{"datHal0", ",", "3"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.410031824292441*^9, 3.410031849759247*^9}, { 3.410103503474145*^9, 3.410103516787772*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "5", ",", "85", ",", "3", ",", "5", ",", "10", ",", "2", ",", "6", ",", "4", ",", "2", ",", "10", ",", "75", ",", "4", ",", "12", ",", "2", ",", "6", ",", "1", ",", "11", ",", "2", ",", "0", ",", "12", ",", "6", ",", "9", ",", "23", ",", "3", ",", "17"}], "}"}]], "Output", CellChangeTimes->{ 3.410031850458216*^9, 3.410034048728015*^9, 3.410101878829506*^9, 3.410184272111056*^9, 3.410363145589695*^9, 3.41053844644894*^9, 3.410539209257378*^9, 3.410539889243517*^9, 3.410546647640192*^9, 3.410547461444022*^9, 3.41625384186402*^9, 3.4165901128718414`*^9, 3.4298792634765096`*^9, 3.4298831361259656`*^9, 3.429890440348954*^9, 3.429898643159047*^9, 3.4299713303318644`*^9, 3.429972756615588*^9, 3.43005454149576*^9, 3.4300613492733326`*^9, 3.430063465045424*^9, 3.4300645722668543`*^9, {3.430065410183992*^9, 3.430062360481367*^9}, 3.4300710979049616`*^9, 3.4300718641316905`*^9}] }, Open ]], Cell["\<\ A maximum likelihood estimate of the mutation rate \[Mu] can be obtained by \ invoking newtonHaldane, which applies the Newton-Raphson method to calculate \ a estimate.\ \>", "Text", CellChangeTimes->{{3.410031652502287*^9, 3.410031653660912*^9}, 3.410537495872966*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "newtonHaldane"}]], "Input"], Cell[BoxData[ StyleBox["\<\"newtonHaldane[data,g,opts] compute the maximum\\nlikelihood \ estimate for \!\(\[Mu]\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718642410707`*^9}, CellTags->"Info3430053864-7255033"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonHaldane", "[", RowBox[{"datHal", ",", "8", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}], ",", " ", RowBox[{"InitialCells", "\[Rule]", "3"}]}], "]"}]], "Input", CellChangeTimes->{{3.410031859501853*^9, 3.410031872363385*^9}, { 3.410103523372756*^9, 3.41010352383728*^9}}], Cell[CellGroupData[{ Cell[BoxData["0.0020656539529808615`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.4300718642723227`*^9}], Cell[BoxData["0.0030859180576825193`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.4300718642723227`*^9}], Cell[BoxData["0.003834883411089199`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.4300718642879486`*^9}], Cell[BoxData["0.004054450482590552`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.430071864303574*^9}], Cell[BoxData["0.004066998505797644`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.430071864303574*^9}], Cell[BoxData["0.004067034969557857`"], "Print", CellChangeTimes->{ 3.399232698008674*^9, 3.399297938870073*^9, 3.405872212501453*^9, 3.405874737412267*^9, 3.409344225661369*^9, 3.409862719896334*^9, 3.409862934826126*^9, 3.409863782355235*^9, 3.410019100504594*^9, 3.410019760764652*^9, 3.410031390700269*^9, 3.410031873575947*^9, 3.41003405013471*^9, 3.410101879783968*^9, 3.410184273646249*^9, 3.410363146936725*^9, 3.410538447584461*^9, 3.410539210605295*^9, 3.410539897607738*^9, 3.410546648750621*^9, 3.410547462587714*^9, 3.41625384309311*^9, 3.416590113028016*^9, 3.4298792636171365`*^9, 3.429883136297659*^9, 3.429890440505151*^9, 3.4298986433309813`*^9, 3.4299713305040216`*^9, 3.429972756771821*^9, 3.4300545416363707`*^9, 3.4300613494295855`*^9, 3.4300634652172813`*^9, 3.430064572438718*^9, { 3.430065410309023*^9, 3.430062361531647*^9}, 3.4300710980455933`*^9, 3.4300718643192*^9}] }, Open ]], Cell[BoxData["0.004067034969863737`"], "Output", CellChangeTimes->{ 3.409862935699761*^9, 3.409863782992733*^9, 3.410019101163153*^9, 3.410019761433659*^9, 3.410031391364605*^9, 3.410031873714521*^9, 3.410034050818822*^9, 3.410101880582799*^9, 3.410184274350171*^9, 3.410363147604697*^9, 3.41053844811546*^9, 3.410539211263295*^9, 3.41053989797822*^9, 3.410546649847823*^9, 3.410547463337648*^9, 3.416253843889853*^9, 3.4165901130904865`*^9, 3.429879263664012*^9, 3.4298831363913097`*^9, 3.4298904405988693`*^9, 3.429898643409133*^9, 3.429971330597926*^9, 3.4299727568343143`*^9, 3.430054541683241*^9, 3.430061349507712*^9, 3.4300634652797747`*^9, 3.430064572501213*^9, { 3.4300654103559103`*^9, 3.430062362188065*^9}, 3.430071098108097*^9, 3.4300718643348255`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonHaldane0", "[", RowBox[{"datHal", ",", "8", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}], ",", " ", RowBox[{"InitialCells", "\[Rule]", "3"}]}], "]"}]], "Input", CellChangeTimes->{{3.410031859501853*^9, 3.410031889101404*^9}, { 3.410103528755896*^9, 3.410103528970493*^9}}], Cell[CellGroupData[{ Cell[BoxData["0.0020656539529808615`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.4300718643348255`*^9}], Cell[BoxData["0.0030859180576825193`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.430071864537961*^9}], Cell[BoxData["0.003834883411089199`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.4300718647254705`*^9}], Cell[BoxData["0.004054450482590553`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.43007186491298*^9}], Cell[BoxData["0.004066998505797644`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.4300718651161156`*^9}], Cell[BoxData["0.004067034969557858`"], "Print", CellChangeTimes->{ 3.410031890348732*^9, 3.410034051036711*^9, 3.410101880851724*^9, 3.410184274574819*^9, 3.410363147896255*^9, 3.410538448334666*^9, 3.410539211562714*^9, 3.41053990190017*^9, 3.41054665010593*^9, 3.410547463591836*^9, 3.416253844138269*^9, 3.416590113106104*^9, 3.429879263664012*^9, 3.4298831364225273`*^9, 3.4298904406144886`*^9, 3.4298986434247637`*^9, 3.429971330613577*^9, 3.4299727568499374`*^9, 3.430054541683241*^9, 3.4300613495233374`*^9, 3.4300634652953987`*^9, 3.430064572516837*^9, {3.430065410371539*^9, 3.430062362435868*^9}, 3.430071098123723*^9, 3.430071865303625*^9}] }, Open ]], Cell[BoxData["0.004067034969863736`"], "Output", CellChangeTimes->{ 3.41003189405352*^9, 3.410034056382206*^9, 3.410101901408962*^9, 3.410184287526691*^9, 3.410363159095202*^9, 3.410538451998104*^9, 3.410539217611835*^9, 3.410539904109518*^9, 3.410546653104653*^9, 3.410547469079179*^9, 3.416253846866756*^9, 3.416590115807931*^9, 3.4298792670546803`*^9, 3.429883139013538*^9, 3.429890440973742*^9, 3.429898643721741*^9, 3.4299713333680997`*^9, 3.4299727578185825`*^9, 3.430054542073826*^9, 3.430061353195283*^9, 3.4300634688887806`*^9, 3.4300645752353954`*^9, {3.43006541063723*^9, 3.430062364803658*^9}, 3.430071098436239*^9, 3.4300718655067606`*^9}] }, Open ]], Cell["\<\ An asymptotic 95% confidence interval for the mutation rate can be obtained \ by invoking CIHaldane. \ \>", "Text", CellChangeTimes->{3.410537689118443*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "CIHaldane"}]], "Input"], Cell[BoxData[ StyleBox["\<\"CIHaldane[data,g,opts] compute an asymptotic confidence \ interval\\nfor the mutation rate.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718656161413`*^9}, CellTags->"Info3430053865-7732867"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CIHaldane", "[", RowBox[{"datHal", ",", "8", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}], ",", " ", RowBox[{"InitialCells", "\[Rule]", "3"}]}], "]"}]], "Input", CellChangeTimes->{{3.410031911130176*^9, 3.410031913901969*^9}, { 3.410101462379918*^9, 3.410101473791139*^9}, {3.41010353463982*^9, 3.410103534823486*^9}}], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for MLE of \\!\\(\[Mu]\\)...\"\>"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718656473927`*^9}], Cell[BoxData["0.0020656539529808615`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718656473927`*^9}], Cell[BoxData["0.0030859180576825193`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718656630187`*^9}], Cell[BoxData["0.003834883411089199`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718656630187`*^9}], Cell[BoxData["0.004054450482590552`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865678644*^9}], Cell[BoxData["0.004066998505797644`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865678644*^9}], Cell[BoxData["0.004067034969557857`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.43007186569427*^9}], Cell[BoxData["\<\"Iterating for lower limit of CI ...\"\>"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.43007186569427*^9}], Cell[BoxData["0.0034944444515550063`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865709896*^9}], Cell[BoxData["0.0027753391250019844`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865709896*^9}], Cell[BoxData["0.002989958104633612`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865725522*^9}], Cell[BoxData["0.003021853655959018`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865725522*^9}], Cell[BoxData["0.0030225139110589133`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718657411475`*^9}], Cell[BoxData["\<\"Iterating for upper limit of CI ...\"\>"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.4300718657411475`*^9}], Cell[BoxData["0.004639625488172467`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865756774*^9}], Cell[BoxData["0.005634822272605693`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865756774*^9}], Cell[BoxData["0.005337644555492653`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865772399*^9}], Cell[BoxData["0.005311696778280044`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865772399*^9}], Cell[BoxData["0.005311482879791037`"], "Print", CellChangeTimes->{ 3.399232701853341*^9, 3.399297941032149*^9, 3.405872216790894*^9, 3.405874741329836*^9, 3.40934422847541*^9, 3.409862721463029*^9, 3.409862941456881*^9, 3.409863783946849*^9, 3.410019102147456*^9, 3.410019762446137*^9, 3.410031392356925*^9, 3.410031916266973*^9, 3.410034057354715*^9, 3.410101902330361*^9, 3.410184288473076*^9, 3.41036316004499*^9, 3.410538452992855*^9, 3.41053921855077*^9, 3.410539912194119*^9, 3.410546653969398*^9, 3.410547470006523*^9, 3.416253847929163*^9, 3.4165901159641066`*^9, 3.429879267179682*^9, 3.429883139169623*^9, 3.429890441129939*^9, 3.429898643893676*^9, 3.4299713335402575`*^9, 3.4299727579904385`*^9, 3.43005454218319*^9, 3.4300613533827863`*^9, 3.4300634690606375`*^9, 3.4300645754072585`*^9, { 3.4300654107622614`*^9, 3.430062365638519*^9}, 3.430071098561245*^9, 3.430071865788025*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"0.003022514190248233`", ",", "0.005311482865175513`"}], "}"}]], "Output", CellChangeTimes->{ 3.399232708236126*^9, 3.399297943535044*^9, 3.405872223769797*^9, 3.405874747305562*^9, 3.409344231736181*^9, 3.409862744648097*^9, 3.409862942915193*^9, 3.409863785813691*^9, 3.410019104001213*^9, 3.410019764343834*^9, 3.410031394269196*^9, 3.410031917910928*^9, 3.410034061883404*^9, 3.410101904284933*^9, 3.410184290400596*^9, 3.410363161883711*^9, 3.410538454838469*^9, 3.410539220409168*^9, 3.4105399143827*^9, 3.41054665594455*^9, 3.410547471868606*^9, 3.416253849817742*^9, 3.416590116167134*^9, 3.4298792673046837`*^9, 3.4298831394037504`*^9, 3.4298904413486147`*^9, 3.429898644128132*^9, 3.4299713337437167`*^9, 3.4299727582091646`*^9, 3.430054542292554*^9, 3.4300613536171656`*^9, 3.430063469263742*^9, 3.430064575594745*^9, { 3.430065410887293*^9, 3.430062367332873*^9}, 3.4300710987331285`*^9, 3.430071865788025*^9}] }, Open ]], Cell["\<\ Historically, the mutation rate \[Mu] was estimated by the method of the \ mean. The method implemented in SALVADOR was that first appeared in Rossman \ et al. (1995).\ \>", "Text", CellChangeTimes->{{3.410537716400706*^9, 3.410537717374817*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "rossman"}]], "Input", CellChangeTimes->{{3.409863283097776*^9, 3.409863283630452*^9}}], Cell[BoxData[ StyleBox["\<\"rossman[data,g,N0] estimates the mutation rate\\n\!\(\[Mu]\) \ by the method of the mean.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718658974056`*^9}, CellTags->"Info3430053865-5358891"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"rossman", "[", RowBox[{"datHal", ",", "8", ",", "3"}], "]"}]], "Input", CellChangeTimes->{{3.409863278958907*^9, 3.409863279641517*^9}, { 3.410362724822462*^9, 3.410362727906221*^9}, {3.410537702153965*^9, 3.4105377065436*^9}}], Cell[BoxData["0.004131307905961723`"], "Output", CellChangeTimes->{ 3.399232709121858*^9, 3.39929794429284*^9, 3.405872224669748*^9, 3.405874748189244*^9, 3.409344232630298*^9, 3.409862746248504*^9, 3.409862954568663*^9, 3.409863288777487*^9, 3.409863786582569*^9, 3.410019104795024*^9, 3.410019765092353*^9, 3.410031395052998*^9, 3.410034067293612*^9, 3.410101948975187*^9, 3.410184318952924*^9, 3.410363189272577*^9, 3.410538465058651*^9, 3.410539236048836*^9, 3.410539933248698*^9, 3.410546663463224*^9, 3.410547485828128*^9, 3.41625385692049*^9, 3.416590121992461*^9, 3.4298792744922757`*^9, 3.429883144914569*^9, 3.4298904422389374`*^9, 3.4298986449096518`*^9, 3.4299713396596813`*^9, 3.4299727606463995`*^9, 3.430054543136217*^9, 3.4300613602735434`*^9, 3.430063476919208*^9, 3.430064575750984*^9, { 3.430065411012324*^9, 3.430062368138749*^9}, 3.430071098873761*^9, 3.4300718659286575`*^9}] }, Open ]], Cell["\<\ Probability mass functions of the Haldane distribution can be computed as \ follows.\ \>", "Text", CellChangeTimes->{{3.41053781443368*^9, 3.410537856307022*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfHaldane"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfHaldane[g, \!\(\[Mu]\), n, \!\(N\_0\)] computes\\nthe first \ n probabilities p(0), p(1), ..., p(n), assuming the population\\nstarts with \ N0 nonmutant cells. Default value for \!\(N\_0\) is unity (1).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718660224123`*^9}, CellTags->"Info3430053865-7117407"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"ppH", "=", RowBox[{"pmfHaldane", "[", RowBox[{"10", ",", "0.01", ",", "200", ",", "1"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.409863303660827*^9, 3.409863326485683*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"g1", "=", RowBox[{"ListPlot", "[", RowBox[{"ppH", ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.3992322456127*^9, 3.399232246157154*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw1lglYjfkex48GqUyWuEqLUylS2qiEpm/7vu/7OZ21RZKGNnUit2GoqbSI VCrrFaXUSTiyjSVG484oE1FXJIShTIx77+P39jzn6fmc7/m83//7/n//U9qx 6/0FciwW6/r/Xv///fVnzHZ7Q+Sb9A9TbOkNPAmbvSrXegnxDKhWHDS4MGJH PBs3Z366/FdSIPE8OLA6IjpCeMSqkK4rzWz+JplYA8HZvKqE6WnEbDg16nbN q5MQ68DZLVurqGY78WKYZenqCFp2EutDKPdydvGxQuKlePfpcWXC0mLiZTB8 dqOvz34PsRFGd1Z1SueVERtj9O6EolppObEpEnXUih2kFcRmmKtwdaQuZy+x OaKmtqVpjjK8AgWJOf0BypXEK2F7vHQa7z2TW+CSmd1V9mmGLZGlN2daRgDD VrDty3XvGmD6VqE8eex4cCTD1mj61Vfpm2vM+lZjRL0y4pUWw2vw/MXqmd5C 5n7Wgnfi/OOMqlJiG1iazDB1vsbc/3ewDxXVnR4qIbZFfah5X/oE87yAny1T oo/KEUuAyv7kg3ryRZTb4ePynrJapZ8ot4OrvMqIj0UB5fbgWu280JC2i3J7 xI9tqtoxxuyXA0qsH86aqN1BuQNUZJ9rsnf/QLkjpP+qzdx/OJ9yR+SmXJzI Gvon5U54oeigs8KSWOKEsp6yMytLmflwhsxlz7NDE3mUO+PtkKXut5HELBdo lJklt0u3Ue4Co6xv2wNmEbNcca/+5S3V0K2Uu6K7q+pGU0ku5W7QdRbftL9E 8ylxg9LCFnFqXw7l7jgkuJ7x1CibcnfwMlXPvt6RRbkHRKP3L5uPZ1DuAfmK Ypfm9HTKPWEmjQ6zUabzIPEE+02KX1XzJsq9oGty4scDsd9T7oWMnJkeG7RS KffG0OWmfVZDKZR7Y+PiNZI9LRso98H06onU0AI6fxIfLPx4Uc94KIlyX7Qq /d71+GziV4YvYh7qfKg+FU+f98XhJMOOrF7xV5b5Yq73uudJkSLy/bC1uF2j zU9Ivh9etWZrK94UkO8H1/S+q9xLxDI/NJq+6y43pM+z/BF2TafRvZ/x/fGw 9UHB1DN0fYk/Wmxd9NxLmH5/1O1eHW/BiyM/AJ8rQjtvzKH1IgB29z4a3Sll 1h8A9ywZp3eQWBaAdyVNgRUTxKxA6OQ9yc+8yfiB+PBIajSTw/iBcDOOjOk8 R32yQASnPWC/HKf1sIKw9++Ng4oaxAjCkxyD27HWzPqDENAzfFAUTPcnC4Jm W8QUWRo9D1YwDu3WNJrcxyc/GHerNYLWnKfvT0kw/HpXpnU/iCU/GF2b9e1G PnDJDwHLM8uiVZkYIQg3Vdy6XY9DfggaF7kvNN4UTX4IOuIMY7oORpIfillq 2qI5t8PJD0WcvPr8wS+h5IdiYsn7pTn2IeSH4tQjiYvc0SDywyCMCyx3tqHv f4Th7LbOtyYzAsgPg5eoobtY3p/8MISIVd4ZWvmRH47CU/sWvcz3JT8clhqF mqf7fcgPh3Bdd9QnmTf54Yj3id+2odmL/AhoDc+s29zgSX4ELp9TEzeXeZAf gVxWZuf6bHfyI9DWONR8NcKN/EgcPhYXF7fElfxIPE3ibQobciY/Eo+OzK57 VeZEfiQcvbVOxHs6kh+F4t4lmzlKDuRHYdkv20+u+oP+PkqiIHmj6bNMBvKj YDzLq/7kBlvyo6HBOq7TL7EhPxopH9qmPDqyhvxoTDX7+bDTE2vyo+H6bEuW ickq8mPQ/V5RoL7LkvwYcP/RUH7hr5Xkx0B65OiswrQV5Mdg0WTQl8bp5uRz 4Nsub2JVa/qV2RwUWZ6Y9tzFhK7HgcLv/0l1W0HM4eDK3teaFyzM6Poc/N3W vlh6lvpqOLA//vb2XsfV1MfB7Z7Mm8NSuv8BDuLU9L9EDTPPjwufOTO499fQ frC5kORP1Awk0P6Ci0+ioOVVlTQfHC5ME5d6mjrQPEm44K1Pr91STfNWw0Xe VEgnT9A8yrh4Jxq0sRbRvA5w8VLPlJNwm5nfWPzbQN0hoZ+YHYsrvTmKa2uJ EYvHHv5yBgbEnFgMT9ffX1RE15fEIu7plUq7Z0x/LG5d2nXFxIZYFov6yrvC 3mJa70AshrRfmx4aZeafB9GtM8cU7IjZPBRll+t5FTDngYeh8ODwx7V0Hjg8 3PBQ6LDWoPMg4eF6xwFJ5w6a/xoeDM6/+YX9lpl3HiYHq5X4gfR8B3i4aH5u 1P6MC/XzcaNA7cdyFZp3Nh/Kc6qM+zJof8DHeNWz8fJJe+rnwzVUIhhuZOab D5Xh0p62StrfGj7k9rnMT9xB8y3jo3CK+6pEp++on4/1vOXFgmCad5YAqr8e TPMrWEv9AlxPVg8s+o3mHwJEZiskXVYl5ghgUG/uNxJE8yUR4Pj4IZf7uXQ+ agTYZrUckgN0PmQCZF7gFv5Rb0X9AijnFflOqaDzwhKiOMljbEayBfUL4Smu 2fKTJc0zhFCe/f17hz/pvHCESD6Cw7adzPwLcbpQZTylhM5PjRC5AXpKQVPp vMiEKIPPnXal5dQvREvMgoa5NobUL0Kldr5fXZ4B9YtwMlqrqfAh/b8NEXQ0 HfSrHfSpX4TSlVFbHTsWU78IjYn32sZsdKlfhNRTnkLvHm3qF0F6dmPT0EY2 9YvgsOB+9Z9uWtQvBrsmpCVVpk79YuxbsWGyI0+N+sW4/1Qhe8tvC6hfjKCu H6L9pxNLxHiteyeKr0JcIwb/zYs2hQlimRj9KpvzhzfS9QbEGIz47KnkRX2s OOxvTWxT1NCk/jgkzFcz6GvVsv0vXTKC0Q== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.39923271070592*^9, 3.399297945891822*^9, 3.405872226254008*^9, 3.405874749783148*^9, 3.40934423410322*^9, 3.409862748857993*^9, 3.409862985088629*^9, {3.409863310918133*^9, 3.409863329862291*^9}, 3.409863787743553*^9, 3.410019105636321*^9, 3.410019766108271*^9, 3.410031396073524*^9, 3.410034068234969*^9, 3.410101949998723*^9, 3.410184319994541*^9, 3.410363190271068*^9, 3.410538466078614*^9, 3.410539237041176*^9, 3.410546664378397*^9, 3.41054748694706*^9, 3.416253857901055*^9, 3.4165901221330185`*^9, 3.429879274632902*^9, 3.42988314507076*^9, 3.429890442395135*^9, 3.429898645081586*^9, 3.429971339816188*^9, 3.429972760818256*^9, 3.4300545432612047`*^9, 3.430061360429796*^9, 3.4300634770754423`*^9, 3.430064575907223*^9, { 3.4300654111529837`*^9, 3.43006236906275*^9}, 3.430071099014393*^9, 3.4300718660536633`*^9}] }, Open ]], Cell["\<\ Now we find the corresponding Luria-Delbruck distribution and make a \ comparison.\ \>", "Text", CellChangeTimes->{{3.410537745039656*^9, 3.410537748729165*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"phi", "=", RowBox[{"1", "-", RowBox[{"1", "/", "1024."}]}]}]], "Input"], Cell[BoxData["0.9990234375`"], "Output", CellChangeTimes->{ 3.399232710809137*^9, 3.399297945995634*^9, 3.405872226357042*^9, 3.405874749895974*^9, 3.409344234205815*^9, 3.409862749018192*^9, 3.409863787848709*^9, 3.410019105855143*^9, 3.410019766274936*^9, 3.410031396176364*^9, 3.410034068435855*^9, 3.410101950100181*^9, 3.410184320097931*^9, 3.410363190423716*^9, 3.410538466180663*^9, 3.410539237204195*^9, 3.410546664547422*^9, 3.41054748705027*^9, 3.41625385806945*^9, 3.4165901221486363`*^9, 3.429879274632902*^9, 3.429883145086379*^9, 3.429890442410754*^9, 3.4298986450972166`*^9, 3.4299713398318386`*^9, 3.4299727608338795`*^9, 3.4300545432612047`*^9, 3.4300613604454217`*^9, 3.4300634770910654`*^9, 3.4300645759228473`*^9, { 3.4300654111529837`*^9, 3.430062369218657*^9}, 3.4300710990300193`*^9, 3.4300718660692897`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "haldaneMutations"}]], "Input"], Cell[BoxData[ StyleBox["\<\"haldaneMutations[\!\(\[Mu]\),g,N0:=1] computes the \ total\\nnumber of mutations accumulated in the gth generation. If Assumption \ C (Kdenall)\\nor the Galton-Waston formulation is adopted, replacing \ \!\(\[Mu]\) by\\n\!\(2\[Mu]\) yields the desired result.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.43007186617867*^9}, CellTags->"Info3430053866-2684086"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"mm", "=", RowBox[{"haldaneMutations", "[", RowBox[{"0.01", ",", "10"}], "]"}]}]], "Input"], Cell[BoxData["9.827644177746974`"], "Output", CellChangeTimes->{ 3.399232711802662*^9, 3.399297947023473*^9, 3.405872227341757*^9, 3.405874750871264*^9, 3.409344235057197*^9, 3.409862750294034*^9, 3.409863788842602*^9, 3.410019106826584*^9, 3.410019767336135*^9, 3.410031397208782*^9, 3.410034069441651*^9, 3.410101951075149*^9, 3.410184321109086*^9, 3.410363191514641*^9, 3.410538467166376*^9, 3.410539238200498*^9, 3.410546665578029*^9, 3.410547488044913*^9, 3.416253858941381*^9, 3.4165901223048115`*^9, 3.429879274773529*^9, 3.4298831452581887`*^9, 3.429890442582571*^9, 3.4298986452535205`*^9, 3.429971340003997*^9, 3.4299727609901123`*^9, 3.4300545433861914`*^9, 3.430061360601675*^9, 3.430063477262923*^9, 3.4300645760790863`*^9, { 3.430065411293644*^9, 3.430062370169396*^9}, 3.4300710991550255`*^9, 3.430071866209922*^9}] }, Open ]], Cell["\<\ Note in passing that the relevancy of Kendall's Assumptions in the present \ context is explained in Zheng (1999). The Galton-Watson formulation is \ explained in Kimmel and Axelrod (1994). Under either formulation the expected \ number of mutations would be computed as follows:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"haldaneMutations", "[", RowBox[{"0.02", ",", "10"}], "]"}]], "Input"], Cell[BoxData["18.87933152671461`"], "Output", CellChangeTimes->{ 3.399232712026381*^9, 3.39929794715372*^9, 3.405872227573282*^9, 3.405874751093462*^9, 3.40934423529854*^9, 3.40986275054527*^9, 3.409863789068538*^9, 3.410019107046631*^9, 3.410019767566106*^9, 3.410031397430234*^9, 3.410034069666279*^9, 3.41010195120255*^9, 3.410184321344251*^9, 3.410363191736672*^9, 3.410538467292756*^9, 3.410539238420725*^9, 3.410546665705596*^9, 3.410547488266527*^9, 3.41625385906902*^9, 3.4165901223048115`*^9, 3.429879274789154*^9, 3.429883145273808*^9, 3.429890442598191*^9, 3.4298986452847815`*^9, 3.429971340019647*^9, 3.4299727610057354`*^9, 3.430054543401815*^9, 3.4300613606173*^9, 3.4300634772785463`*^9, 3.4300645760947104`*^9, { 3.430065411309273*^9, 3.430062370376844*^9}, 3.4300710991706514`*^9, 3.430071866225548*^9}] }, Open ]], Cell["\<\ Now we can compute the corresponding Luria-Delbruck distribution.\ \>", "Text", CellChangeTimes->{{3.410537895401381*^9, 3.410537936443412*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"ppL", "=", RowBox[{"pmfLD0", "[", RowBox[{"10.23", ",", "phi", ",", "200"}], "]"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"g2", "=", RowBox[{"ListPlot", "[", RowBox[{"ppL", ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"Dashing", "[", RowBox[{"{", "0.01", "}"}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.399232252284033*^9, 3.399232252888273*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], Dashing[{0.01}], LineBox[CompressedData[" 1:eJw11gk41AkfB/BJlDYrKeG1GCQlFYpx+xbjGucYxj03Q661SYc0FBWhsZsu u6ntUNErOlTb26zSXTpJrPT2qNAmtZV6t7X7Pv1mnsczz8fX15f/hYU4iyvT YDAYV//5+P/7l9dr73cv7KpWDGh40ydg2HK4aZrTbLI2Mvqb7TYXLSbrwXn8 ytXKp1zydPQUhfbsHxGSjbB7xOpwUWsa+Rvc3GyQroPvyEwE7LViV91cSbZE BD5VGSUqyDMh7A0SZ/esI89C56bf1+j7bCDPhllg4tkHuaVkW5x7cvtmvbCc bAfBJvsFEe8ryfPRaHSw4JShkmyPD02/Pr+uWUV2wPbX0tcGF9R2xNftLmZH eN+TF6J1/lDy1l/UXoS547a9zP1LbSdc4rQEupv9QHbGznrrQwPmarNg5axr kzNRbRckWoW1VT9U913R9mlrwsNqtd2wtfK+RzpbbXeYXbPcxHqu/vk80G1n cvJWgdqeGOFc7s/TVdsLDpr51gu2q39fb6Qys9qPmKoNJNqcW5dcu+WLFUCh rz1vtwWZsRgKk+OnL/vS8VMshl/3Rydb/wrKl+BK39prXRw63oolaG4YHNDi babcB+dZ197sFZZR7gMDl4fynBz1+fIFj6Mb8FXpJsp9YaC1qKD74EbK2dAN a97JukHnW8GG38jUS1EfSij3gznnsT5/Dlnhh0//rnINEhdT7o8teRNuz9+7 nnJ/uB8z1xl9ob6eAuDk8cq80pmsCMC8s54eD0qLKA+ERODF3t9fSHkgVC8P +jzwIzOC0Lx04y7WUbpeFUF4sqFDr8ZEff1y4Ff0n8V7TNdSzsFSk7UZvlMK KA9G3sLtijOT11AejHkLZobX6OdTHgLB3T+y11mtpjwEzN+md37ltYryUDyw X8drF9H9owjFMu+QP7MqVlAeBo3UnMyKC3mUh6G1J1qvnUFmhMOmamxRF3v5 FyMcsR6dLH5VLn19OGayIze/71/2xapwRDfnXkwBmRGBwe+6K5P20P38z91b ZnjxuFKbrIiAhru/5tncHOpHoHfB2aBtL76lPhdlw7M8nwnJ4ML1j1xpWm82 9bm4JpgwcUBIVnERE8605N3Oon4kIqJrRoefZ1I/Encnrc301iYrIlF4oNLo iX0G9SORU9U+dYUonfo89BevuHZkx1Lq8zDD8U6nTRc9rxQ8nJ6k37bLnKzi wb+opP9Meir1o6CtrTPbQyWnfhRcaie87DImK6KQuKG7M2JlCvWjsL3tf43S 3mTqR6N37TqnjgAyomG0JfNDeouM+tG4UihwfWNHVkUDEW9vOByQUp+PaZY7 33y0IoMPv+whN5MDEurz0Taaliq3I6v4GPdzU8zJk2Lqx8Bt8rvH3b5kxCC4 9/rpYx0i6segbtQ3XT+drIrB5pkWjo80yYxYtCSw+p/V0vMesVjz4/CAIciK WPB1lKyaiwLqx+J4/cncTl0yIw5bwvYdr0tKon4ctAI37e5qTqR+HLjnHvs5 65JVcXjVlK9RnpFA/XhMVcyNOnonnvrxkKSp7qS7kRXxKJhbOe7Hg3HUj4dy wDHYwJjMSIDR5Oq+hopY6idgH3PObmiTFQn465WL1qHiGOonwHUpz/jiBDIj EWZex2Oyy/jUT0SxafX+8mlkRSIKxgqcP/8UTf1EzO/kl+yZR2Ykwcs+lp10 Por6SfCuORNkxCMrkpCx2mTDiSEe9ZPw0HXXh29KyAwBJvy8bYezFRkCvM/U Fgy1RlJfAK26LCtrGVklQOif0XtuTSIzhBhfwJXfa6S/30whDp0rvGceR4YQ /PKNjD1aZKEQ740/XvJtjqDvL8Qu4ZzGj2JyrRA6cZnDR6eTVULwSk7F8a6E f3GfEKM3iiWP1pAZIgz87qLn6ERmivDb+KShHT1htC9CqFIiduOShSIszo9v s70eSvsi5PGSQiP8ybUiHLP0sdl6KYT2RShDjaA3gNwngqRl7lODW8G0L8Y7 46vZ1tFkphgXNJqVH/o4tC+Gx5CfMi+TLBSjTv9fucq/gmhfjJD6zHcOSnKt GN5NjOV+s8gqMfQ0Zo39ci6Q9sXo2evJWs8nMySIDU5LKHsbQPsSsPJ/8GpV kiGBbHujq7EjWSjBjJts+8L7/rQvwZJCx5KhFeRaCcaSj5gEmZNVEhhG5QRU XvajfQk0PZZ0NnxLZkiR3pAxbocpmSlFQXlDmu91Nu1LYXbA1HTfKrJQitIR aXH9XLJCip8qJmZxe31pXwru0j5GWRVZJYXPDdVpTgC5T4ruVwszSsd8aF+G HBMZPFvITBn2KWcdjMshQ4bym4airnlkoQx3Tg0sbxxcQvsylEjPszrryLUy hMw47MyWk1UyzOZ4B7yZTe6TIbjOX9ExqP7/NRlRdcULBhvIzGQUfq56Yp1D RjK6DtyLK2KRhcl43rqmevQzaD8ZHNaJi4Vt5Npk6IWdCTCsIKuSUZ1ve6qJ T+5LxtZc7v0QSzIjBfX3LKzbur1pPwUi9yqLjmVkpOD+sqsOF6aQhSnQSbzi UVjvRfspODr2caUWh1ybgpHXpZnsIU/aT4GV16NB53JyXwpan2ho37YnM+QY PpFvPbHDg/bleDt479ndfDLk+Hr6cgdba7JQDttn39tqtrvTvhz/bZ/hFLOK XCvHs52Hhk1tyCo5fg2/5xjywI325Vi+32pK73oyIxVOC7OvX3EiM1Ph/8ji qdYLV++/AdJxecs= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.3992327125701*^9, 3.39929794770846*^9, 3.405872228116761*^9, 3.405874751640376*^9, 3.409344235838514*^9, 3.409862751092838*^9, 3.409863789605216*^9, 3.410019107580642*^9, 3.410019768096186*^9, 3.410031397966823*^9, 3.410034070199608*^9, 3.410101951776201*^9, 3.410184321892704*^9, 3.410363192283253*^9, 3.410538467864849*^9, 3.410539238967135*^9, 3.410546666269948*^9, 3.410547488813311*^9, 3.41625385964285*^9, 3.4165901225546913`*^9, 3.4298792750235324`*^9, 3.4298831455237136`*^9, 3.429890442848106*^9, 3.4298986455192375`*^9, 3.429971340254408*^9, 3.4299727612557087`*^9, 3.430054543636166*^9, 3.430061360867305*^9, 3.4300634775128975`*^9, 3.4300645763603163`*^9, { 3.430065411559335*^9, 3.430062370907507*^9}, 3.430071099420664*^9, 3.430071866459934*^9}] }, Open ]], Cell["Now we can compare the two distributions.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"g1", ",", "g2", ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", " ", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw1lglYjfkex48GqUyWuEqLUylS2qiEpm/7vu/7OZ21RZKGNnUit2GoqbSI VCrrFaXUSTiyjSVG484oE1FXJIShTIx77+P39jzn6fmc7/m83//7/n//U9qx 6/0FciwW6/r/Xv///fVnzHZ7Q+Sb9A9TbOkNPAmbvSrXegnxDKhWHDS4MGJH PBs3Z366/FdSIPE8OLA6IjpCeMSqkK4rzWz+JplYA8HZvKqE6WnEbDg16nbN q5MQ68DZLVurqGY78WKYZenqCFp2EutDKPdydvGxQuKlePfpcWXC0mLiZTB8 dqOvz34PsRFGd1Z1SueVERtj9O6EolppObEpEnXUih2kFcRmmKtwdaQuZy+x OaKmtqVpjjK8AgWJOf0BypXEK2F7vHQa7z2TW+CSmd1V9mmGLZGlN2daRgDD VrDty3XvGmD6VqE8eex4cCTD1mj61Vfpm2vM+lZjRL0y4pUWw2vw/MXqmd5C 5n7Wgnfi/OOMqlJiG1iazDB1vsbc/3ewDxXVnR4qIbZFfah5X/oE87yAny1T oo/KEUuAyv7kg3ryRZTb4ePynrJapZ8ot4OrvMqIj0UB5fbgWu280JC2i3J7 xI9tqtoxxuyXA0qsH86aqN1BuQNUZJ9rsnf/QLkjpP+qzdx/OJ9yR+SmXJzI Gvon5U54oeigs8KSWOKEsp6yMytLmflwhsxlz7NDE3mUO+PtkKXut5HELBdo lJklt0u3Ue4Co6xv2wNmEbNcca/+5S3V0K2Uu6K7q+pGU0ku5W7QdRbftL9E 8ylxg9LCFnFqXw7l7jgkuJ7x1CibcnfwMlXPvt6RRbkHRKP3L5uPZ1DuAfmK Ypfm9HTKPWEmjQ6zUabzIPEE+02KX1XzJsq9oGty4scDsd9T7oWMnJkeG7RS KffG0OWmfVZDKZR7Y+PiNZI9LRso98H06onU0AI6fxIfLPx4Uc94KIlyX7Qq /d71+GziV4YvYh7qfKg+FU+f98XhJMOOrF7xV5b5Yq73uudJkSLy/bC1uF2j zU9Ivh9etWZrK94UkO8H1/S+q9xLxDI/NJq+6y43pM+z/BF2TafRvZ/x/fGw 9UHB1DN0fYk/Wmxd9NxLmH5/1O1eHW/BiyM/AJ8rQjtvzKH1IgB29z4a3Sll 1h8A9ywZp3eQWBaAdyVNgRUTxKxA6OQ9yc+8yfiB+PBIajSTw/iBcDOOjOk8 R32yQASnPWC/HKf1sIKw9++Ng4oaxAjCkxyD27HWzPqDENAzfFAUTPcnC4Jm W8QUWRo9D1YwDu3WNJrcxyc/GHerNYLWnKfvT0kw/HpXpnU/iCU/GF2b9e1G PnDJDwHLM8uiVZkYIQg3Vdy6XY9DfggaF7kvNN4UTX4IOuIMY7oORpIfillq 2qI5t8PJD0WcvPr8wS+h5IdiYsn7pTn2IeSH4tQjiYvc0SDywyCMCyx3tqHv f4Th7LbOtyYzAsgPg5eoobtY3p/8MISIVd4ZWvmRH47CU/sWvcz3JT8clhqF mqf7fcgPh3Bdd9QnmTf54Yj3id+2odmL/AhoDc+s29zgSX4ELp9TEzeXeZAf gVxWZuf6bHfyI9DWONR8NcKN/EgcPhYXF7fElfxIPE3ibQobciY/Eo+OzK57 VeZEfiQcvbVOxHs6kh+F4t4lmzlKDuRHYdkv20+u+oP+PkqiIHmj6bNMBvKj YDzLq/7kBlvyo6HBOq7TL7EhPxopH9qmPDqyhvxoTDX7+bDTE2vyo+H6bEuW ickq8mPQ/V5RoL7LkvwYcP/RUH7hr5Xkx0B65OiswrQV5Mdg0WTQl8bp5uRz 4Nsub2JVa/qV2RwUWZ6Y9tzFhK7HgcLv/0l1W0HM4eDK3teaFyzM6Poc/N3W vlh6lvpqOLA//vb2XsfV1MfB7Z7Mm8NSuv8BDuLU9L9EDTPPjwufOTO499fQ frC5kORP1Awk0P6Ci0+ioOVVlTQfHC5ME5d6mjrQPEm44K1Pr91STfNWw0Xe VEgnT9A8yrh4Jxq0sRbRvA5w8VLPlJNwm5nfWPzbQN0hoZ+YHYsrvTmKa2uJ EYvHHv5yBgbEnFgMT9ffX1RE15fEIu7plUq7Z0x/LG5d2nXFxIZYFov6yrvC 3mJa70AshrRfmx4aZeafB9GtM8cU7IjZPBRll+t5FTDngYeh8ODwx7V0Hjg8 3PBQ6LDWoPMg4eF6xwFJ5w6a/xoeDM6/+YX9lpl3HiYHq5X4gfR8B3i4aH5u 1P6MC/XzcaNA7cdyFZp3Nh/Kc6qM+zJof8DHeNWz8fJJe+rnwzVUIhhuZOab D5Xh0p62StrfGj7k9rnMT9xB8y3jo3CK+6pEp++on4/1vOXFgmCad5YAqr8e TPMrWEv9AlxPVg8s+o3mHwJEZiskXVYl5ghgUG/uNxJE8yUR4Pj4IZf7uXQ+ agTYZrUckgN0PmQCZF7gFv5Rb0X9AijnFflOqaDzwhKiOMljbEayBfUL4Smu 2fKTJc0zhFCe/f17hz/pvHCESD6Cw7adzPwLcbpQZTylhM5PjRC5AXpKQVPp vMiEKIPPnXal5dQvREvMgoa5NobUL0Kldr5fXZ4B9YtwMlqrqfAh/b8NEXQ0 HfSrHfSpX4TSlVFbHTsWU78IjYn32sZsdKlfhNRTnkLvHm3qF0F6dmPT0EY2 9YvgsOB+9Z9uWtQvBrsmpCVVpk79YuxbsWGyI0+N+sW4/1Qhe8tvC6hfjKCu H6L9pxNLxHiteyeKr0JcIwb/zYs2hQlimRj9KpvzhzfS9QbEGIz47KnkRX2s OOxvTWxT1NCk/jgkzFcz6GvVsv0vXTKC0Q== "]]}}, {{}, {}, {Hue[0.67, 0.6, 0.6], Dashing[{0.01}], LineBox[CompressedData[" 1:eJw11gk41AkfB/BJlDYrKeG1GCQlFYpx+xbjGucYxj03Q661SYc0FBWhsZsu u6ntUNErOlTb26zSXTpJrPT2qNAmtZV6t7X7Pv1mnsczz8fX15f/hYU4iyvT YDAYV//5+P/7l9dr73cv7KpWDGh40ydg2HK4aZrTbLI2Mvqb7TYXLSbrwXn8 ytXKp1zydPQUhfbsHxGSjbB7xOpwUWsa+Rvc3GyQroPvyEwE7LViV91cSbZE BD5VGSUqyDMh7A0SZ/esI89C56bf1+j7bCDPhllg4tkHuaVkW5x7cvtmvbCc bAfBJvsFEe8ryfPRaHSw4JShkmyPD02/Pr+uWUV2wPbX0tcGF9R2xNftLmZH eN+TF6J1/lDy1l/UXoS547a9zP1LbSdc4rQEupv9QHbGznrrQwPmarNg5axr kzNRbRckWoW1VT9U913R9mlrwsNqtd2wtfK+RzpbbXeYXbPcxHqu/vk80G1n cvJWgdqeGOFc7s/TVdsLDpr51gu2q39fb6Qys9qPmKoNJNqcW5dcu+WLFUCh rz1vtwWZsRgKk+OnL/vS8VMshl/3Rydb/wrKl+BK39prXRw63oolaG4YHNDi babcB+dZ197sFZZR7gMDl4fynBz1+fIFj6Mb8FXpJsp9YaC1qKD74EbK2dAN a97JukHnW8GG38jUS1EfSij3gznnsT5/Dlnhh0//rnINEhdT7o8teRNuz9+7 nnJ/uB8z1xl9ob6eAuDk8cq80pmsCMC8s54eD0qLKA+ERODF3t9fSHkgVC8P +jzwIzOC0Lx04y7WUbpeFUF4sqFDr8ZEff1y4Ff0n8V7TNdSzsFSk7UZvlMK KA9G3sLtijOT11AejHkLZobX6OdTHgLB3T+y11mtpjwEzN+md37ltYryUDyw X8drF9H9owjFMu+QP7MqVlAeBo3UnMyKC3mUh6G1J1qvnUFmhMOmamxRF3v5 FyMcsR6dLH5VLn19OGayIze/71/2xapwRDfnXkwBmRGBwe+6K5P20P38z91b ZnjxuFKbrIiAhru/5tncHOpHoHfB2aBtL76lPhdlw7M8nwnJ4ML1j1xpWm82 9bm4JpgwcUBIVnERE8605N3Oon4kIqJrRoefZ1I/Encnrc301iYrIlF4oNLo iX0G9SORU9U+dYUonfo89BevuHZkx1Lq8zDD8U6nTRc9rxQ8nJ6k37bLnKzi wb+opP9Meir1o6CtrTPbQyWnfhRcaie87DImK6KQuKG7M2JlCvWjsL3tf43S 3mTqR6N37TqnjgAyomG0JfNDeouM+tG4UihwfWNHVkUDEW9vOByQUp+PaZY7 33y0IoMPv+whN5MDEurz0Taaliq3I6v4GPdzU8zJk2Lqx8Bt8rvH3b5kxCC4 9/rpYx0i6segbtQ3XT+drIrB5pkWjo80yYxYtCSw+p/V0vMesVjz4/CAIciK WPB1lKyaiwLqx+J4/cncTl0yIw5bwvYdr0tKon4ctAI37e5qTqR+HLjnHvs5 65JVcXjVlK9RnpFA/XhMVcyNOnonnvrxkKSp7qS7kRXxKJhbOe7Hg3HUj4dy wDHYwJjMSIDR5Oq+hopY6idgH3PObmiTFQn465WL1qHiGOonwHUpz/jiBDIj EWZex2Oyy/jUT0SxafX+8mlkRSIKxgqcP/8UTf1EzO/kl+yZR2Ykwcs+lp10 Por6SfCuORNkxCMrkpCx2mTDiSEe9ZPw0HXXh29KyAwBJvy8bYezFRkCvM/U Fgy1RlJfAK26LCtrGVklQOif0XtuTSIzhBhfwJXfa6S/30whDp0rvGceR4YQ /PKNjD1aZKEQ740/XvJtjqDvL8Qu4ZzGj2JyrRA6cZnDR6eTVULwSk7F8a6E f3GfEKM3iiWP1pAZIgz87qLn6ERmivDb+KShHT1htC9CqFIiduOShSIszo9v s70eSvsi5PGSQiP8ybUiHLP0sdl6KYT2RShDjaA3gNwngqRl7lODW8G0L8Y7 46vZ1tFkphgXNJqVH/o4tC+Gx5CfMi+TLBSjTv9fucq/gmhfjJD6zHcOSnKt GN5NjOV+s8gqMfQ0Zo39ci6Q9sXo2evJWs8nMySIDU5LKHsbQPsSsPJ/8GpV kiGBbHujq7EjWSjBjJts+8L7/rQvwZJCx5KhFeRaCcaSj5gEmZNVEhhG5QRU XvajfQk0PZZ0NnxLZkiR3pAxbocpmSlFQXlDmu91Nu1LYXbA1HTfKrJQitIR aXH9XLJCip8qJmZxe31pXwru0j5GWRVZJYXPDdVpTgC5T4ruVwszSsd8aF+G HBMZPFvITBn2KWcdjMshQ4bym4airnlkoQx3Tg0sbxxcQvsylEjPszrryLUy hMw47MyWk1UyzOZ4B7yZTe6TIbjOX9ExqP7/NRlRdcULBhvIzGQUfq56Yp1D RjK6DtyLK2KRhcl43rqmevQzaD8ZHNaJi4Vt5Npk6IWdCTCsIKuSUZ1ve6qJ T+5LxtZc7v0QSzIjBfX3LKzbur1pPwUi9yqLjmVkpOD+sqsOF6aQhSnQSbzi UVjvRfspODr2caUWh1ybgpHXpZnsIU/aT4GV16NB53JyXwpan2ho37YnM+QY PpFvPbHDg/bleDt479ndfDLk+Hr6cgdba7JQDttn39tqtrvTvhz/bZ/hFLOK XCvHs52Hhk1tyCo5fg2/5xjywI325Vi+32pK73oyIxVOC7OvX3EiM1Ph/8ji qdYLV++/AdJxecs= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, Frame->True, FrameLabel->{ FormBox["\"Number of mutants\"", TraditionalForm], FormBox["\"Probability\"", TraditionalForm]}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.399232712643772*^9, 3.399297947773406*^9, 3.405872228200881*^9, 3.405874751695392*^9, 3.409344235906361*^9, 3.409862751258508*^9, 3.409863336925954*^9, 3.409863789659589*^9, 3.410019107644142*^9, 3.410019768139842*^9, 3.41003139802086*^9, 3.410034070259508*^9, 3.410101951846509*^9, 3.410184321951111*^9, 3.410363192463089*^9, 3.410538467918679*^9, 3.410539239026655*^9, 3.410546666323224*^9, 3.410547488873705*^9, 3.416253859715683*^9, 3.4165901225703087`*^9, 3.429879275039158*^9, 3.429883145617428*^9, 3.4298904428793454`*^9, 3.429898645550498*^9, 3.4299713404265656`*^9, 3.429972761271332*^9, 3.4300545437924*^9, 3.4300613608829303`*^9, 3.4300634775441437`*^9, 3.4300645763915644`*^9, {3.4300654115749645`*^9, 3.430062370960454*^9}, 3.43007109943629*^9, 3.43007186647556*^9}] }, Open ]], Cell["\<\ As an illustration, we apply the Haldane model to analyze the data given by \ Demerec (1945). To begin with, we estimate g as follows. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"N0", "=", "90"}], ";", RowBox[{"Nt", "=", RowBox[{"1.9", "*", RowBox[{"10", "^", "8"}]}]}], ";"}], "\n", RowBox[{ RowBox[{"Log", "[", RowBox[{"Nt", "/", "N0"}], "]"}], "/", RowBox[{"Log", "[", "2", "]"}]}]}], "Input"], Cell[BoxData["21.009571081325447`"], "Output", CellChangeTimes->{ 3.399232712679007*^9, 3.399297947810293*^9, 3.405872228291808*^9, 3.405874751730953*^9, 3.409344236105496*^9, 3.40986275133487*^9, 3.409863789695603*^9, 3.410019107681749*^9, 3.410019768172765*^9, 3.410031398055641*^9, 3.410034070298047*^9, 3.410101951880062*^9, 3.410184321988345*^9, 3.410363192496742*^9, 3.410538467953437*^9, 3.410539239064942*^9, 3.410546666357284*^9, 3.41054748891148*^9, 3.416253859815793*^9, 3.416590122585926*^9, 3.429879275054783*^9, 3.4298831456486664`*^9, 3.429890442894965*^9, 3.4298986455661287`*^9, 3.429971340442216*^9, 3.429972761302578*^9, 3.4300545437924*^9, 3.4300613609141808`*^9, 3.4300634775597672`*^9, 3.430064576407188*^9, { 3.4300654115905933`*^9, 3.4300623709952*^9}, 3.4300710994519157`*^9, 3.430071866491186*^9}] }, Open ]], Cell["\<\ The above result suggests that a reasonable estimate of g is 21. Under this \ assumption we can now proceed to obtain both point and interval estimates of \ the mutation rate.\ \>", "Text", CellChangeTimes->{{3.410537969285687*^9, 3.410537970519044*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"newtonHaldane", "[", RowBox[{"demerec", ",", "21", ",", RowBox[{"InitialCells", "\[Rule]", "N0"}], ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}], " "}]], "Input", CellChangeTimes->{{3.410538000262738*^9, 3.410538003631364*^9}}], Cell[CellGroupData[{ Cell[BoxData["3.030902384626444`*^-8"], "Print", CellChangeTimes->{ 3.410538467983867*^9, 3.410539239096647*^9, 3.410546666386538*^9, 3.410547489089245*^9, 3.416253859847755*^9, 3.416590122601544*^9, 3.429879275070408*^9, 3.4298831456642857`*^9, 3.4298904429105844`*^9, 3.429898645597389*^9, 3.4299713404578667`*^9, 3.4299727613182015`*^9, 3.4300545438080235`*^9, 3.4300613609298058`*^9, 3.430063477591014*^9, 3.430064576422812*^9, {3.430065411606222*^9, 3.430062371031213*^9}, 3.4300710994675417`*^9, 3.430071866506812*^9}], Cell[BoxData["4.878740530819355`*^-8"], "Print", CellChangeTimes->{ 3.410538467983867*^9, 3.410539239096647*^9, 3.410546666386538*^9, 3.410547489089245*^9, 3.416253859847755*^9, 3.416590122601544*^9, 3.429879275070408*^9, 3.4298831456642857`*^9, 3.4298904429105844`*^9, 3.429898645597389*^9, 3.4299713404578667`*^9, 3.4299727613182015`*^9, 3.4300545438080235`*^9, 3.4300613609298058`*^9, 3.430063477591014*^9, 3.430064576422812*^9, {3.430065411606222*^9, 3.430062371031213*^9}, 3.4300710994675417`*^9, 3.4300718666786957`*^9}], Cell[BoxData["7.010897626882418`*^-8"], "Print", CellChangeTimes->{ 3.410538467983867*^9, 3.410539239096647*^9, 3.410546666386538*^9, 3.410547489089245*^9, 3.416253859847755*^9, 3.416590122601544*^9, 3.429879275070408*^9, 3.4298831456642857`*^9, 3.4298904429105844`*^9, 3.429898645597389*^9, 3.4299713404578667`*^9, 3.4299727613182015`*^9, 3.4300545438080235`*^9, 3.4300613609298058`*^9, 3.430063477591014*^9, 3.430064576422812*^9, {3.430065411606222*^9, 3.430062371031213*^9}, 3.4300710994675417`*^9, 3.4300718668505793`*^9}], Cell[BoxData["7.140002592501701`*^-8"], "Print", CellChangeTimes->{ 3.410538467983867*^9, 3.410539239096647*^9, 3.410546666386538*^9, 3.410547489089245*^9, 3.416253859847755*^9, 3.416590122601544*^9, 3.429879275070408*^9, 3.4298831456642857`*^9, 3.4298904429105844`*^9, 3.429898645597389*^9, 3.4299713404578667`*^9, 3.4299727613182015`*^9, 3.4300545438080235`*^9, 3.4300613609298058`*^9, 3.430063477591014*^9, 3.430064576422812*^9, {3.430065411606222*^9, 3.430062371031213*^9}, 3.4300710994675417`*^9, 3.4300718670380893`*^9}], Cell[BoxData["7.140797218499258`*^-8"], "Print", CellChangeTimes->{ 3.410538467983867*^9, 3.410539239096647*^9, 3.410546666386538*^9, 3.410547489089245*^9, 3.416253859847755*^9, 3.416590122601544*^9, 3.429879275070408*^9, 3.4298831456642857`*^9, 3.4298904429105844`*^9, 3.429898645597389*^9, 3.4299713404578667`*^9, 3.4299727613182015`*^9, 3.4300545438080235`*^9, 3.4300613609298058`*^9, 3.430063477591014*^9, 3.430064576422812*^9, {3.430065411606222*^9, 3.430062371031213*^9}, 3.4300710994675417`*^9, 3.430071867209973*^9}] }, Open ]], Cell[BoxData["7.14079724930282`*^-8"], "Output", CellChangeTimes->{ 3.410538469757511*^9, 3.410539240872974*^9, 3.410546668155099*^9, 3.410547490886546*^9, 3.416253861601362*^9, 3.4165901235073586`*^9, 3.4298792759454193`*^9, 3.4298831465389547`*^9, 3.429890443785288*^9, 3.4298986464726915`*^9, 3.4299713413499565`*^9, 3.4299727621931067`*^9, 3.430054544714181*^9, 3.430061361804823*^9, 3.4300634784659243`*^9, 3.4300645772977505`*^9, {3.430065412512698*^9, 3.430062372796181*^9}, 3.4300711003425865`*^9, 3.430071867381857*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{"CIHaldane", "[", RowBox[{"demerec", ",", "21", ",", RowBox[{"InitialCells", "\[Rule]", "N0"}], ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}], " "}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for MLE of \\!\\(\[Mu]\\)...\"\>"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718674131083`*^9}], Cell[BoxData["3.030902384626444`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718674131083`*^9}], Cell[BoxData["4.878740530819355`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071867600618*^9}], Cell[BoxData["7.010897626882418`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071867772502*^9}], Cell[BoxData["7.140002592501701`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718679443855`*^9}], Cell[BoxData["7.140797218499258`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071868116269*^9}], Cell[BoxData["\<\"Iterating for lower limit of CI ...\"\>"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.43007186852254*^9}], Cell[BoxData["6.530498422127395`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718685537915`*^9}], Cell[BoxData["5.645373400123759`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071868600669*^9}], Cell[BoxData["5.910629952887942`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071868631921*^9}], Cell[BoxData["5.9402862382275275`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718686787977`*^9}], Cell[BoxData["5.940664754519099`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718687100496`*^9}], Cell[BoxData["\<\"Iterating for upper limit of CI ...\"\>"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718687100496`*^9}], Cell[BoxData["7.751096076478245`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718687569275`*^9}], Cell[BoxData["8.70191520653039`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718687881784`*^9}], Cell[BoxData["8.417114495553586`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718688350563`*^9}], Cell[BoxData["8.38813778630758`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.4300718688663073`*^9}], Cell[BoxData["8.3878244410611`*^-8"], "Print", CellChangeTimes->{ 3.399232712842361*^9, 3.399297947843764*^9, 3.405872228428935*^9, 3.405874752000353*^9, 3.405874825545492*^9, 3.409344236308054*^9, 3.409862751531125*^9, 3.409863789718676*^9, 3.410019107723772*^9, 3.410019768195844*^9, 3.410031398084108*^9, 3.410034070333264*^9, 3.410101951919913*^9, 3.410184322170457*^9, 3.410363192520196*^9, 3.410538469934929*^9, 3.410539241056255*^9, 3.410546668340465*^9, 3.410547491069959*^9, 3.416253861791672*^9, 3.416590123538594*^9, 3.429879275992295*^9, 3.4298831465858126`*^9, 3.429890443832147*^9, 3.4298986465195827`*^9, 3.429971341381258*^9, 3.429972762239976*^9, 3.430054544729804*^9, 3.430061361836074*^9, 3.4300634785127945`*^9, 3.4300645773133745`*^9, {3.430065412543956*^9, 3.430062372975499*^9}, 3.430071100373838*^9, 3.430071868913185*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"5.940664677296555`*^-8", ",", "8.387824272723612`*^-8"}], "}"}]], "Output", CellChangeTimes->{ 3.399233154186793*^9, 3.399298385713642*^9, 3.405872675772498*^9, 3.405874752960987*^9, 3.405875270693202*^9, 3.409344674159177*^9, 3.409862754834301*^9, 3.409863793165531*^9, 3.410019111153263*^9, 3.410019771647953*^9, 3.410031401554887*^9, 3.410034073803602*^9, 3.410101955696293*^9, 3.41018432561599*^9, 3.410363195966015*^9, 3.410538473401222*^9, 3.410539245167311*^9, 3.410546671804717*^9, 3.410547495011573*^9, 3.416253865273194*^9, 3.4165901250378737`*^9, 3.429879277789193*^9, 3.429883148069627*^9, 3.4298904453160186`*^9, 3.429898648004471*^9, 3.429971342883725*^9, 3.4299727637241898`*^9, 3.430054546214027*^9, 3.4300613633361025`*^9, 3.430063479997018*^9, 3.4300645788132687`*^9, {3.4300654140599594`*^9, 3.430062376462944*^9}, 3.430071101858289*^9, 3.430071868913185*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["The Bartlett Formulation", "Section", CellChangeTimes->{{3.405797889046735*^9, 3.405797898767687*^9}, { 3.4093396054858*^9, 3.40933961373622*^9}}], Cell["\<\ This formulation of the Luria-Delbruck model was proposed by Bartlett in \ 1952. Under this formulation, nonmutant cells also grow stochastically, \ governed by a Yule birth process. For this reason, Bartlett called this \ formulation a fully stochastic model, in contrast to the Lea-Coulson \ formulation under which nonmutant cells grow deterministically. The mutant \ distribution under this formulation is called the Bartlett distribution, \ which can be computed as follows.\ \>", "Text", CellChangeTimes->{{3.405873086200908*^9, 3.405873331982163*^9}, { 3.405873371668189*^9, 3.4058734877007*^9}, {3.405873542771206*^9, 3.405873618641563*^9}, 3.405874843308882*^9, {3.409339634194318*^9, 3.409339659178836*^9}, {3.409339715714845*^9, 3.409339794880977*^9}, { 3.409339837596298*^9, 3.409339887187403*^9}, {3.410370491754363*^9, 3.410370528049573*^9}, {3.429972260984271*^9, 3.429972263030884*^9}, 3.4299726586418743`*^9, {3.4300571248942037`*^9, 3.430057129924938*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfBartlett"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfBartlett[\!\(\[Alpha],\[Phi]\),n] computes the first\\nn+1 \ probabilities of a Bartlett distribution having \!\(N\_0=1\). Note \ that\\npmfBartlett[\!\(\[Alpha],\[Phi]\),n,k] assumes \!\(N\_0\)=k.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071869038192*^9}, CellTags->"Info3430053868-4904722"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pmfBartlett", "[", RowBox[{"0.00001", ",", "0.999", ",", "12"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.9901088129586381`", ",", "0.00490162132370505`", ",", "0.001658120065365087`", ",", "0.0008332177487069839`", ",", "0.0005010540761054135`", ",", "0.0003344134502532342`", ",", "0.0002390089055181343`", ",", "0.00017931256087105183`", ",", "0.00013948639037820293`", ",", "0.00011159531330540102`", ",", "0.00009130498305392324`", ",", "0.0000760844683517895`", ",", "0.00006437511928083066`"}], "}"}]], "Output", CellChangeTimes->{ 3.405793466583873*^9, {3.405793758193679*^9, 3.405793768137646*^9}, 3.405793877509894*^9, 3.405798062525178*^9, 3.405872676741896*^9, 3.409339384107055*^9, 3.409339925059477*^9, 3.409340666596287*^9, 3.409340714536406*^9, 3.409340806740632*^9, 3.409341434294567*^9, 3.409341804213448*^9, 3.409342038547144*^9, 3.409342383683946*^9, 3.40934291508258*^9, 3.409343252744347*^9, 3.409343358068799*^9, 3.409343455713589*^9, 3.409343524107392*^9, 3.409343593861577*^9, 3.40934467493849*^9, 3.409862755695365*^9, 3.409863794259554*^9, 3.410019112098134*^9, 3.410019772636379*^9, 3.410031402417591*^9, 3.410034074663902*^9, 3.41010195691037*^9, 3.410184326533216*^9, 3.410363197584913*^9, 3.410538474399037*^9, 3.410539246168988*^9, 3.410546672658011*^9, 3.410547496007904*^9, 3.416253866101835*^9, 3.416590125194049*^9, 3.4298792779298196`*^9, 3.429883148241437*^9, 3.429890445487835*^9, 3.429898648176405*^9, 3.4299713430558834`*^9, 3.4299727638960457`*^9, 3.430054546339014*^9, 3.4300568488124685`*^9, 3.430057735362935*^9, 3.4300579472943563`*^9, 3.4300581795353804`*^9, 3.4300594243057985`*^9, 3.4300613635079803`*^9, 3.430063480168875*^9, 3.4300645789851313`*^9, {3.4300654142006197`*^9, 3.430062377359361*^9}, 3.430071102014547*^9, 3.430071869069443*^9}] }, Open ]], Cell["\<\ The following function is for simulation under the Bartlett formulation.\ \>", "Text", CellChangeTimes->{{3.4298983157651825`*^9, 3.4298983477565813`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "simuBartlett"}]], "Input", CellChangeTimes->{{3.429890008382296*^9, 3.4298900120313854`*^9}}], Cell[BoxData[ StyleBox["\<\"simuBartlett[\!\(\[Beta],\[Mu],N\_0\),T] simulates \ the\\nnumbers of nonmutants and mutants using the Bartlett distribution. The \ mutation\\nrate is \!\(\[Alpha]=\[Mu]/\[Beta]\) and the parameter \ \!\(\[Phi]\) is defined by\\n\!\(\[Phi]=1-e\^-\[Beta]T\). The evolution of \ the mutation process can be\\nviewed by setting ShowGrowth->True.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071869163198*^9}, CellTags->"Info3430053869-6652240"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"simuBartlett", "[", RowBox[{"0.1", ",", "0.02", ",", "1", ",", "14.5", ",", RowBox[{"ShowGrowth", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.429890015836419*^9, 3.4298900720158477`*^9}, { 3.4298902235243998`*^9, 3.4298902240552416`*^9}, {3.430056537342372*^9, 3.43005655809038*^9}}], Cell[BoxData["\<\"wild= 1 mutant=0\"\>"], "Print", CellChangeTimes->{{3.4298900473682957`*^9, 3.4298900724061728`*^9}, 3.4298902343910475`*^9, 3.4298984239556913`*^9, 3.429971124885125*^9, 3.4299725510754533`*^9, 3.430054336285244*^9, {3.4300565408576593`*^9, 3.4300565661364827`*^9}, 3.430056848984327*^9, 3.4300577354566755`*^9, 3.430057947388097*^9, 3.4300581796448903`*^9, 3.4300594243995*^9, 3.430061363648608*^9, 3.4300634803251095`*^9, 3.4300645791257467`*^9, { 3.4300654143100214`*^9, 3.430062378319823*^9}, 3.430071102139553*^9, 3.4300718691944494`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]], "Output", CellChangeTimes->{ 3.429890234469113*^9, 3.4298984240650387`*^9, 3.429971124900776*^9, 3.429972551512906*^9, 3.43005433689522*^9, {3.4300565408889065`*^9, 3.4300565661521063`*^9}, 3.4300568490155735`*^9, 3.4300577354566755`*^9, 3.4300579474193435`*^9, 3.4300581796448903`*^9, 3.4300594243995*^9, 3.43006136374236*^9, 3.4300634803251095`*^9, 3.430064579203866*^9, { 3.4300654143256507`*^9, 3.430062378626747*^9}, 3.430071102139553*^9, 3.4300718692100754`*^9}] }, Open ]], Cell["\<\ Now we simulate a fluctuation experiment consisting of n=20 tubes.\ \>", "Text", CellChangeTimes->{{3.409342998539691*^9, 3.409343033933398*^9}, { 3.409343442775415*^9, 3.409343444454112*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"datBart", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"simuBartlett", "[", RowBox[{"1.5", ",", "0.002", ",", "5", ",", "4.5"}], "]"}], ",", RowBox[{"{", "20", "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.405798087496484*^9, 3.405798137462611*^9}, { 3.405798173958898*^9, 3.405798192729578*^9}, {3.410032004036983*^9, 3.410032046585949*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2380", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"6648", ",", "40"}], "}"}], ",", RowBox[{"{", RowBox[{"4342", ",", "12"}], "}"}], ",", RowBox[{"{", RowBox[{"2317", ",", "15"}], "}"}], ",", RowBox[{"{", RowBox[{"4287", ",", "9"}], "}"}], ",", RowBox[{"{", RowBox[{"5918", ",", "47"}], "}"}], ",", RowBox[{"{", RowBox[{"4419", ",", "9"}], "}"}], ",", RowBox[{"{", RowBox[{"2213", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"3890", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"6493", ",", "139"}], "}"}], ",", RowBox[{"{", RowBox[{"2297", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"3523", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"3902", ",", "353"}], "}"}], ",", RowBox[{"{", RowBox[{"2526", ",", "19"}], "}"}], ",", RowBox[{"{", RowBox[{"4855", ",", "9"}], "}"}], ",", RowBox[{"{", RowBox[{"3388", ",", "6"}], "}"}], ",", RowBox[{"{", RowBox[{"3113", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"4886", ",", "22"}], "}"}], ",", RowBox[{"{", RowBox[{"6097", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"2128", ",", "12"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.405793779967176*^9, 3.405793890541845*^9, {3.405798079450366*^9, 3.405798139267997*^9}, {3.405798174783827*^9, 3.405798195317759*^9}, 3.405872680082149*^9, 3.409339387541557*^9, 3.409339957922157*^9, 3.409340503384525*^9, 3.409340670115283*^9, 3.409340718255229*^9, 3.409340809737679*^9, 3.409341807432049*^9, 3.409342041526071*^9, 3.409342387039762*^9, 3.409342453472111*^9, 3.409343046941751*^9, 3.409343258083494*^9, 3.409343361985755*^9, 3.409343459340872*^9, 3.409343528357633*^9, 3.409343598268583*^9, 3.409344679460876*^9, 3.409862761808576*^9, 3.409863799747783*^9, 3.410019116759221*^9, 3.410019778429801*^9, 3.410031407214488*^9, 3.410032011354582*^9, 3.410032050162642*^9, 3.410034079933467*^9, 3.410101962017709*^9, 3.410184330774535*^9, 3.410363203124456*^9, 3.410538479050656*^9, 3.410539252137875*^9, 3.410546677974422*^9, 3.410547500567586*^9, 3.41625387172769*^9, 3.416590126833886*^9, 3.429879279726718*^9, 3.4298831501938243`*^9, 3.4298904468311296`*^9, 3.4298986495987716`*^9, 3.4299713445427*^9, 3.429972348707416*^9, 3.42997276523965*^9, 3.4300545479013543`*^9, 3.430056850484183*^9, {3.4300575969864817`*^9, 3.430057605532481*^9}, 3.4300577369096518`*^9, 3.430057948841073*^9, 3.430058181084166*^9, 3.430059425836255*^9, 3.430061364929883*^9, 3.4300634817155914`*^9, 3.430064580485026*^9, {3.4300654155759625`*^9, 3.430062381424089*^9}, 3.430071103295862*^9, 3.430071870522642*^9}] }, Open ]], Cell["The mutation rate is known in advance.", "Text", CellChangeTimes->{{3.409339980274956*^9, 3.409340025428557*^9}, { 3.409343049021861*^9, 3.409343051789881*^9}, {3.429972358096839*^9, 3.4299723615338993`*^9}, {3.43005784507045*^9, 3.4300578459609838`*^9}, { 3.430057879551294*^9, 3.430057890503297*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"truMu", "=", RowBox[{"0.002", "/", "1.5"}]}]], "Input", CellChangeTimes->{{3.405798152845082*^9, 3.405798153066453*^9}, { 3.405798201684289*^9, 3.405798203864431*^9}}], Cell[BoxData["0.0013333333333333333`"], "Output", CellChangeTimes->{ 3.405793780231245*^9, 3.405793890890162*^9, 3.405798153438524*^9, 3.405798204953546*^9, 3.405872680481881*^9, 3.4093393877475*^9, 3.409340670335202*^9, 3.409340718575379*^9, 3.409340809959884*^9, 3.409341807760211*^9, 3.409342041739376*^9, 3.40934238727282*^9, 3.409342453602182*^9, 3.409343053586002*^9, 3.409343258271142*^9, 3.409343362283692*^9, 3.409343459657891*^9, 3.409343528661047*^9, 3.40934359850232*^9, 3.409344679804076*^9, 3.409862762255801*^9, 3.409863800124365*^9, 3.410019117017955*^9, 3.41001977867457*^9, 3.410031407473605*^9, 3.410032056516605*^9, 3.410034080286042*^9, 3.410101962382829*^9, 3.410184331173408*^9, 3.41036320395677*^9, 3.410538479427385*^9, 3.410539252375419*^9, 3.410546678215338*^9, 3.410547500819922*^9, 3.416253871966471*^9, 3.416590126865121*^9, 3.429879279742343*^9, 3.4298831502250624`*^9, 3.4298904468623686`*^9, 3.4298986496300325`*^9, 3.4299713445740013`*^9, 3.429972363861726*^9, 3.4299727652708964`*^9, 3.430054547916978*^9, 3.4300568505154295`*^9, 3.4300576107819433`*^9, 3.430057736940899*^9, 3.4300579488723197`*^9, 3.4300581811154547`*^9, 3.4300594258674884`*^9, 3.430061364976759*^9, 3.4300634817624617`*^9, 3.4300645805318975`*^9, {3.4300654156072206`*^9, 3.430062381675308*^9}, 3.430071103327114*^9, 3.430071870553894*^9}] }, Open ]], Cell["\<\ We use this data set as an illustrative example. First, let us extract the \ numbers of mutants from the simulated data.\ \>", "Text", CellChangeTimes->{{3.409340045432753*^9, 3.409340047063531*^9}, { 3.409340077892906*^9, 3.409340101966476*^9}, {3.409340176473729*^9, 3.409340192560192*^9}, {3.409340242371934*^9, 3.409340248848574*^9}, { 3.430057240632351*^9, 3.4300572476160107`*^9}, {3.4300572801439295`*^9, 3.430057312812459*^9}, {3.430057369181686*^9, 3.4300573695566473`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"simulated", "=", RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "&"}], "/@", " ", "datBart"}]}]], "Input",\ CellChangeTimes->{{3.410032069450939*^9, 3.410032074413901*^9}, { 3.430059529782341*^9, 3.4300595319374733`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "40", ",", "12", ",", "15", ",", "9", ",", "47", ",", "9", ",", "5", ",", "3", ",", "139", ",", "4", ",", "4", ",", "353", ",", "19", ",", "9", ",", "6", ",", "8", ",", "22", ",", "20", ",", "12"}], "}"}]], "Output", CellChangeTimes->{ 3.40579378055675*^9, 3.405793891132868*^9, 3.405798160112706*^9, 3.405798208396257*^9, 3.405872680625657*^9, 3.409339387856911*^9, 3.409340507967367*^9, 3.409340670448852*^9, 3.409340718784933*^9, 3.409340810073251*^9, 3.409341807962971*^9, 3.409342041852197*^9, 3.409342387401739*^9, 3.409342453712451*^9, 3.409343058185789*^9, 3.409343258380526*^9, 3.409343362476851*^9, 3.409343459867607*^9, 3.409343528859041*^9, 3.409343598698173*^9, 3.409344680021997*^9, 3.409862762377034*^9, 3.409863800377497*^9, 3.410019117264074*^9, 3.410019778808009*^9, 3.410031407720378*^9, {3.410032062079627*^9, 3.410032075635972*^9}, 3.410034080421913*^9, 3.410101962604591*^9, 3.410184331429227*^9, 3.410363204458204*^9, 3.410538479669884*^9, 3.410539252509629*^9, 3.410546678345914*^9, 3.410547501066*^9, 3.416253872105821*^9, 3.4165901268807387`*^9, 3.429879279757968*^9, 3.4298831502406816`*^9, 3.429890446877989*^9, 3.429898649645663*^9, 3.4299713445896516`*^9, 3.4299723671894255`*^9, 3.4299727652708964`*^9, 3.430054547932601*^9, 3.4300568505310535`*^9, 3.4300576134691687`*^9, 3.430057736956522*^9, 3.4300579488879433`*^9, 3.4300581811310987`*^9, 3.4300594258831053`*^9, 3.4300595331712084`*^9, 3.430061364976759*^9, 3.430063481778085*^9, 3.4300645805318975`*^9, {3.4300654156072206`*^9, 3.430062381817038*^9}, 3.430071103327114*^9, 3.43007187056952*^9}] }, Open ]], Cell["Clearly, the parameter \[Phi] is", "Text", CellChangeTimes->{{3.409340251468452*^9, 3.409340278009369*^9}, 3.409340510169483*^9, 3.409341897494967*^9, {3.430057328748327*^9, 3.430057349621189*^9}, {3.43005761531273*^9, 3.4300576168594465`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"phi", "=", RowBox[{"1", "-", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "1.5"}], "*", "4.5"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.405798215449027*^9, 3.405798216039836*^9}, 3.409340282963568*^9}], Cell[BoxData["0.9988291203792088`"], "Output", CellChangeTimes->{ 3.405793780866907*^9, 3.405793891260544*^9, 3.405798216673012*^9, 3.405872680877549*^9, 3.409339388051202*^9, 3.409340511272145*^9, 3.409340670563216*^9, 3.409340718802129*^9, 3.409340810188442*^9, 3.409341807982904*^9, 3.409342041962853*^9, 3.409342387515937*^9, 3.40934245374497*^9, 3.409343060514892*^9, 3.409343258494546*^9, 3.409343362495183*^9, 3.409343459888592*^9, 3.409343528879865*^9, 3.409343598718736*^9, 3.409344680162087*^9, 3.409862762439345*^9, 3.409863800654253*^9, 3.410019117408721*^9, 3.41001977904987*^9, 3.410031407867601*^9, 3.410032077716548*^9, 3.410034080676778*^9, 3.410101962748898*^9, 3.410184331711365*^9, 3.410363204822686*^9, 3.410538479950713*^9, 3.41053925275498*^9, 3.410546678585759*^9, 3.410547501210034*^9, 3.416253872347035*^9, 3.4165901268963566`*^9, 3.429879279773593*^9, 3.429883150256301*^9, 3.429890446893608*^9, 3.429898649661293*^9, 3.4299713445896516`*^9, 3.429972369220415*^9, 3.4299727652865195`*^9, 3.430054547932601*^9, 3.4300568505466766`*^9, 3.430057621155881*^9, 3.430057736972145*^9, 3.4300579489035664`*^9, 3.4300581811467433`*^9, 3.4300594258987226`*^9, 3.430061364992384*^9, 3.430063481778085*^9, 3.4300645805475216`*^9, {3.4300654156228495`*^9, 3.430062381957113*^9}, 3.43007110334274*^9, 3.43007187056952*^9}] }, Open ]], Cell["\<\ Now we apply the maximum likelihood procedure (Zheng 2008) to estimate the \ mutation rate.\ \>", "Text", CellChangeTimes->{{3.405873814840102*^9, 3.405873817120852*^9}, { 3.405873850899935*^9, 3.40587390558504*^9}, {3.409340326723669*^9, 3.409340360031893*^9}, {3.430058164407342*^9, 3.43005816971076*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "newtonBartlett"}]], "Input"], Cell[BoxData[ StyleBox["\<\"newtonBartlett[X, \!\(N\_0, \[Phi]\)] finds the maximum \ \\nlikelihood estimate of the mutation rate \!\(\[Alpha]\) under the Bartlett \ \\nformulation.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718706789007`*^9}, CellTags->"Info3430053870-3381490"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonBartlett", "[", RowBox[{"simulated", ",", "5", ",", "phi"}], "]"}]], "Input", CellChangeTimes->{ 3.409340369995328*^9, {3.430057381992874*^9, 3.4300573835239673`*^9}, { 3.430057419832749*^9, 3.4300574261133556`*^9}, {3.4300576891957884`*^9, 3.430057690633141*^9}, {3.430059536950498*^9, 3.4300595388245263`*^9}}], Cell[BoxData["0.0010992818923167187`"], "Output", CellChangeTimes->{ 3.405793783196289*^9, 3.405793893709667*^9, 3.405798224671057*^9, 3.405872683175473*^9, 3.409339389608349*^9, 3.409340371272492*^9, 3.409340523926227*^9, 3.409340672507613*^9, 3.409340720267718*^9, 3.409340811741477*^9, 3.409341809448368*^9, 3.409342043627143*^9, 3.409342389079326*^9, 3.409342454703733*^9, 3.409343066363057*^9, 3.409343260088564*^9, 3.409343364040012*^9, 3.409343461519166*^9, 3.409343530468097*^9, 3.409343600250733*^9, 3.40934468239855*^9, 3.409862764054721*^9, 3.409863802706408*^9, 3.41001911925007*^9, 3.410019781015459*^9, 3.410031409768406*^9, 3.410032086824857*^9, 3.410034082661043*^9, 3.410101964851635*^9, 3.410184333796626*^9, 3.410363206959482*^9, 3.410538482046035*^9, 3.410539254742232*^9, 3.410546680623602*^9, 3.410547503331699*^9, 3.416253874466867*^9, 3.416590127115001*^9, 3.4298792804298515`*^9, 3.429883150490587*^9, 3.429890447127904*^9, 3.429898649880119*^9, 3.429971344840063*^9, { 3.4299723728137054`*^9, 3.4299723847810483`*^9}, 3.4299727655208693`*^9, 3.430054548120082*^9, 3.4300568507185354`*^9, 3.430057384617605*^9, 3.4300574271288767`*^9, 3.430057514432436*^9, 3.4300576270615263`*^9, 3.430057691492428*^9, 3.430057737112756*^9, 3.430057949044177*^9, 3.4300581813344746`*^9, 3.430059426023658*^9, 3.430059539824008*^9, 3.430061365195513*^9, 3.4300634819811897`*^9, 3.43006458078188*^9, { 3.4300654157791386`*^9, 3.430062383103908*^9}, 3.4300711035458755`*^9, 3.4300718707882814`*^9}] }, Open ]], Cell["\<\ We can also construct an asymptotic confidence interval for the mutation \ rate.\ \>", "Text", CellChangeTimes->{{3.405873944473742*^9, 3.405873958872188*^9}, { 3.409340399576647*^9, 3.409340418808214*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "CIBartlett"}]], "Input"], Cell[BoxData[ StyleBox["\<\"CIBartlett[X, \!\(N\_0, \[Phi]\)] constructs an \ asymptotic\\nconfidence interval for the mutation rate \!\(\[Alpha]\) under \ the Bartlett\\nformulation.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718708976617`*^9}, CellTags->"Info3430053870-9314038"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CIBartlett", "[", RowBox[{"simulated", ",", "5", ",", "phi"}], "]"}]], "Input", CellChangeTimes->{ 3.409340680935142*^9, {3.430057665135752*^9, 3.4300576664793644`*^9}, { 3.430059546523658*^9, 3.430059550115545*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.0007268703468394334`", ",", "0.001604460536701512`"}], "}"}]], "Output", CellChangeTimes->{ 3.405793786274984*^9, 3.405793897793677*^9, 3.405798232596854*^9, 3.405872686537646*^9, 3.409339392105805*^9, 3.40934043036595*^9, 3.40934068950284*^9, 3.409340723112126*^9, 3.40934081451167*^9, 3.409341812247115*^9, 3.40934204630992*^9, 3.409342391897919*^9, 3.409342457693671*^9, 3.409343263024586*^9, 3.409343366692524*^9, 3.409343464412783*^9, 3.409343533546007*^9, 3.409343603179954*^9, 3.409344685866322*^9, 3.40986276810502*^9, 3.409863806348586*^9, 3.410019122766275*^9, 3.410019784225325*^9, 3.410031413276373*^9, 3.410032162260885*^9, 3.410034094362483*^9, 3.410101972981042*^9, 3.410184356724935*^9, 3.41036321212949*^9, 3.410538490055933*^9, 3.410539259546742*^9, 3.410546700091671*^9, 3.410547509658883*^9, 3.416253886960155*^9, 3.4165901345957837`*^9, 3.4298793689931736`*^9, 3.4298831567069893`*^9, 3.4298904502049847`*^9, 3.4298986505991173`*^9, 3.4299713455443444`*^9, 3.429972399545067*^9, 3.429972770926531*^9, 3.430054549151226*^9, 3.4300568581396976`*^9, 3.430057667323028*^9, 3.4300577423622184`*^9, 3.430057949231658*^9, 3.430058181663005*^9, 3.4300594262110605`*^9, 3.430059551021325*^9, 3.4300613654298925`*^9, 3.430063482246787*^9, 3.4300645811568537`*^9, {3.430065415997943*^9, 3.430062384462333*^9}, 3.430071103842766*^9, 3.4300718711633005`*^9}] }, Open ]], Cell["\<\ Now it is straightforward to estimate the mutation rate for the Demerec \ experiment.\ \>", "Text", CellChangeTimes->{{3.409340538850805*^9, 3.409340586232454*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"demerec", "=", RowBox[{"{", RowBox[{ "33", ",", "18", ",", " ", "839", ",", "47", ",", "13", ",", "126", ",", "48", ",", "80", ",", "9", ",", "71", ",", "196", ",", "66", ",", "28", ",", "17", ",", "27", ",", "37", ",", "126", ",", "33", ",", "12", ",", "44", ",", "28", ",", "67", ",", "730", ",", "168", ",", "44", ",", "50", ",", "583", ",", "23", ",", "17", ",", "24"}], "}"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"phi", "=", RowBox[{"1", "-", RowBox[{"90", "/", RowBox[{"(", RowBox[{"1.9", " ", RowBox[{"10", "^", "8"}]}], ")"}]}]}]}]], "Input"], Cell[BoxData["0.9999995263157895`"], "Output", CellChangeTimes->{ 3.405793786596286*^9, 3.405793898013343*^9, 3.405798288272979*^9, 3.405872686828519*^9, 3.409339392274321*^9, 3.409340603375831*^9, 3.409340723355798*^9, 3.409340814681518*^9, 3.409341812429724*^9, 3.409342046565473*^9, 3.409342392074977*^9, 3.409343263214553*^9, 3.409343366944098*^9, 3.409343464667075*^9, 3.409343533735816*^9, 3.409343603379166*^9, 3.409344686162997*^9, 3.409862768306932*^9, 3.409863806569825*^9, 3.410019123083673*^9, 3.410019784435579*^9, 3.410031413577413*^9, 3.41003411799168*^9, 3.410101986763921*^9, 3.410184418132204*^9, 3.410363217349534*^9, 3.410538503532738*^9, 3.410539264587507*^9, 3.410546743889836*^9, 3.410547517998221*^9, 3.416253912842844*^9, 3.416590154914151*^9, 3.4298796161640034`*^9, 3.429883175106289*^9, 3.429890457936736*^9, 3.4298986516619844`*^9, 3.4299713464677353`*^9, 3.429972412324926*^9, 3.4299727852062273`*^9, 3.430054551494736*^9, 3.430056878262766*^9, 3.430057704772318*^9, 3.4300577581262293`*^9, 3.430057949247281*^9, 3.430058181678649*^9, 3.430059426226677*^9, 3.4300613654455175`*^9, 3.430063482262411*^9, 3.4300645811724777`*^9, {3.4300654160135717`*^9, 3.43006238470294*^9}, 3.4300711038583913`*^9, 3.430071871178926*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonBartlett", "[", RowBox[{"demerec", ",", "90", ",", "phi", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["1.590217317193996`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.430071871194552*^9}], Cell[BoxData["3.1360882461326814`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.4300718716633263`*^9}], Cell[BoxData["4.921245150719334`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.430071872116474*^9}], Cell[BoxData["5.698616521938277`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.4300718725696225`*^9}], Cell[BoxData["5.7745228844381766`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.4300718730383964`*^9}], Cell[BoxData["5.775112512010731`*^-8"], "Print", CellChangeTimes->{ 3.405793786615648*^9, 3.405793898032685*^9, 3.405798289818135*^9, 3.405872687018179*^9, 3.409339392363326*^9, 3.409340609004874*^9, 3.409340723375335*^9, 3.409340814869891*^9, 3.409341812529609*^9, 3.409342046584958*^9, 3.409342392224015*^9, 3.409343263314583*^9, 3.409343366965969*^9, 3.409343464689576*^9, 3.409343533906547*^9, 3.40934360348488*^9, 3.409344686321056*^9, 3.409862768455819*^9, 3.409863806757418*^9, 3.410019123207267*^9, 3.410019784627594*^9, 3.410031413603274*^9, 3.410034118015874*^9, 3.410101986871281*^9, 3.410184418262758*^9, 3.410363217466114*^9, 3.410538503640865*^9, 3.410539264618572*^9, 3.410546743999273*^9, 3.410547518109641*^9, 3.416253912962969*^9, 3.4165901549297686`*^9, 3.4298796161952534`*^9, 3.429883175121908*^9, 3.4298904579523563`*^9, 3.4298986516776147`*^9, 3.4299713464833865`*^9, 3.4299724138872557`*^9, 3.4299727852218504`*^9, 3.43005455151036*^9, 3.430056878294013*^9, 3.430057706990841*^9, 3.4300577581418524`*^9, 3.4300579492629046`*^9, 3.430058181709938*^9, 3.4300594262579107`*^9, 3.4300613654611435`*^9, 3.430063482278034*^9, 3.4300645812037253`*^9, {3.4300654160292006`*^9, 3.430062384837865*^9}, 3.4300711038740172`*^9, 3.4300718734915447`*^9}] }, Open ]], Cell[BoxData["5.7751125470636866`*^-8"], "Output", CellChangeTimes->{ 3.405793791838187*^9, 3.405793903213944*^9, 3.405798295571866*^9, 3.405872692702864*^9, 3.409339398008767*^9, 3.409340614584345*^9, 3.409340729182796*^9, 3.409340820052139*^9, 3.409341819097548*^9, 3.40934205234921*^9, 3.409342398201212*^9, 3.409343268535236*^9, 3.40934337220507*^9, 3.409343469980914*^9, 3.409343538946185*^9, 3.409343608701407*^9, 3.4093446914884*^9, 3.409862774917394*^9, 3.409863812185767*^9, 3.410019129385896*^9, 3.41001978973235*^9, 3.410031418897097*^9, 3.410034123379968*^9, 3.410101992188337*^9, 3.410184423601366*^9, 3.410363223938285*^9, 3.410538509000359*^9, 3.410539270004781*^9, 3.410546749367561*^9, 3.41054752344684*^9, 3.416253918304579*^9, 3.4165901576784487`*^9, 3.4298796192577333`*^9, 3.4298831778552504`*^9, 3.4298904606858034`*^9, 3.429898654428565*^9, 3.4299713492222586`*^9, 3.4299724166682034`*^9, 3.4299727879871745`*^9, 3.430054554260078*^9, 3.4300568810281253`*^9, 3.430057709771806*^9, 3.4300577608759475`*^9, 3.4300579519969997`*^9, 3.4300581844476905`*^9, 3.4300594289908686`*^9, 3.430061368195571*^9, 3.4300634850277524`*^9, 3.430064583922284*^9, {3.430065418811145*^9, 3.430062390305761*^9}, 3.4300711065929065`*^9, 3.4300718739446926`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CIBartlett", "[", RowBox[{"demerec", ",", "90", ",", "phi", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for MLE ...\"\>"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.43007187399157*^9}], Cell[BoxData["1.590217317193996`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.43007187399157*^9}], Cell[BoxData["3.1360882461326814`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718744447184`*^9}], Cell[BoxData["4.921245150719334`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718748978662`*^9}], Cell[BoxData["5.698616521938277`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.43007187536664*^9}], Cell[BoxData["5.7745228844381766`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071875819789*^9}], Cell[BoxData["5.775112512010731`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071876272937*^9}], Cell[BoxData["\<\"Iterating for lower limit ...\"\>"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718776480074`*^9}], Cell[BoxData["5.153384384364654`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071878116781*^9}], Cell[BoxData["4.292757190471943`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718785699296`*^9}], Cell[BoxData["4.5507631614911176`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718790230775`*^9}], Cell[BoxData["4.583534239355679`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071879476226*^9}], Cell[BoxData["4.584053668034278`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718799449997`*^9}], Cell[BoxData["4.584053806589249`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071880398148*^9}], Cell[BoxData["4.5840537161152863`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718808512964`*^9}], Cell[BoxData["\<\"Iterating for upper limit ...\"\>"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718808512964`*^9}], Cell[BoxData["6.396840709762719`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718813044443`*^9}], Cell[BoxData["7.400023645837595`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071881773218*^9}], Cell[BoxData["7.099530413340877`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071882226367*^9}], Cell[BoxData["7.070298375747542`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.430071882679515*^9}], Cell[BoxData["7.070006002840305`*^-8"], "Print", CellChangeTimes->{ 3.405793792083911*^9, 3.405793903317469*^9, 3.405798297590439*^9, 3.405872693044308*^9, 3.409339398129217*^9, 3.409340616601526*^9, 3.409340729633364*^9, 3.409340820163899*^9, 3.409341819207083*^9, 3.409342052834971*^9, 3.409342398540915*^9, 3.409343268649605*^9, 3.40934337231707*^9, 3.409343470095128*^9, 3.409343539060351*^9, 3.409343608816327*^9, 3.409344691719077*^9, 3.409862775463625*^9, 3.40986381235771*^9, 3.41001912963923*^9, 3.410019789886864*^9, 3.410031419046709*^9, 3.41003412353016*^9, 3.410101992427573*^9, 3.410184423752079*^9, 3.410363224192767*^9, 3.410538509232012*^9, 3.410539270161926*^9, 3.410546749595248*^9, 3.410547523602861*^9, 3.416253918546617*^9, 3.416590157709684*^9, 3.429879619382733*^9, 3.4298831779021077`*^9, 3.429890460732662*^9, 3.429898654459826*^9, 3.42997134925356*^9, 3.4299724184492598`*^9, 3.429972788018421*^9, 3.4300545542757015`*^9, 3.4300568810749955`*^9, 3.4300577117091074`*^9, 3.4300577609228177`*^9, 3.43005795204387*^9, 3.430058184494623*^9, 3.4300594290377192`*^9, 3.4300613682424464`*^9, 3.430063485074623*^9, 3.4300645839691553`*^9, {3.4300654188424025`*^9, 3.430062390482321*^9}, 3.430071106639784*^9, 3.4300718831326632`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"4.584053744236134`*^-8", ",", "7.070006062016679`*^-8"}], "}"}]], "Output", CellChangeTimes->{ 3.405793809938802*^9, 3.405793921035547*^9, 3.405798315539613*^9, 3.405872711263034*^9, 3.40933941514644*^9, 3.409340632977807*^9, 3.409340747110009*^9, 3.409340836457596*^9, 3.409341835085288*^9, 3.409342068965196*^9, 3.409342414577356*^9, 3.409343285359079*^9, 3.40934338913495*^9, 3.409343486736927*^9, 3.409343558083868*^9, 3.409343626453274*^9, 3.409344708602304*^9, 3.409862797559172*^9, 3.409863830497374*^9, 3.410019150812794*^9, 3.410019806879931*^9, 3.410031435967663*^9, 3.410034142309234*^9, 3.410102009704005*^9, 3.41018444094716*^9, 3.410363241601768*^9, 3.410538526430978*^9, 3.410539287493673*^9, 3.410546767044027*^9, 3.410547540832763*^9, 3.41625393602644*^9, 3.416590166861539*^9, 3.429879628523299*^9, 3.429883186992424*^9, 3.4298904697920885`*^9, 3.4298986635879793`*^9, 3.4299713583584375`*^9, 3.42997242758889*^9, 3.4299727971892986`*^9, 3.4300545633528967`*^9, 3.4300568901834965`*^9, 3.43005772086442*^9, 3.430057770046883*^9, 3.4300579611878853`*^9, 3.430058194334888*^9, 3.430059440391206*^9, 3.4300613773363714`*^9, 3.4300634941986885`*^9, 3.4300645930310173`*^9, {3.430065428125969*^9, 3.430062409252868*^9}, 3.4300711156871223`*^9, 3.4300718831326632`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Plating efficiency", "Section", CellChangeTimes->{{3.416322728861006*^9, 3.416322732595598*^9}}], Cell["\<\ Plating efficiency, denoted by \[Epsilon], refers to the probability that a \ mutant cell living in the tube actually forms a visible colony on a solid \ culture in a dish after being plated (transferred). Imperfect plating \ efficiency (\[Epsilon]<1) can be caused by partial plating or by the cell's \ imperfect ability to survive the plating process. An example of partial \ plating is Luria and Delbruck's experiment #16 (Luria and Delbruck 1943) . In \ this experiment a 0.08-ml portion of each of the 12 0.2-ml cultures was \ plated; thus the plating efficiency is \[Epsilon]=0.4.\ \>", "Text", CellChangeTimes->{{3.416322894750009*^9, 3.416323144722472*^9}, { 3.416323177329584*^9, 3.416323214695262*^9}, {3.430058735796126*^9, 3.4300587859726915`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"e16", "=", RowBox[{"0.08", "/", "0.2"}]}]], "Input", CellChangeTimes->{{3.414439171787294*^9, 3.414439177479653*^9}, { 3.416323637026796*^9, 3.416323637213022*^9}, 3.429971798209203*^9}], Cell[BoxData["0.4`"], "Output", CellChangeTimes->{ 3.414439177813818*^9, 3.41625257703266*^9, 3.416252633055262*^9, 3.416253182627296*^9, 3.416322830610277*^9, 3.416323638766776*^9, 3.416324461803135*^9, 3.416331594129787*^9, 3.4165901668927736`*^9, 3.429879629335794*^9, 3.429883187039281*^9, 3.4298904698389473`*^9, 3.4298986636348705`*^9, 3.4299713584053392`*^9, 3.4299717991468706`*^9, 3.4299719534870234`*^9, 3.429972797220545*^9, 3.4300545633685203`*^9, 3.4300583007155066`*^9, 3.430059386731537*^9, 3.4300613773676214`*^9, 3.4300634942455587`*^9, 3.4300645930778894`*^9, {3.4300654281572275`*^9, 3.43006240941318*^9}, 3.4300711157183733`*^9, 3.4300718831639147`*^9}] }, Open ]], Cell["The original data of the experiment are as follows.", "Text", CellChangeTimes->{{3.416323654711335*^9, 3.416323678130511*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"expt16", "=", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "3", ",", "0", ",", "0", ",", "5", ",", "0", ",", "5", ",", "0", ",", "6", ",", "107", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "0", ",", "64", ",", "0", ",", "35"}], "}"}]}]], "Input", CellChangeTimes->{{3.414439086954578*^9, 3.414439129631743*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "0", ",", "3", ",", "0", ",", "0", ",", "5", ",", "0", ",", "5", ",", "0", ",", "6", ",", "107", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "0", ",", "64", ",", "0", ",", "35"}], "}"}]], "Output", CellChangeTimes->{ 3.414332759384976*^9, 3.414332828337186*^9, 3.414439052061455*^9, 3.414439134583761*^9, 3.416252563394852*^9, 3.416252631207337*^9, 3.416253181010518*^9, 3.416322828915139*^9, 3.416324462138967*^9, 3.416331594184953*^9, 3.416590166908391*^9, 3.4298796293826685`*^9, 3.4298831870549*^9, 3.4298904698545675`*^9, 3.4298986636505013`*^9, 3.429971358420973*^9, 3.429971801506669*^9, 3.429971953533907*^9, 3.429972797236168*^9, 3.430054563384144*^9, 3.430058300762421*^9, 3.4300593867627707`*^9, 3.430061377383247*^9, 3.430063494261182*^9, 3.4300645930935135`*^9, {3.4300654281572275`*^9, 3.430062409526239*^9}, 3.4300711157339993`*^9, 3.4300718831795406`*^9}] }, Open ]], Cell[TextData[{ "The cell population size prior to plating is ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["N", "T"], "=", RowBox[{"5.6", "\[Cross]", "10"}]}], TraditionalForm]]], Cell[BoxData[ SuperscriptBox["", "8"]]], "." }], "Text", CellChangeTimes->{{3.416323248762472*^9, 3.41632326313828*^9}, { 3.416323294812517*^9, 3.416323423581392*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"n16", "=", RowBox[{"5.6", " ", RowBox[{"10", "^", "8"}]}]}]], "Input", CellChangeTimes->{{3.414439147230972*^9, 3.414439157898862*^9}, 3.4299718034601436`*^9}], Cell[BoxData["5.6`*^8"], "Output", CellChangeTimes->{ 3.414332759616327*^9, 3.414332828540363*^9, 3.414439052262004*^9, 3.414439158233316*^9, 3.41625256535191*^9, 3.41625263142287*^9, 3.416253181222288*^9, 3.416322829118661*^9, 3.416324462275775*^9, 3.416331594305369*^9, 3.416590166924009*^9, 3.4298796294295435`*^9, 3.4298831870861387`*^9, 3.429890469870187*^9, 3.4298986636817617`*^9, 3.429971358436607*^9, 3.429971803741444*^9, 3.4299719535651627`*^9, 3.429972797267415*^9, 3.430054563399767*^9, 3.4300583007780595`*^9, 3.430059386778388*^9, 3.4300613773988724`*^9, 3.430063494276805*^9, 3.4300645931091375`*^9, {3.4300654281728563`*^9, 3.430062409573792*^9}, 3.430071115749625*^9, 3.4300718831951666`*^9}] }, Open ]], Cell["\<\ The only existing method to account for plating efficiency is to assume that \ the number of mutants in a tube prior to plating obeys the LD(m,1) \ distribution and that each mutant cell can survive the plating process with \ probability \[Epsilon]. The resulting mutant distribution can be calculated \ by invoking the function pmfLDPlating.\ \>", "Text", CellChangeTimes->{{3.416323744369228*^9, 3.41632395996009*^9}, { 3.416324016682176*^9, 3.416324031997738*^9}, {3.416324676681127*^9, 3.41632468175491*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfLDPlating"}]], "Input"], Cell[BoxData[ StyleBox["\<\"pmfLDPlating[m,\!\(\[Epsilon]\),n] computes probabilities \ for\\nan LD(m) distribution with plating efficiency \!\(\[Epsilon]\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071883320173*^9}, CellTags->"Info3430053883-7446926"] }, Open ]], Cell["\<\ Assume that m = 37.2 and \[Epsilon] = 0.1.\ \>", "Text", CellChangeTimes->{{3.416324035770667*^9, 3.416324051119222*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"dist", "=", RowBox[{"pmfLDPlating", "[", RowBox[{"37.2", ",", "0.1", ",", "150"}], "]"}]}], ";", RowBox[{"dist", "[", RowBox[{"[", RowBox[{"Range", "[", "6", "]"}], "]"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.00007356422544596412`", ",", "0.00047386409861230203`", ",", "0.001625579413881695`", ",", "0.003956802172059684`", ",", "0.007682388414012149`", ",", "0.012681652042429697`"}], "}"}]], "Output", CellChangeTimes->{ 3.414332771580147*^9, 3.414332837240144*^9, 3.41443906125496*^9, 3.41625264120226*^9, 3.416253190828655*^9, 3.416322838645018*^9, 3.416324082521357*^9, 3.416324463489286*^9, 3.416331595673724*^9, 3.4165901670958014`*^9, 3.4298796311170325`*^9, 3.429883187257949*^9, 3.4298904700576234`*^9, 3.4298986638536963`*^9, 3.4299713586242137`*^9, 3.4299718123836174`*^9, 3.429971953674557*^9, 3.429972797439271*^9, 3.4300545635247545`*^9, 3.4300583008875275`*^9, 3.430059386903323*^9, 3.430061377555125*^9, 3.430063494464286*^9, 3.430064593296624*^9, { 3.4300654283135157`*^9, 3.430062411335569*^9}, 3.4300711159058833`*^9, 3.43007188336705*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"{", RowBox[{ RowBox[{"Range", "[", RowBox[{"0", ",", "150"}], "]"}], ",", "dist"}], "}"}], "]"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input", CellChangeTimes->{{3.414332803849389*^9, 3.414332804506964*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw11QlQk2cCxvGooVpdIyuxarUKLCi1iBcYD4SH+z4DJIQridVixY1UFuqK +EnRgrqAnIaCcom1I0gFFFqkaRSH1q7oWnVa3JVqCwVtUalWwaXrDk8yk8n8 5sn/e+fLZBIrrS5800SRSFT68vn/V9MjP8+8s9vXwnVcD10HBhKvLJC40iJM uN9TZl+toqfgwr+6xyY4bafNkX3xR93htD20FFHp2H/zWQ49Bz8sKdtc9qyA ng9jcOqDTCc9bYl5w2kRRdJjtDXsT3265p1p1bQNmgeNDQef1tCLoE6rCSh2 Pk7b4XnvxHr5XZOXYEK242TJiMn2GMleqXqrwmQH2Iac1Fv119LLoXhSHyB+ bLr+CtSu9hrM+9Z0/kqcaM7Kj66qoldhf+XD4S83V9KOCNDsmHsm/ijthOB/ ni66Ly6nV2PD/iMNzV+Z7leGt67OSys/U0qvgTwj87G3sZheCxsLn+3ezwvp dYio96vpjDJ9fuuR5NrvMuW7fNoZfbUSfcFoLr0BKSWyz15kHaJd8Pss5/9M 8ztAu+K5Z33tIfdsGphT+LGQmbR/3AIwsPDCty7GLO5uMMv/8E6S6wfc3VC/ M1z6Wu9e7u5494+29KpKgbs7ci7pR46NZnD3gL7iv4e3DaRz98DOyZcvJ5vt 4u4JxyG3FlHATu6e+G3R19/82pLG3QuJ5QWiLPdU7l5I21e7V/dLCndvWOnL ctubdnD3xr1yF/eugve4++BH7+qNa7KTufvANifEfviw6fvri9lLl/68LFbH 3RfioSkJj1q2cfdDw/UDKjuHJO5+mCGYjVkZ3+Xuj6zu3U+TdVu4+0NvMyl3 cFUi9wA49uJ08fR3uAdgo+yX9oaRTdwD8Uzd9JeK529zD0Trzsn5Q1NoURDs zz1oUizeyD0I0Q+kB+vkWu7BSJ14d/pXhzTcg9HV1urVeU3NPQRV0RfOnrOi hRB412W8Wf17PPdQvCHJ2PFxR9y4EYowv556u9JYvj8UotcvNfbtiRm34eW+ bPC+Ic30exCGhN6kW/W7o9mHwdp25JO2fCX7MJi3toeLGxXsX+7ihR998X0U +3DkTrX4x1JzGuEombXxydGQSPbhGKuRzXzvSAT7cNh2FWr/PChnL8fo3GlF jz1oyOFwY9PB4uPh7OVQPPTf94GENsix9ev4wOCMMPYRMJcezsz7LZR9BHQe paP922khAuuMJUFjP4Wwj0COsXm62ZNg9pFQ9zRv9ZfQiETQ0ZkDLiuC2Eei J9H+w9i4QPaRcJv6eNqiggD2URDtHYha1O3PPgrXrJ5cHLKghSg0OidXzVP7 sY/Cp2s31fg1+bJXIO/i8b8tnE5DgdVp93x9t/mwV+Dyi8//mnLdm70CUs/R F0pXWqTEHk3I+6cbvdgrMTPr4j6nxbSgxARLXfWpak/2Smzd0tb7nTUtioZP xc1P9p3wYB+NW4WDObuW00I0rG5lPMo5784+Gpnzf5ZkBtMiFVxO+pTL7rmx V+GV4Z6zwi5aUGHwiqrVaTZtUMH26iyLFWfBPgY1dqeXhyhpxEAyFlF3e4T/ X0IMFlTJH972pw0xkAVGpmsrXdjHoj9GVrpqdAP7WNimBurmxtBCLES50oE7 Xzizj0Xj5dupkW/SojjolTOG/UvXs4/DgZY/0gtfpYU4dGWIlWJhHfs4ZKma vkkZWcs+Hrqw2X/qeJ9GPDZMOi/9fGQN+3i4SnfofQXaEA+f748NeL5KixLQ 1jGjJ69Yxj4BdyZZt0y1pYUE2B1f/8aRc6vZJ+Bs3xbx/CBapMZr/15Ysusn p3FbqnH+0ujiCoGGGj5C5pLEBbRajZP1htc7Oxx5fTVCE40pFRq6Uo078dfr el6hDWo0R//dbGvDqnH3vvRkG4NMSYs02H0j+aaDmLbUoCzOWuJyZiXP12DW +ZwBuZZWa1DSmX80QUoLGnx0YqUkrGsFz9fgqXty+5wM2qCB+GZr1wknuleD R26n+oZ+Xc7ztfgyX664d5K21OLBjbq7KZtpaKHp110rtaHVWhQVjV7Z07WM 52sRONW/3ehPV2px9Yx5xw/dDjxfiz5twNglhYPr/wD48KMy "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.414332771960198*^9, 3.414332837519637*^9, 3.414439061671761*^9, 3.416252641505534*^9, 3.416253191179311*^9, 3.416322839110094*^9, 3.416324084000231*^9, 3.416324463762606*^9, 3.416331595993981*^9, 3.4165901671114187`*^9, 3.429879631179532*^9, 3.429883187273568*^9, 3.429890470073243*^9, 3.4298986638693266`*^9, 3.4299713586398478`*^9, 3.429971814759043*^9, 3.4299719536901855`*^9, 3.429972797454894*^9, 3.4300545635403776`*^9, 3.430058300918804*^9, 3.43005938691894*^9, 3.4300613775707507`*^9, 3.43006349447991*^9, 3.430064593312248*^9, { 3.430065428329145*^9, 3.430062411778925*^9}, 3.430071115921509*^9, 3.430071883382676*^9}] }, Open ]], Cell["\<\ The first method to account for plating efficiency is to adjust the sample \ mean and then use Luria and Delbruck's method of means. This is the way Luria \ and Delbruck actually analyzed their data in 1943. Because adjusting the \ sample mean is the same as adjusting the raw data, one can proceed as \ follows.\ \>", "Text", CellChangeTimes->{{3.416323744369228*^9, 3.41632395996009*^9}, { 3.416324120050272*^9, 3.416324165659464*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "MethodOfMeans"}]], "Input"], Cell[BoxData[ StyleBox["\<\"MethodOfMeans[data,opts] iteratively solves for m\\nthe \ equation \!\( m log(\[Beta] n m)=X\&_ \), where \!\(\[Beta]\) is \ a\\ncorrection factor, where \!\(X\&_\) is the sample mean, and where n is \ sample size.\\nThe correction suggested by Armitage corresponds to \ \!\(\[Beta]=3.46\)\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071883429553*^9}, CellTags->"Info3430053883-4707819"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "MethodOfMeans", "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Correction", "\[Rule]", "1"}], ",", RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}], ",", RowBox[{"MaxIterations", "\[Rule]", "20"}], ",", RowBox[{"InitialM", "\[Rule]", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.414332761346462*^9, 3.414332829691896*^9, 3.41443905344067*^9, 3.414439162318992*^9, 3.416252575534255*^9, 3.416252632798917*^9, 3.416253182488755*^9, 3.416322830373616*^9, 3.416324464544027*^9, 3.416331596787348*^9, 3.416590167205124*^9, 3.4298796326795225`*^9, 3.4298831873829017`*^9, 3.429890470182581*^9, 3.4298986639787397`*^9, 3.4299713587336507`*^9, 3.4299719537995796`*^9, 3.4299727975642576`*^9, 3.430054563602871*^9, 3.4300583010126343`*^9, 3.4300593870282583`*^9, 3.430061377664502*^9, 3.4300634945892735`*^9, 3.4300645934059916`*^9, { 3.4300654284072895`*^9, 3.430062412673776*^9}, 3.4300711160152636`*^9, 3.430071883476431*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "=", RowBox[{"MethodOfMeans", "[", RowBox[{"expt16", "/", "e16"}], "]"}]}]], "Input", CellChangeTimes->{{3.414439180557882*^9, 3.414439184329845*^9}, { 3.416324188071439*^9, 3.416324200082434*^9}, 3.429971822494804*^9}], Cell[BoxData["5.939480396308497`"], "Output", CellChangeTimes->{ 3.414332761502988*^9, 3.414332829824305*^9, 3.414439053656162*^9, 3.414439184786476*^9, 3.416252578159607*^9, 3.416252633176611*^9, 3.416253182833141*^9, 3.416322830839233*^9, {3.41632419465642*^9, 3.416324201508871*^9}, 3.416324464678696*^9, 3.416331597014512*^9, 3.4165901672207413`*^9, 3.429879632773272*^9, 3.4298831873985205`*^9, 3.4298904701982007`*^9, 3.42989866399437*^9, 3.429971358764919*^9, 3.429971822901127*^9, 3.4299719538152075`*^9, 3.4299727975798807`*^9, 3.4300545636184945`*^9, 3.4300583010439105`*^9, 3.430059387043875*^9, 3.430061377695753*^9, 3.4300634946048965`*^9, 3.430064593437239*^9, { 3.4300654284229183`*^9, 3.430062413221719*^9}, 3.4300711160308895`*^9, 3.4300718834920564`*^9}] }, Open ]], Cell["So the mutation rate is", "Text", CellChangeTimes->{{3.416324204601914*^9, 3.416324209089794*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "/", "n16"}]], "Input", CellChangeTimes->{{3.416324218985651*^9, 3.416324225732965*^9}, 3.4299718264486375`*^9}], Cell[BoxData["1.060621499340803`*^-8"], "Output", CellChangeTimes->{ 3.416324226697679*^9, 3.416324464910812*^9, 3.416331597145586*^9, 3.4165901672363586`*^9, 3.4298796328670216`*^9, 3.4298831874141397`*^9, 3.4298904702138205`*^9, 3.42989866401*^9, 3.429971358780553*^9, 3.4299718267611933`*^9, 3.4299719538308353`*^9, 3.429972797595504*^9, 3.4300545636184945`*^9, 3.430058301059549*^9, 3.430059387059492*^9, 3.430061377695753*^9, 3.43006349462052*^9, 3.430064593437239*^9, { 3.430065428438547*^9, 3.430062413378126*^9}, 3.4300711160308895`*^9, 3.4300718834920564`*^9}] }, Open ]], Cell["\<\ Note that the P0 method is different from the well-known one designed for \ \[Epsilon]=1.\ \>", "Text", CellChangeTimes->{{3.416324262954708*^9, 3.416324345997871*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "P0Plating"}]], "Input"], Cell[BoxData[ StyleBox["\<\"P0Plating[data,\!\(\[Epsilon]\)] estimate\\nthe expected \ number of mutations per culture using the P0 method.\\nIt is assumed that the \ plating efficiency \!\(\[Epsilon]\)\\nsatisfies 0<\!\(\[Epsilon]\)<1.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071883601437*^9}, CellTags->"Info3430053883-8977506"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "=", RowBox[{"P0Plating", "[", RowBox[{"expt16", ",", "0.4"}], "]"}]}]], "Input", CellChangeTimes->{{3.414439192902252*^9, 3.414439201579759*^9}, { 3.416324370573671*^9, 3.41632437168269*^9}}], Cell[BoxData["0.9786800956714168`"], "Output", CellChangeTimes->{ 3.414332763097514*^9, 3.414332830656387*^9, 3.414439054528124*^9, { 3.414439197400277*^9, 3.414439202382908*^9}, 3.416252583933732*^9, 3.416252634212694*^9, 3.4162531838291*^9, 3.416322831780904*^9, { 3.416324354807798*^9, 3.416324372208442*^9}, 3.416324465871067*^9, 3.4163315981846*^9, 3.4165901673769164`*^9, 3.429879633585767*^9, 3.4298831875703306`*^9, 3.429890470370017*^9, 3.429898664150674*^9, 3.4299713589368916`*^9, 3.4299718330591965`*^9, 3.429971953924602*^9, 3.429972797751737*^9, 3.4300545637434816`*^9, 3.4300583011533785`*^9, 3.4300593871531935`*^9, 3.430061377852006*^9, 3.430063494776754*^9, 3.430064593593478*^9, {3.4300654285635786`*^9, 3.430062414096346*^9}, 3.4300711161715217`*^9, 3.4300718836326885`*^9}] }, Open ]], Cell["Hence, the mutation rate is", "Text", CellChangeTimes->{{3.416324358303136*^9, 3.416324363467753*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "/", "n16"}]], "Input", CellChangeTimes->{{3.416324390969393*^9, 3.416324393294217*^9}, 3.4299718349657884`*^9}], Cell[BoxData["1.747643027984673`*^-9"], "Output", CellChangeTimes->{ 3.416324394230551*^9, 3.416324465998817*^9, 3.416331598382257*^9, 3.416590167392534*^9, 3.429879633632642*^9, 3.42988318758595*^9, 3.4298904703856373`*^9, 3.4298986641663046`*^9, 3.4299713589368916`*^9, 3.4299718352314615`*^9, 3.42997195394023*^9, 3.429972797751737*^9, 3.4300545637434816`*^9, 3.430058301169017*^9, 3.4300593871688104`*^9, 3.430061377867631*^9, 3.430063494776754*^9, 3.4300645936091022`*^9, { 3.4300654285635786`*^9, 3.430062414132451*^9}, 3.4300711161715217`*^9, 3.4300718836483145`*^9}] }, Open ]], Cell["\<\ The maximum likelihood method (Zheng 2008a) can be applied as follows.\ \>", "Text", CellChangeTimes->{{3.416331643469462*^9, 3.416331652387729*^9}, { 3.430058849971658*^9, 3.4300588540370703`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "newtonLDPlating"}]], "Input"], Cell[BoxData[ StyleBox["\<\"newtonLDPlating[data,\!\(\[Epsilon]\),opts] estimates\\nthe \ expected number of mutations per culture under the assumption of \ imperfect\\nplating efficiency, that is, \!\(0<\[Epsilon]<1\).\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718837420692`*^9}, CellTags->"Info3430053883-5324659"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "=", RowBox[{"newtonLDPlating", "[", RowBox[{"expt16", ",", "0.4", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.414439258375516*^9, 3.414439259212204*^9}}], Cell[CellGroupData[{ Cell[BoxData["0.9786800956714168`"], "Print", CellChangeTimes->{ 3.414332765815293*^9, 3.414332832832844*^9, 3.414439056697261*^9, 3.414439260736803*^9, 3.416252636739675*^9, 3.416253186375496*^9, 3.416322834131809*^9, 3.416324468094748*^9, 3.416331600535823*^9, 3.4165901675330915`*^9, 3.4298796363201246`*^9, 3.4298831877265215`*^9, 3.4298904705262146`*^9, 3.4298986643226085`*^9, 3.4299713590932302`*^9, 3.4299718395134783`*^9, 3.4299719540339966`*^9, 3.42997279790797*^9, 3.430054563868469*^9, 3.4300583012472086`*^9, 3.430059387246895*^9, 3.430061378008259*^9, 3.430063494932988*^9, 3.430064593765341*^9, { 3.4300654286886096`*^9, 3.430062415077697*^9}, 3.430071116312154*^9, 3.430071883773321*^9}], Cell[BoxData["1.1513822588795282`"], "Print", CellChangeTimes->{ 3.414332765815293*^9, 3.414332832832844*^9, 3.414439056697261*^9, 3.414439260736803*^9, 3.416252636739675*^9, 3.416253186375496*^9, 3.416322834131809*^9, 3.416324468094748*^9, 3.416331600535823*^9, 3.4165901675330915`*^9, 3.4298796363201246`*^9, 3.4298831877265215`*^9, 3.4298904705262146`*^9, 3.4298986643226085`*^9, 3.4299713590932302`*^9, 3.4299718395134783`*^9, 3.4299719540339966`*^9, 3.42997279790797*^9, 3.430054563868469*^9, 3.4300583012472086`*^9, 3.430059387246895*^9, 3.430061378008259*^9, 3.430063494932988*^9, 3.430064593765341*^9, { 3.4300654286886096`*^9, 3.430062415077697*^9}, 3.430071116312154*^9, 3.430071883788947*^9}], Cell[BoxData["1.185379562853652`"], "Print", CellChangeTimes->{ 3.414332765815293*^9, 3.414332832832844*^9, 3.414439056697261*^9, 3.414439260736803*^9, 3.416252636739675*^9, 3.416253186375496*^9, 3.416322834131809*^9, 3.416324468094748*^9, 3.416331600535823*^9, 3.4165901675330915`*^9, 3.4298796363201246`*^9, 3.4298831877265215`*^9, 3.4298904705262146`*^9, 3.4298986643226085`*^9, 3.4299713590932302`*^9, 3.4299718395134783`*^9, 3.4299719540339966`*^9, 3.42997279790797*^9, 3.430054563868469*^9, 3.4300583012472086`*^9, 3.430059387246895*^9, 3.430061378008259*^9, 3.430063494932988*^9, 3.430064593765341*^9, { 3.4300654286886096`*^9, 3.430062415077697*^9}, 3.430071116312154*^9, 3.430071883804572*^9}], Cell[BoxData["1.1863594109955073`"], "Print", CellChangeTimes->{ 3.414332765815293*^9, 3.414332832832844*^9, 3.414439056697261*^9, 3.414439260736803*^9, 3.416252636739675*^9, 3.416253186375496*^9, 3.416322834131809*^9, 3.416324468094748*^9, 3.416331600535823*^9, 3.4165901675330915`*^9, 3.4298796363201246`*^9, 3.4298831877265215`*^9, 3.4298904705262146`*^9, 3.4298986643226085`*^9, 3.4299713590932302`*^9, 3.4299718395134783`*^9, 3.4299719540339966`*^9, 3.42997279790797*^9, 3.430054563868469*^9, 3.4300583012472086`*^9, 3.430059387246895*^9, 3.430061378008259*^9, 3.430063494932988*^9, 3.430064593765341*^9, { 3.4300654286886096`*^9, 3.430062415077697*^9}, 3.430071116312154*^9, 3.430071883804572*^9}], Cell[BoxData["1.186360179896308`"], "Print", CellChangeTimes->{ 3.414332765815293*^9, 3.414332832832844*^9, 3.414439056697261*^9, 3.414439260736803*^9, 3.416252636739675*^9, 3.416253186375496*^9, 3.416322834131809*^9, 3.416324468094748*^9, 3.416331600535823*^9, 3.4165901675330915`*^9, 3.4298796363201246`*^9, 3.4298831877265215`*^9, 3.4298904705262146`*^9, 3.4298986643226085`*^9, 3.4299713590932302`*^9, 3.4299718395134783`*^9, 3.4299719540339966`*^9, 3.42997279790797*^9, 3.430054563868469*^9, 3.4300583012472086`*^9, 3.430059387246895*^9, 3.430061378008259*^9, 3.430063494932988*^9, 3.430064593765341*^9, { 3.4300654286886096`*^9, 3.430062415077697*^9}, 3.430071116312154*^9, 3.430071883820198*^9}] }, Open ]], Cell[BoxData["1.18636017989678`"], "Output", CellChangeTimes->{ 3.414332766515128*^9, 3.414332833485456*^9, 3.414439057300411*^9, 3.414439261113787*^9, 3.416252637301303*^9, 3.416253186994395*^9, 3.416322834734911*^9, 3.416324468725533*^9, 3.416331601202126*^9, 3.4165901675799437`*^9, 3.4298796363826237`*^9, 3.4298831877889977`*^9, 3.429890470588693*^9, 3.4298986643694997`*^9, 3.4299713591557665`*^9, 3.429971839591617*^9, 3.42997195408088*^9, 3.4299727979548397`*^9, 3.4300545639153395`*^9, 3.4300583013097615`*^9, 3.4300593873093624`*^9, 3.4300613780707603`*^9, 3.4300634949798584`*^9, 3.430064593812213*^9, { 3.4300654287354965`*^9, 3.430062415650588*^9}, 3.430071116359031*^9, 3.430071883820198*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", "/", "n16"}]], "Input", CellChangeTimes->{{3.414439263313355*^9, 3.414439263872389*^9}, 3.429971842107693*^9}], Cell[BoxData["2.11850032124425`*^-9"], "Output", CellChangeTimes->{ 3.414332766789622*^9, 3.414332833700465*^9, 3.414439057488827*^9, 3.414439264263037*^9, 3.416252637484815*^9, 3.416253187201172*^9, 3.416322834922674*^9, 3.416324468927208*^9, 3.416331601312984*^9, 3.416590167595561*^9, 3.4298796363982487`*^9, 3.4298831877889977`*^9, 3.429890470604313*^9, 3.42989866438513*^9, 3.4299713591557665`*^9, 3.4299718423889933`*^9, 3.429971954096508*^9, 3.4299727979704633`*^9, 3.4300545639153395`*^9, 3.4300583013254004`*^9, 3.4300593873249793`*^9, 3.4300613780863857`*^9, 3.4300634949954815`*^9, 3.4300645938278365`*^9, { 3.4300654287511253`*^9, 3.430062415838997*^9}, 3.430071116374657*^9, 3.430071883835824*^9}] }, Open ]], Cell["\<\ An asymptotic 95% confidence intervals for m can be constructed as follows.\ \>", "Text", CellChangeTimes->{{3.416331677064704*^9, 3.416331682629985*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "CILDPlating"}]], "Input"], Cell[BoxData[ StyleBox["\<\"CILDPlating[data,\!\(\[Epsilon]\),opts]\\nconstructs a \!\((1-\ \[Alpha])%\) confidence interval for m, the\\nexpected number of mutations \ per culture. Plating efficiency \!\(\[Epsilon]\)\\nmust satisfy \!\(0<\ \[Epsilon]<1\). \"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071883929579*^9}, CellTags->"Info3430053883-8973413"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "CILDPlating", "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"Alpha", "\[Rule]", "0.05`"}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialLowerLimit", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialUpperLimit", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"ShowIterations", "\[Rule]", "False"}], ",", RowBox[{"MaxIterations", "\[Rule]", "20"}], ",", RowBox[{"Tolerance", "\[Rule]", "1.`*^-8"}]}], "}"}]], "Output", CellChangeTimes->{ 3.41433276788056*^9, 3.414332834466168*^9, 3.414439058473666*^9, 3.41625263850474*^9, 3.416253188092778*^9, 3.416322835883166*^9, 3.416324469797821*^9, 3.416331602217112*^9, 3.416590167720501*^9, 3.429879636663872*^9, 3.4298831879451895`*^9, 3.42989047074489*^9, 3.4298986645414343`*^9, 3.429971359312105*^9, 3.429971848061885*^9, 3.4299719541902747`*^9, 3.4299727981266966`*^9, 3.430054564040326*^9, 3.4300583014035916`*^9, 3.430059387418681*^9, 3.430061378227013*^9, 3.4300634951517153`*^9, 3.4300645939684515`*^9, {3.4300654288605275`*^9, 3.430062416811205*^9}, 3.4300711164996634`*^9, 3.4300718839608307`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ci", "=", RowBox[{"CILDPlating", "[", RowBox[{"expt16", ",", "0.4", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.414439269851138*^9, 3.414439270374165*^9}}], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for lower limit ...\"\>"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840389595`*^9}], Cell[BoxData["0.8110505681413445`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840389595`*^9}], Cell[BoxData["0.4538020379202991`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840545855`*^9}], Cell[BoxData["0.5564839759249837`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840545855`*^9}], Cell[BoxData["0.5793884915039692`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840702114`*^9}], Cell[BoxData["0.5803065083033111`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718840702114`*^9}], Cell[BoxData["0.5803079099911405`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.430071884085837*^9}], Cell[BoxData["\<\"Iterating for upper limit ...\"\>"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.430071884085837*^9}], Cell[BoxData["1.5616697916522155`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.430071884101463*^9}], Cell[BoxData["2.330992732616868`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.430071884101463*^9}], Cell[BoxData["2.1054070206626108`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718841170883`*^9}], Cell[BoxData["2.0908703776064157`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718841170883`*^9}], Cell[BoxData["2.090801236715449`"], "Print", CellChangeTimes->{ 3.4143327683338*^9, 3.414332834753238*^9, 3.414439058781273*^9, 3.414439271598568*^9, 3.416252638858765*^9, 3.416253188410803*^9, 3.416322836236581*^9, 3.416324470124356*^9, 3.416331602584233*^9, 3.4165901677985888`*^9, 3.429879636741997*^9, 3.4298831880076656`*^9, 3.4298904708229885`*^9, 3.4298986646039553`*^9, 3.4299713593746405`*^9, 3.4299718498747096`*^9, 3.4299719542527857`*^9, 3.42997279818919*^9, 3.43005456410282*^9, 3.430058301481783*^9, 3.4300593874811487`*^9, 3.4300613782895145`*^9, 3.4300634952142096`*^9, 3.430064594030947*^9, { 3.4300654289230433`*^9, 3.430062417111921*^9}, 3.4300711165621667`*^9, 3.4300718841327143`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"0.5803079099944014`", ",", "2.090801235138148`"}], "}"}]], "Output",\ CellChangeTimes->{ 3.414332770341844*^9, 3.414332836190153*^9, 3.414439060171906*^9, 3.414439273329231*^9, 3.416252640280993*^9, 3.416253189839613*^9, 3.416322837646231*^9, 3.416324471675706*^9, 3.416331603979709*^9, 3.4165901679235287`*^9, 3.4298796367732463`*^9, 3.429883188179476*^9, 3.4298904709479465`*^9, 3.429898664744629*^9, 3.4299713595622473`*^9, 3.4299718500309877`*^9, 3.4299719544090643`*^9, 3.429972798329799*^9, 3.430054564227807*^9, 3.4300583016225276`*^9, 3.430059387637317*^9, 3.430061378430142*^9, 3.4300634953548203`*^9, 3.430064594171562*^9, { 3.4300654290168166`*^9, 3.430062418397992*^9}, 3.430071116671547*^9, 3.43007188414834*^9}] }, Open ]], Cell["Therefore, an CI for the mutation rate is", "Text", CellChangeTimes->{{3.416331702465882*^9, 3.416331714634846*^9}, { 3.430065059076331*^9, 3.4300650609980707`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ci", "/", "n16"}]], "Input", CellChangeTimes->{{3.41443927500774*^9, 3.414439275566432*^9}, 3.4299718830212736`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"1.0362641249900025`*^-9", ",", "3.733573634175264`*^-9"}], "}"}]], "Output", CellChangeTimes->{ 3.414332770558664*^9, 3.414332836377588*^9, 3.41443906036134*^9, 3.414439276073333*^9, 3.416252640471199*^9, 3.416253190027098*^9, 3.416322837869347*^9, 3.416324471917488*^9, 3.416331604202502*^9, 3.416590167954764*^9, 3.4298796368201213`*^9, 3.429883188210714*^9, 3.4298904709791856`*^9, 3.4298986647758904`*^9, 3.429971359609149*^9, 3.429971883411968*^9, 3.4299719544090643`*^9, 3.429972798376669*^9, 3.430054564227807*^9, 3.430058301638166*^9, 3.430059387637317*^9, 3.4300613784770184`*^9, 3.430063495386067*^9, 3.4300645942028103`*^9, { 3.430065429032446*^9, 3.430062418591601*^9}, 3.430071116687173*^9, 3.430071884163966*^9}] }, Open ]], Cell["\<\ Note that SALVADOR also offers Jones median method and Lea and Coulson's \ median method as modified by Angerer.\ \>", "Text", CellChangeTimes->{{3.416332162805771*^9, 3.416332167158678*^9}, { 3.430058944221754*^9, 3.4300589648916206`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "JonesMedianPlating"}]], "Input"], Cell[BoxData[ StyleBox["\<\"JonesMedianPlating[data,\!\(\[Epsilon]\)] estimate\\nthe \ expected number of mutations per culture using the method of the median \ of\\nJones et al. It is assumed that the plating efficiency \ \!\(\[Epsilon]\)\\nsatisfies 0<\!\(\[Epsilon]\)<1.\"\>", "MSG"]], "Print", \ "PrintUsage", CellChangeTimes->{3.4300718842733464`*^9}, CellTags->"Info3430053884-3691012"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"JonesMedianPlating", "[", RowBox[{"expt16", ",", "0.4"}], "]"}]], "Input", CellChangeTimes->{{3.4299718923354425`*^9, 3.42997190379062*^9}}], Cell[BoxData["\<\"Because the sample median is zero, \\n Jones' \ median method is not applicable.\"\>"], "Print", CellChangeTimes->{ 3.4299719047751713`*^9, 3.4299719545184584`*^9, 3.4299727985172787`*^9, 3.4300545643527946`*^9, 3.430058301747634*^9, 3.430059387731019*^9, 3.4300613786176453`*^9, 3.4300634955423007`*^9, 3.430064594359049*^9, { 3.430065429157477*^9, 3.430062419454679*^9}, 3.4300711168278055`*^9, 3.430071884304598*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LCAMedian", "[", RowBox[{"expt16", ",", "0.4"}], "]"}]], "Input", CellChangeTimes->{{3.416332192200096*^9, 3.416332201355344*^9}, { 3.429971920090415*^9, 3.4299719316237316`*^9}}], Cell[BoxData["\<\"Because the sample median is zero,\\n the method \ is not applicable.\"\>"], "Print", "PrintUsage", CellChangeTimes->{ 3.4299713598436575`*^9, {3.429971932217588*^9, 3.429971954534086*^9}, 3.429972798532902*^9, 3.4300545643527946`*^9, 3.4300583017632723`*^9, 3.4300593877622523`*^9, 3.430061378633271*^9, 3.4300634955579243`*^9, 3.430064594374673*^9, {3.4300654291731057`*^9, 3.430062419773682*^9}, 3.4300711168434315`*^9, 3.430071884304598*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["A limiting distribution: a special topic", "Section", CellChangeTimes->{{3.416587165563453*^9, 3.416587175682056*^9}, { 3.416587499078167*^9, 3.416587499580126*^9}, 3.416588713297979*^9, { 3.430059926535362*^9, 3.43005993933109*^9}}], Cell[TextData[{ "The Bartlett mutant distribution gives us an interesting two-parameter \ distribution whose probability generating function is of the form\n \ ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"G", " ", RowBox[{"(", RowBox[{ RowBox[{"z", ";", " ", "A"}], ",", " ", "k"}], ")"}]}], " ", "=", " ", RowBox[{"[", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", " ", "-", " ", RowBox[{ RowBox[{"A", "(", RowBox[{ SuperscriptBox["z", RowBox[{"-", "1"}]], " ", "-", " ", "1"}], ")"}], " ", RowBox[{"log", "(", RowBox[{"1", " ", "-", " ", "z"}], ")"}]}]}], "]"}], RowBox[{"-", "k"}]]}]}], TraditionalForm]]], ",\n where A and k are positive real numbers. This is an infinitely \ divisible distribution with divergent moments (Zheng 2008b). The \ distribution is denoted by ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["B", "0"], "(", RowBox[{"A", ",", "k"}], ")"}], TraditionalForm]]], ".\n The probability mass function can be calculated as follows. \ " }], "Text", CellChangeTimes->{{3.416587574813358*^9, 3.416588084491367*^9}, { 3.416588642127739*^9, 3.41658864313856*^9}, 3.416588788871825*^9, { 3.4300599681253853`*^9, 3.4300599771714497`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "pmfBartzero"}]], "Input", CellChangeTimes->{{3.416588104943234*^9, 3.416588109035593*^9}}], Cell[BoxData[ StyleBox["\<\"pmfBartzero[A,k, n] computes the first n+1 probabilities of \ the\\nBartlett limiting distribution. Note the parameter k can be a \ fractional.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718844139786`*^9}, CellTags->"Info3430053884-2702936"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"prob", "=", RowBox[{"pmfBartzero", "[", RowBox[{"1.3", ",", "5.8", ",", "100"}], "]"}]}], ";", RowBox[{"prob", "[", RowBox[{"[", RowBox[{"Range", "[", "5", "]"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.416588112540403*^9, 3.416588176106813*^9}, { 3.430060853641431*^9, 3.430060881218673*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.007979552769417348`", ",", "0.013079527800305827`", ",", "0.01692756279083059`", ",", "0.019792943654304018`", ",", "0.021869624679473634`"}], "}"}]], "Output", CellChangeTimes->{{3.416588129212165*^9, 3.416588176991362*^9}, 3.416588490739575*^9, {3.416588525689083*^9, 3.416588555163631*^9}, 3.4165901686887865`*^9, 3.4298796452888165`*^9, 3.429883189007288*^9, 3.429890471760171*^9, 3.4298986655574102`*^9, 3.429971360406478*^9, 3.4299727990328474`*^9, 3.43005456483712*^9, 3.430059992420083*^9, 3.4300607651598873`*^9, {3.430060856969449*^9, 3.4300608825155067`*^9}, 3.4300610239960117`*^9, 3.430061378789524*^9, 3.430063495714158*^9, 3.430064594530912*^9, {3.4300654292981367`*^9, 3.430062420527267*^9}, 3.430071116984063*^9, 3.4300718844452305`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{"prob", ",", RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.416588162002581*^9, 3.416588167681094*^9}, { 3.429972468631299*^9, 3.4299724728652134`*^9}, {3.4300608648441973`*^9, 3.43006088898405*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw10glQVAUcx/EFNKA1p0GRY7BAHCAGCIFIEdgf14Kcyy57ISogCAi43MdC 8OSylrOQY4OEAVPkiKBMcSZBEMwpsYhJ4kiSkpRSZkjIccBq+L83s/Pms9/3 2/OZRSuEsZocDif2v8f/581jmdeQkJ5aJ2V49AR6uQ6nU26ryDqY/FJelCn+ kPw6HP0HV9XeZ8k7UfKVYdd6TD3ZEHXbHMzC7zeQTeBSVZyzMNlINsVPBwWP +yPV5D14WeeXMNPIei+6qqPjgqtZW6BkrVX9sZC1FTIGu8xVT9jXs0aarvDh +STWNqgMEUmbJtn3t8OkovzeJzas7XE7+MVqey77efeBM6VdfWGwjuyA3r70 N+5qsHaEjr517DlP9vs6oebFy3luSS35HTjVWxa23PqI7IwPBqLqy7azfhc3 Lj7X/VTO/n77IdwhDWi/VEM+gC21CU0r69VkF8he7bz19xdV5INI9faZ6M2s JLvCq92QK/eqILsh6Waqet2knOyOvD+ap8s12f+PB8PZQefplffJQESssr97 +cymGWBEtCV74J8y6h6wu7qb6eaSGQ+MvNldb/1WKXVPxJuvXPlRUELdEzMZ 3Vo+RcXUvfCgtIVv/HURdS9Y8VWOTzlkjjccfuPKI4NOU/fGkNHn89w29v7z wXeLzp571wup+yA/0cnAZrSAOh9dDaNryqb3qPPR1yG7H12YT90X2a75YteU POq+GBpR159IVlL3Q2tCc7tvVi51P2jbXnULVOVQPwTX+saJxY5s6ocw1KyM OPtDFnV/1GzdcWBCi8z4o2+j6bklL5N6APJ9ntnuKc6gHoCW8Vgb0d106oG4 mepxT2hOZgIxPJUZdb0gjXoQtDru6O3/NZV6EKYvVW6L8ydzgsHd9+f2tYEU 6sEYPzfKa3ybzAlBznzf7+tiBfUQjOufWRyTnqIuwF8Px9q1YpI3DQGcTTMi HJVJdL0AOSbXd82qEzc9JICFgT5PNXyS9qFQjSWHfr+SQPtQ5Is7S/m2ZCYU xiW7GNWpeNqHwj3sl628K3G0FyJxJuoyV5sMIVJFPsPNR07QXojkncaX267F 0l4I9+o8u4ndZI4IEwXKnoWyGNqLIHayl9c+O057EXo0w+60JpCHRGjm9zwa fxBN+zB84+t2fiGSjDDAfH3u4kIU7cNgyX3NZfEkeSgMFscc1xSrkbQXYy6p /Fu9MjLESNzwHm4zIjNi/JzxmfPjqGO0F2NDoR8+3HCU9hIodJkqZvII7SWo ON5vP2NAZiRwUUdYVkRF0F6C/qmlfkHfYdpLYZFmiEevkCGFVEPHzSg6nPZS 5JrOLV8YltNeCjtejfiwFZkjQ2fg0xWNWhntZUiea78Rr0lmZJiVmGlEZklp L4Nd+lHza08ktJeDb8rrCkgkQ45ccZ3e0pKY9y8ttb83 "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{{0., 101.}, {0., 0.024997165966984976`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.416588168300637*^9, 3.416588178267401*^9}, 3.416588491062015*^9, {3.416588525822148*^9, 3.416588555410401*^9}, 3.416590168704404*^9, 3.4298796453356915`*^9, 3.4298831890229073`*^9, 3.42989047179141*^9, 3.4298986655730405`*^9, 3.429971360422112*^9, 3.4299724738963513`*^9, 3.429972799048471*^9, 3.43005456483712*^9, 3.4300599934512405`*^9, 3.4300607651755114`*^9, {3.4300608590475073`*^9, 3.430060889624654*^9}, 3.430061024027261*^9, 3.430061378805149*^9, 3.4300634957297816`*^9, 3.430064594546536*^9, {3.4300654293137655`*^9, 3.430062420778705*^9}, 3.430071116984063*^9, 3.430071884460856*^9}] }, Open ]], Cell[TextData[{ "The following sample was generated from the ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["B", "0"], "(", RowBox[{"1.3", ",", "5.8"}], ")"}], TraditionalForm]]], " distribution." }], "Text", CellChangeTimes->{{3.416588190219389*^9, 3.416588221624346*^9}, { 3.430060213107423*^9, 3.4300602689316177`*^9}, {3.430061127577672*^9, 3.43006113078092*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"simuSample", "=", RowBox[{"{", RowBox[{ "11", ",", "8", ",", "14", ",", "4", ",", "34", ",", "37", ",", "3", ",", "30", ",", "50", ",", "17", ",", "69", ",", "4", ",", "180", ",", "968", ",", "28", ",", "28", ",", "7", ",", "25", ",", "17", ",", "15", ",", "41", ",", "29", ",", "279", ",", "0", ",", "21", ",", "19", ",", "38", ",", "159", ",", "66", ",", "50"}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.430060287664674*^9, 3.430060309022545*^9}, { 3.4300605586047993`*^9, 3.4300605707605047`*^9}, {3.4300607302078805`*^9, 3.430060749879126*^9}, {3.4300609901687527`*^9, 3.4300610126994257`*^9}}], Cell["\<\ Assuming that k=5.8 is known, we can find the maximum likelihood estimate of \ A as follows.\ \>", "Text", CellChangeTimes->{{3.416588264583585*^9, 3.416588295119398*^9}, { 3.4300603355366683`*^9, 3.4300603573638153`*^9}, {3.430063998980985*^9, 3.4300640219948425`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"newtonBartzero", "[", RowBox[{"simuSample", ",", "5.8", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}], ",", RowBox[{"MaxIterations", "\[Rule]", "33"}]}], "]"}]], "Input", CellChangeTimes->{{3.416512671052926*^9, 3.416512699143025*^9}, { 3.416512766495564*^9, 3.416512771911619*^9}, {3.430060364910352*^9, 3.4300603689726706`*^9}, {3.4300609478260865`*^9, 3.4300609514509935`*^9}}],\ Cell[CellGroupData[{ Cell[BoxData["0.7975297148130593`"], "Print", CellChangeTimes->{{3.41658852788614*^9, 3.416588557477136*^9}, 3.416590169594601*^9, 3.429879646991931*^9, 3.4298831899131956`*^9, 3.429890472681733*^9, 3.429898666463973*^9, 3.4299713613288784`*^9, 3.429972799938999*^9, 3.4300545656807833`*^9, {3.430054914477448*^9, 3.4300549434549513`*^9}, {3.430055077687133*^9, 3.4300550890778575`*^9}, { 3.4300551327162247`*^9, 3.4300551511948595`*^9}, {3.4300551995115604`*^9, 3.430055242609173*^9}, 3.430060371722547*^9, 3.430060532277854*^9, 3.430060603602783*^9, {3.4300606862717867`*^9, 3.4300607000213466`*^9}, { 3.4300607524102955`*^9, 3.430060765191136*^9}, 3.4300609521384764`*^9, 3.4300610240428853`*^9, 3.4300613788207746`*^9, 3.4300634957454047`*^9, 3.43006459456216*^9, {3.4300654293293943`*^9, 3.430062421008519*^9}, 3.430071117015315*^9, 3.4300718844921074`*^9}], Cell[BoxData["1.1173089128556328`"], "Print", CellChangeTimes->{{3.41658852788614*^9, 3.416588557477136*^9}, 3.416590169594601*^9, 3.429879646991931*^9, 3.4298831899131956`*^9, 3.429890472681733*^9, 3.429898666463973*^9, 3.4299713613288784`*^9, 3.429972799938999*^9, 3.4300545656807833`*^9, {3.430054914477448*^9, 3.4300549434549513`*^9}, {3.430055077687133*^9, 3.4300550890778575`*^9}, { 3.4300551327162247`*^9, 3.4300551511948595`*^9}, {3.4300551995115604`*^9, 3.430055242609173*^9}, 3.430060371722547*^9, 3.430060532277854*^9, 3.430060603602783*^9, {3.4300606862717867`*^9, 3.4300607000213466`*^9}, { 3.4300607524102955`*^9, 3.430060765191136*^9}, 3.4300609521384764`*^9, 3.4300610240428853`*^9, 3.4300613788207746`*^9, 3.4300634957454047`*^9, 3.43006459456216*^9, {3.4300654293293943`*^9, 3.430062421008519*^9}, 3.430071117015315*^9, 3.4300718845233593`*^9}], Cell[BoxData["1.2818237603695481`"], "Print", CellChangeTimes->{{3.41658852788614*^9, 3.416588557477136*^9}, 3.416590169594601*^9, 3.429879646991931*^9, 3.4298831899131956`*^9, 3.429890472681733*^9, 3.429898666463973*^9, 3.4299713613288784`*^9, 3.429972799938999*^9, 3.4300545656807833`*^9, {3.430054914477448*^9, 3.4300549434549513`*^9}, {3.430055077687133*^9, 3.4300550890778575`*^9}, { 3.4300551327162247`*^9, 3.4300551511948595`*^9}, {3.4300551995115604`*^9, 3.430055242609173*^9}, 3.430060371722547*^9, 3.430060532277854*^9, 3.430060603602783*^9, {3.4300606862717867`*^9, 3.4300607000213466`*^9}, { 3.4300607524102955`*^9, 3.430060765191136*^9}, 3.4300609521384764`*^9, 3.4300610240428853`*^9, 3.4300613788207746`*^9, 3.4300634957454047`*^9, 3.43006459456216*^9, {3.4300654293293943`*^9, 3.430062421008519*^9}, 3.430071117015315*^9, 3.4300718845546107`*^9}], Cell[BoxData["1.310789098555558`"], "Print", CellChangeTimes->{{3.41658852788614*^9, 3.416588557477136*^9}, 3.416590169594601*^9, 3.429879646991931*^9, 3.4298831899131956`*^9, 3.429890472681733*^9, 3.429898666463973*^9, 3.4299713613288784`*^9, 3.429972799938999*^9, 3.4300545656807833`*^9, {3.430054914477448*^9, 3.4300549434549513`*^9}, {3.430055077687133*^9, 3.4300550890778575`*^9}, { 3.4300551327162247`*^9, 3.4300551511948595`*^9}, {3.4300551995115604`*^9, 3.430055242609173*^9}, 3.430060371722547*^9, 3.430060532277854*^9, 3.430060603602783*^9, {3.4300606862717867`*^9, 3.4300607000213466`*^9}, { 3.4300607524102955`*^9, 3.430060765191136*^9}, 3.4300609521384764`*^9, 3.4300610240428853`*^9, 3.4300613788207746`*^9, 3.4300634957454047`*^9, 3.43006459456216*^9, {3.4300654293293943`*^9, 3.430062421008519*^9}, 3.430071117015315*^9, 3.430071884585862*^9}], Cell[BoxData["1.3115179094666523`"], "Print", CellChangeTimes->{{3.41658852788614*^9, 3.416588557477136*^9}, 3.416590169594601*^9, 3.429879646991931*^9, 3.4298831899131956`*^9, 3.429890472681733*^9, 3.429898666463973*^9, 3.4299713613288784`*^9, 3.429972799938999*^9, 3.4300545656807833`*^9, {3.430054914477448*^9, 3.4300549434549513`*^9}, {3.430055077687133*^9, 3.4300550890778575`*^9}, { 3.4300551327162247`*^9, 3.4300551511948595`*^9}, {3.4300551995115604`*^9, 3.430055242609173*^9}, 3.430060371722547*^9, 3.430060532277854*^9, 3.430060603602783*^9, {3.4300606862717867`*^9, 3.4300607000213466`*^9}, { 3.4300607524102955`*^9, 3.430060765191136*^9}, 3.4300609521384764`*^9, 3.4300610240428853`*^9, 3.4300613788207746`*^9, 3.4300634957454047`*^9, 3.43006459456216*^9, {3.4300654293293943`*^9, 3.430062421008519*^9}, 3.430071117015315*^9, 3.430071884617114*^9}] }, Open ]], Cell[BoxData["1.3115183534921602`"], "Output", CellChangeTimes->{{3.430054932439745*^9, 3.4300549435175376`*^9}, { 3.4300550777184258`*^9, 3.4300550899071274`*^9}, {3.4300551327631645`*^9, 3.430055151335679*^9}, {3.4300551995585003`*^9, 3.430055242702964*^9}, 3.430060371816293*^9, 3.430060532340351*^9, 3.430060603680905*^9, { 3.43006068631866*^9, 3.430060700130718*^9}, {3.4300607525196667`*^9, 3.4300607652848835`*^9}, 3.4300609523415956`*^9, 3.430061024214756*^9, 3.430061378992653*^9, 3.430063495917262*^9, 3.430064594734023*^9, { 3.4300654294856834`*^9, 3.430062421450018*^9}, 3.4300711171715727`*^9, 3.4300718846483655`*^9}] }, Open ]], Cell["\<\ Similarly, an asymptotic 95% for the parameter A can be constructed.\ \>", "Text", CellChangeTimes->{{3.416588309096445*^9, 3.416588349889223*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "CIBartzero"}]], "Input", CellChangeTimes->{{3.416588357460326*^9, 3.416588370265984*^9}}], Cell[BoxData[ StyleBox["\<\"CIBartzero[data,k,opts] assumes k is know, and finds mle of A.\ \"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.4300718847733717`*^9}, CellTags->"Info3430053884-2830503"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CIBartzero", "[", RowBox[{"simuSample", ",", "5.8", ",", RowBox[{"ShowIterations", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.416588374146955*^9, 3.416588388958745*^9}, { 3.4300604130019474`*^9, 3.4300604171423874`*^9}, {3.430060967153717*^9, 3.4300609695442805`*^9}}], Cell[CellGroupData[{ Cell[BoxData["\<\"Iterating for mle of A...\"\>"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718848046236`*^9}], Cell[BoxData["0.7975297148130593`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718848046236`*^9}], Cell[BoxData["1.1173089128556328`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718848358755`*^9}], Cell[BoxData["1.2818237603695481`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718848671265`*^9}], Cell[BoxData["1.310789098555558`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718849140043`*^9}], Cell[BoxData["1.3115179094666523`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071884945256*^9}], Cell[BoxData["\<\"Iterating for lower limit ...\"\>"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885039011*^9}], Cell[BoxData["1.1135424385628534`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718850702624`*^9}], Cell[BoxData["0.8742865593130774`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885101514*^9}], Cell[BoxData["0.9454077903048208`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885132766*^9}], Cell[BoxData["0.9559337927062571`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885164017*^9}], Cell[BoxData["0.9561499481262317`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718852108946`*^9}], Cell[BoxData["0.956150038071937`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885242146*^9}], Cell[BoxData["\<\"Iterating for upper limit ...\"\>"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885242146*^9}], Cell[BoxData["1.509494268421467`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718852733974`*^9}], Cell[BoxData["1.8688273499664612`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.4300718853046494`*^9}], Cell[BoxData["1.7625986927347634`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885335901*^9}], Cell[BoxData["1.7548383062301556`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885367152*^9}], Cell[BoxData["1.7547915146281365`"], "Print", CellChangeTimes->{{3.416588529175995*^9, 3.416588558687104*^9}, 3.416590169797629*^9, 3.429879647726301*^9, 3.429883190131863*^9, 3.4298904729004087`*^9, 3.429898666698429*^9, 3.4299713617666273`*^9, 3.429972800126479*^9, 3.4300545693054123`*^9, {3.430055180015897*^9, 3.430055244688202*^9}, 3.4300604198610153`*^9, 3.430060540168125*^9, 3.4300606132898493`*^9, 3.4300607085835724`*^9, {3.430060754582101*^9, 3.4300607653942547`*^9}, {3.4300609618257284`*^9, 3.4300609698723974`*^9}, 3.430061024324128*^9, 3.4300613791489058`*^9, 3.43006349608912*^9, 3.4300645949058857`*^9, {3.4300654296263437`*^9, 3.430062422269328*^9}, 3.430071117327831*^9, 3.430071885398404*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{"0.9561500380719511`", ",", "1.7547915129134526`"}], "}"}]], "Output", CellChangeTimes->{ 3.416588391410652*^9, 3.416588491319917*^9, {3.416588530854828*^9, 3.416588560211057*^9}, 3.416590170000656*^9, 3.4298796478981752`*^9, 3.4298831903505306`*^9, 3.429890473150324*^9, 3.429898666948516*^9, 3.4299713629079022`*^9, 3.429972800345205*^9, 3.430054584491357*^9, { 3.430055180234949*^9, 3.4300552449852066`*^9}, 3.430060420079756*^9, 3.4300605404493628`*^9, 3.430060613539838*^9, 3.4300607088335648`*^9, { 3.4300607548633413`*^9, 3.430060765659871*^9}, {3.4300609624663367`*^9, 3.4300609704817567`*^9}, 3.4300610249022384`*^9, 3.430061379742667*^9, 3.430063496667186*^9, 3.430064595468346*^9, {3.4300654302046127`*^9, 3.43006242457378*^9}, 3.43007111789036*^9, 3.430071885398404*^9}] }, Open ]], Cell[TextData[{ "There is also a P0 method for the ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["B", "0"], "(", RowBox[{"A", ",", "k"}], ")"}], TraditionalForm]]], " distribution." }], "Text", CellChangeTimes->{{3.416588410794234*^9, 3.416588447948193*^9}, 3.430065086386908*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "p0Bartzero"}]], "Input", CellChangeTimes->{{3.416588451149419*^9, 3.416588458244306*^9}}], Cell[BoxData[ StyleBox["\<\"p0Bartzero[data_, k_] estimates the parameter A using the\\nP0 \ methods when k is known.\"\>", "MSG"]], "Print", "PrintUsage", CellChangeTimes->{3.430071885507785*^9}, CellTags->"Info3430053885-1891038"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"p0Bartzero", "[", RowBox[{"simuSample", ",", "5.8"}], "]"}]], "Input", CellChangeTimes->{{3.416587102446657*^9, 3.41658712529394*^9}, { 3.430060432626068*^9, 3.4300604359227953`*^9}, {3.430060975872244*^9, 3.4300609780128136`*^9}}], Cell[BoxData["0.7975297148130593`"], "Output", CellChangeTimes->{{3.416587117977317*^9, 3.416587125598944*^9}, { 3.416588461497143*^9, 3.41658849146218*^9}, {3.416588531509061*^9, 3.416588560814473*^9}, 3.416590170141214*^9, 3.429879648851294*^9, 3.4298831905067215`*^9, 3.429890473290901*^9, 3.4298986670891895`*^9, 3.429971363079875*^9, 3.4299728004858146`*^9, 3.4300545848194485`*^9, 3.430055258991299*^9, 3.430060438500805*^9, 3.430060618289625*^9, { 3.4300607143333883`*^9, 3.4300607187707467`*^9}, {3.430060758878838*^9, 3.4300607657379937`*^9}, 3.430060978325306*^9, 3.430061024995986*^9, 3.4300613799145455`*^9, 3.4300634968390427`*^9, 3.430064595640209*^9, { 3.430065430345273*^9, 3.430062425334531*^9}, 3.430071118030992*^9, 3.4300718855546618`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["A Concluding Example", "Section", CellChangeTimes->{{3.405798389753639*^9, 3.405798405787235*^9}}], Cell["\<\ Boe et al. (1994) meticulously conducted a large scale fluctuation \ experiment, producing the following 1104 observations.\ \>", "Text"], Cell["\<\ boe={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,3,4,4,4,4,\ 6,8,14,15,17,27,29,39,39,66,74,265,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,\ 1,1,1,1,2,2,2,2,3,3,4,4,4,5,5,5,7,8,12,16,18,19,30,42,132,152,513,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,3,4,5,5,6,\ 7,8,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,\ 2,3,4,4,5,6,6,13,18,19,26,36,68,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,\ 1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,4,4,5,6,6,7,12,16,24,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,3,4,4,5,5,6,10,11,12,14,24,27,29,30,\ 73,482,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,\ 1,1,1,1,2,3,3,5,11,16,30,31,49,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,\ 1,1,1,1,2,2,2,2,2,2,2,2,2,4,5,5,6,6,6,7,12,12,12,16,513,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,5,7,8,11,11,18,52,\ 73,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,\ 3,3,4,4,4,5,7,7,7,151,513,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,\ 1,1,1,1,1,1,2,2,3,3,3,4,4,5,6,11,13,16,40,258,320,513,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,11,11,17,107,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,2,3,3,\ 3,4,4,6,6,16,18,20,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,1,1,1,1,1,1,1,2,2,3,3,5,8,8,9,21,21,26,37,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3,3,3,3,4,5,5,6,6,7,7,8,10,12,14,0,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2,3,3,4,5,5,6,13,16,\ 19,26,41,105,116,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,\ 1,1,1,1,2,2,2,3,6,6,6,11,13,19,21,34,140,146,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,9,10,10,11,13,19,20,23,59,69,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,3,3,3,4,4,4,4,4,5,5,\ 8,8,9,10,21,26,192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2,\ 2,2,2,2,2,3,3,4,4,6,9,9,10,14,25,26,29,57,137,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ 0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,5,6,7,8,10,14,16,28,0,0,0,0,0,\ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4,4,6,6,7,\ 7,18,32,35,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,\ 2,3,3,3,3,4,4,5,5,8,10,11,12,19,21};\ \>", "Input"], Cell["\<\ Assuming equal growth rate we obtain the maximum likelihood estimate of m as \ follows.\ \>", "Text"], Cell[CellGroupData[{ Cell["newtonLD[boe]", "Input"], Cell[BoxData["0.736590805157294`"], "Output", CellChangeTimes->{ 3.39923315484516*^9, 3.399298386467165*^9, 3.405872711945457*^9, 3.409344709237033*^9, 3.40986279852812*^9, 3.409863831215263*^9, 3.410019151472208*^9, 3.410019807524262*^9, 3.410031436593008*^9, 3.410034143017368*^9, 3.410102010344963*^9, 3.410184441592747*^9, 3.410363242233343*^9, 3.410538527095855*^9, 3.410539288132086*^9, 3.410546767713924*^9, 3.410547541473108*^9, 3.4162539366726*^9, 3.4165901704535637`*^9, 3.429879649695039*^9, 3.4298831908191037`*^9, 3.4298904736032953`*^9, 3.4298986674017973`*^9, 3.4299713633925533`*^9, 3.4299728007982807`*^9, 3.430054585116293*^9, 3.4300613802270517`*^9, 3.4300634971515107`*^9, 3.4300645959526873`*^9, {3.4300654306422224`*^9, 3.430062425929396*^9}, 3.430071118327882*^9, 3.4300718858515525`*^9}] }, Open ]], Cell["\<\ The fitting is less than perfect, but still an LD distribution catches the \ most prominent features of the data.\ \>", "Text"], Cell[CellGroupData[{ Cell["plotFit[boe,logPlot->True]", "Input"], Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[0.015], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 1, 0], Thickness[0.006], LineBox[CompressedData[" 1:eJw12Xk4FW0bAPCQXTjbzIisoaIFpZKau7Qob6KyVEhKiUSWiLJVtJIkEhFK yhKRJSkkSZSEyFLZK0aoKPTdXfX547h+18yZeZ57eWY5SnYum+35p0yZwo8f f/7//88i1aCqMKmNZpb+nFw1r5tuSi0TXPO9kxYXSPf5FPGVFlh8siT/Q8+/ 7d/pmJFdFw8m99E65/t/rHw8Rsu9yrJ6VPOJ5lec81P8zjjdQstmLrv+mbbY rp3hpvybHk8PDvqg/4V2v7OMzk6cAlaNTdFaOV/+HZ8POEZT2ozY/TRhlvsg y4kf9hWqaIFNP/3fYv+8jnkCsF9f89TD2H762LW6IuKDAGyIttQdf9VPm57T 0ph6cipU/i7cs3qin0550Eg8lxOE/6Rdm1aoDNAKhhuXErcFwc5ot7366oF/ 4xcCY/GtB/ttB2gf/58lTreFYFhA/sx6nwE6ONxJz1dBGN62yi56cWGA1rw3 VUg3VBikvF2le5MH6PAOd99VP4RBXNRw1tj9ATorw+XSvB0i4GojqbuhYoB+ Vr7cy6NQBPiozceohgF68F7txDGeKLib1KRd7higxzQvHk05IAorRaTFGWbg X/xEYfL0uMKaXwN09fTBT5ekxaAdiifuCzL0hRMC+e3WYhDwOmmljRRDq2y4 3LD9lhjMPpHYZkIxtMJkddWSQTEY3WpffF2Roa82iI/dXCQOfOaHVu2axdDb NcINa7zF4VPx0bS4+Qzt9Cy/uK5AHDyGzNx36zJ0bX79yNtRcSh2czn1UJ+h v08rCBxfJAE9QjrhuasYunxYasv2QxJgyTpNbDVk/uVXArJPeKclbGTohxV6 A7M6JKBP0YqTuJmhb60sK38qMw2qZjVvsbFg6IZppxzGjKfBiQOhDc07GHqa m/ayuqBpkNmi5i1ny9DGaaFr7HOngXvY+Rj1PQw9d/m8rY+6p8GdJ3E6UxwY mvWFSwwSknBR53lTqhNDG2wd1xVcKwmwR+SlugtDJ1cmHRb3kITDk2vEjrkx 9IFVFx5KXpcEE/7rdJonQ98fvDB/erUkzNW+2JPnzdCeD0z0l4xKwn5Ca02i L/OvPqXgaWS2k7MfQ2fKpuW9NpICpmG5gWwgQ/+eYvrb1kMKOp/OO59+nKHX p2bcVo2VglvCzT2qwQx9R1/ZYVaZFOhJdtSePMXQEpxSL9c+Kags0E6vOcPQ w5OF24KEpUHxSkwJ33mGNjkwp+qbjDRIbp1PK4Yx9LaY9Os8TWn4uGg3aIQz 9Ma1T8s7l0tDa1RvlUoEQx+ZXTFmv0kaOlvsGsQiGfqstn3LVVtpSHr+2eDD ZYznAfbnU4ekYczQrS8lmqE/t6ifmB8kDRl938/vjGFoWaqjN/yiNLiK3/4s Esv86z9pWDI4cDc5DuMx+1LExWxpcMxdG6gTz9A3VTY0LyyVhruPVb/nJmA+ WLO+xtRKg29XbrxmIkMvrXmQ8PS9NEStChGMTmLoB9MvxRUw0nDrqlbKaDJD K63cd9pzUho8invGjW8ydGXDzJFfEiy4YT7pdTWFoWmLEStjWRYIOe073naL obvnK+scnM2Ci7EqJ6jbDD3jzniD1WIWzFS63bT+DkNbCSfGyK5hQbulYZtb GkOzex+X3tnMgpzyIz0R6Qytr/1fiKQtCxLJpWvTMxh6trEKd40zC1r6N6x7 lInzzco8beLDgrSWIJ3ndxl6dYD3hFYICzyXCpjUZDH/1h8WmCl5t1VlM7R9 3E1+3wQWnFAxnlF2j6GDOu3Od6axwHigc11ODkO/sf8uOquABQe3Fl+Oz2Vo saRRm7XlLAgaTaVP3mfotQ/7HKGWBYOd/Z72eQz9mr44lWxlgYrJAUfIZ2jb Q9a/nveyQK3iqRFRgP12JoO0HmGBw7Df2h60tKaWbM1vnJ8G7+S9QoYutlIt kRdng8b4zAW+DxjawyGleBPBhmXV/gdXFDG0a8Nw6S4lNrBr1thPoK88SvEy 02RDv8HE4vyHDN1RNBGgsZgNr61uibgUM/RosrBf50o2pF1v+qH0CG3UJRL4 Hxt8lCpm1qIdPUbv81mwgeVslX70MUNrzCBk9u1ig8oRo4yZJcy/9ZkNu3zk DCrRWoWy6h892SBeox/sWPpnPQhpH/Vnw4vfEuEiZQz9hbPN/vtpNjiM9/sm oT9e1V30LoINEf4bbZY9YegbejrPUuLYoPk8y/gVOsJ+MMIqhQ1U+hM7u3KG 3rHukdjPu2yQGLHO/Ip+YvL4akAhGwr1zhv6PWVoITO+e4NlbODoJq0UqcDx rI0p2FDNhhgfvfQw9PXkZ7ywBjbIPKPjuM8Y+vw9UY3idjZ4fxxTjkJbHdfZ /raXDc2T0pvISoaO+nCOr+0rG/KrIrUi0WuWdx59+ZMNStNFmqWfY/+dv6Ga LsABZq61xRl0xjpms5cEBwwLBfP5qhg6z/Xmtnk8DniFDYt6obc0nD73egYH Cievbf+ErjyyWn+PGgdcR8Xzdrxg/l3fOJDaW6NRhTa693WD6WIOfDFjlS+p Zui+y24r02kOFK25HJqMnj1TuPPHOg7McyyOkKxh6J7ZQ0e0TDiQJnuu/TB6 285Sw+2WHChXSjnail41z/aSmy0HXm209Vz1kqGzhqbH+zhwoKUvp+4Guup+ bqqbKwfsJk2vC79i6Huu7sPbvTkw4BrVsw9t90y5UCeAA00TMZlP0Z2Os/Um QjjAktLgn1nL0JqDoRl5YXi+Q7U9/mgnS2HT3VE43i/1Ds3oSNWJbVPiOTCU D+d1XjO0F+/qlLCbHBBta7E6i44LqPeRyuAAn4de+wf02C73icBcDkRX3ZVd XIf9Lk4WdReh/WxlzqJtTq3tW/6EA0b7F7W3ouUL3O+HVHFgcWiv+/w3DC0s P3Xrk9ccWN7F1+aPrtll+XW4iQPTyWaVl+i/9w8cALVYoxn1mH+7jx2avRwY Fly3wxE904svQpfhQJBipuV99IDzk2863zFf1f7r+Rrwejr0Tld1ggPr8/V1 jNBze2QDxKZyoW+JgewldIxx4M8OMS40xlUJtaC3TFlSk8Xiwt79n34qN+L6 Pz9B2YPiglZQ+LgDelXJFnkNBS6ctQiXzkD7HNHoaVDlgtvPK8uG0D9HDRK9 NLkQrKEftOgtQ++L5PeYpsOFUzafer3QViLTA6KXcqHh3ph7ATprNLSPAi5s 701U/4mmdha9Dl3LhS36AiJ6TbieVVhY//yPC/tMZ8gcQYe6et7esYULFlOa bfLQhhvONWdv40KRmmjrCNq3/si0KbZcmO5sF6XVzNBJnSftDPZy4ZZgcLgz OpfeO3r0ABdk9kzU3EI/1ljVn+bGhbSBZVs60Dsbc23qvHF8t+KVZrzDfKbX 7x/040JF46Hl5ui/929cELzekxqKNvzUWCx5FuOVpOz4FC33zhKkw7mQcEYr cAJ9Ymrlc5EoLiTHSQ/ptDB0iM8T79FYLggY3n60Hy0dcmhPeyLG51rjl2vo BdbHUx7e4sKKdtujdei4fP0dERlckOqfcBVuZehljm7RtjlcmFVhXq2HXvj6 vJdqIReMxwUuOaMtDcOkPz7iwqbpYRXxaGN3ad/L5Vy4K+PuWIvWCFtbs6qK C8/K5fz52xh6PGmqUs8rLuxQ+iysg36V9vD08QYu9FfMF96Nzs4MlqdauPDW aL7/RbRGBfUt+QPmJ1zJrQSdMaNOeU4PF46raX9k0LvfFRWlfOFCVnRA7Yx2 hm4UCmmcMcSFJ08VVxmh2yxDQ8794AJXS1bXG600tfX98DgX7q91zkxGF7pq /tjCzwPTu6J3X6F1v3S3pgnzIDb67dJxtJ3x7FuTEjyIGMozVn+P2yOeOKxn 8+DYQ99BU/QSR1r7PMmDhrUDikfRf++veTDf8dWHG+gSlROzpijzgHzZtPAl ev+eb97z1XmgqlogO4oOro6SsdTkgboNN1rxA/ZD7CVZHy0eXO4+dccQPWha Fxapy4PNLXcsXNEufL+Cby/jQZGB2LUo9I1Id1YB8EB/2eyAYvQvyX10yRoe 0HODf3eiPQpKFcs24P5TomaIf2ToOTuWlBdv4sF6w+fvFqCP7aD1c7by4K1L yDJztGIHLzJpGw+4ffNW+KL1v5W0nbPhQYD59K54dEcge5brbh5syY3VeoL+ dSjBf6MDDxSC+VV70bVpL4dnOvPAbCT8sXgHQ58jX138fogHyeNnBOejr4Re cyw9zIO1F9W/maLNmgRPn/LF8ZZdveCB5o+O/2UYwIOYd7ymy2gDzfqXAid5 cDOk+GU+enXse3bBafz+t3zPZnSqa3WtQyjmb0T5xS+0y/kjMpwIHkgTvDdy nQzdJXj5e14UD95XJYYuR7d/TvG0iOXBxInmcWu07nTRpK8JPPCrKlfwQ1f9 7D0TfIMHZ233j8ah/z4f8eCVRXnIQ3TMc3ZhQgYPtLTra1rQd1gDlNo9Hrz4 EVbzC10/68Cum3kYX9PekOldDF1mOHxNqQiPn/Di1xL08RNlLVGPeeBKqWtY oCfdfqiKlvMg400r4YmufHPipGclD4jB148uonfqLhdqrebB75hOtbvoL6E1 2fRrHtQu6P+vGn3rXVlkXAMP2BvLtD+hv+WdLPjezIOO9qVNQt04v6Hts4za eTC+UnGlCjp8xv4vMR1Yf4arnGh0jGKuVHcPDxaYO1juQAuXqMRqfuGBzyEL US+0n6bP1YODPBjaXOt3EX3Gz4ZMG+HBPe9LBenoagNLma5RHqgttip8hj79 89VtmQkeFFe+D+xAH7nArV/PR8Da3Y3Sk2j1NtPrnoIEVC8f2kf1MPQjhatU nCgB6rffh2ij9zl1GzyeRgBPYdOh/9CrVSU121kEiBv2zNyLnnmotmmMR0AM xyTJH/3x+hsz6ekEnCiZ2x+Njrp5/ZayPAGeg0oC2ehrnreaFygT4Hynqus5 OsCTHtFTI6DhcEVkB/pFR9IEzCFgg3UmZxz99/mXgGnj0225vfh8dcF4ykpt AvTD4n010aKTl0SX6RKQPfFy72q0x89UZS09Am526itbob/mbd6isoKAqUke Ge7oyIDlSaxVBJzcIyBxFp0gxT99fA0BgZruyxLRgX1Kjz6ux+3vjZYXoJWz RWLKNxJwezOH/QqdGCiRnWxKQKbRxsJutOPig5IBZgQ0X/LVnUAXVG27b7GN gDg++RBOH/ZDfPddDWsCBI9kp81G51WRguO2BIxM5qTQ6LoDLQXP9hCg/DDe 2wwtNCjVEO5AwFfxzwpO6FwrH1uLAwSI+k67FoAOjHu1U8aVgPIm3+FI9LuK nOZGdwIO0amKd9Bgd7/xohcBVhxhtcdo3dTN1ht8CbjPFZxajxavGzk06Yfx tWM96EObbP4umxlEgEhQtNEkWpuM32UVTIC9g+B99ieGjn2pul7oDAFR/iU/ 1dB6anffpp0nIDlj4fRlaKspWwiTcAKMbMu5m9DFhWyRwUsEvDj99pMdeo19 x71z0RjPrNrYw+ibE7cU1GIJOPiNrXEGLZG62LQongB31kRkHPrhly3Gm5Iw 3vZM6130g65sufabBOwdXyfwBP33/QcB8y7sFmpEx6SWGHxLJ+BieFxP35/9 z11I8c0ioE3TJGUcbVf8fmgyh4DcTW/WSH1maEGPGRr++QSczggsU0Jr5iaZ jT8gYKwyQ3Eh+um5Uq/Djwhgj9y1XouOXvrgcn8p1q9Zi48lesC6JG/XUwJs h457O6Kd5v1qf11JQGLmmPlRtFJCIHdlNQEuFqFEKPptpO32tFcEKF0Lz4tH X5OIus99Q0CL2ma9LHT4OnKeTyMB8qdmxJeih38+LW9pJkDbBLrr0KGH/YP0 2wiIFBWS7kJvfzlt/5UPBCynC+S+owNEdPyGOwmoCUiSEP7C0GnLkp9u6CWg YO+09yQ677HYuvjPBKy7vCJqFjpz69SpXwcICC0/pr0UvQRU+GGIgK2PpLPX o7cdG1hz7hsB7/fqE9vRN1o+1NWPEnDvweqdjuiq2Qfvyo0TsKj1wHkfdMym sXbb31hPkj8SzqAdfNv2JvKT8C5/ZkwMmqEPrv8gSMK6Q7pHbqNj8wbOzhAl 4cWY04pCtPnNq9oWEiQ0rpn6qRKdG3NzZagUCeuPLT/ahH4sufhhKZuE1N9b v/Wi5U85po7wSDDaF2I2in6Rt1VspgwJu89Jxwn34/X6yu8OEzkSJE5pvCDQ f9+PkbAyj92hii49F8ZKUibh6cPfHxaiC+S2OT9TJUHgtEalAboyMs308ywS 6jfXRG9Gf9CwLxXXJME4WcF0F/qrpFnZ7PkkOFqaD7mgh4PXWK7RJiH32q2j fugAqR8nbBaR0DthNHgOPeGmtNFzCQne5p4br6L3dLnnnF5GgkyX5aVUdJx8 ZPHVFSQsXjOnPA/t46HicmclCTvd5d6Xo01GcirzV5OQ/HJXVx1a7Whjbdk6 EoYUNOs/oMPqpM++2ECC9cW0TAYt/6Rt9PVGEmwecTwn/sxfK0++0YQEybRw VfEBjI+WyJSmLSSYvDArodDblJckvDUn4dvUMEM1dEnZDf6GbSQ0pDs90EGX Gt2aU2tFwscImekr0SJ+YbLPd5Kg9qt8jzG6vCTp7WM7EqoS4q7uQHsuVrPP tSdB/OGLYge0cY3JkxQHEmQF/Ws80bbbzMeinEhgpbc/D0I7J9sJBx8koXi/ TE4Y2vVUzNdDh0gIcjM/E4t+91v2wQ4PEnjHH29MRZ/Tm9xr4EXCxtaAyVz0 kSzT0Vk+WD8bHseWogk9RTeJYyT0y6fMeol2k3Fu7PcngW+JdeI7NI9cpFEd RMIePjGxXvTlsIOut0+S0OHxZucIuj9Y9PbJUxg/uY6kKQyer5BptjlLwnaO VYME+u/7VRJOi9j/oND7G1TniYeTsIlWEVZFS3rPMW+LIGF5+ANBLbTe546A zMsknHLZPKyP1omYkeV3hYQjneKvDNHTRmL7jGJJvH6Ix25Fc8qU5pLxJJiV eFjYoge/2/u9v47zW+fIfwCd1jjjfUoyCd3JknFef84vObrVOQXzN3Jc/Tj6 c05c+4LbJGR/+3w99I/3ZAcNpWH9CjtIxKCXrnsD2ZkkPJwrs+8G+rpyrJxr NgmjLMXsu+hUxzhKM5cEHYG4/gdonvHexd15mK/RTJkK9JJyf99rhSTUhnnr vkbLJTj3bH1Igi+HWN2Kdr+UcUz0McbbK2VVL3qnUREUlWJ/bjfSHkYLuojr OJeTUCmmyJlEj+aJW8g9I+HKcYMukUGsn5/qmZXPSTjvUneLg/bQebrcs5qE R7P7reXRpyPXCSq8IiGnOH3qbHRCpIhIxWs8fr9WnA469IetoXM9CYtmXVZf 8ef7zUnPWG9JELr8PckQPfFE4WxOMwlyHBf2FvThLPmLZq0kKGjLulujc2W6 20facf1YTjzdh+7izzt88SMJyrq+4m5oVdEay3ldJLx8u8fgKPq34+5Tz3pI iIzpdw5GP+beEd71iQTmzvyzF9Apd968/fGFhIVjq6/GoIeixSfPMSS4aKy7 lox+wvU6ojiE9ZK66VIGmlmgtzF7hITEKK9j+ei/7++xPpobt5WiY1m0UO0Y CXPJ07NfoOddyWasx0koyEr6Uo+u3/Fhad8kCfq1dFI7Ot2wuduNj4J3Np4b +9AWe2+N/hSgoEfI6vMQuqNl86FAIQriloofG0ef+N2yWUiUgg6NGH6hr1gv 5mvjT4tTIPRW4agU2ijljKW4JAUuk9l9FDp7SmLAWWkKdqg5Gimjd5YEyIhx KAi9tuO6BtohkVQN4VHA7xf3eSFa6vGWG/wUBdHJa+asQD9IlI89Op2CRw/2 W69D16yzEf8mR4HiYoWTJmibOd9GnBQoMDDzvb4NXW9Uuv2DEgWLFCOy7dA+ +tdXmM2kQP2gb74T+p2KY2KFGgVSHw3veaCVKr+GLJlNweovUknH0Guvin5N 0aBApqozJPjP/Ar823nzKPA6+25XGPr9mLxZ0AIK3ERFtKL/jHckY0u/NgWt g8e+JaAthEZazBehH5pkpqKf22QOFS+mwPthhE02Ook//rKqHgWqktsFHqAb 6489P6NPgVnC/bgydHiiwIWBFRTwLS6a+wIdodjVa7KSgnkOx+69QZ8er2vI MsDxxEnMb0VDu98O1lqMJ/doQhf6qUe4t4shBSXtrcID6ED3nPkvNlBwpNvA /jtaIel8kPpGCh50PcqfRAd1PHIL3ERBoutufuEh7A+dz3zNphS0DdKrpNA9 eWlaWlsp0EjZ602io0uuCYSYU/D8Tm+yAjrtjeWRd5YUjA40VKij//5+RIHd 0lUf5qNVNnqaB1hjPjWXfV2MfjU8+vjVTgoCDF7/oNEzdELqFewoKH9NfluH NhhIjXTeg/kQlevbhPbY1ctfuJeCY4MDdRboQfUKecH9FPw6kJC7Ey266tkn Yyec7woI3YeWkXVyiHKmIJOvzdoFbR2meaXNhYKBuadneqGrvwb7zXSjwJQy /eiHfssaktnvgfU1tDoqGE2s7DiQdpiC8BfuBqHoPstq7wFvCn5c/NIdiRZ/ rEjP96XAklUcGIfmuBqVHDxGQdbX75wb6Pc/86ek+1MwUnQjLg3Nd+H1ZF8g BXvevZXPQQvy/y5SPUHB4KVrUQ/QJVWJ+rbBFISxBEXK0Md5iv5XTmG8tk13 fY7WL2w4WXuGgunmX17W/on/fzM3i5zH+q49pd6EFpbb07U8jIKDhycOv0cX LWXALZwCgTqL4h503DG5vTciKADzGxMDaOWzYN4YScFr0+GF39FzGtLZItEU ED+N90ygy1JyYhfHUHBgb/nZqcMM3a2c9M0+loKT4bvviKMV1pfLR1yjIHub bhkbrf17j8yjBAq0AjfUyaAzWM+7+xKx3jLS3imiPZbqneLcoCD4wP4WdfQC xbHJZSkUqGicr5+HfrnH8L/dqRQspGdWLEK/i9936PQdCn5/1MvSR7/dd8kl Ix37Tbc1wgB9zkzM8HUmBU406bIBvUZEYHwki4LJvpFVpmjhOffPETkUFIgE SVmii9y3/dK9T0Hf1udvbNAmWYrrzfOxPw82XbRH//19k4JZbYXrD/w5Xub7 4PAiCjpZPmNuaPGzi4+kF1Pw1VY58Qja9crBTc8eU6Ar9sggAF2x8q7Yx1IK 3i/c0RaMXkGopv18QsH1QT638+j7jcML2RUU9C8qnoxAhx1ZeXNWJX6/O+ZE DNpeVYtvRRUFc14kClxHv1jRuXZzNe5/9b1vCnpir4+3/UtcH4Zt+tPR3gGs KK9ajN/2WZY56BvZ5Umn6ihYvmpdUSF6p3NWfHQ9BV3CT2VK0EEH+s+mNFIw 9DXDtQK9/8GF/blNFIhqS5RUo+3y7y4tfUfBy84esTdoJWrXRHUrBTPZ/xk3 oxX77uW+bcfzp686+x79+3LB7o8fKNgcWV/Sja7vDxD53EHBh0uSQ1/QfjPI G0NdWF92P2SH0S1FIXpjPVgfiVfoMTS3uqVysg/r4+Ok1W90cZH8VoEvFFTE L/AQHGFottPWZqEBCoQNlpwUR4tpHLcWHcT1W1nhAgt99GlGm9gQBYYBA5dI 9NzAJhvxEQo+nc+MmIFuk53aLvadAvn9TudU0Jsa59qKjmJ/4mPdbPT/AKQB whk= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, DisplayFunction->Identity, Frame->True, PlotRange->All, PlotRangeClipping->True]], "Output", CellChangeTimes->{ 3.399233155409574*^9, 3.399298387020932*^9, 3.405872712517816*^9, 3.409344709783892*^9, 3.409862799371942*^9, 3.409863831754538*^9, 3.410019151999555*^9, 3.41001980806579*^9, 3.4100314371179*^9, 3.41003414366701*^9, 3.410102010889082*^9, 3.410184442138004*^9, 3.41036324277152*^9, 3.41053852763705*^9, 3.410539288677407*^9, 3.410546768283902*^9, 3.410547542019378*^9, 3.416253937218279*^9, 3.416590170765914*^9, 3.4298796500387864`*^9, 3.429883191131486*^9, 3.4298904739313087`*^9, 3.429898667730036*^9, 3.4299713637208652`*^9, 3.42997280112637*^9, 3.430054585428761*^9, 3.4300613805395575`*^9, 3.430063497463979*^9, 3.430064596280789*^9, {3.4300654309704294`*^9, 3.430062426583343*^9}, 3.430071118656024*^9, 3.430071886179694*^9}] }, Open ]], Cell["\<\ If we use the differential growth model, we can improve the fitting \ significantly.\ \>", "Text"], Cell[CellGroupData[{ Cell["newtonM[boe]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"0.7139394740998702`", ",", "0.8379963656154868`"}], "}"}]], "Output", CellChangeTimes->{ 3.399233157377934*^9, 3.399298388746881*^9, 3.405872714339837*^9, 3.409344711528192*^9, 3.409862802125579*^9, 3.409863834068762*^9, 3.410019153867746*^9, 3.41001980980406*^9, 3.410031438882263*^9, 3.410034145609716*^9, 3.410102012615543*^9, 3.410184443884355*^9, 3.410363244514281*^9, 3.410538529367887*^9, 3.41053929042717*^9, 3.410546770611145*^9, 3.410547543741749*^9, 3.416253938972161*^9, 3.4165901719059916`*^9, 3.429879651241904*^9, 3.42988319227168*^9, 3.4298904750559273`*^9, 3.4298986688554244`*^9, 3.429971364830872*^9, 3.4299728022512474`*^9, 3.430054586553646*^9, 3.430061381648954*^9, 3.4300634985888634`*^9, 3.4300645974057093`*^9, {3.4300654321113386`*^9, 3.430062428243131*^9}, 3.4300711197654552`*^9, 3.430071887289126*^9}] }, Open ]], Cell[CellGroupData[{ Cell["plotFit[boe,DifferentialGrowth->True,logPlot->True]", "Input"], Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[0.015], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 1, 0], Thickness[0.006], LineBox[CompressedData[" 1:eJw12Xk4Vd/XAHBJhpThDucc8xBJpKiE0llNGkkhUUmFJjKPlakiJUMUIUTR gCJDpAyREJVCIRKR6B5JhaJ3/Z5vrz+u5/PcM+y911p773Ou0n7n7fb8fHx8 /Pjxv////6dQrxjvZNlFM/oTU6u1+uiRa9YT4dW9tOj0bL8vMd/orT0et5c4 9P/7/ifd7/d2zUv+AXrxha+/VpWP067y/oNa0l9ofsX5E6J3/tAnwg4ITe/9 Qlta6+S4Kf+lfZjPckUnBmn3O8vpvDQ+yOWIhZiPDv67/jT4m+aZFW8+RBMW BQ9zj/LD4aktcdXpQ/SWZQFFPVrTwV3UIVS8b4g+mfy6lOieDrZnBtbayX+l t4VrawicEQCdKLf5nSZf6cyHrUSd7Axo3U9UiPh+pRU2GOsTt2fA6bCGKMnk r//aLwirHsfdaHv8lfYLmKg4elsQ+umaO2THVzok+qjBcQUhuLCKYO34+ZXW vC8gqBshBIOiMmuFxHh0dI/78dW/hEBE5OD60Dk8OjfHOVZrlzCc2hcWobSM Rz+rNvT2KBGGvTom4ZyNPHr4/qvJk1wRyH/74kCsFY8e17x4ItNRBGKEQ0af H+L9Gz8RKHJZdKzHi0c3SA9/iZWYCQFdUed/neLRUaenP+jaMxOmvZA/pxLF o+dsutxifXMmnFxaxwtK5NEKUw31esMzwS0kZY5KBo9ObBEdz1gqClWKxC/Z ezzaWiN6Q6OPKExMpU0/Ucyjjz578Ph1sSjodUcLbK3k0a8eNI++HROFWV8m ZNLqePTP2cVBf5bOgt1QPyuwiUdXfxc3s3adBR1+C4+OvOP9i+8saDi2sHpa N49+VGPAm9czCyobB6oK+nn0zVVPqp9KzYYFWjHGXB6Pbpl99tC4yWyQHVKK nTvKo2e76Sx/HTwbnqgdWMKM82iTrIh19gWzQV5bco3HXx69wFDLvKxvNqTd PLinRIChJYc4xDAhBnbTEwurRRh6jfkf3RlGYpA5N3ROghhDX69N9xL1EANz kzaV5WyGdlwd9UjsGrrwB3OHZOjC4aiF0g1icHP0vhcjw9CeD01X6I2JQflc w2PCisy//BQHo7szLcbnMPRdmayips3iIP9H16dKjaH/8m37a+shDlnO2mNH NRh6462c26pJ4lD7+cvzb1oMfWeF8qF5T8RBam94raUOQ89iV3q7DIiDRPDT lJSlDP19qsQqWEgCuOo1H+v0GNrUcX79DykJIK90ibQvZ2irhOxrXE0JcFT8 5PZqJUMbGz2t7jWUgGOrzO3urmJoX/WacfutEtAebijutZahz+vYdyTaSsA9 G/7ouesZerYja/CsqwTY9vaNVmxk6MEOtdMLgyXAXcV/6cYtDC1D9XyOvigB W9RHDR+ZMP/qTwLUGf1B+W04HuqxMRfzJCB2HTHb2YyhM+ZsaltSKQE73eUP 5lgw9ALJed8SXknAKHkl970lQ+s3Pkx9+kECtE8YJ0xaMfRD6dirxYwEZK5Z VS22m6GVVh0M85ySABV9hwZJG4aubVEZ/T1LEjhl+uuEbBmathzdbSIjCfKr LYuYfQzdt1B58TF1STjXN5VRf4Ch5e78adm9TBKaQ6OjEu0ZerdQWoLMOkkI F5j+Ze9BhmZ9Lq+8s10SHhWumSN1mKFX6GwJFbOVhH0fr2XUHGFodZM5nHVO kvC6cc67o47Y39y7YaZ+kuCt1S4teIyh1wb6TGqHSkLCQZ2ay87Mv/kHz1+z ZKm8K0PbX83gP54qCS/8GouS3Bg6uHf/hd4sSbgaIZ7M8mDoN/Y/ReYVS8LR LbaLAz0Zemb6mI1RtSTcsy4u++TF0EaPBo7AK0nIlG0OXePD0E30RQHyvSQo 69k0XPFlaFvXPb/rPmN/+GRefPZj6J/ncsg9o5LgLEDULjrB0BKa2jKNfyUh +MeTUdeTDP14t2qFvCgL9sqrhWX5M7THoczHWwkWZMYOl3wIYGiXlu+V+5RY 4LQ9pVQsiKGvlGV6W2iygGtz9bFuMEP3lE4GaixjQYHKLmbnKYYeuy7k37uK Bd/UDh/3PI3e/Ek4aAsLSuWiLoSfYegjHmOF0yxZ0H613yQ5hKE15Aipg/tY MOA12Hc7lPk3P7MguDLyeN5ZhtYukVH76In3bzTTLghjcD4I7RoLYMEQz0zj /jmGHmJb2f8MY0HdFuvzWecZ+mOi7tL2GBbYlvNcr4Uz9A2Dxc8yr7LAs9Z+ KvoCQ8fYD8fszmRBfh7PxD+CoXetL5s5cY8F+3mpgQ6RDF1lWp4YWMKC8Qdn 726KYmhBi2n3h5+wwGb2/Z/zo7E9RgnFmxpYcP2HnovQRYa+dv0ZN7KFBa6r Ny39gL5wX0TjcRcLvPKW2RTEYH6dWmz99jMLCi+e4A+NZei47vBpnd9Y8Lyr Rs/iEkOvM+w98WKCBQ8ZAVLxMtbfhRuq2dPZcPjOgbx+dM56Zrv3LDbssLFV yIpj6CKXDCstLhsqlOtdneIZ2qwlLLxJjg3fmcZSjStYD75rV9jNZQPXdIzV j/5vfWNDQuXykJQEht58/9umbcvYwLz4rWaRyNADl91WZdNseNUkJiKchPmt ItT7az0bfI5X6T9A96uP+GqbsmGvxGCt/VWcT/ZWbrDeyYY9Lm+eSSQz9Got 21g3WzYceGe9rhidOyKd4neIDTLen4z3pjB0fWHBLTcXNuwudRzmT2Xo+y7u 36192GB6zt/gOnr/M+WSxYFs+KC2Wn/NNYbuPaJuMBmK7RM9Md6F1hyOyCmK ZEPRiehQvzSGPrpTaNuBODZ4C4YzrHSGvqQ6acWXwoZz9bKGt9De3ES+yAw2 NN9NOW54naGvBjb7ieewwXGffOEL9Pg+98mgAjYogNmvvTew3kXJ0r5SNsSr Zm3koW3OGg0YVrEhTty4yC+DoeWL3QtD69lQks3aNCOToYXkBcyrmtiw8k2s aAS6cd/Ob9/fseHHm3kzuDeZf/sHNjwq66ET0Lv3f+zR/MyG2PNJVXK3GFrF e1qMLsMGZ3VeYgqa51T1Y/FPNjQF6Tcq3GZo65F2XdVJNiyyyTyQjF7QLxM4 U4ADUyvn28ncYegEk6CJnpkcsFIIbL2MNuPTa8yV5IC02pJqiSyc/xemKntQ HFDakrokDL26wkxeQ4EDCT08Tb5shvbz1ehvUeXA8BzZAk/0xNiaNG9NPD7+ 1+sB9MFL/B6zF3OAfUY1ancOtl9YOjBenwNhqxSHG9C5YxEDFHBga5D+hOFd hqb2ljZFGHFALTYxPwsdXGO5Z2ILB/iubFKVvsfQES6et3eZceDnDdXtIegN m8Lb8qw4EPepH76hjzf7zuaz5UDHLfVf1rkMnd57Zv8aBw4Ye+7ze4IuoB3G Tjhy4O5E74v5eQxdrrH6a5YbB26wv/yJQu9tLbB57cOBzJxQwZ9oVnbz4WF/ DmTkF36zus/8279xILdv+5NS9IYvrY/FzmP/78sEyucztGz7TpCI5sAm4QLN APRpgdo64TgOjLNvNnSiQ/2qfMaSOGA+y+6gYQHOn6Gudl1pHJDpWzmVgF60 51Tmo5scOCnidfkX+uqDFbticjigzLdwiVkhQy8/4hZvm88BBzmf9mz0kqYL 3qolHBBT2hglVMTQOzdESnws40Dym1M7bNEm7hLHL1dzICZ9VPsBWiPSqHF1 PQfuaJnNFX/A0H/SBZT6X+L12lYvs0e/zHoUdqqFA5M7zQ6VoPPuhshTHRz4 vHDaI7FiPL+G+nG9mwOa+oV6+9E5cq+V5/dzIFaxrjMffaC9tDRzCOPTEZwn WMLQrYKhrXIjHMhX5RZZojt3RoSG/+JARO91JhOtJPD+w/c/HJhIX7f3F7rE RfOXGT8XZk5MCBs9ZGjdob73WUJckBp+wMSg95uo35yaxYWNB+2I7v99H1N1 aCOLCz98XwcsKGVovSO0zgWSC3ptDVq+6P/211xIXjB7bhW6Ys7peXzKXCAc DA+JPWLow3Y/fBaqcWE1NfnLEh3SECe1U5MLBi/et6aizZJiZfy0ufB+j93M AfTwtteRl3S5ULpA5OKixwztPO13yO3l6PN6rt7oG5fcJYuBC8Ej228/Qv8W O0hXrONC4fZsenoZrofFlYpPNnFhuVX04g3o+bv0qh9v5cKe+4Znw9End9Er 8s2xv9v66JdoxR7upXQrLgTcyN/NLsf9w4+KznAbLqz/VPPBAt0TxJrncoAL N9csbYxD/3ZNDTA+xAW/BcJq79Cvsl58V3HiwoPg1V+lKhg6nHx58acrFw43 dihbo69EJB+p9OIC38mntVfQFu9mhJ09zoU1kn09b9H88Sm/NwRy4bGllDtZ iftZzeYX089woSV+qa8Fem3SB1ZxGBf8a4XGLqJvuTS8OhTBhasl5t9eoJ0v +EqxYzAe6985zHrC0J9mXP5ZFMcFy6BN1hvQXYOZnpZJXHjy3qLhFFpXWiT9 WyoX4m2uVTxG1098PhdygwslpfV64+j/no+4oBvluGRxFc5fdayS1BwuxHlz Ch3RdyR51Nz7XFi60rjsBrp5nuO+jCIuhExL2NaJfrLhe7JSKY6nhfcxopqh T51+0hFXjv0/tIs0QU+5/VIVqebC/jmFxmfQtW9On/Gs5YK86TdWKXqvrqHg +wbsX4HLoRH0UERjHt3EhWUGF7fOe8rQN9ufXLragufz59TuQf8oOlP8s40L CpHE24to3RHreZu7uJDaTp2oQUfLHR5K6OGCvt+fwt/oBMUC8b5+Lly+N/3c whpcHyrmJGkOYTxijv7cj/bX9Es8Noz9UXScvIQ+529DZo3i8dZ6qc/QDWt2 Sn0a44LGvqmuCXTYxMvbUpNc8DzX/0jzGe7PozjNG6cR4H2cWm6DVuvcds1z BgGNdO7OSHSZQiJ1VYSAPtsGshx98GjfmvLZBGT8OeU7jF6rKqbZJUlAZHu/ v2Itrj+ur96NcwmwDBFSN0V/vPbGQkKaAMFdX30C0HEZ124qyxMQdS3FOQed 7HmzbZEyAb9SFMXeowM96VGDuQSMZR+zEK1j6Oc96ZMwn4CVG04b6aP/e/4l QHPOzo8OaMkoE75VOgQsNnyvHosWmYoVWa5LQPkwv3wF2mPilrK2AQEVMwrK vqK/FW03m7OSgOrKdnHpelzfAw3TJVcTUDK5S9wInSrOL/1nHQEbNckyV3TQ gFLZx40EtLoPKlxFK+cJJ1QbEzC/+L7OM3Ra0Ky869sIyL+7fmwEfWTZMbFA CwLCPh93lXvO0MX1VoWWVgTwdSulrEffSum7p7GHAAFJ4WBXdFE9OeOPLQGS 4+PSiejXjh3Fz+wI6F9YfqQKLTgs3hJ9iACes6LbV3TBbj9bS0cCzK+/1yYa sH1XX+6VciHg/Y+i2yvR7TX5ba3uBHi0Or53QMP+wtaL3gQ4s4rqItC6t7bv 2XScgLgmE/dCtOjrUdcpfwKGcgda36NNt/+UuRtMgEaVwbhAI0PrkCn7dodg +9JGWjXQSS9UNwqeI+CQR5nHdrTB3Htvsy4Q0Dy15aUPejefGWEajfe7vXYw Gf24hCU8HEuAVJTx0yr0Ovue++HxBGQFz9r/BZ0xeVNhbhIBvZRKmfgLfP68 tWxbaQoBykVLOpegHw2ZmWxNJ2A4vqPMCv3wU55sVwYBu9uK7PzR/73/IEA+ yLYhDZ1wq2LNj2wCYs4cm3j6v+PDozKP5xIQ1O499AW9//GHkal8Aor9JK6L vWToGR5yGgEPCDh1sE5JB61ZkG7x5yHme8lSBwv00/BKb68yzKfbH1x90PH6 Dy9/rSTgYbTlukQ0b09F0b6nBLB/qXQ/Qh/V+t3VVEuA4eVX6z6glVKDOKsa CNjj0OvO/4qh316ytc56SUDatY9HVdDJs+IKOW8I8Hy+VcsIHb2e1PJrJSC0 NPvhQfT3iafVHW0EPEo5wQlDR3gFBK/oJGCcf7n+bbT1i9mHr3QTUPbWfn49 OlB4sf/3XmxvgM/nQXTW8utPN30mYEXtkPusJsy38pnrUwYJMPlr0KCJvmsu IPCNRwBr8N3oFrQezOGHEQJy21YOOqKtTvLWhf8gwDTz/b1w9I2O7tfNYwR0 l8wzykLXqx+7J/sH64MbfacenbB1vMv2LwGV5iHdX9CHjnc6pPGT0FDg9Vnk NdYvfWxj9wwS5sq/KJ+HTirinZcTIcFI4feR9egdGYk6lrNIUPtj12+PLkjI WBUhTsLuHE/d0+hysWWPKlkkcAdjd6ah5c8euTXKJUF4nrpJOfp5kflMFSkS 1qfGkZ1osyt/e0xlSfi9c23Bb/R/78dIEJ97UU3qDUNXhkdKpiuT8Cjn4zFd dLGsldMzVRIk3S6fN0PXXsraNjiPhM31s/xd0N0a9pWimiTo/Uw3uoD+Jmbx RH0hCc7s4k+30N9D1u1cp0NCkObNXU/RgeK/TtssJUFC7/nNj+hJNyVjTz0S 3skFNEyh7T6554ctJyGzRKpOuhn3d/KXHieuJEG/93uyLtrPY47znVXYHie7 LdvRpqP5tQ/W4v3nVTQ5oeeeaH31ZD0JQ0M2OmHoyNcS559vImFVQvTR62j5 qs6xJmMS7kln+ZehQ7SL5FtNSYg/yOfYhjbTFuZ7Z0bC3fCuxT/QVsp6qW93 kLDvzpUW8RbcHz25wd9iRYLq1Enz+ejKzTfnv9pNQkV7W/ZatLB/pEzdXhIC SiY/2qCrK9Lflu8nwWLx4lEftOeyufYF9iRMm1HTfRFt0mhalXkI40cKZGWh ba12jMcdJeHHiSVmT9FO1/cLhRzDfPG51tqFdjmb8M3VlQQv/xj9cXT7X5mH uzxIMNXd7stqxf2LwZTDGm+MZ6BKnAbaN3fb2Dw/bI+nacxaNGGg6DbrJI6X k8yxPWg3KafWrwEYz8laNS80l1yq0RBMQtdkSnkE+nLkMZfbZ0ioPf9BLxP9 NUTk9pmzJLBFG6PK/ne/EqbN5jwJx9VvP2tF//d+lYTBDwUfGPThFlUt0WgS un213wm9ZWgxn/k7OmNIeHFhd54C2mCwJ/DuZRI8Rbwcl6EXx8jl+l8hQWNh qdBW9OzRpIHNSVgfVxxPO6DZT5QWkCkk5C+v+ngSPfzT3v/DNRKOHPyrfAmd 1Sr3IfM6CVvrrdZloQ+LjZk7ZWK+e4lteoIezL/ateg2xr/DUrvtf7bLCx7J IsHutfPvYbT++jeQd5eE5/GRN4XeMfQ15SRZlzwSrF4zevLoW0euUpoFJGjG PstaguaaOCzrK8J6s9omsBmtVx1wPLmEBF2xCnofWjbVqd/8EQn2EiZ7vdHu sTknRcpJOKWldeACeu/mUiitJOH8ncub09EznEUXO1WTsA1KqWL0WJGopewz ElbLva5rRHtOqN2trSNBeUhsfy/aY/FTQ88GEh6/SuscR4ddWj9D4SUJic4V IN6G6/clYeGaJhKSPyWdVUFH/LLd4NRMQtZrh0J9tEdb+jPJtzjf7DKtM0FP Vimcz28jQU7pXNUBtFeu/EWL9ySkmqy94YMukOrrGu0i4UxMjuMF9Cf+Iq+L HzF/1Mak09CqIo07tT6R8KBu671C9N8jB84+68d41PZo1qPLOXeE9n3Bepno jupCZ9558/bXEAm7qrw7vqNH4kWnwhkSHKWbxIXbGbqK4+2rOEJCRpCchiya WWRgnDdKgp9EiNYi9H/v70lwdVkmvRadJEkLvhrHfOzazbNEa13JY/b8IQG0 le4cRTfv6tYfmMJ4v8wxDUBnb2jrc5tGwYuyhV0X0ZYON8cmplMwkNiwIwPd 07HdNUiQgubE3KJi9Om/HdsFRSjIuCjA34DW32GUEiZKQcwwb+kH9ObMcztF xShQrIo3+47O40sLPC9BwaaH6rsEOzDeFYFSM9kU3FKp3SKFPpRGqoZy/3f+ 1XmaaPFysxv8FAVL8hp5K9EP0+STTkhTcDs1KGUbunG9jegPWQqo+A4DO7TN /B+jRxUoKJCeUeGFbt5cad2tRMG7bYo6YWi/FddWWqhQIChuFpGIbp9zJK1m LgW85xXN2Wil2m+heuoUuN2LEi5HGyWKfMvUoCAtrGduE1q/OKCLq4XXf/N+ US/6w7i8RfAiCqY9TJv783/tHc0x+6pDAcO2EBZ+j+MnONqxYymOnz3ZIoWu s7k78ngZBRv6RaM00On8KZdVDShYGWCua4hubT5Zd24FBQ+fsmpN0NFp06N4 KykwFTm0wRYdo/jps+kqCsSNPPNd0WF/XrfkrqHgyKJds0+hoct/l6QRBSLa Bmax6Kce0T7OGyi47qATcgMd5J6/8PkmClozDmQUohXSLwSrGVPwzf/r/Rp0 cE+ZW9BWCqqXMDlv0RGLB6e1baPAoyY0bgDdX5SlrW1OwdLhZqcJdHxF8vTQ HRQozBnTFu3E+ebNTt/2nRR8jpzVK4P+7/cjjK+y9mlN9Bxjzx2BeyhIPH2K ZYh++X2s/OVeCt7IKkUao+UWhzYr7Kfgr4TaxB70Gt6tS052FLCN8syOoT32 feYvccD+7etK9EcPq9XIzzhMQURNXVMEWmT1sy8mRynITY0aS0ZLyRw9FOdE wcXmLbPvovdEal7pdKZAjCUjWYZu+Bbir+JGgUM1IfAC/VZyROqwBwX9yrv6 OtHEqh7HLC8KopSnP+ChB3Y2+PB8KMgLUvedQouWK9ILj2O+PvmsLtaF87HL 5opjJymYqbOrTg79YeIBX3YABXKdCdYL0NOimqYGgrD/qRVtK9Az+P+Wqp6m IF96YNMWdEV92grbEAqiC+ff2YU+xVUMuHKWgr7MlN9H0CtKWs68OkdB6JDt Cj90/BaV7cIXKBjbEuoUhhaStftkGEnB790akfHoUn0G3KKx/k7YX8tEXz0p 63AjhoItLcbXC9HK52FH6yUK1tv9iatGz2/JZgnHU7Bq6OyJN+gnmflJyxIo sOYX3d6D7lNO/2GfRIGqSAI1glbYWC0fk0zBAh3jl3wf8Hngr51UWSrmi/9y X3F0jmRd30AaBaOPj7Pl0R76BmfZN3A8LqmkaKIXKY5PLc+kYLv7Ftnl6Bd2 G7YcuEXB/qsi5zei21MOuobdoUBA3W3QEv32YKxzTjYFxlOJhg7ocIuZG5ru UjDvbVKQB3qd8PQ/o7kU1K09VxSMFppfGE7kU6CW4dsVhS51t/qtW0jBAZ3A 8WS0aa7ixh0PKFgzmjcjG/3f75sUJNfPFXj4v+vd/RASXUrBM6fh0Wdo0fPL fLMfU8DvoPK2Be1y5djWZ+UU9HJbs3vRNavuzfxYSUFNgazXCHoloZo1UUXB QgsRbb5uhi5s/b6EVUPB4vZ7nbPRkb6rMubVUtAtqBYgg7ZX1Z62sp6CG84B LHX085W9RtsbKMg50xCvi5508POxf0HB1osqrLVon0DJOO9XFOx7EOe/DX0j rzr97Gs8f1S/0wa91yk3Jb6ZAiV5eW1HdLDj1/OZrRQE9u3w9kUffhh1uOAd Bc5tP++FoPc/uKdf2Y75tE+iMwatRO2bbHhPQVd5wVQqWnHgfsHbLgrGiXFW Dvrv5eIDH7sxH22HpB+im78GCg/2YD16XSOeof3lyBsjnzA/xOcLNqM7SkMN xvspGHkUN9CN5jR01E4NULBo9Hc5D/24VN58+hAF5tMOhf9Gs46atwnycP5n f90s/JGhZ2qc2iMyjPWqm/SXgz7xNKdz5ggFF3aEZCqhFwS9sxEdxfVhZeka LXSnjEDXzJ8UOF0xeWOA3tq6wFZkDPv/zdhqPfr/AKUZiRU= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, DisplayFunction->Identity, Frame->True, PlotRange->All, PlotRangeClipping->True]], "Output", CellChangeTimes->{ 3.39923315937148*^9, 3.399298390637139*^9, 3.405872716261766*^9, 3.409344713371539*^9, 3.40986280472859*^9, 3.409863836064032*^9, 3.410019155768166*^9, 3.410019811644987*^9, 3.410031440734395*^9, 3.410034147702478*^9, 3.41010201448772*^9, 3.410184445757897*^9, 3.410363246624373*^9, 3.410538531228004*^9, 3.410539292272902*^9, 3.410546772704907*^9, 3.410547545507699*^9, 3.416253940837934*^9, 3.416590173046069*^9, 3.429879652413771*^9, 3.429883193411874*^9, 3.4298904762117853`*^9, 3.429898670012074*^9, 3.4299713659877806`*^9, 3.4299728034073715`*^9, 3.430054587694154*^9, 3.4300613828052263`*^9, 3.430063499744995*^9, 3.430064598546254*^9, {3.4300654332835064`*^9, 3.430062430073738*^9}, 3.430071120921765*^9, 3.4300718884454355`*^9}] }, Open ]], Cell["\<\ By setting options appropriately, one can use plotFit to produce informative \ graphics. \ \>", "Text"], Cell[CellGroupData[{ Cell["Options[plotFit]", "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"logPlot", "\[Rule]", "False"}], ",", RowBox[{"DifferentialGrowth", "\[Rule]", "False"}], ",", RowBox[{"dataStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"PointSize", "[", "0.015`", "]"}]}], "}"}]}], ",", RowBox[{"fitStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"0", ",", "1", ",", "0"}], "]"}], ",", RowBox[{"Thickness", "[", "0.006`", "]"}]}], "}"}]}], ",", RowBox[{"InitialM", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"InitialR", "\[Rule]", RowBox[{"-", "1"}]}], ",", RowBox[{"Phi", "\[Rule]", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.399233159580173*^9, 3.399298390795748*^9, 3.405872716398995*^9, 3.409344713550746*^9, 3.40986280479506*^9, 3.409863836231016*^9, 3.410019155924089*^9, 3.410019811795835*^9, 3.410031440881871*^9, 3.410034148059067*^9, 3.410102014569526*^9, 3.410184445909176*^9, 3.410363246823966*^9, 3.410538531380228*^9, 3.410539292425973*^9, 3.410546772785923*^9, 3.410547545658957*^9, 3.416253940925241*^9, 3.416590173077304*^9, 3.429879652445021*^9, 3.429883193427493*^9, 3.4298904762274046`*^9, 3.4298986700277042`*^9, 3.4299713660190487`*^9, 3.4299728034386187`*^9, 3.4300545877097774`*^9, 3.4300613828208513`*^9, 3.4300634997762423`*^9, 3.4300645985775023`*^9, {3.430065433299135*^9, 3.430062430243548*^9}, 3.430071120937391*^9, 3.4300718884610605`*^9}] }, Open ]], Cell["\<\ Note that when you set the option logPlot to True, the horizontal axis is \ log(x+1) in stead of log(x), to avoid log(0). The meaning of the two options \ InitialM and Initial R is the same as in newtonM and newtonLD. As a \ illustrative example, we now use graphics to compare the two models fitted to \ the Boe el al. (1994) data.\ \>", "Text", CellChangeTimes->{{3.430062840163254*^9, 3.43006287000119*^9}}], Cell[CellGroupData[{ Cell["\<\ graphic1=plotFit[boe,fitStyle->{RGBColor[0,0,0],Dashing[{0.015}]},dataStyle->{\ RGBColor[0,0,0],PointSize[0.012]},logPlot->True]\ \>", "Input"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0, 0, 0], PointSize[0.012], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 0, 0], Dashing[{0.015}], LineBox[CompressedData[" 1:eJw12Xk4FW0bAPCQXTjbzIisoaIFpZKau7Qob6KyVEhKiUSWiLJVtJIkEhFK yhKRJSkkSZSEyFLZK0aoKPTdXfX547h+18yZeZ57eWY5SnYum+35p0yZwo8f f/7//88i1aCqMKmNZpb+nFw1r5tuSi0TXPO9kxYXSPf5FPGVFlh8siT/Q8+/ 7d/pmJFdFw8m99E65/t/rHw8Rsu9yrJ6VPOJ5lec81P8zjjdQstmLrv+mbbY rp3hpvybHk8PDvqg/4V2v7OMzk6cAlaNTdFaOV/+HZ8POEZT2ozY/TRhlvsg y4kf9hWqaIFNP/3fYv+8jnkCsF9f89TD2H762LW6IuKDAGyIttQdf9VPm57T 0ph6cipU/i7cs3qin0550Eg8lxOE/6Rdm1aoDNAKhhuXErcFwc5ot7366oF/ 4xcCY/GtB/ttB2gf/58lTreFYFhA/sx6nwE6ONxJz1dBGN62yi56cWGA1rw3 VUg3VBikvF2le5MH6PAOd99VP4RBXNRw1tj9ATorw+XSvB0i4GojqbuhYoB+ Vr7cy6NQBPiozceohgF68F7txDGeKLib1KRd7higxzQvHk05IAorRaTFGWbg X/xEYfL0uMKaXwN09fTBT5ekxaAdiifuCzL0hRMC+e3WYhDwOmmljRRDq2y4 3LD9lhjMPpHYZkIxtMJkddWSQTEY3WpffF2Roa82iI/dXCQOfOaHVu2axdDb NcINa7zF4VPx0bS4+Qzt9Cy/uK5AHDyGzNx36zJ0bX79yNtRcSh2czn1UJ+h v08rCBxfJAE9QjrhuasYunxYasv2QxJgyTpNbDVk/uVXArJPeKclbGTohxV6 A7M6JKBP0YqTuJmhb60sK38qMw2qZjVvsbFg6IZppxzGjKfBiQOhDc07GHqa m/ayuqBpkNmi5i1ny9DGaaFr7HOngXvY+Rj1PQw9d/m8rY+6p8GdJ3E6UxwY mvWFSwwSknBR53lTqhNDG2wd1xVcKwmwR+SlugtDJ1cmHRb3kITDk2vEjrkx 9IFVFx5KXpcEE/7rdJonQ98fvDB/erUkzNW+2JPnzdCeD0z0l4xKwn5Ca02i L/OvPqXgaWS2k7MfQ2fKpuW9NpICpmG5gWwgQ/+eYvrb1kMKOp/OO59+nKHX p2bcVo2VglvCzT2qwQx9R1/ZYVaZFOhJdtSePMXQEpxSL9c+Kags0E6vOcPQ w5OF24KEpUHxSkwJ33mGNjkwp+qbjDRIbp1PK4Yx9LaY9Os8TWn4uGg3aIQz 9Ma1T8s7l0tDa1RvlUoEQx+ZXTFmv0kaOlvsGsQiGfqstn3LVVtpSHr+2eDD ZYznAfbnU4ekYczQrS8lmqE/t6ifmB8kDRl938/vjGFoWaqjN/yiNLiK3/4s Esv86z9pWDI4cDc5DuMx+1LExWxpcMxdG6gTz9A3VTY0LyyVhruPVb/nJmA+ WLO+xtRKg29XbrxmIkMvrXmQ8PS9NEStChGMTmLoB9MvxRUw0nDrqlbKaDJD K63cd9pzUho8invGjW8ydGXDzJFfEiy4YT7pdTWFoWmLEStjWRYIOe073naL obvnK+scnM2Ci7EqJ6jbDD3jzniD1WIWzFS63bT+DkNbCSfGyK5hQbulYZtb GkOzex+X3tnMgpzyIz0R6Qytr/1fiKQtCxLJpWvTMxh6trEKd40zC1r6N6x7 lInzzco8beLDgrSWIJ3ndxl6dYD3hFYICzyXCpjUZDH/1h8WmCl5t1VlM7R9 3E1+3wQWnFAxnlF2j6GDOu3Od6axwHigc11ODkO/sf8uOquABQe3Fl+Oz2Vo saRRm7XlLAgaTaVP3mfotQ/7HKGWBYOd/Z72eQz9mr44lWxlgYrJAUfIZ2jb Q9a/nveyQK3iqRFRgP12JoO0HmGBw7Df2h60tKaWbM1vnJ8G7+S9QoYutlIt kRdng8b4zAW+DxjawyGleBPBhmXV/gdXFDG0a8Nw6S4lNrBr1thPoK88SvEy 02RDv8HE4vyHDN1RNBGgsZgNr61uibgUM/RosrBf50o2pF1v+qH0CG3UJRL4 Hxt8lCpm1qIdPUbv81mwgeVslX70MUNrzCBk9u1ig8oRo4yZJcy/9ZkNu3zk DCrRWoWy6h892SBeox/sWPpnPQhpH/Vnw4vfEuEiZQz9hbPN/vtpNjiM9/sm oT9e1V30LoINEf4bbZY9YegbejrPUuLYoPk8y/gVOsJ+MMIqhQ1U+hM7u3KG 3rHukdjPu2yQGLHO/Ip+YvL4akAhGwr1zhv6PWVoITO+e4NlbODoJq0UqcDx rI0p2FDNhhgfvfQw9PXkZ7ywBjbIPKPjuM8Y+vw9UY3idjZ4fxxTjkJbHdfZ /raXDc2T0pvISoaO+nCOr+0rG/KrIrUi0WuWdx59+ZMNStNFmqWfY/+dv6Ga LsABZq61xRl0xjpms5cEBwwLBfP5qhg6z/Xmtnk8DniFDYt6obc0nD73egYH Cievbf+ErjyyWn+PGgdcR8Xzdrxg/l3fOJDaW6NRhTa693WD6WIOfDFjlS+p Zui+y24r02kOFK25HJqMnj1TuPPHOg7McyyOkKxh6J7ZQ0e0TDiQJnuu/TB6 285Sw+2WHChXSjnail41z/aSmy0HXm209Vz1kqGzhqbH+zhwoKUvp+4Guup+ bqqbKwfsJk2vC79i6Huu7sPbvTkw4BrVsw9t90y5UCeAA00TMZlP0Z2Os/Um QjjAktLgn1nL0JqDoRl5YXi+Q7U9/mgnS2HT3VE43i/1Ds3oSNWJbVPiOTCU D+d1XjO0F+/qlLCbHBBta7E6i44LqPeRyuAAn4de+wf02C73icBcDkRX3ZVd XIf9Lk4WdReh/WxlzqJtTq3tW/6EA0b7F7W3ouUL3O+HVHFgcWiv+/w3DC0s P3Xrk9ccWN7F1+aPrtll+XW4iQPTyWaVl+i/9w8cALVYoxn1mH+7jx2avRwY Fly3wxE904svQpfhQJBipuV99IDzk2863zFf1f7r+Rrwejr0Tld1ggPr8/V1 jNBze2QDxKZyoW+JgewldIxx4M8OMS40xlUJtaC3TFlSk8Xiwt79n34qN+L6 Pz9B2YPiglZQ+LgDelXJFnkNBS6ctQiXzkD7HNHoaVDlgtvPK8uG0D9HDRK9 NLkQrKEftOgtQ++L5PeYpsOFUzafer3QViLTA6KXcqHh3ph7ATprNLSPAi5s 701U/4mmdha9Dl3LhS36AiJ6TbieVVhY//yPC/tMZ8gcQYe6et7esYULFlOa bfLQhhvONWdv40KRmmjrCNq3/si0KbZcmO5sF6XVzNBJnSftDPZy4ZZgcLgz OpfeO3r0ABdk9kzU3EI/1ljVn+bGhbSBZVs60Dsbc23qvHF8t+KVZrzDfKbX 7x/040JF46Hl5ui/929cELzekxqKNvzUWCx5FuOVpOz4FC33zhKkw7mQcEYr cAJ9Ymrlc5EoLiTHSQ/ptDB0iM8T79FYLggY3n60Hy0dcmhPeyLG51rjl2vo BdbHUx7e4sKKdtujdei4fP0dERlckOqfcBVuZehljm7RtjlcmFVhXq2HXvj6 vJdqIReMxwUuOaMtDcOkPz7iwqbpYRXxaGN3ad/L5Vy4K+PuWIvWCFtbs6qK C8/K5fz52xh6PGmqUs8rLuxQ+iysg36V9vD08QYu9FfMF96Nzs4MlqdauPDW aL7/RbRGBfUt+QPmJ1zJrQSdMaNOeU4PF46raX9k0LvfFRWlfOFCVnRA7Yx2 hm4UCmmcMcSFJ08VVxmh2yxDQ8794AJXS1bXG600tfX98DgX7q91zkxGF7pq /tjCzwPTu6J3X6F1v3S3pgnzIDb67dJxtJ3x7FuTEjyIGMozVn+P2yOeOKxn 8+DYQ99BU/QSR1r7PMmDhrUDikfRf++veTDf8dWHG+gSlROzpijzgHzZtPAl ev+eb97z1XmgqlogO4oOro6SsdTkgboNN1rxA/ZD7CVZHy0eXO4+dccQPWha Fxapy4PNLXcsXNEufL+Cby/jQZGB2LUo9I1Id1YB8EB/2eyAYvQvyX10yRoe 0HODf3eiPQpKFcs24P5TomaIf2ToOTuWlBdv4sF6w+fvFqCP7aD1c7by4K1L yDJztGIHLzJpGw+4ffNW+KL1v5W0nbPhQYD59K54dEcge5brbh5syY3VeoL+ dSjBf6MDDxSC+VV70bVpL4dnOvPAbCT8sXgHQ58jX138fogHyeNnBOejr4Re cyw9zIO1F9W/maLNmgRPn/LF8ZZdveCB5o+O/2UYwIOYd7ymy2gDzfqXAid5 cDOk+GU+enXse3bBafz+t3zPZnSqa3WtQyjmb0T5xS+0y/kjMpwIHkgTvDdy nQzdJXj5e14UD95XJYYuR7d/TvG0iOXBxInmcWu07nTRpK8JPPCrKlfwQ1f9 7D0TfIMHZ233j8ah/z4f8eCVRXnIQ3TMc3ZhQgYPtLTra1rQd1gDlNo9Hrz4 EVbzC10/68Cum3kYX9PekOldDF1mOHxNqQiPn/Di1xL08RNlLVGPeeBKqWtY oCfdfqiKlvMg400r4YmufHPipGclD4jB148uonfqLhdqrebB75hOtbvoL6E1 2fRrHtQu6P+vGn3rXVlkXAMP2BvLtD+hv+WdLPjezIOO9qVNQt04v6Hts4za eTC+UnGlCjp8xv4vMR1Yf4arnGh0jGKuVHcPDxaYO1juQAuXqMRqfuGBzyEL US+0n6bP1YODPBjaXOt3EX3Gz4ZMG+HBPe9LBenoagNLma5RHqgttip8hj79 89VtmQkeFFe+D+xAH7nArV/PR8Da3Y3Sk2j1NtPrnoIEVC8f2kf1MPQjhatU nCgB6rffh2ij9zl1GzyeRgBPYdOh/9CrVSU121kEiBv2zNyLnnmotmmMR0AM xyTJH/3x+hsz6ekEnCiZ2x+Njrp5/ZayPAGeg0oC2ehrnreaFygT4Hynqus5 OsCTHtFTI6DhcEVkB/pFR9IEzCFgg3UmZxz99/mXgGnj0225vfh8dcF4ykpt AvTD4n010aKTl0SX6RKQPfFy72q0x89UZS09Am526itbob/mbd6isoKAqUke Ge7oyIDlSaxVBJzcIyBxFp0gxT99fA0BgZruyxLRgX1Kjz6ux+3vjZYXoJWz RWLKNxJwezOH/QqdGCiRnWxKQKbRxsJutOPig5IBZgQ0X/LVnUAXVG27b7GN gDg++RBOH/ZDfPddDWsCBI9kp81G51WRguO2BIxM5qTQ6LoDLQXP9hCg/DDe 2wwtNCjVEO5AwFfxzwpO6FwrH1uLAwSI+k67FoAOjHu1U8aVgPIm3+FI9LuK nOZGdwIO0amKd9Bgd7/xohcBVhxhtcdo3dTN1ht8CbjPFZxajxavGzk06Yfx tWM96EObbP4umxlEgEhQtNEkWpuM32UVTIC9g+B99ieGjn2pul7oDAFR/iU/ 1dB6anffpp0nIDlj4fRlaKspWwiTcAKMbMu5m9DFhWyRwUsEvDj99pMdeo19 x71z0RjPrNrYw+ibE7cU1GIJOPiNrXEGLZG62LQongB31kRkHPrhly3Gm5Iw 3vZM6130g65sufabBOwdXyfwBP33/QcB8y7sFmpEx6SWGHxLJ+BieFxP35/9 z11I8c0ioE3TJGUcbVf8fmgyh4DcTW/WSH1maEGPGRr++QSczggsU0Jr5iaZ jT8gYKwyQ3Eh+um5Uq/Djwhgj9y1XouOXvrgcn8p1q9Zi48lesC6JG/XUwJs h457O6Kd5v1qf11JQGLmmPlRtFJCIHdlNQEuFqFEKPptpO32tFcEKF0Lz4tH X5OIus99Q0CL2ma9LHT4OnKeTyMB8qdmxJeih38+LW9pJkDbBLrr0KGH/YP0 2wiIFBWS7kJvfzlt/5UPBCynC+S+owNEdPyGOwmoCUiSEP7C0GnLkp9u6CWg YO+09yQ677HYuvjPBKy7vCJqFjpz69SpXwcICC0/pr0UvQRU+GGIgK2PpLPX o7cdG1hz7hsB7/fqE9vRN1o+1NWPEnDvweqdjuiq2Qfvyo0TsKj1wHkfdMym sXbb31hPkj8SzqAdfNv2JvKT8C5/ZkwMmqEPrv8gSMK6Q7pHbqNj8wbOzhAl 4cWY04pCtPnNq9oWEiQ0rpn6qRKdG3NzZagUCeuPLT/ahH4sufhhKZuE1N9b v/Wi5U85po7wSDDaF2I2in6Rt1VspgwJu89Jxwn34/X6yu8OEzkSJE5pvCDQ f9+PkbAyj92hii49F8ZKUibh6cPfHxaiC+S2OT9TJUHgtEalAboyMs308ywS 6jfXRG9Gf9CwLxXXJME4WcF0F/qrpFnZ7PkkOFqaD7mgh4PXWK7RJiH32q2j fugAqR8nbBaR0DthNHgOPeGmtNFzCQne5p4br6L3dLnnnF5GgkyX5aVUdJx8 ZPHVFSQsXjOnPA/t46HicmclCTvd5d6Xo01GcirzV5OQ/HJXVx1a7Whjbdk6 EoYUNOs/oMPqpM++2ECC9cW0TAYt/6Rt9PVGEmwecTwn/sxfK0++0YQEybRw VfEBjI+WyJSmLSSYvDArodDblJckvDUn4dvUMEM1dEnZDf6GbSQ0pDs90EGX Gt2aU2tFwscImekr0SJ+YbLPd5Kg9qt8jzG6vCTp7WM7EqoS4q7uQHsuVrPP tSdB/OGLYge0cY3JkxQHEmQF/Ws80bbbzMeinEhgpbc/D0I7J9sJBx8koXi/ TE4Y2vVUzNdDh0gIcjM/E4t+91v2wQ4PEnjHH29MRZ/Tm9xr4EXCxtaAyVz0 kSzT0Vk+WD8bHseWogk9RTeJYyT0y6fMeol2k3Fu7PcngW+JdeI7NI9cpFEd RMIePjGxXvTlsIOut0+S0OHxZucIuj9Y9PbJUxg/uY6kKQyer5BptjlLwnaO VYME+u/7VRJOi9j/oND7G1TniYeTsIlWEVZFS3rPMW+LIGF5+ANBLbTe546A zMsknHLZPKyP1omYkeV3hYQjneKvDNHTRmL7jGJJvH6Ix25Fc8qU5pLxJJiV eFjYoge/2/u9v47zW+fIfwCd1jjjfUoyCd3JknFef84vObrVOQXzN3Jc/Tj6 c05c+4LbJGR/+3w99I/3ZAcNpWH9CjtIxKCXrnsD2ZkkPJwrs+8G+rpyrJxr NgmjLMXsu+hUxzhKM5cEHYG4/gdonvHexd15mK/RTJkK9JJyf99rhSTUhnnr vkbLJTj3bH1Igi+HWN2Kdr+UcUz0McbbK2VVL3qnUREUlWJ/bjfSHkYLuojr OJeTUCmmyJlEj+aJW8g9I+HKcYMukUGsn5/qmZXPSTjvUneLg/bQebrcs5qE R7P7reXRpyPXCSq8IiGnOH3qbHRCpIhIxWs8fr9WnA469IetoXM9CYtmXVZf 8ef7zUnPWG9JELr8PckQPfFE4WxOMwlyHBf2FvThLPmLZq0kKGjLulujc2W6 20facf1YTjzdh+7izzt88SMJyrq+4m5oVdEay3ldJLx8u8fgKPq34+5Tz3pI iIzpdw5GP+beEd71iQTmzvyzF9Apd968/fGFhIVjq6/GoIeixSfPMSS4aKy7 lox+wvU6ojiE9ZK66VIGmlmgtzF7hITEKK9j+ei/7++xPpobt5WiY1m0UO0Y CXPJ07NfoOddyWasx0koyEr6Uo+u3/Fhad8kCfq1dFI7Ot2wuduNj4J3Np4b +9AWe2+N/hSgoEfI6vMQuqNl86FAIQriloofG0ef+N2yWUiUgg6NGH6hr1gv 5mvjT4tTIPRW4agU2ijljKW4JAUuk9l9FDp7SmLAWWkKdqg5Gimjd5YEyIhx KAi9tuO6BtohkVQN4VHA7xf3eSFa6vGWG/wUBdHJa+asQD9IlI89Op2CRw/2 W69D16yzEf8mR4HiYoWTJmibOd9GnBQoMDDzvb4NXW9Uuv2DEgWLFCOy7dA+ +tdXmM2kQP2gb74T+p2KY2KFGgVSHw3veaCVKr+GLJlNweovUknH0Guvin5N 0aBApqozJPjP/Ar823nzKPA6+25XGPr9mLxZ0AIK3ERFtKL/jHckY0u/NgWt g8e+JaAthEZazBehH5pkpqKf22QOFS+mwPthhE02Ook//rKqHgWqktsFHqAb 6489P6NPgVnC/bgydHiiwIWBFRTwLS6a+wIdodjVa7KSgnkOx+69QZ8er2vI MsDxxEnMb0VDu98O1lqMJ/doQhf6qUe4t4shBSXtrcID6ED3nPkvNlBwpNvA /jtaIel8kPpGCh50PcqfRAd1PHIL3ERBoutufuEh7A+dz3zNphS0DdKrpNA9 eWlaWlsp0EjZ602io0uuCYSYU/D8Tm+yAjrtjeWRd5YUjA40VKij//5+RIHd 0lUf5qNVNnqaB1hjPjWXfV2MfjU8+vjVTgoCDF7/oNEzdELqFewoKH9NfluH NhhIjXTeg/kQlevbhPbY1ctfuJeCY4MDdRboQfUKecH9FPw6kJC7Ey266tkn Yyec7woI3YeWkXVyiHKmIJOvzdoFbR2meaXNhYKBuadneqGrvwb7zXSjwJQy /eiHfssaktnvgfU1tDoqGE2s7DiQdpiC8BfuBqHoPstq7wFvCn5c/NIdiRZ/ rEjP96XAklUcGIfmuBqVHDxGQdbX75wb6Pc/86ek+1MwUnQjLg3Nd+H1ZF8g BXvevZXPQQvy/y5SPUHB4KVrUQ/QJVWJ+rbBFISxBEXK0Md5iv5XTmG8tk13 fY7WL2w4WXuGgunmX17W/on/fzM3i5zH+q49pd6EFpbb07U8jIKDhycOv0cX LWXALZwCgTqL4h503DG5vTciKADzGxMDaOWzYN4YScFr0+GF39FzGtLZItEU ED+N90ygy1JyYhfHUHBgb/nZqcMM3a2c9M0+loKT4bvviKMV1pfLR1yjIHub bhkbrf17j8yjBAq0AjfUyaAzWM+7+xKx3jLS3imiPZbqneLcoCD4wP4WdfQC xbHJZSkUqGicr5+HfrnH8L/dqRQspGdWLEK/i9936PQdCn5/1MvSR7/dd8kl Ix37Tbc1wgB9zkzM8HUmBU406bIBvUZEYHwki4LJvpFVpmjhOffPETkUFIgE SVmii9y3/dK9T0Hf1udvbNAmWYrrzfOxPw82XbRH//19k4JZbYXrD/w5Xub7 4PAiCjpZPmNuaPGzi4+kF1Pw1VY58Qja9crBTc8eU6Ar9sggAF2x8q7Yx1IK 3i/c0RaMXkGopv18QsH1QT638+j7jcML2RUU9C8qnoxAhx1ZeXNWJX6/O+ZE DNpeVYtvRRUFc14kClxHv1jRuXZzNe5/9b1vCnpir4+3/UtcH4Zt+tPR3gGs KK9ajN/2WZY56BvZ5Umn6ihYvmpdUSF6p3NWfHQ9BV3CT2VK0EEH+s+mNFIw 9DXDtQK9/8GF/blNFIhqS5RUo+3y7y4tfUfBy84esTdoJWrXRHUrBTPZ/xk3 oxX77uW+bcfzp686+x79+3LB7o8fKNgcWV/Sja7vDxD53EHBh0uSQ1/QfjPI G0NdWF92P2SH0S1FIXpjPVgfiVfoMTS3uqVysg/r4+Ok1W90cZH8VoEvFFTE L/AQHGFottPWZqEBCoQNlpwUR4tpHLcWHcT1W1nhAgt99GlGm9gQBYYBA5dI 9NzAJhvxEQo+nc+MmIFuk53aLvadAvn9TudU0Jsa59qKjmJ/4mPdbPT/AKQB whk= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, DisplayFunction->Identity, Frame->True, PlotRange->All, PlotRangeClipping->True]], "Output", CellChangeTimes->{ 3.399233160269143*^9, 3.399298391346072*^9, 3.405872717004526*^9, 3.409344714115066*^9, 3.409862805411375*^9, 3.409863836794159*^9, 3.410019156485029*^9, 3.410019812347787*^9, 3.410031441431144*^9, 3.410034148803893*^9, 3.410102015126533*^9, 3.410184446468122*^9, 3.410363247351791*^9, 3.410538531945412*^9, 3.410539292963615*^9, 3.410546773358723*^9, 3.41054754621567*^9, 3.416253941481423*^9, 3.4165901733896537`*^9, 3.429879652773144*^9, 3.429883193755494*^9, 3.4298904765554185`*^9, 3.4298986703559427`*^9, 3.42997136634736*^9, 3.4299728037667074`*^9, 3.4300545880222454`*^9, 3.430061383148983*^9, 3.430063500104334*^9, 3.430064598905604*^9, {3.4300654336117134`*^9, 3.430062430772655*^9}, 3.4300711212655325`*^9, 3.4300718887892027`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ graphic2=plotFit[boe, \ DifferentialGrowth->True,fitStyle->RGBColor[0,0,0],dataStyle->{RGBColor[1,1,1]\ },logPlot->True]\ \>", "Input"], Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 1, 1], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 0, 0], LineBox[CompressedData[" 1:eJw12Xk4Vd/XAHBJhpThDucc8xBJpKiE0llNGkkhUUmFJjKPlakiJUMUIUTR gCJDpAyREJVCIRKR6B5JhaJ3/Z5vrz+u5/PcM+y911p773Ou0n7n7fb8fHx8 /Pjxv////6dQrxjvZNlFM/oTU6u1+uiRa9YT4dW9tOj0bL8vMd/orT0et5c4 9P/7/ifd7/d2zUv+AXrxha+/VpWP067y/oNa0l9ofsX5E6J3/tAnwg4ITe/9 Qlta6+S4Kf+lfZjPckUnBmn3O8vpvDQ+yOWIhZiPDv67/jT4m+aZFW8+RBMW BQ9zj/LD4aktcdXpQ/SWZQFFPVrTwV3UIVS8b4g+mfy6lOieDrZnBtbayX+l t4VrawicEQCdKLf5nSZf6cyHrUSd7Axo3U9UiPh+pRU2GOsTt2fA6bCGKMnk r//aLwirHsfdaHv8lfYLmKg4elsQ+umaO2THVzok+qjBcQUhuLCKYO34+ZXW vC8gqBshBIOiMmuFxHh0dI/78dW/hEBE5OD60Dk8OjfHOVZrlzCc2hcWobSM Rz+rNvT2KBGGvTom4ZyNPHr4/qvJk1wRyH/74kCsFY8e17x4ItNRBGKEQ0af H+L9Gz8RKHJZdKzHi0c3SA9/iZWYCQFdUed/neLRUaenP+jaMxOmvZA/pxLF o+dsutxifXMmnFxaxwtK5NEKUw31esMzwS0kZY5KBo9ObBEdz1gqClWKxC/Z ezzaWiN6Q6OPKExMpU0/Ucyjjz578Ph1sSjodUcLbK3k0a8eNI++HROFWV8m ZNLqePTP2cVBf5bOgt1QPyuwiUdXfxc3s3adBR1+C4+OvOP9i+8saDi2sHpa N49+VGPAm9czCyobB6oK+nn0zVVPqp9KzYYFWjHGXB6Pbpl99tC4yWyQHVKK nTvKo2e76Sx/HTwbnqgdWMKM82iTrIh19gWzQV5bco3HXx69wFDLvKxvNqTd PLinRIChJYc4xDAhBnbTEwurRRh6jfkf3RlGYpA5N3ROghhDX69N9xL1EANz kzaV5WyGdlwd9UjsGrrwB3OHZOjC4aiF0g1icHP0vhcjw9CeD01X6I2JQflc w2PCisy//BQHo7szLcbnMPRdmayips3iIP9H16dKjaH/8m37a+shDlnO2mNH NRh6462c26pJ4lD7+cvzb1oMfWeF8qF5T8RBam94raUOQ89iV3q7DIiDRPDT lJSlDP19qsQqWEgCuOo1H+v0GNrUcX79DykJIK90ibQvZ2irhOxrXE0JcFT8 5PZqJUMbGz2t7jWUgGOrzO3urmJoX/WacfutEtAebijutZahz+vYdyTaSsA9 G/7ouesZerYja/CsqwTY9vaNVmxk6MEOtdMLgyXAXcV/6cYtDC1D9XyOvigB W9RHDR+ZMP/qTwLUGf1B+W04HuqxMRfzJCB2HTHb2YyhM+ZsaltSKQE73eUP 5lgw9ALJed8SXknAKHkl970lQ+s3Pkx9+kECtE8YJ0xaMfRD6dirxYwEZK5Z VS22m6GVVh0M85ySABV9hwZJG4aubVEZ/T1LEjhl+uuEbBmathzdbSIjCfKr LYuYfQzdt1B58TF1STjXN5VRf4Ch5e78adm9TBKaQ6OjEu0ZerdQWoLMOkkI F5j+Ze9BhmZ9Lq+8s10SHhWumSN1mKFX6GwJFbOVhH0fr2XUHGFodZM5nHVO kvC6cc67o47Y39y7YaZ+kuCt1S4teIyh1wb6TGqHSkLCQZ2ay87Mv/kHz1+z ZKm8K0PbX83gP54qCS/8GouS3Bg6uHf/hd4sSbgaIZ7M8mDoN/Y/ReYVS8LR LbaLAz0Zemb6mI1RtSTcsy4u++TF0EaPBo7AK0nIlG0OXePD0E30RQHyvSQo 69k0XPFlaFvXPb/rPmN/+GRefPZj6J/ncsg9o5LgLEDULjrB0BKa2jKNfyUh +MeTUdeTDP14t2qFvCgL9sqrhWX5M7THoczHWwkWZMYOl3wIYGiXlu+V+5RY 4LQ9pVQsiKGvlGV6W2iygGtz9bFuMEP3lE4GaixjQYHKLmbnKYYeuy7k37uK Bd/UDh/3PI3e/Ek4aAsLSuWiLoSfYegjHmOF0yxZ0H613yQ5hKE15Aipg/tY MOA12Hc7lPk3P7MguDLyeN5ZhtYukVH76In3bzTTLghjcD4I7RoLYMEQz0zj /jmGHmJb2f8MY0HdFuvzWecZ+mOi7tL2GBbYlvNcr4Uz9A2Dxc8yr7LAs9Z+ KvoCQ8fYD8fszmRBfh7PxD+CoXetL5s5cY8F+3mpgQ6RDF1lWp4YWMKC8Qdn 726KYmhBi2n3h5+wwGb2/Z/zo7E9RgnFmxpYcP2HnovQRYa+dv0ZN7KFBa6r Ny39gL5wX0TjcRcLvPKW2RTEYH6dWmz99jMLCi+e4A+NZei47vBpnd9Y8Lyr Rs/iEkOvM+w98WKCBQ8ZAVLxMtbfhRuq2dPZcPjOgbx+dM56Zrv3LDbssLFV yIpj6CKXDCstLhsqlOtdneIZ2qwlLLxJjg3fmcZSjStYD75rV9jNZQPXdIzV j/5vfWNDQuXykJQEht58/9umbcvYwLz4rWaRyNADl91WZdNseNUkJiKchPmt ItT7az0bfI5X6T9A96uP+GqbsmGvxGCt/VWcT/ZWbrDeyYY9Lm+eSSQz9Got 21g3WzYceGe9rhidOyKd4neIDTLen4z3pjB0fWHBLTcXNuwudRzmT2Xo+y7u 36192GB6zt/gOnr/M+WSxYFs+KC2Wn/NNYbuPaJuMBmK7RM9Md6F1hyOyCmK ZEPRiehQvzSGPrpTaNuBODZ4C4YzrHSGvqQ6acWXwoZz9bKGt9De3ES+yAw2 NN9NOW54naGvBjb7ieewwXGffOEL9Pg+98mgAjYogNmvvTew3kXJ0r5SNsSr Zm3koW3OGg0YVrEhTty4yC+DoeWL3QtD69lQks3aNCOToYXkBcyrmtiw8k2s aAS6cd/Ob9/fseHHm3kzuDeZf/sHNjwq66ET0Lv3f+zR/MyG2PNJVXK3GFrF e1qMLsMGZ3VeYgqa51T1Y/FPNjQF6Tcq3GZo65F2XdVJNiyyyTyQjF7QLxM4 U4ADUyvn28ncYegEk6CJnpkcsFIIbL2MNuPTa8yV5IC02pJqiSyc/xemKntQ HFDakrokDL26wkxeQ4EDCT08Tb5shvbz1ehvUeXA8BzZAk/0xNiaNG9NPD7+ 1+sB9MFL/B6zF3OAfUY1ancOtl9YOjBenwNhqxSHG9C5YxEDFHBga5D+hOFd hqb2ljZFGHFALTYxPwsdXGO5Z2ILB/iubFKVvsfQES6et3eZceDnDdXtIegN m8Lb8qw4EPepH76hjzf7zuaz5UDHLfVf1rkMnd57Zv8aBw4Ye+7ze4IuoB3G Tjhy4O5E74v5eQxdrrH6a5YbB26wv/yJQu9tLbB57cOBzJxQwZ9oVnbz4WF/ DmTkF36zus/8279xILdv+5NS9IYvrY/FzmP/78sEyucztGz7TpCI5sAm4QLN APRpgdo64TgOjLNvNnSiQ/2qfMaSOGA+y+6gYQHOn6Gudl1pHJDpWzmVgF60 51Tmo5scOCnidfkX+uqDFbticjigzLdwiVkhQy8/4hZvm88BBzmf9mz0kqYL 3qolHBBT2hglVMTQOzdESnws40Dym1M7bNEm7hLHL1dzICZ9VPsBWiPSqHF1 PQfuaJnNFX/A0H/SBZT6X+L12lYvs0e/zHoUdqqFA5M7zQ6VoPPuhshTHRz4 vHDaI7FiPL+G+nG9mwOa+oV6+9E5cq+V5/dzIFaxrjMffaC9tDRzCOPTEZwn WMLQrYKhrXIjHMhX5RZZojt3RoSG/+JARO91JhOtJPD+w/c/HJhIX7f3F7rE RfOXGT8XZk5MCBs9ZGjdob73WUJckBp+wMSg95uo35yaxYWNB+2I7v99H1N1 aCOLCz98XwcsKGVovSO0zgWSC3ptDVq+6P/211xIXjB7bhW6Ys7peXzKXCAc DA+JPWLow3Y/fBaqcWE1NfnLEh3SECe1U5MLBi/et6aizZJiZfy0ufB+j93M AfTwtteRl3S5ULpA5OKixwztPO13yO3l6PN6rt7oG5fcJYuBC8Ej228/Qv8W O0hXrONC4fZsenoZrofFlYpPNnFhuVX04g3o+bv0qh9v5cKe+4Znw9End9Er 8s2xv9v66JdoxR7upXQrLgTcyN/NLsf9w4+KznAbLqz/VPPBAt0TxJrncoAL N9csbYxD/3ZNDTA+xAW/BcJq79Cvsl58V3HiwoPg1V+lKhg6nHx58acrFw43 dihbo69EJB+p9OIC38mntVfQFu9mhJ09zoU1kn09b9H88Sm/NwRy4bGllDtZ iftZzeYX089woSV+qa8Fem3SB1ZxGBf8a4XGLqJvuTS8OhTBhasl5t9eoJ0v +EqxYzAe6985zHrC0J9mXP5ZFMcFy6BN1hvQXYOZnpZJXHjy3qLhFFpXWiT9 WyoX4m2uVTxG1098PhdygwslpfV64+j/no+4oBvluGRxFc5fdayS1BwuxHlz Ch3RdyR51Nz7XFi60rjsBrp5nuO+jCIuhExL2NaJfrLhe7JSKY6nhfcxopqh T51+0hFXjv0/tIs0QU+5/VIVqebC/jmFxmfQtW9On/Gs5YK86TdWKXqvrqHg +wbsX4HLoRH0UERjHt3EhWUGF7fOe8rQN9ufXLragufz59TuQf8oOlP8s40L CpHE24to3RHreZu7uJDaTp2oQUfLHR5K6OGCvt+fwt/oBMUC8b5+Lly+N/3c whpcHyrmJGkOYTxijv7cj/bX9Es8Noz9UXScvIQ+529DZo3i8dZ6qc/QDWt2 Sn0a44LGvqmuCXTYxMvbUpNc8DzX/0jzGe7PozjNG6cR4H2cWm6DVuvcds1z BgGNdO7OSHSZQiJ1VYSAPtsGshx98GjfmvLZBGT8OeU7jF6rKqbZJUlAZHu/ v2Itrj+ur96NcwmwDBFSN0V/vPbGQkKaAMFdX30C0HEZ124qyxMQdS3FOQed 7HmzbZEyAb9SFMXeowM96VGDuQSMZR+zEK1j6Oc96ZMwn4CVG04b6aP/e/4l QHPOzo8OaMkoE75VOgQsNnyvHosWmYoVWa5LQPkwv3wF2mPilrK2AQEVMwrK vqK/FW03m7OSgOrKdnHpelzfAw3TJVcTUDK5S9wInSrOL/1nHQEbNckyV3TQ gFLZx40EtLoPKlxFK+cJJ1QbEzC/+L7OM3Ra0Ky869sIyL+7fmwEfWTZMbFA CwLCPh93lXvO0MX1VoWWVgTwdSulrEffSum7p7GHAAFJ4WBXdFE9OeOPLQGS 4+PSiejXjh3Fz+wI6F9YfqQKLTgs3hJ9iACes6LbV3TBbj9bS0cCzK+/1yYa sH1XX+6VciHg/Y+i2yvR7TX5ba3uBHi0Or53QMP+wtaL3gQ4s4rqItC6t7bv 2XScgLgmE/dCtOjrUdcpfwKGcgda36NNt/+UuRtMgEaVwbhAI0PrkCn7dodg +9JGWjXQSS9UNwqeI+CQR5nHdrTB3Htvsy4Q0Dy15aUPejefGWEajfe7vXYw Gf24hCU8HEuAVJTx0yr0Ovue++HxBGQFz9r/BZ0xeVNhbhIBvZRKmfgLfP68 tWxbaQoBykVLOpegHw2ZmWxNJ2A4vqPMCv3wU55sVwYBu9uK7PzR/73/IEA+ yLYhDZ1wq2LNj2wCYs4cm3j6v+PDozKP5xIQ1O499AW9//GHkal8Aor9JK6L vWToGR5yGgEPCDh1sE5JB61ZkG7x5yHme8lSBwv00/BKb68yzKfbH1x90PH6 Dy9/rSTgYbTlukQ0b09F0b6nBLB/qXQ/Qh/V+t3VVEuA4eVX6z6glVKDOKsa CNjj0OvO/4qh316ytc56SUDatY9HVdDJs+IKOW8I8Hy+VcsIHb2e1PJrJSC0 NPvhQfT3iafVHW0EPEo5wQlDR3gFBK/oJGCcf7n+bbT1i9mHr3QTUPbWfn49 OlB4sf/3XmxvgM/nQXTW8utPN30mYEXtkPusJsy38pnrUwYJMPlr0KCJvmsu IPCNRwBr8N3oFrQezOGHEQJy21YOOqKtTvLWhf8gwDTz/b1w9I2O7tfNYwR0 l8wzykLXqx+7J/sH64MbfacenbB1vMv2LwGV5iHdX9CHjnc6pPGT0FDg9Vnk NdYvfWxj9wwS5sq/KJ+HTirinZcTIcFI4feR9egdGYk6lrNIUPtj12+PLkjI WBUhTsLuHE/d0+hysWWPKlkkcAdjd6ah5c8euTXKJUF4nrpJOfp5kflMFSkS 1qfGkZ1osyt/e0xlSfi9c23Bb/R/78dIEJ97UU3qDUNXhkdKpiuT8Cjn4zFd dLGsldMzVRIk3S6fN0PXXsraNjiPhM31s/xd0N0a9pWimiTo/Uw3uoD+Jmbx RH0hCc7s4k+30N9D1u1cp0NCkObNXU/RgeK/TtssJUFC7/nNj+hJNyVjTz0S 3skFNEyh7T6554ctJyGzRKpOuhn3d/KXHieuJEG/93uyLtrPY47znVXYHie7 LdvRpqP5tQ/W4v3nVTQ5oeeeaH31ZD0JQ0M2OmHoyNcS559vImFVQvTR62j5 qs6xJmMS7kln+ZehQ7SL5FtNSYg/yOfYhjbTFuZ7Z0bC3fCuxT/QVsp6qW93 kLDvzpUW8RbcHz25wd9iRYLq1Enz+ejKzTfnv9pNQkV7W/ZatLB/pEzdXhIC SiY/2qCrK9Lflu8nwWLx4lEftOeyufYF9iRMm1HTfRFt0mhalXkI40cKZGWh ba12jMcdJeHHiSVmT9FO1/cLhRzDfPG51tqFdjmb8M3VlQQv/xj9cXT7X5mH uzxIMNXd7stqxf2LwZTDGm+MZ6BKnAbaN3fb2Dw/bI+nacxaNGGg6DbrJI6X k8yxPWg3KafWrwEYz8laNS80l1yq0RBMQtdkSnkE+nLkMZfbZ0ioPf9BLxP9 NUTk9pmzJLBFG6PK/ne/EqbN5jwJx9VvP2tF//d+lYTBDwUfGPThFlUt0WgS un213wm9ZWgxn/k7OmNIeHFhd54C2mCwJ/DuZRI8Rbwcl6EXx8jl+l8hQWNh qdBW9OzRpIHNSVgfVxxPO6DZT5QWkCkk5C+v+ngSPfzT3v/DNRKOHPyrfAmd 1Sr3IfM6CVvrrdZloQ+LjZk7ZWK+e4lteoIezL/ateg2xr/DUrvtf7bLCx7J IsHutfPvYbT++jeQd5eE5/GRN4XeMfQ15SRZlzwSrF4zevLoW0euUpoFJGjG PstaguaaOCzrK8J6s9omsBmtVx1wPLmEBF2xCnofWjbVqd/8EQn2EiZ7vdHu sTknRcpJOKWldeACeu/mUiitJOH8ncub09EznEUXO1WTsA1KqWL0WJGopewz ElbLva5rRHtOqN2trSNBeUhsfy/aY/FTQ88GEh6/SuscR4ddWj9D4SUJic4V IN6G6/clYeGaJhKSPyWdVUFH/LLd4NRMQtZrh0J9tEdb+jPJtzjf7DKtM0FP Vimcz28jQU7pXNUBtFeu/EWL9ySkmqy94YMukOrrGu0i4UxMjuMF9Cf+Iq+L HzF/1Mak09CqIo07tT6R8KBu671C9N8jB84+68d41PZo1qPLOXeE9n3Bepno jupCZ9558/bXEAm7qrw7vqNH4kWnwhkSHKWbxIXbGbqK4+2rOEJCRpCchiya WWRgnDdKgp9EiNYi9H/v70lwdVkmvRadJEkLvhrHfOzazbNEa13JY/b8IQG0 le4cRTfv6tYfmMJ4v8wxDUBnb2jrc5tGwYuyhV0X0ZYON8cmplMwkNiwIwPd 07HdNUiQgubE3KJi9Om/HdsFRSjIuCjA34DW32GUEiZKQcwwb+kH9ObMcztF xShQrIo3+47O40sLPC9BwaaH6rsEOzDeFYFSM9kU3FKp3SKFPpRGqoZy/3f+ 1XmaaPFysxv8FAVL8hp5K9EP0+STTkhTcDs1KGUbunG9jegPWQqo+A4DO7TN /B+jRxUoKJCeUeGFbt5cad2tRMG7bYo6YWi/FddWWqhQIChuFpGIbp9zJK1m LgW85xXN2Wil2m+heuoUuN2LEi5HGyWKfMvUoCAtrGduE1q/OKCLq4XXf/N+ US/6w7i8RfAiCqY9TJv783/tHc0x+6pDAcO2EBZ+j+MnONqxYymOnz3ZIoWu s7k78ngZBRv6RaM00On8KZdVDShYGWCua4hubT5Zd24FBQ+fsmpN0NFp06N4 KykwFTm0wRYdo/jps+kqCsSNPPNd0WF/XrfkrqHgyKJds0+hoct/l6QRBSLa Bmax6Kce0T7OGyi47qATcgMd5J6/8PkmClozDmQUohXSLwSrGVPwzf/r/Rp0 cE+ZW9BWCqqXMDlv0RGLB6e1baPAoyY0bgDdX5SlrW1OwdLhZqcJdHxF8vTQ HRQozBnTFu3E+ebNTt/2nRR8jpzVK4P+7/cjjK+y9mlN9Bxjzx2BeyhIPH2K ZYh++X2s/OVeCt7IKkUao+UWhzYr7Kfgr4TaxB70Gt6tS052FLCN8syOoT32 feYvccD+7etK9EcPq9XIzzhMQURNXVMEWmT1sy8mRynITY0aS0ZLyRw9FOdE wcXmLbPvovdEal7pdKZAjCUjWYZu+Bbir+JGgUM1IfAC/VZyROqwBwX9yrv6 OtHEqh7HLC8KopSnP+ChB3Y2+PB8KMgLUvedQouWK9ILj2O+PvmsLtaF87HL 5opjJymYqbOrTg79YeIBX3YABXKdCdYL0NOimqYGgrD/qRVtK9Az+P+Wqp6m IF96YNMWdEV92grbEAqiC+ff2YU+xVUMuHKWgr7MlN9H0CtKWs68OkdB6JDt Cj90/BaV7cIXKBjbEuoUhhaStftkGEnB790akfHoUn0G3KKx/k7YX8tEXz0p 63AjhoItLcbXC9HK52FH6yUK1tv9iatGz2/JZgnHU7Bq6OyJN+gnmflJyxIo sOYX3d6D7lNO/2GfRIGqSAI1glbYWC0fk0zBAh3jl3wf8Hngr51UWSrmi/9y X3F0jmRd30AaBaOPj7Pl0R76BmfZN3A8LqmkaKIXKY5PLc+kYLv7Ftnl6Bd2 G7YcuEXB/qsi5zei21MOuobdoUBA3W3QEv32YKxzTjYFxlOJhg7ocIuZG5ru UjDvbVKQB3qd8PQ/o7kU1K09VxSMFppfGE7kU6CW4dsVhS51t/qtW0jBAZ3A 8WS0aa7ixh0PKFgzmjcjG/3f75sUJNfPFXj4v+vd/RASXUrBM6fh0Wdo0fPL fLMfU8DvoPK2Be1y5djWZ+UU9HJbs3vRNavuzfxYSUFNgazXCHoloZo1UUXB QgsRbb5uhi5s/b6EVUPB4vZ7nbPRkb6rMubVUtAtqBYgg7ZX1Z62sp6CG84B LHX085W9RtsbKMg50xCvi5508POxf0HB1osqrLVon0DJOO9XFOx7EOe/DX0j rzr97Gs8f1S/0wa91yk3Jb6ZAiV5eW1HdLDj1/OZrRQE9u3w9kUffhh1uOAd Bc5tP++FoPc/uKdf2Y75tE+iMwatRO2bbHhPQVd5wVQqWnHgfsHbLgrGiXFW Dvrv5eIDH7sxH22HpB+im78GCg/2YD16XSOeof3lyBsjnzA/xOcLNqM7SkMN xvspGHkUN9CN5jR01E4NULBo9Hc5D/24VN58+hAF5tMOhf9Gs46atwnycP5n f90s/JGhZ2qc2iMyjPWqm/SXgz7xNKdz5ggFF3aEZCqhFwS9sxEdxfVhZeka LXSnjEDXzJ8UOF0xeWOA3tq6wFZkDPv/zdhqPfr/AKUZiRU= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, DisplayFunction->Identity, Frame->True, PlotRange->All, PlotRangeClipping->True]], "Output", CellChangeTimes->{ 3.399233161966844*^9, 3.399298393026508*^9, 3.405872718937075*^9, 3.409344715930083*^9, 3.409862807623833*^9, 3.409863839272453*^9, 3.410019158182199*^9, 3.410019814045812*^9, 3.410031443114562*^9, 3.410034150679374*^9, 3.410102016823458*^9, 3.410184448155327*^9, 3.410363249133071*^9, 3.410538533640024*^9, 3.410539294774404*^9, 3.410546775210985*^9, 3.410547547919418*^9, 3.416253943184943*^9, 3.4165901745297313`*^9, 3.4298796539293866`*^9, 3.4298831948956885`*^9, 3.429890477695657*^9, 3.429898671481332*^9, 3.429971367488635*^9, 3.4299728049072084`*^9, 3.4300545891627536`*^9, 3.4300613842740045`*^9, 3.4300635012448416`*^9, 3.430064600046149*^9, {3.430065434768252*^9, 3.430062432600262*^9}, 3.4300711223905897`*^9, 3.4300718899142604`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Show[graphic2,graphic1,FrameLabel->{\"log of k+1\", \"prob. of no more than k \ mutants\"}]\ \>", "Input"], Cell[BoxData[ GraphicsBox[{{ {RGBColor[1, 1, 1], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 0, 0], LineBox[CompressedData[" 1:eJw12Xk4Vd/XAHBJhpThDucc8xBJpKiE0llNGkkhUUmFJjKPlakiJUMUIUTR gCJDpAyREJVCIRKR6B5JhaJ3/Z5vrz+u5/PcM+y911p773Ou0n7n7fb8fHx8 /Pjxv////6dQrxjvZNlFM/oTU6u1+uiRa9YT4dW9tOj0bL8vMd/orT0et5c4 9P/7/ifd7/d2zUv+AXrxha+/VpWP067y/oNa0l9ofsX5E6J3/tAnwg4ITe/9 Qlta6+S4Kf+lfZjPckUnBmn3O8vpvDQ+yOWIhZiPDv67/jT4m+aZFW8+RBMW BQ9zj/LD4aktcdXpQ/SWZQFFPVrTwV3UIVS8b4g+mfy6lOieDrZnBtbayX+l t4VrawicEQCdKLf5nSZf6cyHrUSd7Axo3U9UiPh+pRU2GOsTt2fA6bCGKMnk r//aLwirHsfdaHv8lfYLmKg4elsQ+umaO2THVzok+qjBcQUhuLCKYO34+ZXW vC8gqBshBIOiMmuFxHh0dI/78dW/hEBE5OD60Dk8OjfHOVZrlzCc2hcWobSM Rz+rNvT2KBGGvTom4ZyNPHr4/qvJk1wRyH/74kCsFY8e17x4ItNRBGKEQ0af H+L9Gz8RKHJZdKzHi0c3SA9/iZWYCQFdUed/neLRUaenP+jaMxOmvZA/pxLF o+dsutxifXMmnFxaxwtK5NEKUw31esMzwS0kZY5KBo9ObBEdz1gqClWKxC/Z ezzaWiN6Q6OPKExMpU0/Ucyjjz578Ph1sSjodUcLbK3k0a8eNI++HROFWV8m ZNLqePTP2cVBf5bOgt1QPyuwiUdXfxc3s3adBR1+C4+OvOP9i+8saDi2sHpa N49+VGPAm9czCyobB6oK+nn0zVVPqp9KzYYFWjHGXB6Pbpl99tC4yWyQHVKK nTvKo2e76Sx/HTwbnqgdWMKM82iTrIh19gWzQV5bco3HXx69wFDLvKxvNqTd PLinRIChJYc4xDAhBnbTEwurRRh6jfkf3RlGYpA5N3ROghhDX69N9xL1EANz kzaV5WyGdlwd9UjsGrrwB3OHZOjC4aiF0g1icHP0vhcjw9CeD01X6I2JQflc w2PCisy//BQHo7szLcbnMPRdmayips3iIP9H16dKjaH/8m37a+shDlnO2mNH NRh6462c26pJ4lD7+cvzb1oMfWeF8qF5T8RBam94raUOQ89iV3q7DIiDRPDT lJSlDP19qsQqWEgCuOo1H+v0GNrUcX79DykJIK90ibQvZ2irhOxrXE0JcFT8 5PZqJUMbGz2t7jWUgGOrzO3urmJoX/WacfutEtAebijutZahz+vYdyTaSsA9 G/7ouesZerYja/CsqwTY9vaNVmxk6MEOtdMLgyXAXcV/6cYtDC1D9XyOvigB W9RHDR+ZMP/qTwLUGf1B+W04HuqxMRfzJCB2HTHb2YyhM+ZsaltSKQE73eUP 5lgw9ALJed8SXknAKHkl970lQ+s3Pkx9+kECtE8YJ0xaMfRD6dirxYwEZK5Z VS22m6GVVh0M85ySABV9hwZJG4aubVEZ/T1LEjhl+uuEbBmathzdbSIjCfKr LYuYfQzdt1B58TF1STjXN5VRf4Ch5e78adm9TBKaQ6OjEu0ZerdQWoLMOkkI F5j+Ze9BhmZ9Lq+8s10SHhWumSN1mKFX6GwJFbOVhH0fr2XUHGFodZM5nHVO kvC6cc67o47Y39y7YaZ+kuCt1S4teIyh1wb6TGqHSkLCQZ2ay87Mv/kHz1+z ZKm8K0PbX83gP54qCS/8GouS3Bg6uHf/hd4sSbgaIZ7M8mDoN/Y/ReYVS8LR LbaLAz0Zemb6mI1RtSTcsy4u++TF0EaPBo7AK0nIlG0OXePD0E30RQHyvSQo 69k0XPFlaFvXPb/rPmN/+GRefPZj6J/ncsg9o5LgLEDULjrB0BKa2jKNfyUh +MeTUdeTDP14t2qFvCgL9sqrhWX5M7THoczHWwkWZMYOl3wIYGiXlu+V+5RY 4LQ9pVQsiKGvlGV6W2iygGtz9bFuMEP3lE4GaixjQYHKLmbnKYYeuy7k37uK Bd/UDh/3PI3e/Ek4aAsLSuWiLoSfYegjHmOF0yxZ0H613yQ5hKE15Aipg/tY MOA12Hc7lPk3P7MguDLyeN5ZhtYukVH76In3bzTTLghjcD4I7RoLYMEQz0zj /jmGHmJb2f8MY0HdFuvzWecZ+mOi7tL2GBbYlvNcr4Uz9A2Dxc8yr7LAs9Z+ KvoCQ8fYD8fszmRBfh7PxD+CoXetL5s5cY8F+3mpgQ6RDF1lWp4YWMKC8Qdn 726KYmhBi2n3h5+wwGb2/Z/zo7E9RgnFmxpYcP2HnovQRYa+dv0ZN7KFBa6r Ny39gL5wX0TjcRcLvPKW2RTEYH6dWmz99jMLCi+e4A+NZei47vBpnd9Y8Lyr Rs/iEkOvM+w98WKCBQ8ZAVLxMtbfhRuq2dPZcPjOgbx+dM56Zrv3LDbssLFV yIpj6CKXDCstLhsqlOtdneIZ2qwlLLxJjg3fmcZSjStYD75rV9jNZQPXdIzV j/5vfWNDQuXykJQEht58/9umbcvYwLz4rWaRyNADl91WZdNseNUkJiKchPmt ItT7az0bfI5X6T9A96uP+GqbsmGvxGCt/VWcT/ZWbrDeyYY9Lm+eSSQz9Got 21g3WzYceGe9rhidOyKd4neIDTLen4z3pjB0fWHBLTcXNuwudRzmT2Xo+y7u 36192GB6zt/gOnr/M+WSxYFs+KC2Wn/NNYbuPaJuMBmK7RM9Md6F1hyOyCmK ZEPRiehQvzSGPrpTaNuBODZ4C4YzrHSGvqQ6acWXwoZz9bKGt9De3ES+yAw2 NN9NOW54naGvBjb7ieewwXGffOEL9Pg+98mgAjYogNmvvTew3kXJ0r5SNsSr Zm3koW3OGg0YVrEhTty4yC+DoeWL3QtD69lQks3aNCOToYXkBcyrmtiw8k2s aAS6cd/Ob9/fseHHm3kzuDeZf/sHNjwq66ET0Lv3f+zR/MyG2PNJVXK3GFrF e1qMLsMGZ3VeYgqa51T1Y/FPNjQF6Tcq3GZo65F2XdVJNiyyyTyQjF7QLxM4 U4ADUyvn28ncYegEk6CJnpkcsFIIbL2MNuPTa8yV5IC02pJqiSyc/xemKntQ HFDakrokDL26wkxeQ4EDCT08Tb5shvbz1ehvUeXA8BzZAk/0xNiaNG9NPD7+ 1+sB9MFL/B6zF3OAfUY1ancOtl9YOjBenwNhqxSHG9C5YxEDFHBga5D+hOFd hqb2ljZFGHFALTYxPwsdXGO5Z2ILB/iubFKVvsfQES6et3eZceDnDdXtIegN m8Lb8qw4EPepH76hjzf7zuaz5UDHLfVf1rkMnd57Zv8aBw4Ye+7ze4IuoB3G Tjhy4O5E74v5eQxdrrH6a5YbB26wv/yJQu9tLbB57cOBzJxQwZ9oVnbz4WF/ DmTkF36zus/8279xILdv+5NS9IYvrY/FzmP/78sEyucztGz7TpCI5sAm4QLN APRpgdo64TgOjLNvNnSiQ/2qfMaSOGA+y+6gYQHOn6Gudl1pHJDpWzmVgF60 51Tmo5scOCnidfkX+uqDFbticjigzLdwiVkhQy8/4hZvm88BBzmf9mz0kqYL 3qolHBBT2hglVMTQOzdESnws40Dym1M7bNEm7hLHL1dzICZ9VPsBWiPSqHF1 PQfuaJnNFX/A0H/SBZT6X+L12lYvs0e/zHoUdqqFA5M7zQ6VoPPuhshTHRz4 vHDaI7FiPL+G+nG9mwOa+oV6+9E5cq+V5/dzIFaxrjMffaC9tDRzCOPTEZwn WMLQrYKhrXIjHMhX5RZZojt3RoSG/+JARO91JhOtJPD+w/c/HJhIX7f3F7rE RfOXGT8XZk5MCBs9ZGjdob73WUJckBp+wMSg95uo35yaxYWNB+2I7v99H1N1 aCOLCz98XwcsKGVovSO0zgWSC3ptDVq+6P/211xIXjB7bhW6Ys7peXzKXCAc DA+JPWLow3Y/fBaqcWE1NfnLEh3SECe1U5MLBi/et6aizZJiZfy0ufB+j93M AfTwtteRl3S5ULpA5OKixwztPO13yO3l6PN6rt7oG5fcJYuBC8Ej228/Qv8W O0hXrONC4fZsenoZrofFlYpPNnFhuVX04g3o+bv0qh9v5cKe+4Znw9End9Er 8s2xv9v66JdoxR7upXQrLgTcyN/NLsf9w4+KznAbLqz/VPPBAt0TxJrncoAL N9csbYxD/3ZNDTA+xAW/BcJq79Cvsl58V3HiwoPg1V+lKhg6nHx58acrFw43 dihbo69EJB+p9OIC38mntVfQFu9mhJ09zoU1kn09b9H88Sm/NwRy4bGllDtZ iftZzeYX089woSV+qa8Fem3SB1ZxGBf8a4XGLqJvuTS8OhTBhasl5t9eoJ0v +EqxYzAe6985zHrC0J9mXP5ZFMcFy6BN1hvQXYOZnpZJXHjy3qLhFFpXWiT9 WyoX4m2uVTxG1098PhdygwslpfV64+j/no+4oBvluGRxFc5fdayS1BwuxHlz Ch3RdyR51Nz7XFi60rjsBrp5nuO+jCIuhExL2NaJfrLhe7JSKY6nhfcxopqh T51+0hFXjv0/tIs0QU+5/VIVqebC/jmFxmfQtW9On/Gs5YK86TdWKXqvrqHg +wbsX4HLoRH0UERjHt3EhWUGF7fOe8rQN9ufXLragufz59TuQf8oOlP8s40L CpHE24to3RHreZu7uJDaTp2oQUfLHR5K6OGCvt+fwt/oBMUC8b5+Lly+N/3c whpcHyrmJGkOYTxijv7cj/bX9Es8Noz9UXScvIQ+529DZo3i8dZ6qc/QDWt2 Sn0a44LGvqmuCXTYxMvbUpNc8DzX/0jzGe7PozjNG6cR4H2cWm6DVuvcds1z BgGNdO7OSHSZQiJ1VYSAPtsGshx98GjfmvLZBGT8OeU7jF6rKqbZJUlAZHu/ v2Itrj+ur96NcwmwDBFSN0V/vPbGQkKaAMFdX30C0HEZ124qyxMQdS3FOQed 7HmzbZEyAb9SFMXeowM96VGDuQSMZR+zEK1j6Oc96ZMwn4CVG04b6aP/e/4l QHPOzo8OaMkoE75VOgQsNnyvHosWmYoVWa5LQPkwv3wF2mPilrK2AQEVMwrK vqK/FW03m7OSgOrKdnHpelzfAw3TJVcTUDK5S9wInSrOL/1nHQEbNckyV3TQ gFLZx40EtLoPKlxFK+cJJ1QbEzC/+L7OM3Ra0Ky869sIyL+7fmwEfWTZMbFA CwLCPh93lXvO0MX1VoWWVgTwdSulrEffSum7p7GHAAFJ4WBXdFE9OeOPLQGS 4+PSiejXjh3Fz+wI6F9YfqQKLTgs3hJ9iACes6LbV3TBbj9bS0cCzK+/1yYa sH1XX+6VciHg/Y+i2yvR7TX5ba3uBHi0Or53QMP+wtaL3gQ4s4rqItC6t7bv 2XScgLgmE/dCtOjrUdcpfwKGcgda36NNt/+UuRtMgEaVwbhAI0PrkCn7dodg +9JGWjXQSS9UNwqeI+CQR5nHdrTB3Htvsy4Q0Dy15aUPejefGWEajfe7vXYw Gf24hCU8HEuAVJTx0yr0Ovue++HxBGQFz9r/BZ0xeVNhbhIBvZRKmfgLfP68 tWxbaQoBykVLOpegHw2ZmWxNJ2A4vqPMCv3wU55sVwYBu9uK7PzR/73/IEA+ yLYhDZ1wq2LNj2wCYs4cm3j6v+PDozKP5xIQ1O499AW9//GHkal8Aor9JK6L vWToGR5yGgEPCDh1sE5JB61ZkG7x5yHme8lSBwv00/BKb68yzKfbH1x90PH6 Dy9/rSTgYbTlukQ0b09F0b6nBLB/qXQ/Qh/V+t3VVEuA4eVX6z6glVKDOKsa CNjj0OvO/4qh316ytc56SUDatY9HVdDJs+IKOW8I8Hy+VcsIHb2e1PJrJSC0 NPvhQfT3iafVHW0EPEo5wQlDR3gFBK/oJGCcf7n+bbT1i9mHr3QTUPbWfn49 OlB4sf/3XmxvgM/nQXTW8utPN30mYEXtkPusJsy38pnrUwYJMPlr0KCJvmsu IPCNRwBr8N3oFrQezOGHEQJy21YOOqKtTvLWhf8gwDTz/b1w9I2O7tfNYwR0 l8wzykLXqx+7J/sH64MbfacenbB1vMv2LwGV5iHdX9CHjnc6pPGT0FDg9Vnk NdYvfWxj9wwS5sq/KJ+HTirinZcTIcFI4feR9egdGYk6lrNIUPtj12+PLkjI WBUhTsLuHE/d0+hysWWPKlkkcAdjd6ah5c8euTXKJUF4nrpJOfp5kflMFSkS 1qfGkZ1osyt/e0xlSfi9c23Bb/R/78dIEJ97UU3qDUNXhkdKpiuT8Cjn4zFd dLGsldMzVRIk3S6fN0PXXsraNjiPhM31s/xd0N0a9pWimiTo/Uw3uoD+Jmbx RH0hCc7s4k+30N9D1u1cp0NCkObNXU/RgeK/TtssJUFC7/nNj+hJNyVjTz0S 3skFNEyh7T6554ctJyGzRKpOuhn3d/KXHieuJEG/93uyLtrPY47znVXYHie7 LdvRpqP5tQ/W4v3nVTQ5oeeeaH31ZD0JQ0M2OmHoyNcS559vImFVQvTR62j5 qs6xJmMS7kln+ZehQ7SL5FtNSYg/yOfYhjbTFuZ7Z0bC3fCuxT/QVsp6qW93 kLDvzpUW8RbcHz25wd9iRYLq1Enz+ejKzTfnv9pNQkV7W/ZatLB/pEzdXhIC SiY/2qCrK9Lflu8nwWLx4lEftOeyufYF9iRMm1HTfRFt0mhalXkI40cKZGWh ba12jMcdJeHHiSVmT9FO1/cLhRzDfPG51tqFdjmb8M3VlQQv/xj9cXT7X5mH uzxIMNXd7stqxf2LwZTDGm+MZ6BKnAbaN3fb2Dw/bI+nacxaNGGg6DbrJI6X k8yxPWg3KafWrwEYz8laNS80l1yq0RBMQtdkSnkE+nLkMZfbZ0ioPf9BLxP9 NUTk9pmzJLBFG6PK/ne/EqbN5jwJx9VvP2tF//d+lYTBDwUfGPThFlUt0WgS un213wm9ZWgxn/k7OmNIeHFhd54C2mCwJ/DuZRI8Rbwcl6EXx8jl+l8hQWNh qdBW9OzRpIHNSVgfVxxPO6DZT5QWkCkk5C+v+ngSPfzT3v/DNRKOHPyrfAmd 1Sr3IfM6CVvrrdZloQ+LjZk7ZWK+e4lteoIezL/ateg2xr/DUrvtf7bLCx7J IsHutfPvYbT++jeQd5eE5/GRN4XeMfQ15SRZlzwSrF4zevLoW0euUpoFJGjG PstaguaaOCzrK8J6s9omsBmtVx1wPLmEBF2xCnofWjbVqd/8EQn2EiZ7vdHu sTknRcpJOKWldeACeu/mUiitJOH8ncub09EznEUXO1WTsA1KqWL0WJGopewz ElbLva5rRHtOqN2trSNBeUhsfy/aY/FTQ88GEh6/SuscR4ddWj9D4SUJic4V IN6G6/clYeGaJhKSPyWdVUFH/LLd4NRMQtZrh0J9tEdb+jPJtzjf7DKtM0FP Vimcz28jQU7pXNUBtFeu/EWL9ySkmqy94YMukOrrGu0i4UxMjuMF9Cf+Iq+L HzF/1Mak09CqIo07tT6R8KBu671C9N8jB84+68d41PZo1qPLOXeE9n3Bepno jupCZ9558/bXEAm7qrw7vqNH4kWnwhkSHKWbxIXbGbqK4+2rOEJCRpCchiya WWRgnDdKgp9EiNYi9H/v70lwdVkmvRadJEkLvhrHfOzazbNEa13JY/b8IQG0 le4cRTfv6tYfmMJ4v8wxDUBnb2jrc5tGwYuyhV0X0ZYON8cmplMwkNiwIwPd 07HdNUiQgubE3KJi9Om/HdsFRSjIuCjA34DW32GUEiZKQcwwb+kH9ObMcztF xShQrIo3+47O40sLPC9BwaaH6rsEOzDeFYFSM9kU3FKp3SKFPpRGqoZy/3f+ 1XmaaPFysxv8FAVL8hp5K9EP0+STTkhTcDs1KGUbunG9jegPWQqo+A4DO7TN /B+jRxUoKJCeUeGFbt5cad2tRMG7bYo6YWi/FddWWqhQIChuFpGIbp9zJK1m LgW85xXN2Wil2m+heuoUuN2LEi5HGyWKfMvUoCAtrGduE1q/OKCLq4XXf/N+ US/6w7i8RfAiCqY9TJv783/tHc0x+6pDAcO2EBZ+j+MnONqxYymOnz3ZIoWu s7k78ngZBRv6RaM00On8KZdVDShYGWCua4hubT5Zd24FBQ+fsmpN0NFp06N4 KykwFTm0wRYdo/jps+kqCsSNPPNd0WF/XrfkrqHgyKJds0+hoct/l6QRBSLa Bmax6Kce0T7OGyi47qATcgMd5J6/8PkmClozDmQUohXSLwSrGVPwzf/r/Rp0 cE+ZW9BWCqqXMDlv0RGLB6e1baPAoyY0bgDdX5SlrW1OwdLhZqcJdHxF8vTQ HRQozBnTFu3E+ebNTt/2nRR8jpzVK4P+7/cjjK+y9mlN9Bxjzx2BeyhIPH2K ZYh++X2s/OVeCt7IKkUao+UWhzYr7Kfgr4TaxB70Gt6tS052FLCN8syOoT32 feYvccD+7etK9EcPq9XIzzhMQURNXVMEWmT1sy8mRynITY0aS0ZLyRw9FOdE wcXmLbPvovdEal7pdKZAjCUjWYZu+Bbir+JGgUM1IfAC/VZyROqwBwX9yrv6 OtHEqh7HLC8KopSnP+ChB3Y2+PB8KMgLUvedQouWK9ILj2O+PvmsLtaF87HL 5opjJymYqbOrTg79YeIBX3YABXKdCdYL0NOimqYGgrD/qRVtK9Az+P+Wqp6m IF96YNMWdEV92grbEAqiC+ff2YU+xVUMuHKWgr7MlN9H0CtKWs68OkdB6JDt Cj90/BaV7cIXKBjbEuoUhhaStftkGEnB790akfHoUn0G3KKx/k7YX8tEXz0p 63AjhoItLcbXC9HK52FH6yUK1tv9iatGz2/JZgnHU7Bq6OyJN+gnmflJyxIo sOYX3d6D7lNO/2GfRIGqSAI1glbYWC0fk0zBAh3jl3wf8Hngr51UWSrmi/9y X3F0jmRd30AaBaOPj7Pl0R76BmfZN3A8LqmkaKIXKY5PLc+kYLv7Ftnl6Bd2 G7YcuEXB/qsi5zei21MOuobdoUBA3W3QEv32YKxzTjYFxlOJhg7ocIuZG5ru UjDvbVKQB3qd8PQ/o7kU1K09VxSMFppfGE7kU6CW4dsVhS51t/qtW0jBAZ3A 8WS0aa7ixh0PKFgzmjcjG/3f75sUJNfPFXj4v+vd/RASXUrBM6fh0Wdo0fPL fLMfU8DvoPK2Be1y5djWZ+UU9HJbs3vRNavuzfxYSUFNgazXCHoloZo1UUXB QgsRbb5uhi5s/b6EVUPB4vZ7nbPRkb6rMubVUtAtqBYgg7ZX1Z62sp6CG84B LHX085W9RtsbKMg50xCvi5508POxf0HB1osqrLVon0DJOO9XFOx7EOe/DX0j rzr97Gs8f1S/0wa91yk3Jb6ZAiV5eW1HdLDj1/OZrRQE9u3w9kUffhh1uOAd Bc5tP++FoPc/uKdf2Y75tE+iMwatRO2bbHhPQVd5wVQqWnHgfsHbLgrGiXFW Dvrv5eIDH7sxH22HpB+im78GCg/2YD16XSOeof3lyBsjnzA/xOcLNqM7SkMN xvspGHkUN9CN5jR01E4NULBo9Hc5D/24VN58+hAF5tMOhf9Gs46atwnycP5n f90s/JGhZ2qc2iMyjPWqm/SXgz7xNKdz5ggFF3aEZCqhFwS9sxEdxfVhZeka LXSnjEDXzJ8UOF0xeWOA3tq6wFZkDPv/zdhqPfr/AKUZiRU= "]]}}}, { {RGBColor[0, 0, 0], PointSize[0.012], PointBox[CompressedData[" 1:eJw1k39MlHUcx4lDTnju4ODwCVFAaG1XHKSQnoLs/QHnjzBIMWoRbuRgOq+6 5WE2zB84sViGEKw5sXK6AXJ2DdvJryycYCy10pvg0ukSR4X3fL/HROUYUc/z 3ON3++754/vZ5/N5v9+vJ2WLo7gyNCQkhOSrfJ+e5ef/KXRU3wVfMT2bnzGG gpnDsTh1H4Lu2+rxpgk8arXJFX9p74/hqPa23Jn8G1mfS0/y+gNYJZ5tqLWO I3TRi9OCawbuxKN2/dg43izNdO9I/Q9vDeXLFQ/gdOXg7MkQwqmB3ywTD7T+ z1BFiiCX+CCWePo67aG0pu6bjfe2+vCqbV/XaIaOgvv4sOdr7w/inzqKvuLR OSUfNh5ekhZWG0ZOqb8sZ7GEtr4R8ZeFc6hEPRKS1xWuEDvmUFCfpO0fTsp2 f9RIqN43fcHeEU7H70zKCiUcarRn707W0+acxSNRVyRYvw8LX1av1/aV0Djq 3J3/RE8Hej4sdycydLodzRlvz6WgfoahwdxdVb1z6fm9igKGgPWLj9vejaBD VkUh0/yK0PQxXE3wjzebIqlNsdfB0HBQ1313cySpz80MzxV8OVzaHkmuDuUw JM9evbzcH0mCaihDy7AQaF0qULpqIENpWuO6Xz8SqEgNiME+1P2jt0egYB4M 17pvTN6cEjT/GAYfRm8q/cBAwTyZlp+BfrdMZBXMMJz/OZtZRg2kuOHRcbTn XRy8NN9IjbWKIA7jjswc7wEjFcvbTs3nKDpTv7rSYyTFjYoUjvTcjNd/GjOS WTWQI8YXJ/rFKC0vju8WnOm6vj6alOmtNg7XytRtlovR9LIaOEfhmkuD93NN JDeXLeX4LLPydku5iYI8yv1jLBPHrpm0vDn6Epq/6uEmOqdTJnCk5G2t2zlr IjWeCo5E18xwmS2GVDlOjjL9yWMLVsdofHA0VfqbytpiNT44Bjb0t+zvjaWA Mr6Ow72WF+8ymCnIM4fVX+/uOmKmXgWHoxyBd5z/1njMlKACwJHU4zz3yWUz qfa2crD3Bh5lPTbTrRoFII4NL51IrYqPIxU3D0f+hU1JaclxGo8cW4peaJ81 zCMV/wGOqunTqUuyRY1Pju2296P2l4ikru+V5326/fTkvGcpSRUg9+9c9Mob 3fGk4niP47WR9PKIqXgK/vV+/A/WkNuz "]]}, {{}, {}, {RGBColor[0, 0, 0], Dashing[{0.015}], LineBox[CompressedData[" 1:eJw12Xk4FW0bAPCQXTjbzIisoaIFpZKau7Qob6KyVEhKiUSWiLJVtJIkEhFK yhKRJSkkSZSEyFLZK0aoKPTdXfX547h+18yZeZ57eWY5SnYum+35p0yZwo8f f/7//88i1aCqMKmNZpb+nFw1r5tuSi0TXPO9kxYXSPf5FPGVFlh8siT/Q8+/ 7d/pmJFdFw8m99E65/t/rHw8Rsu9yrJ6VPOJ5lec81P8zjjdQstmLrv+mbbY rp3hpvybHk8PDvqg/4V2v7OMzk6cAlaNTdFaOV/+HZ8POEZT2ozY/TRhlvsg y4kf9hWqaIFNP/3fYv+8jnkCsF9f89TD2H762LW6IuKDAGyIttQdf9VPm57T 0ph6cipU/i7cs3qin0550Eg8lxOE/6Rdm1aoDNAKhhuXErcFwc5ot7366oF/ 4xcCY/GtB/ttB2gf/58lTreFYFhA/sx6nwE6ONxJz1dBGN62yi56cWGA1rw3 VUg3VBikvF2le5MH6PAOd99VP4RBXNRw1tj9ATorw+XSvB0i4GojqbuhYoB+ Vr7cy6NQBPiozceohgF68F7txDGeKLib1KRd7higxzQvHk05IAorRaTFGWbg X/xEYfL0uMKaXwN09fTBT5ekxaAdiifuCzL0hRMC+e3WYhDwOmmljRRDq2y4 3LD9lhjMPpHYZkIxtMJkddWSQTEY3WpffF2Roa82iI/dXCQOfOaHVu2axdDb NcINa7zF4VPx0bS4+Qzt9Cy/uK5AHDyGzNx36zJ0bX79yNtRcSh2czn1UJ+h v08rCBxfJAE9QjrhuasYunxYasv2QxJgyTpNbDVk/uVXArJPeKclbGTohxV6 A7M6JKBP0YqTuJmhb60sK38qMw2qZjVvsbFg6IZppxzGjKfBiQOhDc07GHqa m/ayuqBpkNmi5i1ny9DGaaFr7HOngXvY+Rj1PQw9d/m8rY+6p8GdJ3E6UxwY mvWFSwwSknBR53lTqhNDG2wd1xVcKwmwR+SlugtDJ1cmHRb3kITDk2vEjrkx 9IFVFx5KXpcEE/7rdJonQ98fvDB/erUkzNW+2JPnzdCeD0z0l4xKwn5Ca02i L/OvPqXgaWS2k7MfQ2fKpuW9NpICpmG5gWwgQ/+eYvrb1kMKOp/OO59+nKHX p2bcVo2VglvCzT2qwQx9R1/ZYVaZFOhJdtSePMXQEpxSL9c+Kags0E6vOcPQ w5OF24KEpUHxSkwJ33mGNjkwp+qbjDRIbp1PK4Yx9LaY9Os8TWn4uGg3aIQz 9Ma1T8s7l0tDa1RvlUoEQx+ZXTFmv0kaOlvsGsQiGfqstn3LVVtpSHr+2eDD ZYznAfbnU4ekYczQrS8lmqE/t6ifmB8kDRl938/vjGFoWaqjN/yiNLiK3/4s Esv86z9pWDI4cDc5DuMx+1LExWxpcMxdG6gTz9A3VTY0LyyVhruPVb/nJmA+ WLO+xtRKg29XbrxmIkMvrXmQ8PS9NEStChGMTmLoB9MvxRUw0nDrqlbKaDJD K63cd9pzUho8invGjW8ydGXDzJFfEiy4YT7pdTWFoWmLEStjWRYIOe073naL obvnK+scnM2Ci7EqJ6jbDD3jzniD1WIWzFS63bT+DkNbCSfGyK5hQbulYZtb GkOzex+X3tnMgpzyIz0R6Qytr/1fiKQtCxLJpWvTMxh6trEKd40zC1r6N6x7 lInzzco8beLDgrSWIJ3ndxl6dYD3hFYICzyXCpjUZDH/1h8WmCl5t1VlM7R9 3E1+3wQWnFAxnlF2j6GDOu3Od6axwHigc11ODkO/sf8uOquABQe3Fl+Oz2Vo saRRm7XlLAgaTaVP3mfotQ/7HKGWBYOd/Z72eQz9mr44lWxlgYrJAUfIZ2jb Q9a/nveyQK3iqRFRgP12JoO0HmGBw7Df2h60tKaWbM1vnJ8G7+S9QoYutlIt kRdng8b4zAW+DxjawyGleBPBhmXV/gdXFDG0a8Nw6S4lNrBr1thPoK88SvEy 02RDv8HE4vyHDN1RNBGgsZgNr61uibgUM/RosrBf50o2pF1v+qH0CG3UJRL4 Hxt8lCpm1qIdPUbv81mwgeVslX70MUNrzCBk9u1ig8oRo4yZJcy/9ZkNu3zk DCrRWoWy6h892SBeox/sWPpnPQhpH/Vnw4vfEuEiZQz9hbPN/vtpNjiM9/sm oT9e1V30LoINEf4bbZY9YegbejrPUuLYoPk8y/gVOsJ+MMIqhQ1U+hM7u3KG 3rHukdjPu2yQGLHO/Ip+YvL4akAhGwr1zhv6PWVoITO+e4NlbODoJq0UqcDx rI0p2FDNhhgfvfQw9PXkZ7ywBjbIPKPjuM8Y+vw9UY3idjZ4fxxTjkJbHdfZ /raXDc2T0pvISoaO+nCOr+0rG/KrIrUi0WuWdx59+ZMNStNFmqWfY/+dv6Ga LsABZq61xRl0xjpms5cEBwwLBfP5qhg6z/Xmtnk8DniFDYt6obc0nD73egYH Cievbf+ErjyyWn+PGgdcR8Xzdrxg/l3fOJDaW6NRhTa693WD6WIOfDFjlS+p Zui+y24r02kOFK25HJqMnj1TuPPHOg7McyyOkKxh6J7ZQ0e0TDiQJnuu/TB6 285Sw+2WHChXSjnail41z/aSmy0HXm209Vz1kqGzhqbH+zhwoKUvp+4Guup+ bqqbKwfsJk2vC79i6Huu7sPbvTkw4BrVsw9t90y5UCeAA00TMZlP0Z2Os/Um QjjAktLgn1nL0JqDoRl5YXi+Q7U9/mgnS2HT3VE43i/1Ds3oSNWJbVPiOTCU D+d1XjO0F+/qlLCbHBBta7E6i44LqPeRyuAAn4de+wf02C73icBcDkRX3ZVd XIf9Lk4WdReh/WxlzqJtTq3tW/6EA0b7F7W3ouUL3O+HVHFgcWiv+/w3DC0s P3Xrk9ccWN7F1+aPrtll+XW4iQPTyWaVl+i/9w8cALVYoxn1mH+7jx2avRwY Fly3wxE904svQpfhQJBipuV99IDzk2863zFf1f7r+Rrwejr0Tld1ggPr8/V1 jNBze2QDxKZyoW+JgewldIxx4M8OMS40xlUJtaC3TFlSk8Xiwt79n34qN+L6 Pz9B2YPiglZQ+LgDelXJFnkNBS6ctQiXzkD7HNHoaVDlgtvPK8uG0D9HDRK9 NLkQrKEftOgtQ++L5PeYpsOFUzafer3QViLTA6KXcqHh3ph7ATprNLSPAi5s 701U/4mmdha9Dl3LhS36AiJ6TbieVVhY//yPC/tMZ8gcQYe6et7esYULFlOa bfLQhhvONWdv40KRmmjrCNq3/si0KbZcmO5sF6XVzNBJnSftDPZy4ZZgcLgz OpfeO3r0ABdk9kzU3EI/1ljVn+bGhbSBZVs60Dsbc23qvHF8t+KVZrzDfKbX 7x/040JF46Hl5ui/929cELzekxqKNvzUWCx5FuOVpOz4FC33zhKkw7mQcEYr cAJ9Ymrlc5EoLiTHSQ/ptDB0iM8T79FYLggY3n60Hy0dcmhPeyLG51rjl2vo BdbHUx7e4sKKdtujdei4fP0dERlckOqfcBVuZehljm7RtjlcmFVhXq2HXvj6 vJdqIReMxwUuOaMtDcOkPz7iwqbpYRXxaGN3ad/L5Vy4K+PuWIvWCFtbs6qK C8/K5fz52xh6PGmqUs8rLuxQ+iysg36V9vD08QYu9FfMF96Nzs4MlqdauPDW aL7/RbRGBfUt+QPmJ1zJrQSdMaNOeU4PF46raX9k0LvfFRWlfOFCVnRA7Yx2 hm4UCmmcMcSFJ08VVxmh2yxDQ8794AJXS1bXG600tfX98DgX7q91zkxGF7pq /tjCzwPTu6J3X6F1v3S3pgnzIDb67dJxtJ3x7FuTEjyIGMozVn+P2yOeOKxn 8+DYQ99BU/QSR1r7PMmDhrUDikfRf++veTDf8dWHG+gSlROzpijzgHzZtPAl ev+eb97z1XmgqlogO4oOro6SsdTkgboNN1rxA/ZD7CVZHy0eXO4+dccQPWha Fxapy4PNLXcsXNEufL+Cby/jQZGB2LUo9I1Id1YB8EB/2eyAYvQvyX10yRoe 0HODf3eiPQpKFcs24P5TomaIf2ToOTuWlBdv4sF6w+fvFqCP7aD1c7by4K1L yDJztGIHLzJpGw+4ffNW+KL1v5W0nbPhQYD59K54dEcge5brbh5syY3VeoL+ dSjBf6MDDxSC+VV70bVpL4dnOvPAbCT8sXgHQ58jX138fogHyeNnBOejr4Re cyw9zIO1F9W/maLNmgRPn/LF8ZZdveCB5o+O/2UYwIOYd7ymy2gDzfqXAid5 cDOk+GU+enXse3bBafz+t3zPZnSqa3WtQyjmb0T5xS+0y/kjMpwIHkgTvDdy nQzdJXj5e14UD95XJYYuR7d/TvG0iOXBxInmcWu07nTRpK8JPPCrKlfwQ1f9 7D0TfIMHZ233j8ah/z4f8eCVRXnIQ3TMc3ZhQgYPtLTra1rQd1gDlNo9Hrz4 EVbzC10/68Cum3kYX9PekOldDF1mOHxNqQiPn/Di1xL08RNlLVGPeeBKqWtY oCfdfqiKlvMg400r4YmufHPipGclD4jB148uonfqLhdqrebB75hOtbvoL6E1 2fRrHtQu6P+vGn3rXVlkXAMP2BvLtD+hv+WdLPjezIOO9qVNQt04v6Hts4za eTC+UnGlCjp8xv4vMR1Yf4arnGh0jGKuVHcPDxaYO1juQAuXqMRqfuGBzyEL US+0n6bP1YODPBjaXOt3EX3Gz4ZMG+HBPe9LBenoagNLma5RHqgttip8hj79 89VtmQkeFFe+D+xAH7nArV/PR8Da3Y3Sk2j1NtPrnoIEVC8f2kf1MPQjhatU nCgB6rffh2ij9zl1GzyeRgBPYdOh/9CrVSU121kEiBv2zNyLnnmotmmMR0AM xyTJH/3x+hsz6ekEnCiZ2x+Njrp5/ZayPAGeg0oC2ehrnreaFygT4Hynqus5 OsCTHtFTI6DhcEVkB/pFR9IEzCFgg3UmZxz99/mXgGnj0225vfh8dcF4ykpt AvTD4n010aKTl0SX6RKQPfFy72q0x89UZS09Am526itbob/mbd6isoKAqUke Ge7oyIDlSaxVBJzcIyBxFp0gxT99fA0BgZruyxLRgX1Kjz6ux+3vjZYXoJWz RWLKNxJwezOH/QqdGCiRnWxKQKbRxsJutOPig5IBZgQ0X/LVnUAXVG27b7GN gDg++RBOH/ZDfPddDWsCBI9kp81G51WRguO2BIxM5qTQ6LoDLQXP9hCg/DDe 2wwtNCjVEO5AwFfxzwpO6FwrH1uLAwSI+k67FoAOjHu1U8aVgPIm3+FI9LuK nOZGdwIO0amKd9Bgd7/xohcBVhxhtcdo3dTN1ht8CbjPFZxajxavGzk06Yfx tWM96EObbP4umxlEgEhQtNEkWpuM32UVTIC9g+B99ieGjn2pul7oDAFR/iU/ 1dB6anffpp0nIDlj4fRlaKspWwiTcAKMbMu5m9DFhWyRwUsEvDj99pMdeo19 x71z0RjPrNrYw+ibE7cU1GIJOPiNrXEGLZG62LQongB31kRkHPrhly3Gm5Iw 3vZM6130g65sufabBOwdXyfwBP33/QcB8y7sFmpEx6SWGHxLJ+BieFxP35/9 z11I8c0ioE3TJGUcbVf8fmgyh4DcTW/WSH1maEGPGRr++QSczggsU0Jr5iaZ jT8gYKwyQ3Eh+um5Uq/Djwhgj9y1XouOXvrgcn8p1q9Zi48lesC6JG/XUwJs h457O6Kd5v1qf11JQGLmmPlRtFJCIHdlNQEuFqFEKPptpO32tFcEKF0Lz4tH X5OIus99Q0CL2ma9LHT4OnKeTyMB8qdmxJeih38+LW9pJkDbBLrr0KGH/YP0 2wiIFBWS7kJvfzlt/5UPBCynC+S+owNEdPyGOwmoCUiSEP7C0GnLkp9u6CWg YO+09yQ677HYuvjPBKy7vCJqFjpz69SpXwcICC0/pr0UvQRU+GGIgK2PpLPX o7cdG1hz7hsB7/fqE9vRN1o+1NWPEnDvweqdjuiq2Qfvyo0TsKj1wHkfdMym sXbb31hPkj8SzqAdfNv2JvKT8C5/ZkwMmqEPrv8gSMK6Q7pHbqNj8wbOzhAl 4cWY04pCtPnNq9oWEiQ0rpn6qRKdG3NzZagUCeuPLT/ahH4sufhhKZuE1N9b v/Wi5U85po7wSDDaF2I2in6Rt1VspgwJu89Jxwn34/X6yu8OEzkSJE5pvCDQ f9+PkbAyj92hii49F8ZKUibh6cPfHxaiC+S2OT9TJUHgtEalAboyMs308ywS 6jfXRG9Gf9CwLxXXJME4WcF0F/qrpFnZ7PkkOFqaD7mgh4PXWK7RJiH32q2j fugAqR8nbBaR0DthNHgOPeGmtNFzCQne5p4br6L3dLnnnF5GgkyX5aVUdJx8 ZPHVFSQsXjOnPA/t46HicmclCTvd5d6Xo01GcirzV5OQ/HJXVx1a7Whjbdk6 EoYUNOs/oMPqpM++2ECC9cW0TAYt/6Rt9PVGEmwecTwn/sxfK0++0YQEybRw VfEBjI+WyJSmLSSYvDArodDblJckvDUn4dvUMEM1dEnZDf6GbSQ0pDs90EGX Gt2aU2tFwscImekr0SJ+YbLPd5Kg9qt8jzG6vCTp7WM7EqoS4q7uQHsuVrPP tSdB/OGLYge0cY3JkxQHEmQF/Ws80bbbzMeinEhgpbc/D0I7J9sJBx8koXi/ TE4Y2vVUzNdDh0gIcjM/E4t+91v2wQ4PEnjHH29MRZ/Tm9xr4EXCxtaAyVz0 kSzT0Vk+WD8bHseWogk9RTeJYyT0y6fMeol2k3Fu7PcngW+JdeI7NI9cpFEd RMIePjGxXvTlsIOut0+S0OHxZucIuj9Y9PbJUxg/uY6kKQyer5BptjlLwnaO VYME+u/7VRJOi9j/oND7G1TniYeTsIlWEVZFS3rPMW+LIGF5+ANBLbTe546A zMsknHLZPKyP1omYkeV3hYQjneKvDNHTRmL7jGJJvH6Ix25Fc8qU5pLxJJiV eFjYoge/2/u9v47zW+fIfwCd1jjjfUoyCd3JknFef84vObrVOQXzN3Jc/Tj6 c05c+4LbJGR/+3w99I/3ZAcNpWH9CjtIxKCXrnsD2ZkkPJwrs+8G+rpyrJxr NgmjLMXsu+hUxzhKM5cEHYG4/gdonvHexd15mK/RTJkK9JJyf99rhSTUhnnr vkbLJTj3bH1Igi+HWN2Kdr+UcUz0McbbK2VVL3qnUREUlWJ/bjfSHkYLuojr OJeTUCmmyJlEj+aJW8g9I+HKcYMukUGsn5/qmZXPSTjvUneLg/bQebrcs5qE R7P7reXRpyPXCSq8IiGnOH3qbHRCpIhIxWs8fr9WnA469IetoXM9CYtmXVZf 8ef7zUnPWG9JELr8PckQPfFE4WxOMwlyHBf2FvThLPmLZq0kKGjLulujc2W6 20facf1YTjzdh+7izzt88SMJyrq+4m5oVdEay3ldJLx8u8fgKPq34+5Tz3pI iIzpdw5GP+beEd71iQTmzvyzF9Apd968/fGFhIVjq6/GoIeixSfPMSS4aKy7 lox+wvU6ojiE9ZK66VIGmlmgtzF7hITEKK9j+ei/7++xPpobt5WiY1m0UO0Y CXPJ07NfoOddyWasx0koyEr6Uo+u3/Fhad8kCfq1dFI7Ot2wuduNj4J3Np4b +9AWe2+N/hSgoEfI6vMQuqNl86FAIQriloofG0ef+N2yWUiUgg6NGH6hr1gv 5mvjT4tTIPRW4agU2ijljKW4JAUuk9l9FDp7SmLAWWkKdqg5Gimjd5YEyIhx KAi9tuO6BtohkVQN4VHA7xf3eSFa6vGWG/wUBdHJa+asQD9IlI89Op2CRw/2 W69D16yzEf8mR4HiYoWTJmibOd9GnBQoMDDzvb4NXW9Uuv2DEgWLFCOy7dA+ +tdXmM2kQP2gb74T+p2KY2KFGgVSHw3veaCVKr+GLJlNweovUknH0Guvin5N 0aBApqozJPjP/Ar823nzKPA6+25XGPr9mLxZ0AIK3ERFtKL/jHckY0u/NgWt g8e+JaAthEZazBehH5pkpqKf22QOFS+mwPthhE02Ook//rKqHgWqktsFHqAb 6489P6NPgVnC/bgydHiiwIWBFRTwLS6a+wIdodjVa7KSgnkOx+69QZ8er2vI MsDxxEnMb0VDu98O1lqMJ/doQhf6qUe4t4shBSXtrcID6ED3nPkvNlBwpNvA /jtaIel8kPpGCh50PcqfRAd1PHIL3ERBoutufuEh7A+dz3zNphS0DdKrpNA9 eWlaWlsp0EjZ602io0uuCYSYU/D8Tm+yAjrtjeWRd5YUjA40VKij//5+RIHd 0lUf5qNVNnqaB1hjPjWXfV2MfjU8+vjVTgoCDF7/oNEzdELqFewoKH9NfluH NhhIjXTeg/kQlevbhPbY1ctfuJeCY4MDdRboQfUKecH9FPw6kJC7Ey266tkn Yyec7woI3YeWkXVyiHKmIJOvzdoFbR2meaXNhYKBuadneqGrvwb7zXSjwJQy /eiHfssaktnvgfU1tDoqGE2s7DiQdpiC8BfuBqHoPstq7wFvCn5c/NIdiRZ/ rEjP96XAklUcGIfmuBqVHDxGQdbX75wb6Pc/86ek+1MwUnQjLg3Nd+H1ZF8g BXvevZXPQQvy/y5SPUHB4KVrUQ/QJVWJ+rbBFISxBEXK0Md5iv5XTmG8tk13 fY7WL2w4WXuGgunmX17W/on/fzM3i5zH+q49pd6EFpbb07U8jIKDhycOv0cX LWXALZwCgTqL4h503DG5vTciKADzGxMDaOWzYN4YScFr0+GF39FzGtLZItEU ED+N90ygy1JyYhfHUHBgb/nZqcMM3a2c9M0+loKT4bvviKMV1pfLR1yjIHub bhkbrf17j8yjBAq0AjfUyaAzWM+7+xKx3jLS3imiPZbqneLcoCD4wP4WdfQC xbHJZSkUqGicr5+HfrnH8L/dqRQspGdWLEK/i9936PQdCn5/1MvSR7/dd8kl Ix37Tbc1wgB9zkzM8HUmBU406bIBvUZEYHwki4LJvpFVpmjhOffPETkUFIgE SVmii9y3/dK9T0Hf1udvbNAmWYrrzfOxPw82XbRH//19k4JZbYXrD/w5Xub7 4PAiCjpZPmNuaPGzi4+kF1Pw1VY58Qja9crBTc8eU6Ar9sggAF2x8q7Yx1IK 3i/c0RaMXkGopv18QsH1QT638+j7jcML2RUU9C8qnoxAhx1ZeXNWJX6/O+ZE DNpeVYtvRRUFc14kClxHv1jRuXZzNe5/9b1vCnpir4+3/UtcH4Zt+tPR3gGs KK9ajN/2WZY56BvZ5Umn6ihYvmpdUSF6p3NWfHQ9BV3CT2VK0EEH+s+mNFIw 9DXDtQK9/8GF/blNFIhqS5RUo+3y7y4tfUfBy84esTdoJWrXRHUrBTPZ/xk3 oxX77uW+bcfzp686+x79+3LB7o8fKNgcWV/Sja7vDxD53EHBh0uSQ1/QfjPI G0NdWF92P2SH0S1FIXpjPVgfiVfoMTS3uqVysg/r4+Ok1W90cZH8VoEvFFTE L/AQHGFottPWZqEBCoQNlpwUR4tpHLcWHcT1W1nhAgt99GlGm9gQBYYBA5dI 9NzAJhvxEQo+nc+MmIFuk53aLvadAvn9TudU0Jsa59qKjmJ/4mPdbPT/AKQB whk= "]]}}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, DisplayFunction->Identity, Frame->True, FrameLabel->{ FormBox["\"log of k+1\"", TraditionalForm], FormBox["\"prob. of no more than k mutants\"", TraditionalForm]}, PlotRange->All, PlotRangeClipping->True]], "Output", CellChangeTimes->{ 3.399233162160375*^9, 3.399298393229545*^9, 3.405872719100918*^9, 3.409344716127325*^9, 3.40986280918503*^9, 3.409863839684613*^9, 3.410019158360131*^9, 3.410019814219352*^9, 3.410031443277948*^9, 3.410034150897041*^9, 3.410102017003246*^9, 3.41018444833074*^9, 3.410363249342877*^9, 3.4105385338103*^9, 3.410539294952315*^9, 3.410546775381047*^9, 3.410547548092943*^9, 3.416253943360255*^9, 3.4165901745609665`*^9, 3.429879653976261*^9, 3.4298831949269266`*^9, 3.4298904777268963`*^9, 3.429898671528223*^9, 3.4299713675199027`*^9, 3.4299728049228315`*^9, 3.4300545891940002`*^9, 3.43006138428963*^9, 3.4300635012760887`*^9, 3.4300646000773964`*^9, {3.4300654347995095`*^9, 3.430062432788219*^9}, 3.4300711224218416`*^9, 3.430071889945512*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["References", "Section"], Cell["\<\ W. P. Angerer, An explicit representation of the Luria-Delbruck \ distribution. J. Math. Biol. 42 (2001) 145-174. P. Armitage, The statistical theory of bacterial populations subject to \ mutation, J. R. Statist. Soc. B 14 (1952) 1-33. M.S. Bartlett, An Introduction to Stochastic Processes With Special Reference \ to Methods and Applications, third edition, Cambridge University Press, 1978. L. Boe, T. Tolker-Nielsen, K.-M. Eegholm, H. Spliid, A. Vrang, Fluctuation \ analysis of mutations to nalidixic acid resistance in Escherichia coli. J. \ Bacteriol. 176 (1994) 2781-2787. J. Cairns, J. Overbaugh, S. Miller, The origin of mutants. Nature 335 (1988) \ 142-145. K.S. Crump, D.G. Hoel, Mathematical models for estimating mutation rates in \ cell populations. Biometrika 61 (1974) 237-252. M. Demerec, Production of staphylococcus strains resistant to various \ concentrations of penicillin, Proc. Nat. Acad. Sci. USA 31 (1945) 16-24. J.W. Drake, A constant rate of spontaneous mutation in DNA-based microbes, \ Proc. Nat. Acad. Sci. USA 88 (1991) 7160-7164. M.E. Jones, S. M. Thomas and A. Rogers, Luria-Delbruck fluctuation \ experiments: design and analysis. Genetics 136 (1994) 1209-1216. M. Kimmel, D.E. Axelrod, Fluctuation test for two-stage mutations: \ application to gene amplification, Mutation Res. 306 (1994) 45-60. A.L. Koch, Mutation and growth rates from Luria-Delbruck fluctuation tests. \ Mutation Res. 95 (1982) 129-143. E.A. Lea, C.A. Coulson, The distribution of the numbers of mutants in \ bacterial populations. J. Genetics 49 (1949) 264-285. S.E. Luria, M. Delbruck, Mutations of bacteria from virus sensitivity to \ virus resistance. Genetics 28 (1943) 491-511. W.T. Ma, G. vH. Sandri, S. Sarkar, Analysis of the Luria and Delbruck \ distribution using discrete convolution powers. J. Appl. Prob. 29 (1992) \ 255-267. B. Mandelbrot, A population birth-and-mutation process, I: Explicit \ distributions for the number of mutants in an old culture of bacteria. J. \ Appl. Prob. 11 (1974) 437-444. W.A. Rosche, P. L. Foster, Determining mutation rates in bacterial \ populations. Methods, 20 (2000) 4-17. T.G. Rossman, E.I. Goncharova, A. Nadas, Modeling and measurement of the \ spontaneous mutation rate in mammalian cells, Mutation Res. 328 (1995) 21-30. S. Sarkar, Haldane's solution of the Luria-Delbruck distribution, Genetics \ 127 (1991) 257-261. F.M. Stewart, D.M. Gordon, B.R. Levin, Fluctuation analysis: the probability \ distribution of the number of mutants under different conditions, Genetics \ 124 (1990) 175-185. Q. Zheng, Progress of a half century in the study of the Luria-Delbruck \ distribution, Math. Biosci. 162 (1999) 1-32. Q. Zheng, Statistical and algorithmic methods for fluctuation analysis with \ SALVADOR as an implementation, Math. Biosci. 176 (2002) 237-252. Q. Zheng, New algorithms for Luria-Delbruck fluctuation analysis, Math. \ Biosci. 196 (2005) 198-214. Q. Zheng, On Haldane's formulation of Luria and Delbruck's mutation model, \ Math. Biosci. 209 (2007) 500-513. Q. Zheng, On Bartlett's formulation of the Luria-Delbruck mutation model, \ Math. Biosci. 215 (2008) 48-54. Q. Zheng, A note on plating efficiency in fluctuation experiments, to appear \ in Math. Biosci. (2008a). Q. Zheng, On a limiting distribution derived from the Bartlett formulation of \ the Luria-Delbruck mutation model, preprint, (2008b).\ \>", "Text", CellChangeTimes->{{3.405797658006746*^9, 3.405797719540607*^9}, { 3.405797859009001*^9, 3.405797863469506*^9}, {3.410364063992406*^9, 3.410364144453671*^9}, 3.410370566618645*^9, {3.416337245552069*^9, 3.416337280394264*^9}, {3.416588734655744*^9, 3.416588778451216*^9}, { 3.4298796786479783`*^9, 3.429879758663091*^9}, {3.4298797924909997`*^9, 3.429879797100345*^9}, {3.429879857474959*^9, 3.42987985805308*^9}, 3.4298799005371833`*^9}] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"Presentation", WindowSize->{1159, 590}, WindowMargins->{{368, Automatic}, {Automatic, 21}}, DockedCells->(FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, Placeholder]}]& ), PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"Magnification"->1., "PaperOrientation"->"Portrait", "PaperSize"->{611.25, 789.5625}, "PostScriptOutputFile"->"u05/vancouver/good2.nb.ps"}, ShowSelection->True, FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (June 19, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "Info3430053780-3362690"->{ Cell[9196, 217, 271, 5, 59, "Print", CellTags->"Info3430053780-3362690"]}, "Info3430053780-4056072"->{ Cell[10600, 252, 281, 5, 59, "Print", CellTags->"Info3430053780-4056072"]}, "Info3430053780-3497384"->{ Cell[12007, 287, 525, 8, 114, "Print", CellTags->"Info3430053780-3497384"]}, "Info3430053781-8974776"->{ Cell[14311, 344, 534, 8, 109, "Print", CellTags->"Info3430053781-8974776"]}, "Info3430053781-3895988"->{ Cell[31010, 664, 294, 5, 61, "Print", CellTags->"Info3430053781-3895988"]}, "Info3430053781-6282249"->{ Cell[32892, 712, 366, 6, 77, "Print", CellTags->"Info3430053781-6282249"]}, "Info3430053781-9194219"->{ Cell[39989, 872, 544, 9, 131, "Print", CellTags->"Info3430053781-9194219"]}, "Info3430053781-6469246"->{ Cell[42205, 925, 422, 7, 94, "Print", CellTags->"Info3430053781-6469246"]}, "Info3430053782-2659468"->{ Cell[45738, 1010, 359, 6, 77, "Print", CellTags->"Info3430053782-2659468"]}, "Info3430053782-1486419"->{ Cell[49422, 1106, 240, 4, 58, "Print", CellTags->"Info3430053782-1486419"]}, "Info3430053782-9484289"->{ Cell[64481, 1398, 250, 5, 58, "Print", CellTags->"Info3430053782-9484289"]}, "Info3430053783-6762549"->{ Cell[67511, 1475, 498, 8, 109, "Print", CellTags->"Info3430053783-6762549"]}, "Info3430053784-9086444"->{ Cell[86479, 1833, 339, 6, 83, "Print", CellTags->"Info3430053784-9086444"]}, "Info3430053809-3357107"->{ Cell[90143, 1917, 263, 5, 58, "Print", CellTags->"Info3430053809-3357107"]}, "Info3430053810-4078900"->{ Cell[91791, 1958, 263, 5, 58, "Print", CellTags->"Info3430053810-4078900"]}, "Info3430053862-6070048"->{ Cell[127012, 2680, 246, 5, 60, "Print", CellTags->"Info3430053862-6070048"]}, "Info3430053862-5530159"->{ Cell[128494, 2719, 435, 7, 92, "Print", CellTags->"Info3430053862-5530159"]}, "Info3430053863-2140964"->{ Cell[144521, 3017, 350, 6, 77, "Print", CellTags->"Info3430053863-2140964"]}, "Info3430053863-2297694"->{ Cell[153252, 3185, 440, 7, 117, "Print", CellTags->"Info3430053863-2297694"]}, "Info3430053863-1206427"->{ Cell[167147, 3444, 381, 6, 100, "Print", CellTags->"Info3430053863-1206427"]}, "Info3430053863-9079730"->{ Cell[168725, 3483, 233, 4, 58, "Print", CellTags->"Info3430053863-9079730"]}, "Info3430053863-2784273"->{ Cell[171166, 3547, 309, 5, 75, "Print", CellTags->"Info3430053863-2784273"]}, "Info3430053864-7255033"->{ Cell[184873, 3836, 235, 4, 58, "Print", CellTags->"Info3430053864-7255033"]}, "Info3430053865-7732867"->{ Cell[197495, 4076, 239, 4, 58, "Print", CellTags->"Info3430053865-7732867"]}, "Info3430053865-5358891"->{ Cell[217681, 4434, 237, 4, 58, "Print", CellTags->"Info3430053865-5358891"]}, "Info3430053865-7117407"->{ Cell[219434, 4478, 357, 6, 78, "Print", CellTags->"Info3430053865-7117407"]}, "Info3430053866-2684086"->{ Cell[225661, 4612, 407, 7, 92, "Print", CellTags->"Info3430053866-2684086"]}, "Info3430053868-4904722"->{ Cell[264558, 5351, 349, 6, 78, "Print", CellTags->"Info3430053868-4904722"]}, "Info3430053869-6652240"->{ Cell[267217, 5409, 491, 8, 112, "Print", CellTags->"Info3430053869-6652240"]}, "Info3430053870-3381490"->{ Cell[279610, 5680, 301, 5, 76, "Print", CellTags->"Info3430053870-3381490"]}, "Info3430053870-9314038"->{ Cell[282210, 5736, 303, 5, 76, "Print", CellTags->"Info3430053870-9314038"]}, "Info3430053883-7446926"->{ Cell[330967, 6589, 278, 5, 58, "Print", CellTags->"Info3430053883-7446926"]}, "Info3430053883-4707819"->{ Cell[336770, 6722, 435, 7, 92, "Print", CellTags->"Info3430053883-4707819"]}, "Info3430053883-8977506"->{ Cell[340608, 6815, 357, 6, 92, "Print", CellTags->"Info3430053883-8977506"]}, "Info3430053883-5324659"->{ Cell[343284, 6881, 342, 6, 75, "Print", CellTags->"Info3430053883-5324659"]}, "Info3430053883-8973413"->{ Cell[349600, 7012, 375, 6, 92, "Print", CellTags->"Info3430053883-8973413"]}, "Info3430053884-3691012"->{ Cell[363622, 7289, 395, 7, 92, "Print", CellTags->"Info3430053884-3691012"]}, "Info3430053884-2702936"->{ Cell[367233, 7387, 291, 5, 58, "Print", CellTags->"Info3430053884-2702936"]}, "Info3430053884-2830503"->{ Cell[378931, 7625, 212, 4, 40, "Print", CellTags->"Info3430053884-2830503"]}, "Info3430053885-1891038"->{ Cell[395241, 7908, 235, 4, 58, "Print", CellTags->"Info3430053885-1891038"]} } *) (*CellTagsIndex CellTagsIndex->{ {"Info3430053780-3362690", 481444, 9468}, {"Info3430053780-4056072", 481553, 9471}, {"Info3430053780-3497384", 481663, 9474}, {"Info3430053781-8974776", 481774, 9477}, {"Info3430053781-3895988", 481885, 9480}, {"Info3430053781-6282249", 481995, 9483}, {"Info3430053781-9194219", 482105, 9486}, {"Info3430053781-6469246", 482216, 9489}, {"Info3430053782-2659468", 482326, 9492}, {"Info3430053782-1486419", 482437, 9495}, {"Info3430053782-9484289", 482548, 9498}, {"Info3430053783-6762549", 482659, 9501}, {"Info3430053784-9086444", 482771, 9504}, {"Info3430053809-3357107", 482882, 9507}, {"Info3430053810-4078900", 482993, 9510}, {"Info3430053862-6070048", 483104, 9513}, {"Info3430053862-5530159", 483216, 9516}, {"Info3430053863-2140964", 483328, 9519}, {"Info3430053863-2297694", 483440, 9522}, {"Info3430053863-1206427", 483553, 9525}, {"Info3430053863-9079730", 483666, 9528}, {"Info3430053863-2784273", 483778, 9531}, {"Info3430053864-7255033", 483890, 9534}, {"Info3430053865-7732867", 484002, 9537}, {"Info3430053865-5358891", 484114, 9540}, {"Info3430053865-7117407", 484226, 9543}, {"Info3430053866-2684086", 484338, 9546}, {"Info3430053868-4904722", 484450, 9549}, {"Info3430053869-6652240", 484562, 9552}, {"Info3430053870-3381490", 484675, 9555}, {"Info3430053870-9314038", 484787, 9558}, {"Info3430053883-7446926", 484899, 9561}, {"Info3430053883-4707819", 485011, 9564}, {"Info3430053883-8977506", 485123, 9567}, {"Info3430053883-5324659", 485235, 9570}, {"Info3430053883-8973413", 485347, 9573}, {"Info3430053884-3691012", 485459, 9576}, {"Info3430053884-2702936", 485571, 9579}, {"Info3430053884-2830503", 485683, 9582}, {"Info3430053885-1891038", 485795, 9585} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 250, 5, 59, "Title"], Cell[843, 30, 525, 13, 183, "Text"], Cell[CellGroupData[{ Cell[1393, 47, 31, 0, 77, "Section"], Cell[1427, 49, 2848, 44, 303, "Text"], Cell[CellGroupData[{ Cell[4300, 97, 394, 6, 36, "Input"], Cell[4697, 105, 919, 13, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5653, 123, 291, 4, 36, "Input"], Cell[5947, 129, 1058, 17, 36, "Output"] }, Open ]], Cell[7020, 149, 248, 5, 36, "Input"], Cell[7271, 156, 271, 6, 63, "Text"], Cell[7545, 164, 37, 0, 36, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[7619, 169, 44, 1, 67, "Section"], Cell[7666, 172, 1136, 26, 135, "Text"], Cell[8805, 200, 307, 10, 36, "Input"], Cell[CellGroupData[{ Cell[9137, 214, 56, 1, 36, "Input"], Cell[9196, 217, 271, 5, 59, "Print", CellTags->"Info3430053780-3362690"] }, Open ]], Cell[CellGroupData[{ Cell[9504, 227, 124, 2, 36, "Input"], Cell[9631, 231, 874, 13, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10542, 249, 55, 1, 36, "Input"], Cell[10600, 252, 281, 5, 59, "Print", CellTags->"Info3430053780-4056072"] }, Open ]], Cell[CellGroupData[{ Cell[10918, 262, 123, 2, 36, "Input"], Cell[11044, 266, 869, 13, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11950, 284, 54, 1, 36, "Input"], Cell[12007, 287, 525, 8, 114, "Print", CellTags->"Info3430053780-3497384"] }, Open ]], Cell[12547, 298, 85, 2, 39, "Text"], Cell[CellGroupData[{ Cell[12657, 304, 205, 5, 36, "Input"], Cell[12865, 311, 1109, 19, 36, "Output"] }, Open ]], Cell[13989, 333, 240, 4, 63, "Text"], Cell[CellGroupData[{ Cell[14254, 341, 54, 1, 36, "Input"], Cell[14311, 344, 534, 8, 109, "Print", CellTags->"Info3430053781-8974776"] }, Open ]], Cell[CellGroupData[{ Cell[14882, 357, 207, 4, 36, "Input"], Cell[CellGroupData[{ Cell[15114, 365, 1162, 19, 26, "Print"], Cell[16279, 386, 1162, 19, 26, "Print"], Cell[17444, 407, 1162, 19, 26, "Print"], Cell[18609, 428, 1162, 19, 26, "Print"], Cell[19774, 449, 1162, 19, 26, "Print"], Cell[20939, 470, 1162, 19, 26, "Print"], Cell[22104, 491, 1162, 19, 26, "Print"], Cell[23269, 512, 1162, 19, 26, "Print"], Cell[24434, 533, 1162, 19, 26, "Print"], Cell[25599, 554, 1162, 19, 26, "Print"], Cell[26764, 575, 1162, 19, 26, "Print"], Cell[27929, 596, 1162, 19, 26, "Print"] }, Open ]], Cell[29106, 618, 884, 13, 36, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[30039, 637, 57, 1, 67, "Section"], Cell[30099, 640, 830, 17, 135, "Text"], Cell[CellGroupData[{ Cell[30954, 661, 53, 1, 36, "Input"], Cell[31010, 664, 294, 5, 61, "Print", CellTags->"Info3430053781-3895988"] }, Open ]], Cell[CellGroupData[{ Cell[31341, 674, 90, 2, 36, "Input"], Cell[31434, 678, 1229, 21, 60, "Output"] }, Open ]], Cell[32678, 702, 138, 3, 39, "Text"], Cell[CellGroupData[{ Cell[32841, 709, 48, 1, 36, "Input"], Cell[32892, 712, 366, 6, 77, "Print", CellTags->"Info3430053781-6282249"] }, Open ]], Cell[CellGroupData[{ Cell[33295, 723, 236, 7, 36, "Input"], Cell[33534, 732, 1197, 20, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34768, 757, 212, 6, 36, "Input"], Cell[34983, 765, 1193, 20, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36213, 790, 392, 10, 36, "Input"], Cell[36608, 802, 3192, 58, 246, "Output"] }, Open ]], Cell[39815, 863, 99, 2, 39, "Text"], Cell[CellGroupData[{ Cell[39939, 869, 47, 1, 36, "Input"], Cell[39989, 872, 544, 9, 131, "Print", CellTags->"Info3430053781-9194219"] }, Open ]], Cell[CellGroupData[{ Cell[40570, 886, 96, 2, 36, "Input"], Cell[40669, 890, 1244, 21, 60, "Output"] }, Open ]], Cell[41928, 914, 198, 4, 63, "Text"], Cell[CellGroupData[{ Cell[42151, 922, 51, 1, 36, "Input"], Cell[42205, 925, 422, 7, 94, "Print", CellTags->"Info3430053781-6469246"] }, Open ]], Cell[CellGroupData[{ Cell[42664, 937, 100, 2, 36, "Input"], Cell[42767, 941, 1248, 21, 60, "Output"] }, Open ]], Cell[44030, 965, 112, 3, 39, "Text"], Cell[CellGroupData[{ Cell[44167, 972, 111, 2, 36, "Input"], Cell[44281, 976, 1240, 21, 60, "Output"] }, Open ]], Cell[45536, 1000, 122, 3, 39, "Text"], Cell[CellGroupData[{ Cell[45683, 1007, 52, 1, 36, "Input"], Cell[45738, 1010, 359, 6, 77, "Print", CellTags->"Info3430053782-2659468"] }, Open ]], Cell[CellGroupData[{ Cell[46134, 1021, 110, 2, 36, "Input"], Cell[46247, 1025, 1241, 21, 60, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[47537, 1052, 68, 1, 67, "Section"], Cell[47608, 1055, 725, 13, 113, "Text"], Cell[48336, 1070, 241, 8, 36, "Input"], Cell[48580, 1080, 93, 2, 39, "Text"], Cell[48676, 1084, 472, 9, 60, "Input"], Cell[49151, 1095, 192, 4, 63, "Text"], Cell[CellGroupData[{ Cell[49368, 1103, 51, 1, 36, "Input"], Cell[49422, 1106, 240, 4, 58, "Print", CellTags->"Info3430053782-1486419"] }, Open ]], Cell[CellGroupData[{ Cell[49699, 1115, 67, 1, 36, "Input"], Cell[49769, 1118, 870, 13, 36, "Output"] }, Open ]], Cell[50654, 1134, 230, 4, 63, "Text"], Cell[CellGroupData[{ Cell[50909, 1142, 34, 0, 36, "Input"], Cell[50946, 1144, 1155, 21, 41, "Output"] }, Open ]], Cell[52116, 1168, 324, 6, 63, "Text"], Cell[CellGroupData[{ Cell[52465, 1178, 67, 0, 36, "Input"], Cell[CellGroupData[{ Cell[52557, 1182, 858, 13, 26, "Print"], Cell[53418, 1197, 878, 13, 26, "Print"], Cell[54299, 1212, 873, 13, 26, "Print"], Cell[55175, 1227, 878, 13, 26, "Print"], Cell[56056, 1242, 876, 13, 26, "Print"], Cell[56935, 1257, 878, 13, 26, "Print"] }, Open ]], Cell[57828, 1273, 883, 13, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[58748, 1291, 68, 0, 36, "Input"], Cell[CellGroupData[{ Cell[58841, 1295, 857, 13, 26, "Print"], Cell[59701, 1310, 874, 13, 26, "Print"], Cell[60578, 1325, 876, 13, 26, "Print"], Cell[61457, 1340, 874, 13, 26, "Print"], Cell[62334, 1355, 874, 13, 26, "Print"] }, Open ]], Cell[63223, 1371, 878, 13, 36, "Output"] }, Open ]], Cell[64116, 1387, 312, 5, 63, "Text"], Cell[CellGroupData[{ Cell[64453, 1396, 25, 0, 36, "Input"], Cell[64481, 1398, 250, 5, 58, "Print", CellTags->"Info3430053782-9484289"] }, Open ]], Cell[CellGroupData[{ Cell[64768, 1408, 33, 0, 36, "Input"], Cell[64804, 1410, 914, 15, 36, "Output"] }, Open ]], Cell[65733, 1428, 68, 0, 39, "Text"], Cell[CellGroupData[{ Cell[65826, 1432, 33, 0, 36, "Input"], Cell[65862, 1434, 1161, 21, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[67072, 1461, 56, 0, 77, "Section"], Cell[67131, 1463, 322, 6, 63, "Text"], Cell[CellGroupData[{ Cell[67478, 1473, 30, 0, 36, "Input"], Cell[67511, 1475, 498, 8, 109, "Print", CellTags->"Info3430053783-6762549"] }, Open ]], Cell[68024, 1486, 93, 2, 39, "Text"], Cell[CellGroupData[{ Cell[68142, 1492, 38, 0, 36, "Input"], Cell[68183, 1494, 905, 15, 36, "Output"] }, Open ]], Cell[69103, 1512, 218, 4, 39, "Text"], Cell[CellGroupData[{ Cell[69346, 1520, 49, 0, 36, "Input"], Cell[69398, 1522, 915, 15, 36, "Output"] }, Open ]], Cell[70328, 1540, 68, 0, 39, "Text"], Cell[CellGroupData[{ Cell[70421, 1544, 38, 0, 36, "Input"], Cell[70462, 1546, 1321, 25, 66, "Output"] }, Open ]], Cell[71798, 1574, 699, 10, 111, "Text"], Cell[CellGroupData[{ Cell[72522, 1588, 104, 3, 36, "Input"], Cell[CellGroupData[{ Cell[72651, 1595, 860, 12, 26, "Print"], Cell[73514, 1609, 824, 12, 26, "Print"], Cell[74341, 1623, 841, 12, 26, "Print"], Cell[75185, 1637, 841, 12, 26, "Print"], Cell[76029, 1651, 841, 12, 26, "Print"], Cell[76873, 1665, 841, 12, 26, "Print"], Cell[77717, 1679, 843, 12, 26, "Print"], Cell[78563, 1693, 843, 12, 26, "Print"], Cell[79409, 1707, 862, 12, 26, "Print"], Cell[80274, 1721, 824, 12, 26, "Print"], Cell[81101, 1735, 841, 12, 26, "Print"], Cell[81945, 1749, 842, 12, 26, "Print"], Cell[82790, 1763, 842, 12, 26, "Print"], Cell[83635, 1777, 842, 12, 26, "Print"], Cell[84480, 1791, 842, 12, 26, "Print"] }, Open ]], Cell[85337, 1806, 923, 15, 36, "Output"] }, Open ]], Cell[86275, 1824, 146, 3, 39, "Text"], Cell[CellGroupData[{ Cell[86446, 1831, 30, 0, 36, "Input"], Cell[86479, 1833, 339, 6, 83, "Print", CellTags->"Info3430053784-9086444"] }, Open ]], Cell[CellGroupData[{ Cell[86855, 1844, 39, 0, 36, "Input"], Cell[86897, 1846, 858, 12, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[87792, 1863, 46, 0, 36, "Input"], Cell[87841, 1865, 852, 12, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88730, 1882, 75, 0, 36, "Input"], Cell[88808, 1884, 918, 15, 36, "Output"] }, Open ]], Cell[89741, 1902, 113, 3, 39, "Text"], Cell[89857, 1907, 224, 4, 63, "Text"], Cell[CellGroupData[{ Cell[90106, 1915, 34, 0, 36, "Input"], Cell[90143, 1917, 263, 5, 58, "Print", CellTags->"Info3430053809-3357107"] }, Open ]], Cell[CellGroupData[{ Cell[90443, 1927, 42, 0, 36, "Input"], Cell[90488, 1929, 912, 15, 36, "Output"] }, Open ]], Cell[91415, 1947, 314, 5, 63, "Text"], Cell[CellGroupData[{ Cell[91754, 1956, 34, 0, 36, "Input"], Cell[91791, 1958, 263, 5, 58, "Print", CellTags->"Info3430053810-4078900"] }, Open ]], Cell[CellGroupData[{ Cell[92091, 1968, 47, 0, 36, "Input"], Cell[92141, 1970, 917, 15, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93095, 1990, 59, 0, 36, "Input"], Cell[93157, 1992, 1094, 21, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94288, 2018, 63, 0, 36, "Input"], Cell[94354, 2020, 1048, 19, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[95439, 2044, 70, 0, 36, "Input"], Cell[95512, 2046, 909, 15, 36, "Output"] }, Open ]], Cell[96436, 2064, 113, 3, 39, "Text"], Cell[96552, 2069, 68, 0, 39, "Text"], Cell[CellGroupData[{ Cell[96645, 2073, 54, 0, 36, "Input"], Cell[96702, 2075, 924, 15, 36, "Output"] }, Open ]], Cell[97641, 2093, 112, 3, 39, "Text"], Cell[CellGroupData[{ Cell[97778, 2100, 42, 0, 36, "Input"], Cell[97823, 2102, 917, 15, 36, "Output"] }, Open ]], Cell[98755, 2120, 114, 3, 39, "Text"], Cell[98872, 2125, 132, 3, 39, "Text"], Cell[CellGroupData[{ Cell[99029, 2132, 42, 0, 36, "Input"], Cell[99074, 2134, 1492, 30, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[100603, 2169, 111, 3, 36, "Input"], Cell[CellGroupData[{ Cell[100739, 2176, 866, 12, 26, "Print"], Cell[101608, 2190, 895, 14, 26, "Print"], Cell[102506, 2206, 915, 15, 26, "Print"], Cell[103424, 2223, 912, 15, 26, "Print"], Cell[104339, 2240, 914, 15, 26, "Print"], Cell[105256, 2257, 912, 15, 26, "Print"], Cell[106171, 2274, 910, 14, 26, "Print"], Cell[107084, 2290, 914, 15, 26, "Print"], Cell[108001, 2307, 909, 14, 26, "Print"], Cell[108913, 2323, 868, 12, 26, "Print"], Cell[109784, 2337, 898, 14, 26, "Print"], Cell[110685, 2353, 911, 14, 26, "Print"], Cell[111599, 2369, 909, 14, 26, "Print"], Cell[112511, 2385, 911, 15, 26, "Print"], Cell[113425, 2402, 915, 15, 26, "Print"], Cell[114343, 2419, 909, 14, 26, "Print"] }, Open ]], Cell[115267, 2436, 912, 15, 36, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[116228, 2457, 61, 0, 77, "Section"], Cell[116292, 2459, 2106, 44, 135, "Text"], Cell[CellGroupData[{ Cell[118423, 2507, 85, 2, 36, "Input"], Cell[118511, 2511, 1375, 23, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[119923, 2539, 68, 0, 36, "Input"], Cell[CellGroupData[{ Cell[120016, 2543, 853, 13, 26, "Print"], Cell[120872, 2558, 871, 13, 26, "Print"], Cell[121746, 2573, 869, 13, 26, "Print"], Cell[122618, 2588, 869, 13, 26, "Print"], Cell[123490, 2603, 871, 13, 26, "Print"], Cell[124364, 2618, 868, 13, 26, "Print"] }, Open ]], Cell[125247, 2634, 863, 13, 36, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[126159, 2653, 64, 1, 67, "Section"], Cell[126226, 2656, 546, 9, 87, "Text"], Cell[126775, 2667, 156, 6, 39, "Text"], Cell[CellGroupData[{ Cell[126956, 2677, 53, 1, 36, "Input"], Cell[127012, 2680, 246, 5, 60, "Print", CellTags->"Info3430053862-6070048"] }, Open ]], Cell[CellGroupData[{ Cell[127295, 2690, 69, 1, 36, "Input"], Cell[127367, 2693, 891, 13, 26, "Print"] }, Open ]], Cell[128273, 2709, 137, 3, 39, "Text"], Cell[CellGroupData[{ Cell[128435, 2716, 56, 1, 36, "Input"], Cell[128494, 2719, 435, 7, 92, "Print", CellTags->"Info3430053862-5530159"] }, Open ]], Cell[CellGroupData[{ Cell[128966, 2731, 72, 1, 36, "Input"], Cell[129041, 2734, 1108, 19, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[130186, 2758, 141, 3, 36, "Input"], Cell[CellGroupData[{ Cell[130352, 2765, 834, 12, 26, "Print"], Cell[131189, 2779, 850, 12, 26, "Print"], Cell[132042, 2793, 850, 12, 26, "Print"], Cell[132895, 2807, 850, 12, 26, "Print"], Cell[133748, 2821, 850, 12, 26, "Print"], Cell[134601, 2835, 850, 12, 26, "Print"], Cell[135454, 2849, 850, 12, 26, "Print"] }, Open ]], Cell[136319, 2864, 853, 12, 36, "Output"] }, Open ]], Cell[137187, 2879, 82, 2, 39, "Text"], Cell[CellGroupData[{ Cell[137294, 2885, 193, 4, 36, "Input"], Cell[CellGroupData[{ Cell[137512, 2893, 827, 12, 26, "Print"], Cell[138342, 2907, 843, 12, 26, "Print"], Cell[139188, 2921, 843, 12, 26, "Print"], Cell[140034, 2935, 843, 12, 26, "Print"], Cell[140880, 2949, 841, 12, 26, "Print"], Cell[141724, 2963, 842, 12, 26, "Print"], Cell[142569, 2977, 843, 12, 26, "Print"] }, Open ]], Cell[143427, 2992, 852, 12, 36, "Output"] }, Open ]], Cell[144294, 3007, 145, 3, 39, "Text"], Cell[CellGroupData[{ Cell[144464, 3014, 54, 1, 36, "Input"], Cell[144521, 3017, 350, 6, 77, "Print", CellTags->"Info3430053863-2140964"] }, Open ]], Cell[CellGroupData[{ Cell[144908, 3028, 70, 1, 36, "Input"], Cell[144981, 3031, 1069, 18, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[146087, 3054, 139, 3, 36, "Input"], Cell[CellGroupData[{ Cell[146251, 3061, 832, 12, 26, "Print"], Cell[147086, 3075, 833, 12, 26, "Print"], Cell[147922, 3089, 848, 12, 26, "Print"], Cell[148773, 3103, 848, 12, 26, "Print"], Cell[149624, 3117, 848, 12, 26, "Print"], Cell[150475, 3131, 848, 12, 26, "Print"], Cell[151326, 3145, 850, 12, 26, "Print"] }, Open ]], Cell[152191, 3160, 851, 12, 36, "Output"] }, Open ]], Cell[153057, 3175, 109, 3, 39, "Text"], Cell[CellGroupData[{ Cell[153191, 3182, 58, 1, 36, "Input"], Cell[153252, 3185, 440, 7, 117, "Print", CellTags->"Info3430053863-2297694"] }, Open ]], Cell[CellGroupData[{ Cell[153729, 3197, 148, 3, 36, "Input"], Cell[CellGroupData[{ Cell[153902, 3204, 831, 12, 26, "Print"], Cell[154736, 3218, 846, 12, 26, "Print"], Cell[155585, 3232, 847, 12, 26, "Print"], Cell[156435, 3246, 847, 12, 26, "Print"], Cell[157285, 3260, 847, 12, 26, "Print"], Cell[158135, 3274, 847, 12, 26, "Print"] }, Open ]], Cell[158997, 3289, 855, 12, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[159889, 3306, 90, 2, 36, "Input"], Cell[159982, 3310, 827, 12, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[160846, 3327, 144, 3, 36, "Input"], Cell[CellGroupData[{ Cell[161015, 3334, 824, 12, 26, "Print"], Cell[161842, 3348, 839, 12, 26, "Print"], Cell[162684, 3362, 843, 12, 26, "Print"], Cell[163530, 3376, 843, 12, 26, "Print"], Cell[164376, 3390, 843, 12, 26, "Print"], Cell[165222, 3404, 843, 12, 26, "Print"] }, Open ]], Cell[166080, 3419, 841, 12, 36, "Output"] }, Open ]], Cell[166936, 3434, 133, 3, 39, "Text"], Cell[CellGroupData[{ Cell[167094, 3441, 50, 1, 36, "Input"], Cell[167147, 3444, 381, 6, 100, "Print", CellTags->"Info3430053863-1206427"] }, Open ]], Cell[CellGroupData[{ Cell[167565, 3455, 66, 1, 36, "Input"], Cell[167634, 3458, 847, 12, 36, "Output"] }, Open ]], Cell[168496, 3473, 147, 3, 39, "Text"], Cell[CellGroupData[{ Cell[168668, 3480, 54, 1, 36, "Input"], Cell[168725, 3483, 233, 4, 58, "Print", CellTags->"Info3430053863-9079730"] }, Open ]], Cell[CellGroupData[{ Cell[168995, 3492, 46, 3, 54, "Input"], Cell[169044, 3497, 847, 12, 36, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[169940, 3515, 40, 0, 77, "Section"], Cell[169983, 3517, 1101, 23, 159, "Text"], Cell[CellGroupData[{ Cell[171109, 3544, 54, 1, 36, "Input"], Cell[171166, 3547, 309, 5, 75, "Print", CellTags->"Info3430053863-2784273"] }, Open ]], Cell[CellGroupData[{ Cell[171512, 3557, 208, 4, 36, "Input"], Cell[CellGroupData[{ Cell[171745, 3565, 942, 16, 26, "Print"], Cell[172690, 3583, 942, 16, 26, "Print"], Cell[173635, 3601, 942, 16, 26, "Print"], Cell[174580, 3619, 944, 16, 26, "Print"], Cell[175527, 3637, 944, 16, 26, "Print"], Cell[176474, 3655, 944, 16, 26, "Print"], Cell[177421, 3673, 946, 16, 26, "Print"], Cell[178370, 3691, 946, 16, 26, "Print"] }, Open ]], Cell[179331, 3710, 884, 13, 36, "Output"] }, Open ]], Cell[180230, 3726, 163, 3, 39, "Text"], Cell[CellGroupData[{ Cell[180418, 3733, 417, 9, 36, "Input"], Cell[180838, 3744, 1765, 27, 60, "Output"] }, Open ]], Cell[182618, 3774, 535, 15, 63, "Text"], Cell[CellGroupData[{ Cell[183178, 3793, 340, 9, 36, "Input"], Cell[183521, 3804, 969, 16, 36, "Output"] }, Open ]], Cell[184505, 3823, 284, 6, 39, "Text"], Cell[CellGroupData[{ Cell[184814, 3833, 56, 1, 36, "Input"], Cell[184873, 3836, 235, 4, 58, "Print", CellTags->"Info3430053864-7255033"] }, Open ]], Cell[CellGroupData[{ Cell[185145, 3845, 320, 6, 36, "Input"], Cell[CellGroupData[{ Cell[185490, 3855, 949, 14, 26, "Print"], Cell[186442, 3871, 949, 14, 26, "Print"], Cell[187394, 3887, 948, 14, 26, "Print"], Cell[188345, 3903, 946, 14, 26, "Print"], Cell[189294, 3919, 946, 14, 26, "Print"], Cell[190243, 3935, 944, 14, 26, "Print"] }, Open ]], Cell[191202, 3952, 807, 12, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[192046, 3969, 322, 6, 36, "Input"], Cell[CellGroupData[{ Cell[192393, 3979, 689, 10, 26, "Print"], Cell[193085, 3991, 687, 10, 26, "Print"], Cell[193775, 4003, 688, 10, 26, "Print"], Cell[194466, 4015, 685, 10, 26, "Print"], Cell[195154, 4027, 688, 10, 26, "Print"], Cell[195845, 4039, 686, 10, 26, "Print"] }, Open ]], Cell[196546, 4052, 687, 10, 36, "Output"] }, Open ]], Cell[197248, 4065, 167, 4, 39, "Text"], Cell[CellGroupData[{ Cell[197440, 4073, 52, 1, 36, "Input"], Cell[197495, 4076, 239, 4, 58, "Print", CellTags->"Info3430053865-7732867"] }, Open ]], Cell[CellGroupData[{ Cell[197771, 4085, 365, 7, 36, "Input"], Cell[CellGroupData[{ Cell[198161, 4096, 971, 14, 26, "Print"], Cell[199135, 4112, 947, 14, 26, "Print"], Cell[200085, 4128, 947, 14, 26, "Print"], Cell[201035, 4144, 946, 14, 26, "Print"], Cell[201984, 4160, 944, 14, 26, "Print"], Cell[202931, 4176, 944, 14, 26, "Print"], Cell[203878, 4192, 943, 14, 26, "Print"], Cell[204824, 4208, 965, 14, 26, "Print"], Cell[205792, 4224, 945, 14, 26, "Print"], Cell[206740, 4240, 945, 14, 26, "Print"], Cell[207688, 4256, 944, 14, 26, "Print"], Cell[208635, 4272, 944, 14, 26, "Print"], Cell[209582, 4288, 947, 14, 26, "Print"], Cell[210532, 4304, 968, 14, 26, "Print"], Cell[211503, 4320, 944, 14, 26, "Print"], Cell[212450, 4336, 944, 14, 26, "Print"], Cell[213397, 4352, 944, 14, 26, "Print"], Cell[214344, 4368, 944, 14, 26, "Print"], Cell[215291, 4384, 944, 14, 26, "Print"] }, Open ]], Cell[216250, 4401, 1014, 17, 36, "Output"] }, Open ]], Cell[217279, 4421, 258, 5, 39, "Text"], Cell[CellGroupData[{ Cell[217562, 4430, 116, 2, 36, "Input"], Cell[217681, 4434, 237, 4, 58, "Print", CellTags->"Info3430053865-5358891"] }, Open ]], Cell[CellGroupData[{ Cell[217955, 4443, 260, 5, 36, "Input"], Cell[218218, 4450, 947, 14, 36, "Output"] }, Open ]], Cell[219180, 4467, 173, 4, 39, "Text"], Cell[CellGroupData[{ Cell[219378, 4475, 53, 1, 36, "Input"], Cell[219434, 4478, 357, 6, 78, "Print", CellTags->"Info3430053865-7117407"] }, Open ]], Cell[219806, 4487, 227, 6, 36, "Input"], Cell[CellGroupData[{ Cell[220058, 4497, 265, 6, 36, "Input"], Cell[220326, 4505, 4042, 70, 238, "Output"] }, Open ]], Cell[224383, 4578, 172, 4, 39, "Text"], Cell[CellGroupData[{ Cell[224580, 4586, 102, 3, 36, "Input"], Cell[224685, 4591, 877, 13, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[225599, 4609, 59, 1, 36, "Input"], Cell[225661, 4612, 407, 7, 92, "Print", CellTags->"Info3430053866-2684086"] }, Open ]], Cell[CellGroupData[{ Cell[226105, 4624, 121, 3, 36, "Input"], Cell[226229, 4629, 876, 13, 36, "Output"] }, Open ]], Cell[227120, 4645, 303, 5, 63, "Text"], Cell[CellGroupData[{ Cell[227448, 4654, 96, 2, 36, "Input"], Cell[227547, 4658, 867, 13, 36, "Output"] }, Open ]], Cell[228429, 4674, 155, 3, 39, "Text"], Cell[228587, 4679, 146, 4, 36, "Input"], Cell[CellGroupData[{ Cell[228758, 4687, 383, 9, 36, "Input"], Cell[229144, 4698, 3911, 68, 240, "Output"] }, Open ]], Cell[233070, 4769, 57, 0, 39, "Text"], Cell[CellGroupData[{ Cell[233152, 4773, 282, 7, 36, "Input"], Cell[233437, 4782, 6992, 121, 247, "Output"] }, Open ]], Cell[240444, 4906, 160, 3, 39, "Text"], Cell[CellGroupData[{ Cell[240629, 4913, 276, 9, 60, "Input"], Cell[240908, 4924, 869, 13, 36, "Output"] }, Open ]], Cell[241792, 4940, 265, 5, 39, "Text"], Cell[CellGroupData[{ Cell[242082, 4949, 291, 6, 36, "Input"], Cell[CellGroupData[{ Cell[242398, 4959, 551, 8, 28, "Print"], Cell[242952, 4969, 553, 8, 28, "Print"], Cell[243508, 4979, 553, 8, 28, "Print"], Cell[244064, 4989, 553, 8, 28, "Print"], Cell[244620, 4999, 551, 8, 28, "Print"] }, Open ]], Cell[245186, 5010, 555, 8, 38, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[245778, 5023, 227, 5, 36, "Input"], Cell[CellGroupData[{ Cell[246030, 5032, 921, 13, 26, "Print"], Cell[246954, 5047, 897, 13, 28, "Print"], Cell[247854, 5062, 895, 13, 28, "Print"], Cell[248752, 5077, 895, 13, 28, "Print"], Cell[249650, 5092, 897, 13, 28, "Print"], Cell[250550, 5107, 895, 13, 28, "Print"], Cell[251448, 5122, 915, 13, 26, "Print"], Cell[252366, 5137, 897, 13, 28, "Print"], Cell[253266, 5152, 895, 13, 28, "Print"], Cell[254164, 5167, 895, 13, 28, "Print"], Cell[255062, 5182, 898, 13, 28, "Print"], Cell[255963, 5197, 897, 13, 28, "Print"], Cell[256863, 5212, 918, 13, 26, "Print"], Cell[257784, 5227, 897, 13, 28, "Print"], Cell[258684, 5242, 896, 13, 28, "Print"], Cell[259583, 5257, 897, 13, 28, "Print"], Cell[260483, 5272, 896, 13, 28, "Print"], Cell[261382, 5287, 893, 13, 28, "Print"] }, Open ]], Cell[262290, 5303, 968, 16, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[263307, 5325, 155, 2, 77, "Section"], Cell[263465, 5329, 1011, 15, 87, "Text"], Cell[CellGroupData[{ Cell[264501, 5348, 54, 1, 36, "Input"], Cell[264558, 5351, 349, 6, 78, "Print", CellTags->"Info3430053868-4904722"] }, Open ]], Cell[CellGroupData[{ Cell[264944, 5362, 108, 2, 36, "Input"], Cell[265055, 5366, 1830, 29, 60, "Output"] }, Open ]], Cell[266900, 5398, 166, 3, 39, "Text"], Cell[CellGroupData[{ Cell[267091, 5405, 123, 2, 36, "Input"], Cell[267217, 5409, 491, 8, 112, "Print", CellTags->"Info3430053869-6652240"] }, Open ]], Cell[CellGroupData[{ Cell[267745, 5422, 337, 6, 36, "Input"], Cell[268085, 5430, 590, 8, 26, "Print"], Cell[268678, 5440, 558, 10, 36, "Output"] }, Open ]], Cell[269251, 5453, 205, 4, 39, "Text"], Cell[CellGroupData[{ Cell[269481, 5461, 396, 9, 36, "Input"], Cell[269880, 5472, 2814, 64, 83, "Output"] }, Open ]], Cell[272709, 5539, 316, 4, 39, "Text"], Cell[CellGroupData[{ Cell[273050, 5547, 197, 4, 36, "Input"], Cell[273250, 5553, 1420, 20, 36, "Output"] }, Open ]], Cell[274685, 5576, 505, 8, 39, "Text"], Cell[CellGroupData[{ Cell[275215, 5588, 286, 8, 36, "Input"], Cell[275504, 5598, 1723, 27, 36, "Output"] }, Open ]], Cell[277242, 5628, 259, 3, 39, "Text"], Cell[CellGroupData[{ Cell[277526, 5635, 247, 7, 36, "Input"], Cell[277776, 5644, 1410, 20, 36, "Output"] }, Open ]], Cell[279201, 5667, 324, 6, 39, "Text"], Cell[CellGroupData[{ Cell[279550, 5677, 57, 1, 36, "Input"], Cell[279610, 5680, 301, 5, 76, "Print", CellTags->"Info3430053870-3381490"] }, Open ]], Cell[CellGroupData[{ Cell[279948, 5690, 355, 6, 36, "Input"], Cell[280306, 5698, 1589, 23, 36, "Output"] }, Open ]], Cell[281910, 5724, 219, 5, 39, "Text"], Cell[CellGroupData[{ Cell[282154, 5733, 53, 1, 36, "Input"], Cell[282210, 5736, 303, 5, 76, "Print", CellTags->"Info3430053870-9314038"] }, Open ]], Cell[CellGroupData[{ Cell[282550, 5746, 249, 5, 36, "Input"], Cell[282802, 5753, 1486, 23, 36, "Output"] }, Open ]], Cell[284303, 5779, 175, 4, 39, "Text"], Cell[284481, 5785, 472, 9, 60, "Input"], Cell[CellGroupData[{ Cell[284978, 5798, 180, 6, 36, "Input"], Cell[285161, 5806, 1321, 19, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[286519, 5830, 165, 3, 36, "Input"], Cell[CellGroupData[{ Cell[286709, 5837, 1333, 19, 28, "Print"], Cell[288045, 5858, 1336, 19, 28, "Print"], Cell[289384, 5879, 1333, 19, 28, "Print"], Cell[290720, 5900, 1335, 19, 28, "Print"], Cell[292058, 5921, 1336, 19, 28, "Print"], Cell[293397, 5942, 1335, 19, 28, "Print"] }, Open ]], Cell[294747, 5964, 1333, 19, 38, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[296117, 5988, 161, 3, 36, "Input"], Cell[CellGroupData[{ Cell[296303, 5995, 1327, 19, 26, "Print"], Cell[297633, 6016, 1320, 19, 28, "Print"], Cell[298956, 6037, 1324, 19, 28, "Print"], Cell[300283, 6058, 1323, 19, 28, "Print"], Cell[301609, 6079, 1320, 19, 28, "Print"], Cell[302932, 6100, 1322, 19, 28, "Print"], Cell[304257, 6121, 1321, 19, 28, "Print"], Cell[305581, 6142, 1338, 19, 26, "Print"], Cell[306922, 6163, 1321, 19, 28, "Print"], Cell[308246, 6184, 1323, 19, 28, "Print"], Cell[309572, 6205, 1324, 19, 28, "Print"], Cell[310899, 6226, 1321, 19, 28, "Print"], Cell[312223, 6247, 1323, 19, 28, "Print"], Cell[313549, 6268, 1321, 19, 28, "Print"], Cell[314873, 6289, 1324, 19, 28, "Print"], Cell[316200, 6310, 1338, 19, 26, "Print"], Cell[317541, 6331, 1323, 19, 28, "Print"], Cell[318867, 6352, 1321, 19, 28, "Print"], Cell[320191, 6373, 1321, 19, 28, "Print"], Cell[321515, 6394, 1321, 19, 28, "Print"], Cell[322839, 6415, 1323, 19, 28, "Print"] }, Open ]], Cell[324177, 6437, 1395, 22, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[325621, 6465, 103, 1, 77, "Section"], Cell[325727, 6468, 777, 12, 87, "Text"], Cell[CellGroupData[{ Cell[326529, 6484, 217, 4, 36, "Input"], Cell[326749, 6490, 708, 10, 36, "Output"] }, Open ]], Cell[327472, 6503, 133, 1, 39, "Text"], Cell[CellGroupData[{ Cell[327630, 6508, 365, 7, 36, "Input"], Cell[327998, 6517, 981, 16, 36, "Output"] }, Open ]], Cell[328994, 6536, 374, 12, 39, "Text"], Cell[CellGroupData[{ Cell[329393, 6552, 196, 5, 36, "Input"], Cell[329592, 6559, 749, 11, 38, "Output"] }, Open ]], Cell[330356, 6573, 528, 9, 63, "Text"], Cell[CellGroupData[{ Cell[330909, 6586, 55, 1, 36, "Input"], Cell[330967, 6589, 278, 5, 58, "Print", CellTags->"Info3430053883-7446926"] }, Open ]], Cell[331260, 6597, 132, 3, 39, "Text"], Cell[CellGroupData[{ Cell[331417, 6604, 246, 7, 36, "Input"], Cell[331666, 6613, 942, 16, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[332645, 6634, 442, 11, 36, "Input"], Cell[333090, 6647, 3130, 56, 243, "Output"] }, Open ]], Cell[336235, 6706, 451, 9, 87, "Text"], Cell[CellGroupData[{ Cell[336711, 6719, 56, 1, 36, "Input"], Cell[336770, 6722, 435, 7, 92, "Print", CellTags->"Info3430053883-4707819"] }, Open ]], Cell[CellGroupData[{ Cell[337242, 6734, 72, 1, 36, "Input"], Cell[337317, 6737, 1013, 18, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[338367, 6760, 258, 5, 36, "Input"], Cell[338628, 6767, 814, 12, 36, "Output"] }, Open ]], Cell[339457, 6782, 105, 1, 39, "Text"], Cell[CellGroupData[{ Cell[339587, 6787, 145, 3, 36, "Input"], Cell[339735, 6792, 599, 9, 38, "Output"] }, Open ]], Cell[340349, 6804, 179, 4, 39, "Text"], Cell[CellGroupData[{ Cell[340553, 6812, 52, 1, 36, "Input"], Cell[340608, 6815, 357, 6, 92, "Print", CellTags->"Info3430053883-8977506"] }, Open ]], Cell[CellGroupData[{ Cell[341002, 6826, 230, 5, 36, "Input"], Cell[341235, 6833, 835, 12, 36, "Output"] }, Open ]], Cell[342085, 6848, 109, 1, 39, "Text"], Cell[CellGroupData[{ Cell[342219, 6853, 145, 3, 36, "Input"], Cell[342367, 6858, 604, 9, 38, "Output"] }, Open ]], Cell[342986, 6870, 212, 4, 39, "Text"], Cell[CellGroupData[{ Cell[343223, 6878, 58, 1, 36, "Input"], Cell[343284, 6881, 342, 6, 75, "Print", CellTags->"Info3430053883-5324659"] }, Open ]], Cell[CellGroupData[{ Cell[343663, 6892, 245, 5, 36, "Input"], Cell[CellGroupData[{ Cell[343933, 6901, 741, 11, 26, "Print"], Cell[344677, 6914, 741, 11, 26, "Print"], Cell[345421, 6927, 740, 11, 26, "Print"], Cell[346164, 6940, 741, 11, 26, "Print"], Cell[346908, 6953, 740, 11, 26, "Print"] }, Open ]], Cell[347663, 6967, 744, 11, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[348444, 6983, 143, 3, 36, "Input"], Cell[348590, 6988, 748, 11, 38, "Output"] }, Open ]], Cell[349353, 7002, 165, 3, 39, "Text"], Cell[CellGroupData[{ Cell[349543, 7009, 54, 1, 36, "Input"], Cell[349600, 7012, 375, 6, 92, "Print", CellTags->"Info3430053883-8973413"] }, Open ]], Cell[CellGroupData[{ Cell[350012, 7023, 70, 1, 36, "Input"], Cell[350085, 7026, 1152, 22, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[351274, 7053, 242, 5, 36, "Input"], Cell[CellGroupData[{ Cell[351541, 7062, 762, 11, 26, "Print"], Cell[352306, 7075, 744, 11, 26, "Print"], Cell[353053, 7088, 744, 11, 26, "Print"], Cell[353800, 7101, 744, 11, 26, "Print"], Cell[354547, 7114, 744, 11, 26, "Print"], Cell[355294, 7127, 744, 11, 26, "Print"], Cell[356041, 7140, 742, 11, 26, "Print"], Cell[356786, 7153, 760, 11, 26, "Print"], Cell[357549, 7166, 742, 11, 26, "Print"], Cell[358294, 7179, 741, 11, 26, "Print"], Cell[359038, 7192, 744, 11, 26, "Print"], Cell[359785, 7205, 744, 11, 26, "Print"], Cell[360532, 7218, 743, 11, 26, "Print"] }, Open ]], Cell[361290, 7232, 804, 14, 36, "Output"] }, Open ]], Cell[362109, 7249, 174, 2, 39, "Text"], Cell[CellGroupData[{ Cell[362308, 7255, 145, 3, 36, "Input"], Cell[362456, 7260, 807, 14, 41, "Output"] }, Open ]], Cell[363278, 7277, 255, 5, 39, "Text"], Cell[CellGroupData[{ Cell[363558, 7286, 61, 1, 36, "Input"], Cell[363622, 7289, 395, 7, 92, "Print", CellTags->"Info3430053884-3691012"] }, Open ]], Cell[CellGroupData[{ Cell[364054, 7301, 168, 3, 36, "Input"], Cell[364225, 7306, 463, 7, 50, "Print"] }, Open ]], Cell[CellGroupData[{ Cell[364725, 7318, 209, 4, 36, "Input"], Cell[364937, 7324, 491, 7, 69, "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[365477, 7337, 246, 3, 77, "Section"], Cell[365726, 7342, 1359, 37, 116, "Text"], Cell[CellGroupData[{ Cell[367110, 7383, 120, 2, 36, "Input"], Cell[367233, 7387, 291, 5, 58, "Print", CellTags->"Info3430053884-2702936"] }, Open ]], Cell[CellGroupData[{ Cell[367561, 7397, 359, 9, 36, "Input"], Cell[367923, 7408, 840, 14, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[368800, 7427, 292, 6, 36, "Input"], Cell[369095, 7435, 2448, 44, 242, "Output"] }, Open ]], Cell[371558, 7482, 393, 11, 39, "Text"], Cell[371954, 7495, 682, 12, 60, "Input"], Cell[372639, 7509, 286, 6, 39, "Text"], Cell[CellGroupData[{ Cell[372950, 7519, 426, 7, 36, "Input"], Cell[CellGroupData[{ Cell[373403, 7531, 905, 12, 26, "Print"], Cell[374311, 7545, 905, 12, 26, "Print"], Cell[375219, 7559, 905, 12, 26, "Print"], Cell[376127, 7573, 902, 12, 26, "Print"], Cell[377032, 7587, 903, 12, 26, "Print"] }, Open ]], Cell[377950, 7602, 661, 9, 36, "Output"] }, Open ]], Cell[378626, 7614, 158, 3, 39, "Text"], Cell[CellGroupData[{ Cell[378809, 7621, 119, 2, 36, "Input"], Cell[378931, 7625, 212, 4, 40, "Print", CellTags->"Info3430053884-2830503"] }, Open ]], Cell[CellGroupData[{ Cell[379180, 7634, 323, 6, 36, "Input"], Cell[CellGroupData[{ Cell[379528, 7644, 766, 10, 26, "Print"], Cell[380297, 7656, 752, 10, 26, "Print"], Cell[381052, 7668, 752, 10, 26, "Print"], Cell[381807, 7680, 752, 10, 26, "Print"], Cell[382562, 7692, 751, 10, 26, "Print"], Cell[383316, 7704, 750, 10, 26, "Print"], Cell[384069, 7716, 768, 10, 26, "Print"], Cell[384840, 7728, 752, 10, 26, "Print"], Cell[385595, 7740, 750, 10, 26, "Print"], Cell[386348, 7752, 750, 10, 26, "Print"], Cell[387101, 7764, 750, 10, 26, "Print"], Cell[387854, 7776, 752, 10, 26, "Print"], Cell[388609, 7788, 749, 10, 26, "Print"], Cell[389361, 7800, 768, 10, 26, "Print"], Cell[390132, 7812, 751, 10, 26, "Print"], Cell[390886, 7824, 752, 10, 26, "Print"], Cell[391641, 7836, 750, 10, 26, "Print"], Cell[392394, 7848, 750, 10, 26, "Print"], Cell[393147, 7860, 750, 10, 26, "Print"] }, Open ]], Cell[393912, 7873, 861, 14, 36, "Output"] }, Open ]], Cell[394788, 7890, 306, 10, 39, "Text"], Cell[CellGroupData[{ Cell[395119, 7904, 119, 2, 36, "Input"], Cell[395241, 7908, 235, 4, 58, "Print", CellTags->"Info3430053885-1891038"] }, Open ]], Cell[CellGroupData[{ Cell[395513, 7917, 264, 5, 36, "Input"], Cell[395780, 7924, 797, 11, 36, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[396626, 7941, 105, 1, 77, "Section"], Cell[396734, 7944, 147, 3, 39, "Text"], Cell[396884, 7949, 2441, 32, 36, "Input"], Cell[399328, 7983, 112, 3, 39, "Text"], Cell[CellGroupData[{ Cell[399465, 7990, 30, 0, 36, "Input"], Cell[399498, 7992, 854, 12, 36, "Output"] }, Open ]], Cell[400367, 8007, 137, 3, 39, "Text"], Cell[CellGroupData[{ Cell[400529, 8014, 43, 0, 36, "Input"], Cell[400575, 8016, 12128, 204, 246, "Output"] }, Open ]], Cell[412718, 8223, 108, 3, 39, "Text"], Cell[CellGroupData[{ Cell[412851, 8230, 29, 0, 36, "Input"], Cell[412883, 8232, 916, 15, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[413836, 8252, 68, 0, 36, "Input"], Cell[413907, 8254, 12239, 205, 246, "Output"] }, Open ]], Cell[426161, 8462, 113, 3, 39, "Text"], Cell[CellGroupData[{ Cell[426299, 8469, 33, 0, 36, "Input"], Cell[426335, 8471, 1589, 33, 60, "Output"] }, Open ]], Cell[427939, 8507, 422, 7, 63, "Text"], Cell[CellGroupData[{ Cell[428386, 8518, 153, 3, 36, "Input"], Cell[428542, 8523, 12139, 204, 246, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[440718, 8732, 145, 4, 36, "Input"], Cell[440866, 8738, 12212, 205, 246, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[453115, 8948, 116, 3, 36, "Input"], Cell[453234, 8953, 23486, 393, 253, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[476769, 9352, 29, 0, 77, "Section"], Cell[476801, 9354, 3916, 89, 1263, "Text"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)