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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 452841, 23098]*) (*NotebookOutlinePosition[ 453922, 23133]*) (* CellTagsIndexPosition[ 453878, 23129]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Modeling Growth \nwith \nL-Systems & ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" ", Evaluatable->False, AspectRatioFixed->True] }], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica in Education and Research", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["\nVol. 4 No.3\nCopyright 1995 TELOS/Springer-Verlag", Evaluatable->False, AspectRatioFixed->True] }], "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "The symbolic and graphic capabilities of Mathematica are used to implement \ and visualize parallel rewrite systems."], "Subsubtitle", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, TextAlignment->Left, AspectRatioFixed->True], Cell[TextData["by Christian Jacob"], "Subsubtitle", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, TextAlignment->Left, AspectRatioFixed->True, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData["Introduction"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Rewriting has proved to be a useful technique for defining complex objects \ by successively replacing parts of simple initial objects using a set of \ rewrite rules or productions. Rewriting systems operating on character \ strings have been successfully used for describing syntactic features of \ natural languages or for formal definitions of programming languages [Cho56], \ [Bac59]."], "Text", Evaluatable->False, PageBreakBelow->False, AspectRatioFixed->True], Cell[TextData[ "Here we want to focus on a special type of rewrite systems, commonly termed \ L-systems, which are used in theoretical biology in order to describe and \ simulate natural growth processes. The introduction of L-systems dates back \ until 1968 when the biologist Aristid Lindenmayer (hence L-systems) defined a \ formal rule system (production system) where all letters in a given word are \ replaced in parallel and simultaneously [Lin68]. This feature makes L-systems \ especially suitable for desribing fractal structures, cell divisions in \ multicellular organisms or flowering stages of herbaceous plants [Pru90]."], "Text", Evaluatable->False, PageBreakBelow->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Formal definition of L-systems"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Context-free L-systems"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "D0L-systems (D0 means deterministic with no context) are the simplest type \ of L-systems. 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Let us have a \ closer look at how to simulate development of multicellular filaments. The \ following growth process can be observed with various algae and especially in \ the blue-green bacteria Anabaena catenula [Pru89]."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Suppose that we want to represent two cytological states, termed a and b, of \ the cells which characterize their size and readiness to divide. 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With p", Evaluatable->False, AspectRatioFixed->True], StyleBox["3 ", Evaluatable->False, AspectRatioFixed->True, FontSize->10, FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["and p", Evaluatable->False, AspectRatioFixed->True], StyleBox["4 ", Evaluatable->False, AspectRatioFixed->True, FontSize->10, FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["a ", Evaluatable->False, AspectRatioFixed->True], StyleBox["b", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["-cell converts into an according ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "-cell.\nStarting with the axiom string this rewrite system generates the \ following sequence of words:\n\n\t\ta", Evaluatable->False, AspectRatioFixed->True], StyleBox["r", Evaluatable->False, AspectRatioFixed->True, FontSize->10, FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox["\n\t\ta", 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FontSize->10, FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[ " matching a predecessor (the left side of the rule) is replaced by the \ according successor (the right side string of the rule). This replacement is \ done simultaneously within each generation step.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Before we show how to implement these concepts in Mathe- matica we will have \ a brief look at the (biologically more relevant) extension to L-systems rules \ depending on context."], "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Context-sensitive L-systems"], "Subsection", Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "Up to now we have discussed context-independent rewriting, i.e. the way a \ letter is rewritten depends on the letter only, adjacent letters have no \ influence on the rewrite process. However, if there is a need to simulate \ interaction (e.g. of cells within a layer) context-sensitive L-systems, \ commonly known as ", Evaluatable->False, AspectRatioFixed->True], StyleBox["IL-systems", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[", have to be used. ", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "In the most general definition of IL-systems the rewriting of a letter \ depends on m of its left and n of its right neighbors, where m and n are \ fixed integers. These systems are denoted as (m,n)L-systems which resemble \ context-sensitive Chomsky- grammars, but - as L-system rewriting is parallel \ in nature - every symbol is rewritten in each derivation step; this is \ especially important whenever there is an overlap of context strings."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "In order to make the following examples easier for demonstration we will \ focus on (1,1)L-systems (or 2L-systems) in the sequel. This means that each \ rule of IL-systems we will discuss has the form\n\n\t\tl < p > r -> s\n\nwith \ l, p, r and s denoting left context, predecessor, right context and \ successor, respectively. The symbols \"<\" and \">\" only separate context \ and predecessor strings. Thus an 0L-system as discussed in the previous \ section consists of rules with no left or right context of the form \n\n\t\t< \ p > -> s \n\t\t\nor simply \n\n\t\tp -> s."], "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["How does it look in ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["?", Evaluatable->False, AspectRatioFixed->True] }], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Now let us examine how we can represent L-systems in ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[". We first load the notebook package ", Evaluatable->False, AspectRatioFixed->True], StyleBox["kLSystems.ma", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" ", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["<< kLSystems.ma"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["The ", Evaluatable->False, AspectRatioFixed->True], StyleBox["kLSystems", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " package contains defintions for the application of parallel rewrite rules \ of L-systems with left and right contexts with arbitrary length. Each rule of \ the form l < p > r -> s as described above is represented by a ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" expression of the form", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData[ "\<\ LRule[ LEFT[ l ], PRED[ p ], RIGHT[ r ], SUCC[ s ] ]\ \>", "\<\ LRule[LEFT[l], PRED[p], RIGHT[r], SUCC[s]]\ \>"], "Input", AspectRatioFixed->True], Cell[TextData[ "Accordingly, we define the production set as an LRULES expression"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData["\<\ LRULES[ LRule[...], LRule[...], ... ]\ \>", "\<\ $Failed\ \>"], "Input", AspectRatioFixed->True], Cell[TextData["and an L-system is described as follows:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["LSystem[ Axiom[...], LRULES[ ... ] ]"], "Input", AspectRatioFixed->True], Cell[TextData[ "With this representation we can easily derive the type of the expressions \ and subexpressions by only looking at their head symbols."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "This notation leads to the following description of the example L-sytem \ for ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Anabaena catenula ", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["presented in the previous section:", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "axiom = AXIOM[ aR ];\n\nlrules =\n LRULES[ \n LRule[LEFT[], PRED[ aR \ ], RIGHT[], \n SUCC[ aL,bR ]],\n LRule[LEFT[], PRED[ aL \ ], RIGHT[], \n SUCC[ bL,aR ]],\n LRule[LEFT[], PRED[ bR \ ], RIGHT[], \n SUCC[ aR ]],\n LRule[LEFT[], PRED[ bL \ ], RIGHT[], \n SUCC[ aL ]]\n ];\n \nlsystem = \ LSystem[axiom,lrules];\n\nskipPattern = {Null};\n"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["The ", Evaluatable->False, AspectRatioFixed->True], StyleBox["skipPattern", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[ " list includes all symbols that should not be considered as context. \ However, these skip patterns will not be used in the following examples.\nIn \ order to get formatted output of the resulting strings we define formatting \ patterns for the L-system expressions:", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Format[AXIOM[x___]] := SequenceForm[x]\n\nFormat[aR] := Subscripted[a[r]]\n\ Format[aL] := Subscripted[a[l]]\nFormat[bR] := Subscripted[b[r]]\nFormat[bL] \ := Subscripted[b[l]]\n\nFormat[LRule[LEFT[l___],PRED[p___],\n \ RIGHT[r___],SUCC[s___]]] :=\n SequenceForm[l,\" < \",p,\" > \",r,\" -> \",s]\ \n \nFormat[LSystem[a_,l_]] := \n TableForm[{\n SequenceForm[\"Axiom: \ \",a],\n SequenceForm[\"Rules: \",\n ColumnForm[Apply[List,l]]]\n \ }]"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[ "This enables us to display our rewrite rules in the notation commonly used \ in L-system literature:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["lsystem"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ LSystem[AXIOM[aR], LRULES[LRule[LEFT[], PRED[aR], RIGHT[], SUCC[aL, \ bR]], LRule[LEFT[], PRED[aL], RIGHT[], SUCC[bL, aR]], LRule[LEFT[], PRED[bR], \ RIGHT[], SUCC[aR]], LRule[LEFT[], PRED[bL], RIGHT[], SUCC[aL]]]]\ \>", "\<\ Axiom: a r Rules: < a > -> a b r l r < a > -> b a l l r < b > -> a r r < b > -> a l l\ \>"], "Output", Evaluatable->False, LineSpacing->{0.6, 0}, AspectRatioFixed->True] }, Closed]], Cell[TextData[{ StyleBox["Now we are ready to start an L-system simulation. The function ", Evaluatable->False, AspectRatioFixed->True], StyleBox["runKLSystem[lsys_LSystem,n_Integer]", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" takes an L-system expression ", Evaluatable->False, AspectRatioFixed->True], StyleBox["lsys", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and the number ", Evaluatable->False, AspectRatioFixed->True], StyleBox["n", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " of rewrite steps as arguments and performs parallel expression rewriting \ starting with the axiom expression of ", Evaluatable->False, AspectRatioFixed->True], StyleBox["lsys.", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["anabaenaGrowth = runKLSystem[lsystem, 6]\n\n"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {AXIOM[aR], AXIOM[aL, bR], AXIOM[bL, aR, aR], AXIOM[aL, aL, bR, aL, bR], AXIOM[bL, aR, bL, aR, aR, bL, aR, aR], AXIOM[aL, aL, bR, aL, aL, bR, aL, bR, aL, aL, bR, aL, bR], AXIOM[bL, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR]}\ \>", "\<\ {a , a b , b a a , a a b a b , b a b a a b a a , r l r l r r l l r l r l r l r r l r r a a b a a b a b a a b a b , l l r l l r l r l l r l r b a b a a b a b a a b a a b a b a a b a a } l r l r r l r l r r l r r l r l r r l r r\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[TextData[ "This output does not resemble growing cell layers, but the following \ formatted outputs are a nice, however very simple, visualization:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["ColumnForm[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ AXIOM[aR] AXIOM[aL, bR] AXIOM[bL, aR, aR] AXIOM[aL, aL, bR, aL, bR] AXIOM[bL, aR, bL, aR, aR, bL, aR, aR] AXIOM[aL, aL, bR, aL, aL, bR, aL, bR, aL, aL, bR, aL, bR] AXIOM[bL, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR]\ \>", "\<\ a r a b l r b a a l r r a a b a b l l r l r b a b a a b a a l r l r r l r r a a b a a b a b a a b a b l l r l l r l r l l r l r b a b a a b a b a a b a a b a b a a b a a l r l r r l r l r r l r r l r l r r l r r\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["ColumnForm[%%,Center]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ AXIOM[aR] AXIOM[aL, bR] AXIOM[bL, aR, aR] AXIOM[aL, aL, bR, aL, bR] AXIOM[bL, aR, bL, aR, aR, bL, aR, aR] AXIOM[aL, aL, bR, aL, aL, bR, aL, bR, aL, aL, bR, aL, bR] AXIOM[bL, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR, bL, aR, bL, aR, aR, bL, aR, aR]\ \>", "\<\ a r a b l r b a a l r r a a b a b l l r l r b a b a a b a a l r l r r l r r a a b a a b a b a a b a b l l r l l r l r l l r l r b a b a a b a b a a b a a b a b a a b a a l r l r r l r l r r l r r l r l r r l r r\ \>"], "Output", Evaluatable->False, LineSpacing->{0.6, 0}, AspectRatioFixed->True] }, Closed]], Cell[TextData[{ StyleBox["\nPlease note that ", Evaluatable->False, AspectRatioFixed->True], StyleBox["runKLSystem[lsys,n]", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" returns a list of expressions with head ", Evaluatable->False, AspectRatioFixed->True], StyleBox["AXIOM", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[", the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Format", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" definition for the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["AXIOM", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" expressions strip off the head.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["L-System string interpretation"], "Section", CellMargins->{{Inherited, Inherited}, {Inherited, 10}}, Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[ "The following definitions tell how the generated strings are interpreted as \ cell layers. As a side effect the interpretation function generates graphics \ objects that are used for visualization."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "ClearAll[interpret];\n\ninterpret[AXIOM[z__]] := \nModule[{x = 0, y = 0},\n \ First[Take[Fold[interpret[#1,#2]&,\n {x,y,{}},{z}],-1]]\n];\n\n\ interpret[{x_,y_,l_}, aL ] := \n {x+2,y,Append[l,ArrowedCircle[{x+1, y}, \ {1,.5},\n Direction -> Left]]};\ninterpret[{x_,y_,l_}, aR \ ] := \n {x+2,y,Append[l,ArrowedDisk[{x+1, y}, {1,.5},\n \ Direction -> Right]]};\ninterpret[{x_,y_,l_}, bL ] := \n \ {x+1,y,Append[l,ArrowedCircle[{x+.5, y}, {.5,.5},\n \ Direction -> Left]]};\ninterpret[{x_,y_,l_}, bR ] := \n \ {x+1,y,Append[l,ArrowedDisk[{x+.5, y}, {.5,.5},\n \ Direction -> Right]]};\n"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["The interpretation for each of the symbols ", Evaluatable->False, AspectRatioFixed->True], StyleBox["aL, aR, bL", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["bR", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" is defined by the function ", Evaluatable->False, AspectRatioFixed->True], StyleBox["interpret[{x,y,l},symbol] ", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " which first of all receives the x- and y-coordinates of the current cell \ and returns a coordinate pair for the following cell. The y-coordinate \ remains unchanged as we only consider layers growing horizontally but not \ vertically. Through the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["l", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["-parameter a supplemented list of graphics objects (", Evaluatable->False, AspectRatioFixed->True], StyleBox["ArrowedCircle, ArrowedDisk", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[") is passed on. This list is returned by the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["AXIOM", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " interpretation function which takes only one argument, keeps the \ coordinates as local variables and folds ", Evaluatable->False, AspectRatioFixed->True], StyleBox["interpret", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" over each subexpression of the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["AXIOM", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" term.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Needs[\"Graphics`Arrow`\"];\n\nArrowedDisk[{x_,y_},{r1_,r2_},opts___] :=\n \n\ Graphics[{\n Thickness[0.001],\n GrayLevel[(1 - HueValue) /. {opts} /. \ Options[ArrowedDisk]],\n Disk[{x,y},{r1,r2}],Hue[0],\n \n If[(Direction \ /. {opts}) === Left,\n Arrow[{x+ .8 r1,y},{x- .8 r1,y},\n \ HeadScaling -> Relative],\n Arrow[{x- .8 r1,y},{x+ .8 r1,y},\n \ HeadScaling -> Relative]\n ], \n \n Hue[0.75],\n \ Circle[{x,y},{r1,r2}]\n }]"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[ "Options[ArrowedDisk] :=\n{\n HueValue -> 0.1,\n Direction -> Right\n}"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[ "ArrowedCircle[coords:{_,_},radii:{_,_},opts___] :=\n \ ArrowedDisk[coords,radii,opts,HueValue -> 0]"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["The listing above shows the definitions of the ", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], StyleBox["ArrowedDisk", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and ", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], StyleBox["ArrowedCircle", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " graphics objects. After mapping the interpretation function on the \ L-system generated expressions the resulting graphics can be easily animated \ which gives instant insight into the simulated growth process. An auxiliary \ single point is put at the maximum horizontal coordinate in order to ensure \ all graphics keeping the same length.", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "disksAndCircles = Map[interpret,anabaenaGrowth];\n\nmaxX = \ Max[Cases[disksAndCircles,Circle[x___],\n Infinity] /. \ Circle[{x_,_},_] :> x];\nMap[\n Show[Graphics[#],Graphics[{Hue[0],\n \ Point[{maxX+2,0}]}],\n AspectRatio -> Automatic,\n PlotRange -> All\n \ ]&,\n disksAndCircles\n];\n"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .02857 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.027211 0.014286 0.027211 [ [ 0 0 0 0 ] [ 1 .02857 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P % Start 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Cell \ orientation is visualized through different greylevels as well as arrows \ pointing left (white) and right (grey).", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "A more elegant functional style formulation of an interpretation function \ using ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "'s pattern matching and upvalue definition capabilities is the following.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "SetAttributes[CellLayerGraphics, {Listable}]\n\n\ CellLayerGraphics[AXIOM[z__]] :=\n Fold[CellCircle[#2,#1]&,{{0,0},{}},{z}]\n\ \naL/: CellCircle[aL, {{x_,y_},g_List}] := \n {{x+2,y},\n \ Append[g,ArrowedDisk[{x+1, y}, {1,0.5},\n Direction -> \ Left]]}\n\naR/: CellCircle[aR, {{x_,y_},g_List}] := \n {{x+2,y},\n \ Append[g,ArrowedDisk[{x+1, y}, {1,0.5},\n HueValue -> \ 0.9,\n Direction -> Right]]}\n\nbL/: CellCircle[bL, \ {{x_,y_},g_List}] := \n {{x+1,y},\n Append[g,ArrowedDisk[{x+.5, \ y}, {.5,0.5},\n Direction -> Left]]}\n\nbR/: CellCircle[bR, \ {{x_,y_},g_List}] := \n {{x+1,y},\n Append[g,ArrowedDisk[{x+.5, \ y}, {.5,0.5},\n HueValue -> 0.9,\n \ Direction -> Right]]}"], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["We define a listable function ", Evaluatable->False, AspectRatioFixed->True], StyleBox["CellLayerGraphics", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " which returns a Graphics object and the maximum x- and y-coordinate. The \ following command shows that the produced cell layer graphics extend \ horizontally up to a length of 34.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["CellLayerGraphics[anabaenaGrowth] // Short"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ Short[\"<<>>\"]\ \>", "\<\ {{{2, 0}, {-Graphics-}}, {<<2>>}, <<4>>, {{34, 0}, <<1>>}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Show[% // Last // Last, AspectRatio -> Automatic];"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .02941 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0280112 0.0147059 0.0280112 [ [ 0 0 0 0 ] [ 1 .02941 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .02941 L 0 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For ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["b", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" only one context (left or right) is important whereas ", Evaluatable->False, AspectRatioFixed->True], StyleBox["c", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" is only replace by ", Evaluatable->False, AspectRatioFixed->True], StyleBox["d", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" if ", Evaluatable->False, AspectRatioFixed->True], StyleBox["c", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" appears within a (", Evaluatable->False, AspectRatioFixed->True], StyleBox["c,d)", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "-context. We only give the formatted output of the rule system which is \ defined in the same notation as described above.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "\nILAxiom1 = AXIOM[ b,a,a,a,a,a,a,a,d ];\n\nILRules1 =\n LRULES[ \n \ LRule[LEFT[ b ], PRED[ a ], RIGHT[ ], \n SUCC[ b ]],\n \ LRule[LEFT[ ], PRED[ b ], RIGHT[ b ], \n SUCC[ c ]],\n\ LRule[LEFT[ ], PRED[ b ], RIGHT[ d ], \n SUCC[ c \ ]],\n LRule[LEFT[ c ], PRED[ c ], RIGHT[ d ], \n SUCC[ \ d ]]\n ];\n \nILSystem1 = LSystem[ILAxiom1,ILRules1];\n\nskipPattern = \ {Null};\n"], "Input", CellOpen->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["ILSystem1"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ LSystem[AXIOM[b, a, a, a, a, a, a, a, d], LRULES[LRule[LEFT[b], PRED[a], RIGHT[], SUCC[b]], LRule[LEFT[], PRED[b], RIGHT[b], SUCC[c]], LRule[LEFT[], PRED[b], RIGHT[d], SUCC[c]], LRule[LEFT[c], PRED[c], RIGHT[d], SUCC[d]]]]\ \>", "\<\ Axiom: baaaaaaad Rules: b < a > -> b < b > b -> c < b > d -> c c < c > d -> d\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]], Cell[TextData[ "These rules generate the following string sequence starting from the defined \ axiom:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["anabaenaGrowth1 = runKLSystem[ILSystem1, 15]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {AXIOM[b, a, a, a, a, a, a, a, d], AXIOM[b, b, a, a, a, a, a, a, d], AXIOM[c, b, b, a, a, a, a, a, d], AXIOM[c, c, b, b, a, a, a, a, d], AXIOM[c, c, c, b, b, a, a, a, d], AXIOM[c, c, c, c, b, b, a, a, d], AXIOM[c, c, c, c, c, b, b, a, d], AXIOM[c, c, c, c, c, c, b, b, d], AXIOM[c, c, c, c, c, c, c, c, d], AXIOM[c, c, c, c, c, c, c, d, d], AXIOM[c, c, c, c, c, c, d, d, d], AXIOM[c, c, c, c, c, d, d, d, d], AXIOM[c, c, c, c, d, d, d, d, d], AXIOM[c, c, c, d, d, d, d, d, d], AXIOM[c, c, d, d, d, d, d, d, d], AXIOM[c, d, d, d, d, d, d, d, d]}\ \>", "\<\ {baaaaaaad, bbaaaaaad, cbbaaaaad, ccbbaaaad, cccbbaaad, ccccbbaad, cccccbbad, ccccccbbd, ccccccccd, cccccccdd, ccccccddd, cccccdddd, ccccddddd, cccdddddd, ccddddddd, cdddddddd}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[TextData[{ StyleBox["In columnform the spreading of the ", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], StyleBox["c", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" symbols through the string is more obvious:", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True] }], "Text", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["ColumnForm[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ AXIOM[b, a, a, a, a, a, a, a, d] AXIOM[b, b, a, a, a, a, a, a, d] AXIOM[c, b, b, a, a, a, a, a, d] AXIOM[c, c, b, b, a, a, a, a, d] AXIOM[c, c, c, b, b, a, a, a, d] AXIOM[c, c, c, c, b, b, a, a, d] AXIOM[c, c, c, c, c, b, b, a, d] AXIOM[c, c, c, c, c, c, b, b, d] AXIOM[c, c, c, c, c, c, c, c, d] AXIOM[c, c, c, c, c, c, c, d, d] AXIOM[c, c, c, c, c, c, d, d, d] AXIOM[c, c, c, c, c, d, d, d, d] AXIOM[c, c, c, c, d, d, d, d, d] AXIOM[c, c, c, d, d, d, d, d, d] AXIOM[c, c, d, d, d, d, d, d, d] AXIOM[c, d, d, d, d, d, d, d, d]\ \>", "\<\ baaaaaaad bbaaaaaad cbbaaaaad ccbbaaaad cccbbaaad ccccbbaad cccccbbad ccccccbbd ccccccccd cccccccdd ccccccddd cccccdddd ccccddddd cccdddddd ccddddddd cdddddddd\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]], Cell[TextData[{ StyleBox[ "This can be interpreted as an example of cellular interaction, where a \ hormone (", Evaluatable->False, AspectRatioFixed->True], StyleBox["c", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ ") diffuses along a filament. However, there is at least one shortcoming \ with this rewrite system: the cell layer extension is predefined by the \ length of the axiom string. The rule system would become more flexible if we \ could parametrize the layer extension. We use this concept of parametrization \ in the next section.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Parametrized L-systems "], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Up to now we only used simple symbols as the rule system alphabet. If we \ parametrize these symbols - which means that we use expressions instead of \ symbols -we are able to control rule applications by environment variables."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "We introduce an environment variable w to control cell layer width"], "Text",\ Evaluatable->False, AspectRatioFixed->True], Cell[TextData["w = 11; (* cell layer width *)"], "Input", AspectRatioFixed->True], Cell[TextData[ "and use this variable in the following parametrized L-system."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "\nILAxiom2 := AXIOM[ a[1],b ];\n\nILRules2 :=\n LRULES[ \n LRule[LEFT[ \ a[i_ /; i < w] ], PRED[ b ], \n RIGHT[ ], SUCC[ a[i+1],b ]],\n \ LRule[LEFT[ ], PRED[ a[i_ /; i > 1] ], \n RIGHT[ c ], SUCC[ c ]],\n\ LRule[LEFT[ a[w] ], PRED[ b ], \n RIGHT[ ], SUCC[ c ]],\n \ LRule[LEFT[ c ], PRED[ b ], \n RIGHT[ ], SUCC[ \"\" ]],\n \ LRule[LEFT[ a[i_ /; i > 1] ], PRED[ c ], \n RIGHT[ ], SUCC[ \"\" \ ]],\n LRule[LEFT[ a[1] ], PRED[ c ], \n RIGHT[ ], SUCC[ b ]]\n \ ];\n \nILSystem2 := LSystem[ILAxiom2,ILRules2];\n\nskipPattern = {Null};\n\n\ postProcessingFunction := (Flatten[#,Infinity,List])&;\n"], "Input", CellOpen->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["ILSystem2"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ LSystem[AXIOM[a[1], b], LRULES[LRule[LEFT[a[i_ /; i < w]], PRED[b], RIGHT[], SUCC[a[1 + i], b]], LRule[LEFT[], PRED[a[i_ /; i > 1]], RIGHT[c], SUCC[c]], LRule[LEFT[a[15]], PRED[b], RIGHT[], SUCC[c]], LRule[LEFT[c], PRED[b], RIGHT[], SUCC[\"\"]], LRule[LEFT[a[i_ /; i > 1]], PRED[c], RIGHT[], SUCC[\"\"]], LRule[LEFT[a[1]], PRED[c], RIGHT[], SUCC[b]]]]\ \>", "\<\ Axiom: a[1]b Rules: a[i_ /; i < w] < b > -> a[1 + i]b < a[i_ /; i > 1] > c -> c a[15] < b > -> c c < b > -> a[i_ /; i > 1] < c > -> a[1] < c > -> b\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "anabaenaGrowth2 = runKLSystem[ILSystem2, 30];\n\n\ ColumnForm[anabaenaGrowth2,Center]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ AXIOM [a[1], b] AXIOM [a[1], a[2], b] AXIOM[a[1], a[2], a[3], b] AXIOM[a[1], a[2], a[3], a[4], b] AXIOM[a[1], a[2], a[3], a[4], a[5], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], b] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], c] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], c, \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], c, \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], c, \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], c, \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[ 6], c, \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[ 5], c, \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[ 4], c, \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[ 3], c, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[ 2], c, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[ 1], c, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[ 1], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[ 2], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[ 3], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[ 4], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[ 5], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[ 6], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"] AXIOM[a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[ 9], b, \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"]\ \>", "\<\ a[1]b a[1]a[2]b a[1]a[2]a[3]b a[1]a[2]a[3]a[4]b a[1]a[2]a[3]a[4]a[5]b a[1]a[2]a[3]a[4]a[5]a[6]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]a[10]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]a[10]a[11]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]a[10]a[11]c a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]a[10]c a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]c a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]c a[1]a[2]a[3]a[4]a[5]a[6]a[7]c a[1]a[2]a[3]a[4]a[5]a[6]c a[1]a[2]a[3]a[4]a[5]c a[1]a[2]a[3]a[4]c a[1]a[2]a[3]c a[1]a[2]c a[1]c a[1]b a[1]a[2]b a[1]a[2]a[3]b a[1]a[2]a[3]a[4]b a[1]a[2]a[3]a[4]a[5]b a[1]a[2]a[3]a[4]a[5]a[6]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]b a[1]a[2]a[3]a[4]a[5]a[6]a[7]a[8]a[9]b\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Anabaena catenula alga growth"], "Subsection", Evaluatable->False, PageBreakAbove->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox["We come back to our ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Anabaena catenula", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " example. Now we want to control the cells' lifetime; at the end of their \ development time the cells of type ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["b ", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["divide into two successor cells.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "lifeTimeA = 3; (* development time cells a and b *)\nlifeTimeB = 2;\n"], "Input", AspectRatioFixed->True], Cell[TextData[ "These environment variables are used in the following L-system:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "ILAxiom3 := AXIOM[ Al[1] ];\n\nILRules3 :=\n LRULES[ \n LRule[LEFT[], \ PRED[ Al[lifeTimeA] ], RIGHT[], \n SUCC[ Al[1],Br[1] ]\n \ ],\n LRule[LEFT[], PRED[ Ar[lifeTimeA] ], RIGHT[], \n \ SUCC[ Bl[1],Ar[1] ]\n ],\n LRule[LEFT[], PRED[ Bl[lifeTimeB] ], \ RIGHT[], \n SUCC[ Al[1],Br[1] ]\n ],\n LRule[LEFT[], \ PRED[ Br[lifeTimeB] ], RIGHT[], \n SUCC[ Bl[1],Ar[1] ]\n \ ],\n LRule[LEFT[], PRED[ Al[i_ /; i < lifeTimeA] ], \n RIGHT[], \n\ SUCC[ Al[i+1] ]\n ],\n LRule[LEFT[], PRED[ Ar[i_ /; i \ < lifeTimeA] ], \n RIGHT[], \n SUCC[ Ar[i+1] ]\n \ ],\n LRule[LEFT[], PRED[ Bl[i_ /; i < lifeTimeB] ], \n RIGHT[], \n\ SUCC[ Bl[i+1] ]\n ],\n LRule[LEFT[], PRED[ Br[i_ /; i \ < lifeTimeB] ], \n RIGHT[], \n SUCC[ Br[i+1] ]\n \ ]\n ];"], "Input", AspectRatioFixed->True], Cell[TextData[ "ILSystem3 := LSystem[ILAxiom3,ILRules3];\n\nskipPattern = {Null};\n\n\ postProcessingFunction := (Flatten[#,Infinity,List])&;\n"], "Input", AspectRatioFixed->True], Cell[TextData[ "Format[Ar[i_]] := Subscripted[A[r,i],{1}]\nFormat[Al[i_]] := \ Subscripted[A[l,i],{1}]\nFormat[Br[i_]] := Subscripted[B[r,i],{1}]\n\ Format[Bl[i_]] := Subscripted[B[l,i],{1}]\n"], "Input", CellOpen->False, InitializationCell->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["ILSystem3"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ LSystem[AXIOM[Al[1]], LRULES[LRule[LEFT[], PRED[Al[3]], RIGHT[], SUCC[Al[1], Br[1]]], LRule[LEFT[], PRED[Ar[3]], RIGHT[], SUCC[Bl[1], Ar[1]]], LRule[LEFT[], PRED[Bl[2]], RIGHT[], SUCC[Al[1], Br[1]]], LRule[LEFT[], PRED[Br[2]], RIGHT[], SUCC[Bl[1], Ar[1]]], LRule[LEFT[], PRED[Al[i_ /; i < lifeTimeA]], RIGHT[], SUCC[Al[1 + i]]], LRule[LEFT[], PRED[Ar[i_ /; i < lifeTimeA]], RIGHT[], SUCC[Ar[1 + i]]], LRule[LEFT[], PRED[Bl[i_ /; i < lifeTimeB]], RIGHT[], SUCC[Bl[1 + i]]], LRule[LEFT[], PRED[Br[i_ /; i < lifeTimeB]], RIGHT[], SUCC[Br[1 + i]]]]]\ \>", "\<\ Axiom: A [1] l Rules: < A [3] > -> A [1]B [1] l l r < A [3] > -> B [1]A [1] r l r < B [2] > -> A [1]B [1] l l r < B [2] > -> B [1]A [1] r l r < A [i_ /; i < lifeTimeA] > -> A [1 + i] l l < A [i_ /; i < lifeTimeA] > -> A [1 + i] r r < B [i_ /; i < lifeTimeB] > -> B [1 + i] l l < B [i_ /; i < lifeTimeB] > -> B [1 + i] r r\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "anabaenaGrowth3 = runKLSystem[ILSystem3, 9];\n\n\ ColumnForm[anabaenaGrowth3]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ AXIOM[Al[1]] AXIOM[Al[2]] AXIOM[Al[3]] AXIOM[Al[1], Br[1]] AXIOM[Al[2], Br[2]] AXIOM[Al[3], Bl[1], Ar[1]] AXIOM[Al[1], Br[1], Bl[2], Ar[2]] AXIOM[Al[2], Br[2], Al[1], Br[1], Ar[3]] AXIOM[Al[3], Bl[1], Ar[1], Al[2], Br[2], Bl[1], Ar[1]] AXIOM[Al[1], Br[1], Bl[2], Ar[2], Al[3], Bl[1], Ar[1], Bl[2], Ar[2]]\ \>", "\<\ A [1] l A [2] l A [3] l A [1]B [1] l r A [2]B [2] l r A [3]B [1]A [1] l l r A [1]B [1]B [2]A [2] l r l r A [2]B [2]A [1]B [1]A [3] l r l r r A [3]B [1]A [1]A [2]B [2]B [1]A [1] l l r l r l r A [1]B [1]B [2]A [2]A [3]B [1]A [1]B [2]A [2] l r l r l l r l r\ \>"], "Output", Evaluatable->False, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Graphical Interpretation"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "The interpretation function only has to be extended in order to take into \ account the lifetime of the two cell classes ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["b", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ ". The developmental states of the cells are depicted by letting the cells \ become darker with growing age. 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Each ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "-cell needs three timesteps to mature. Then the cell divides into a new ", Evaluatable->False, AspectRatioFixed->True], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["-cell (with same orientation) and a smaller ", Evaluatable->False, AspectRatioFixed->True], StyleBox["b", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["-cell with opposite orientation. 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arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl arrl scale [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto fill -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto -0.2 0.05 lineto stroke grestore } def % End of user PostScript p p 1 g .001 w .0499 .0137 m matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix F 1 0 0 r p .07078 .0137 m .02903 .0137 L s % Start of user PostScript 1.8 0 0.2 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix s P p 1 g .001 w .08904 .0137 m .08904 .0137 .01305 0 365.73 arc F 1 0 0 r p .0786 .0137 m .09948 .0137 L s % Start of user PostScript 2.1 0 2.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .08904 .0137 .01305 0 365.73 arc s P .008 w .97619 .0137 Mdot P 0 0 m 1 0 L 1 .0274 L 0 .0274 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{427, 13}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgIoc>Ic3>IVC>IIS>II03=Voc=Vc3=V VC=VIS=V:IP00o`21000030000fH0000>0005 RP0008X020000fH0003o07l0000;0003IP00010000>:08X02@000hX0003o07l0000;0003RP000140 00>:IP002@000hX0003o07h0000:0003RP0S018S00=VRR<02B<00fH0003o07400ol:00002P000fH0 000200038`0000h000=V00001@0012<008[o07<00ol:00002P000hYV000B0003IXX000T000=V0000 o`1a00?o2P0000`000=V00003`000fJ:IP090003IXX00?l0O`0000d000=V000030000hYV00020003 IP0000D000=V0000o`2000003P000fJ:00090003IXX000D000=V00000`000fH0003o0840000@000: RVJ:IXYVRVJ:IPT000EVRVJ:IP3o08@00000\ \>"], ImageRangeCache->{{{0, 426}, {12, 0}} -> {-0.912692, -0.539741, 0.0899658, 0.0899658}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .0274 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0260926 0.0136986 0.0260926 [ [ 0 0 0 0 ] [ 1 .0274 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl arrl scale [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto fill -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto -0.2 0.05 lineto stroke grestore } def % End of user PostScript p p .8 g .001 w .0499 .0137 m matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix F 1 0 0 r p .07078 .0137 m .02903 .0137 L s % Start of user PostScript 1.8 0 0.2 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix s P p .8 g .001 w .08904 .0137 m .08904 .0137 .01305 0 365.73 arc F 1 0 0 r p .0786 .0137 m .09948 .0137 L s % Start of user PostScript 2.1 0 2.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .08904 .0137 .01305 0 365.73 arc s P .008 w .97619 .0137 Mdot P 0 0 m 1 0 L 1 .0274 L 0 .0274 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{427, 13}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgIoc>Ic3>IVC>IIS>II03=Voc=Vc3=V VC=VIS=V:IP00o`21000030000fH[:`0>:`05 RP0008X022/00fH0003o07l0000;0003IR/[010[00>:08X02B/00hX0003o07l0000;0003RR/[014[ 00>:IR/02B/00hX0003o07h0000:0003RR/S018S00=VRR<02B<00fH0003o07400ol:00002P000fH[ :`02:`038b/[00h[00=V:b/01B/012<[:h[o07<00ol:00002P000hYV:`0B:`03IXX[00T[00=V0000 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mul arrl div arrx arrl div 0 0 ] concat -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto fill -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto -0.2 0.05 lineto stroke grestore } def % End of user PostScript p p 1 g .001 w .0499 .0137 m matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix F 1 0 0 r p .07078 .0137 m .02903 .0137 L s % Start of user PostScript 1.8 0 0.2 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix s P p 1 g .001 w .08904 .0137 m .08904 .0137 .01305 0 365.73 arc F 1 0 0 r p .0786 .0137 m .09948 .0137 L s % Start of user PostScript 2.1 0 2.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .08904 .0137 .01305 0 365.73 arc s P p .6 g .001 w .11513 .0137 m .11513 .0137 .01305 0 365.73 arc F 1 0 0 r p .1047 .0137 m .12557 .0137 L s % Start of user PostScript 3.1 0 3.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .11513 .0137 .01305 0 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grestore } def % End of user PostScript p p .8 g .001 w .0499 .0137 m matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix F 1 0 0 r p .07078 .0137 m .02903 .0137 L s % Start of user PostScript 1.8 0 0.2 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix s P p .8 g .001 w .08904 .0137 m .08904 .0137 .01305 0 365.73 arc F 1 0 0 r p .0786 .0137 m .09948 .0137 L s % Start of user PostScript 2.1 0 2.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .08904 .0137 .01305 0 365.73 arc s P p .4 g .001 w .11513 .0137 m .11513 .0137 .01305 0 365.73 arc F 1 0 0 r p .1047 .0137 m .12557 .0137 L s % Start of user PostScript 3.1 0 3.9 0 MAarrowhead1 % End of user PostScript P .5 0 1 r newpath .11513 .0137 .01305 0 365.73 arc s P .008 w .97619 .0137 Mdot P 0 0 m 1 0 L 1 .0274 L 0 .0274 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", 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%%Creator: Mathematica %%AspectRatio: .0274 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0260926 0.0136986 0.0260926 [ [ 0 0 0 0 ] [ 1 .0274 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl arrl scale [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto fill -0.2 0.05 moveto 0 0 lineto -0.2 -0.05 lineto -0.2 0.05 lineto stroke grestore } def % End of user PostScript p p 1 g .001 w .0499 .0137 m matrix currentmatrix .02609 .01305 scale 1.91242 1.0501 1 0 365.73 arc setmatrix F 1 0 0 r p .07078 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.87174 m .43598 .88035 L .43825 .88392 L p .578 .488 .717 r F P s P p .002 w .42807 .88486 m .4283 .88633 L p .43161 .87174 L .804 .669 .715 r F P s P p .002 w .43161 .87174 m .42884 .88084 L .42807 .88486 L p .804 .669 .715 r F P s P p .2 1 0 r 2 Mabswid .43163 .87174 m .43695 .86997 L s P p .2 1 0 r 2 Mabswid .58657 .15757 m .58951 .16005 L s P p .2 1 0 r 2 Mabswid .44228 .86786 m .43695 .86997 L s P p .002 w .26285 .79031 m .2606 .79275 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .26584 .78641 m .26285 .79031 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .2606 .79275 m .25686 .79617 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .28407 .792 m .28201 .79711 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .28357 .78901 m .28407 .792 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .28002 .78515 m .28357 .78901 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .28201 .79711 m .27971 .80073 L p .27035 .77953 L .802 .667 .715 r F P s P p .2 1 0 r 2 Mabswid .58951 .16005 m .59268 .16294 L s P p .002 w .27971 .80073 m .27434 .80349 L .27035 .77953 L p .802 .667 .715 r F P s P p .002 w .25686 .79617 m .25422 .79837 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .26947 .80925 m .27434 .80349 L p .27035 .77953 L .802 .667 .715 r F P s P p .2 1 0 r 2 Mabswid .44759 .86543 m .44228 .86786 L s P p .002 w .25422 .79837 m .25232 .79912 L .27035 .77953 L p .83 .987 .717 r F P s P p .002 w .26666 .80988 m .26947 .80925 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .26359 .80903 m .26666 .80988 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .24962 .78726 m .25356 .78897 L .27035 .77953 L p .585 .165 .21 r F P s P p .002 w .24924 .78553 m .24962 .78726 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .24991 .78321 m .24924 .78553 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .25202 .78203 m .24991 .78321 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .25765 .78082 m .25202 .78203 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .25541 .79187 m .25356 .78897 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .24815 .80233 m .25232 .79912 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .24775 .80209 m .24815 .80233 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .24849 .80062 m .24775 .80209 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .25076 .79816 m .24849 .80062 L p .27035 .77953 L .83 .987 .717 r F P s P p .002 w .27035 .77953 m .25681 .79225 L .25076 .79816 L p .83 .987 .717 r F P s P p .002 w .25792 .79243 m .25541 .79187 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .2615 .79239 m .25792 .79243 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .26361 .7912 m .2615 .79239 L p .27035 .77953 L .585 .165 .21 r F P s P p .002 w .27035 .77953 m .26636 .78766 L .26361 .7912 L p .585 .165 .21 r F P s P p .002 w .28852 .80517 m .29 .8032 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .28585 .8061 m .28852 .80517 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .27256 .78273 m .27662 .7871 L .27035 .77953 L p .599 .126 0 r F P s P p .002 w .28347 .80402 m .28585 .8061 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .27035 .77953 m .27899 .79685 L .28347 .80402 L p .572 .484 .716 r F P s P p .002 w .26308 .80603 m .26359 .80903 L p .27035 .77953 L .802 .667 .715 r F P s P p .002 w .27035 .77953 m .26465 .7979 L .26308 .80603 L p .802 .667 .715 r F P s P p .002 w .26994 .77983 m .27256 .78273 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .26694 .77648 m .26994 .77983 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .26616 .77554 m .26694 .77648 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .26683 .77607 m .26616 .77554 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .29 .8032 m .28938 .79613 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .28147 .79242 m .27662 .7871 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .2833 .79437 m .28147 .79242 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .28473 .79582 m .2833 .79437 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .28393 .79486 m .28473 .79582 L p .27035 .77953 L .599 .126 0 r F P s P p .002 w .27035 .77953 m .28011 .79052 L .28393 .79486 L p .599 .126 0 r F P s P p .002 w .29115 .79114 m .28938 .79613 L .27035 .77953 L p .572 .484 .716 r F P s P p .002 w .29024 .78708 m .29115 .79114 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .28813 .78198 m .29024 .78708 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .28575 .7799 m .28813 .78198 L p .27035 .77953 L .572 .484 .716 r F P s P p .002 w .2807 .77877 m .28575 .7799 L p .27035 .77953 L .572 .484 .716 r F P s P p .2 1 0 r 2 Mabswid .27035 .77953 m .27764 .77452 L s P p .2 1 0 r 2 Mabswid .59268 .16294 m .5961 .16624 L s P p .2 1 0 r 2 Mabswid .45296 .86297 m .44759 .86543 L s P p .2 1 0 r 2 Mabswid .285 .76925 m .27764 .77452 L s P p .002 w .34147 .78715 m .33922 .78962 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .34456 .7832 m .34147 .78715 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .33922 .78962 m .33555 .79307 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .36298 .78886 m .36092 .79402 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .3625 .78584 m .36298 .78886 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .35897 .78193 m .3625 .78584 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .36092 .79402 m .35862 .79768 L p .34936 .77624 L .804 .669 .715 r F P s P p .2 1 0 r 2 Mabswid .5961 .16624 m .59956 .16957 L s P p .2 1 0 r 2 Mabswid .29242 .76373 m .285 .76925 L s P p .002 w .35862 .79768 m .35327 .80047 L .34936 .77624 L p .804 .669 .715 r F P s P p .002 w .33555 .79307 m .33299 .79529 L p .34936 .77624 L .804 .977 .688 r F P s P p .2 1 0 r 2 Mabswid .45832 .86017 m .45296 .86297 L s P p .002 w .34841 .80629 m .35327 .80047 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .33299 .79529 m .33126 .79604 L .34936 .77624 L p .804 .977 .688 r F P s P p .002 w .3456 .80693 m .34841 .80629 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .34255 .80606 m .3456 .80693 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .32897 .78403 m .3331 .78575 L .34936 .77624 L p .583 .16 .204 r F P s P p .002 w .32845 .78228 m .32897 .78403 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .32895 .77994 m .32845 .78228 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .33099 .77876 m .32895 .77994 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .33661 .77754 m .33099 .77876 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .3352 .78868 m .3331 .78575 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .32725 .79928 m .33126 .79604 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .32694 .79903 m .32725 .79928 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .32777 .79754 m .32694 .79903 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .33005 .79505 m .32777 .79754 L p .34936 .77624 L .804 .977 .688 r F P s P p .002 w .34936 .77624 m .33604 .78908 L .33005 .79505 L p .804 .977 .688 r F P s P p .002 w .33779 .78924 m .3352 .78868 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .34141 .78921 m .33779 .78924 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .34345 .788 m .34141 .78921 L p .34936 .77624 L .583 .16 .204 r F P s P p .002 w .34936 .77624 m .34596 .78443 L .34345 .788 L p .583 .16 .204 r F P s P p .002 w .36952 .80016 m .3689 .79301 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .35243 .77944 m .35652 .78385 L .34936 .77624 L p 0 0 .454 r F P s P p .002 w .37074 .78796 m .3689 .79301 L .34936 .77624 L p .573 .485 .716 r F P s P p .002 w .34971 .77652 m .35243 .77944 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .36982 .78385 m .37074 .78796 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .36767 .7787 m .36982 .78385 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .36522 .7766 m .36767 .7787 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .36002 .77547 m .36522 .7766 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .34655 .77312 m .34971 .77652 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .34567 .77218 m .34655 .77312 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .34615 .77273 m .34567 .77218 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .36152 .78924 m .35652 .78385 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .36334 .7912 m .36152 .78924 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .3647 .79268 m .36334 .7912 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .36378 .79171 m .3647 .79268 L p .34936 .77624 L 0 0 .454 r F P s P p .002 w .34936 .77624 m .3597 .78734 L .36378 .79171 L p 0 0 .454 r F P s P p .002 w .36798 .80216 m .36952 .80016 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .36523 .80309 m .36798 .80216 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .36278 .80099 m .36523 .80309 L p .34936 .77624 L .573 .485 .716 r F P s P p .002 w .34936 .77624 m .3582 .79374 L .36278 .80099 L p .573 .485 .716 r F P s P p .002 w .34206 .80303 m .34255 .80606 L p .34936 .77624 L .804 .669 .715 r F P s P p .002 w .34936 .77624 m .34364 .79481 L .34206 .80303 L p .804 .669 .715 r F P s P p .2 1 0 r 2 Mabswid .34942 .7762 m .35679 .77124 L s P p .2 1 0 r 2 Mabswid .29991 .75817 m .29242 .76373 L s P p .2 1 0 r 2 Mabswid .59956 .16957 m .60326 .1733 L s P p .2 1 0 r 2 Mabswid .46368 .85704 m .45832 .86017 L s P p .2 1 0 r 2 Mabswid .36428 .76598 m .35679 .77124 L s P p .2 1 0 r 2 Mabswid .30746 .75236 m .29991 .75817 L s P p .2 1 0 r 2 Mabswid .60326 .1733 m .60723 .17745 L s P p .2 1 0 r 2 Mabswid .4691 .85386 m .46368 .85704 L s P p .2 1 0 r 2 Mabswid .37183 .76046 m .36428 .76598 L s P p .002 w .42611 .81736 m .42385 .81986 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .42932 .81338 m .42611 .81736 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .42385 .81986 m .42025 .8234 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .44796 .81911 m .4459 .82435 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .44749 .81605 m .44796 .81911 L p .43443 .80642 L .807 .672 .715 r F P s P p .2 1 0 r 2 Mabswid .31509 .7463 m .30746 .75236 L s P p .002 w .44399 .81212 m .44749 .81605 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .4459 .82435 m .44359 .82806 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .44359 .82806 m .43826 .83091 L .43443 .80642 L p .807 .672 .715 r F P s P p .002 w .42025 .8234 m .41778 .82569 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .4334 .83683 m .43826 .83091 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .41778 .82569 m .41624 .82652 L .43443 .80642 L p .757 .952 .636 r F P s P p .002 w .4306 .8375 m .4334 .83683 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .42757 .83663 m .4306 .8375 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .41441 .81454 m .41874 .81633 L .43443 .80642 L p .586 .167 .212 r F P s P p .002 w .41373 .81271 m .41441 .81454 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .41404 .81027 m .41373 .81271 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .41601 .80904 m .41404 .81027 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .4216 .80777 m .41601 .80904 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .42112 .81939 m .41874 .81633 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .41241 .82988 m .41624 .82652 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .4122 .82968 m .41241 .82988 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .41313 .8282 m .4122 .82968 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .41542 .82567 m .41313 .8282 L p .43443 .80642 L .757 .952 .636 r F P s P p .002 w .43443 .80642 m .42134 .81957 L .41542 .82567 L p .757 .952 .636 r F P s P p .002 w .42379 .81998 m .42112 .81939 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .42746 .81994 m .42379 .81998 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .42943 .81868 m .42746 .81994 L p .43443 .80642 L .586 .167 .212 r F P s P p .002 w .43443 .80642 m .43167 .81497 L .42943 .81868 L p .586 .167 .212 r F P s P p .002 w .45516 .83076 m .45455 .82353 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .43845 .80998 m .44258 .81445 L .43443 .80642 L p 0 0 .493 r F P s P p .002 w .45647 .81843 m .45455 .82353 L .43443 .80642 L p .574 .485 .716 r F P s P p .002 w .45553 .81427 m .45647 .81843 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .43562 .807 m .43845 .80998 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .45334 .80904 m .45553 .81427 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .45081 .8069 m .45334 .80904 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .44545 .80571 m .45081 .8069 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .43229 .80351 m .43562 .807 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .43128 .80252 m .43229 .80351 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .43157 .803 m .43128 .80252 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .44775 .81994 m .44258 .81445 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .44955 .82192 m .44775 .81994 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .45084 .82338 m .44955 .82192 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .4498 .82236 m .45084 .82338 L p .43443 .80642 L 0 0 .493 r F P s P p .002 w .43443 .80642 m .44541 .81784 L .4498 .82236 L p 0 0 .493 r F P s P p .002 w .45357 .83277 m .45516 .83076 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .45072 .8337 m .45357 .83277 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .4482 .83155 m .45072 .8337 L p .43443 .80642 L .574 .485 .716 r F P s P p .002 w .43443 .80642 m .4435 .82419 L .4482 .83155 L p .574 .485 .716 r F P s P p .002 w .42709 .83357 m .42757 .83663 L p .43443 .80642 L .807 .672 .715 r F P s P p .002 w .43443 .80642 m .42868 .82525 L .42709 .83357 L p .807 .672 .715 r F P s P p .2 1 0 r 2 Mabswid .43481 .80615 m .44122 .80151 L s P p .2 1 0 r 2 Mabswid .37944 .75489 m .37183 .76046 L s P p .2 1 0 r 2 Mabswid .60723 .17745 m .61123 .18163 L s P p .2 1 0 r 2 Mabswid .47452 .85035 m .4691 .85386 L s P p .2 1 0 r 2 Mabswid .32279 .74018 m .31509 .7463 L s P p .2 1 0 r 2 Mabswid .38712 .74905 m .37944 .75489 L s P p .2 1 0 r 2 Mabswid .44805 .7963 m .44122 .80151 L s P p 0 1 .1 r .001 w .47071 .86672 Mdot P p .2 1 0 r 2 Mabswid .47301 .86169 m .47071 .86672 L s P p .2 1 0 r 2 Mabswid .33056 .73382 m .32279 .74018 L s P p .2 1 0 r 2 Mabswid .61123 .18163 m .6155 .18622 L s P p .2 1 0 r 2 Mabswid .47995 .84648 m .47452 .85035 L s P p 0 1 .1 r .002 w .47301 .86169 Mdot P p .2 1 0 r 2 Mabswid .47531 .85663 m .47301 .86169 L s P p 0 1 .1 r .001 w .47507 .87107 Mdot P p .2 1 0 r 2 Mabswid .47628 .86494 m .47507 .87107 L s P p 0 1 .1 r .003 w .47531 .85663 Mdot P p .2 1 0 r 2 Mabswid .47763 .85156 m .47531 .85663 L s P p 0 1 .1 r .002 w .47628 .86494 Mdot P p .2 1 0 r 2 Mabswid .4775 .85879 m .47628 .86494 L s P p .2 1 0 r 2 Mabswid .39488 .74295 m .38712 .74905 L s P p .2 1 0 r 2 Mabswid .33842 .72721 m .33056 .73382 L s P p .2 1 0 r 2 Mabswid .45493 .79078 m .44805 .7963 L s P p 0 1 .1 r .003 w .4775 .85879 Mdot P p .2 1 0 r 2 Mabswid .47872 .85264 m .4775 .85879 L s P p 0 1 .1 r .004 w .47763 .85156 Mdot P p .2 1 0 r 2 Mabswid .47995 .84648 m .47763 .85156 L s P p 0 1 .1 r .004 w .47872 .85264 Mdot P p .2 1 0 r 2 Mabswid .47995 .84648 m .47872 .85264 L s P p 0 1 .1 r .0015 w .32837 .75206 Mdot P p .2 1 0 r 2 Mabswid .33088 .74586 m .32837 .75206 L s P p .2 1 0 r 2 Mabswid .6155 .18622 m .62003 .19121 L s P p 0 1 .1 r .003 w .33088 .74586 Mdot P p .2 1 0 r 2 Mabswid .33339 .73965 m .33088 .74586 L s P p .2 1 0 r 2 Mabswid .48543 .84257 m .47995 .84648 L s P p 0 1 .1 r .0045 w .33339 .73965 Mdot P p .2 1 0 r 2 Mabswid .3359 .73344 m .33339 .73965 L s P p 0 1 .1 r .006 w .3359 .73344 Mdot P p .2 1 0 r 2 Mabswid .33842 .72721 m .3359 .73344 L s P p 0 1 .1 r .0015 w .33472 .75484 Mdot P p .2 1 0 r 2 Mabswid .33565 .74794 m .33472 .75484 L s P p 0 1 .1 r .003 w .33565 .74794 Mdot P p .2 1 0 r 2 Mabswid .33657 .74103 m .33565 .74794 L s P p .2 1 0 r 2 Mabswid .4027 .73679 m .39488 .74295 L s P p 0 1 .1 r .0045 w .33657 .74103 Mdot P p .2 1 0 r 2 Mabswid .3375 .73412 m .33657 .74103 L s P p 0 1 .1 r .006 w .3375 .73412 Mdot P p .2 1 0 r 2 Mabswid .33842 .72721 m .3375 .73412 L s P p .2 1 0 r 2 Mabswid .34635 .72055 m .33842 .72721 L s P p .002 w .4714 .90426 m .46682 .90939 L p .48876 .88261 L .693 .911 .568 r F P s P p .002 w .47801 .89631 m .4714 .90426 L p .48876 .88261 L .693 .911 .568 r F P s P p .2 1 0 r 2 Mabswid .46188 .7852 m .45493 .79078 L s P p .002 w .46682 .90939 m .46544 .91082 L .46901 .90583 L p .693 .911 .568 r F P s P p .46901 .90583 m .48876 .88261 L .46682 .90939 L .693 .911 .568 r F P p .002 w .51598 .90796 m .51518 .91001 L .50438 .90706 L p .81 .675 .714 r F P s P p .50438 .90706 m .48876 .88261 L .51598 .90796 L .81 .675 .714 r F P p .002 w .51503 .90177 m .51598 .90796 L p .48876 .88261 L .81 .675 .714 r F P s P p .002 w .50802 .8939 m .51503 .90177 L p .48876 .88261 L .81 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .62003 .19121 m .62461 .19626 L s P p .2 1 0 r 2 Mabswid .49093 .8383 m .48543 .84257 L s P p .2 1 0 r 2 Mabswid .41059 .73038 m .4027 .73679 L s P p .2 1 0 r 2 Mabswid .35436 .71365 m .34635 .72055 L s P p .002 w .50438 .90706 m .49836 .90541 L p .48876 .88261 L .81 .675 .714 r F P s P p .002 w .32279 .66324 m .31929 .66702 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .32757 .65693 m .32279 .66324 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .31929 .66702 m .31353 .67211 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .46901 .90583 m .47101 .90303 L p .48876 .88261 L .693 .911 .568 r F P s P p .2 1 0 r 2 Mabswid .46889 .77933 m .46188 .7852 L s P p .002 w .49836 .90541 m .492 .90367 L .48876 .88261 L p .81 .675 .714 r F P s P p .002 w .35618 .66574 m .35298 .67372 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .35543 .66101 m .35618 .66574 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .34994 .65478 m .35543 .66101 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .35298 .67372 m .3494 .67934 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .3494 .67934 m .34107 .6835 L .33495 .64551 L p .807 .672 .715 r F P s P p .002 w .48805 .90259 m .492 .90367 L p .48876 .88261 L .81 .675 .714 r F P s P p .002 w .31353 .67211 m .30951 .67531 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .47101 .90303 m .47313 .90008 L .48876 .88261 L p .693 .911 .568 r F P s P p .002 w .48635 .90212 m .48805 .90259 L p .48876 .88261 L .81 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .36246 .7065 m .35436 .71365 L s P p .2 1 0 r 2 Mabswid .41857 .7237 m .41059 .73038 L s P p .002 w .48446 .90161 m .48635 .90212 L p .48876 .88261 L .81 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .62461 .19626 m .62947 .2017 L s P p .002 w .33349 .69241 m .34107 .6835 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .46788 .89184 m .47565 .89176 L .48876 .88261 L p .595 .185 .234 r F P s P p .002 w .46051 .89192 m .46788 .89184 L p .48876 .88261 L .595 .185 .234 r F P s P p .46051 .89192 m .48876 .88261 L .44732 .89102 L .595 .185 .234 r F P p .002 w .45128 .8883 m .44732 .89102 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .46264 .88552 m .45128 .8883 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .47444 .89825 m .47313 .90008 L p .48876 .88261 L .693 .911 .568 r F P s P p .002 w .47501 .89745 m .47444 .89825 L p .48876 .88261 L .693 .911 .568 r F P s P p .002 w .47563 .89658 m .47501 .89745 L p .48876 .88261 L .693 .911 .568 r F P s P p .002 w .47589 .89622 m .47563 .89658 L p .48876 .88261 L .693 .911 .568 r F P s P p .002 w .48876 .88261 m .47608 .89595 L .47589 .89622 L p .693 .911 .568 r F P s P p .002 w .48046 .89171 m .47565 .89176 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .48254 .89169 m .48046 .89171 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .48484 .89167 m .48254 .89169 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .48575 .89166 m .48484 .89167 L p .48876 .88261 L .595 .185 .234 r F P s P p .002 w .48371 .9014 m .48446 .90161 L p .48876 .88261 L .81 .675 .714 r F P s P p .002 w .48876 .88261 m .48311 .90124 L .48371 .9014 L p .81 .675 .714 r F P s P p .002 w .48876 .88261 m .48648 .89165 L .48575 .89166 L p .595 .185 .234 r F P s P p .002 w .50252 .8988 m .50632 .89763 L p .48876 .88261 L .572 .484 .716 r F P s P p .002 w .49366 .88727 m .49629 .89023 L .48876 .88261 L p 0 0 .481 r F P s P p .002 w .51247 .89575 m .50632 .89763 L .48876 .88261 L p .572 .484 .716 r F P s P p .002 w .49116 .88444 m .49366 .88727 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .51833 .89395 m .51247 .89575 L p .48876 .88261 L .572 .484 .716 r F P s P p .51833 .89395 m .48876 .88261 L .52804 .88864 L .572 .484 .716 r F P p .002 w .52278 .88417 m .52804 .88864 L p .48876 .88261 L .572 .484 .716 r F P s P p .002 w .51162 .88155 m .52278 .88417 L p .48876 .88261 L .572 .484 .716 r F P s P p .49116 .88444 m .48876 .88261 L .48528 .87791 L 0 0 .481 r F P p .002 w .48305 .87565 m .48528 .87791 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .48338 .87629 m .48305 .87565 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .49791 .89206 m .49629 .89023 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .49861 .89284 m .49791 .89206 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .49938 .89371 m .49861 .89284 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .49969 .89406 m .49938 .89371 L p .48876 .88261 L 0 0 .481 r F P s P p .002 w .48876 .88261 m .49993 .89433 L .49969 .89406 L p 0 0 .481 r F P s P p .002 w .50089 .8993 m .50252 .8988 L p .48876 .88261 L .572 .484 .716 r F P s P p .002 w .49908 .89985 m .50089 .8993 L p .48876 .88261 L .572 .484 .716 r F P s P p .002 w .49836 .90008 m .49908 .89985 L p .48876 .88261 L .572 .484 .716 r F P s P p .002 w .48876 .88261 m .49779 .90025 L .49836 .90008 L p .572 .484 .716 r F P s P p .2 1 0 r 2 Mabswid .48904 .88209 m .49309 .87464 L s P p .2 1 0 r 2 Mabswid .49645 .83367 m .49093 .8383 L s P p .2 1 0 r 2 Mabswid .41104 .7425 m .40854 .74875 L s P p .002 w .30951 .67531 m .30673 .67602 L .33495 .64551 L p .837 .99 .726 r F P s P p .002 w .32912 .69331 m .33349 .69241 L p .33495 .64551 L .807 .672 .715 r F P s P p .2 1 0 r 2 Mabswid .47595 .77315 m .46889 .77933 L s P p .2 1 0 r 2 Mabswid .41354 .73624 m .41104 .7425 L s P p .002 w .32435 .69185 m .32912 .69331 L p .33495 .64551 L .807 .672 .715 r F P s P p .2 1 0 r 2 Mabswid .41605 .72998 m .41354 .73624 L s P p .002 w .30294 .6562 m .30932 .65854 L .33495 .64551 L p .548 .093 .123 r F P s P p .002 w .30219 .65381 m .30294 .6562 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .30307 .65062 m .30219 .65381 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .30629 .649 m .30307 .65062 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .31507 .64732 m .30629 .649 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .3125 .66255 m .30932 .65854 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .3011 .67745 m .29984 .67997 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .30466 .6736 m .3011 .67745 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .33495 .64551 m .31406 .6646 L .30466 .6736 L p .837 .99 .726 r F P s P p .002 w .31654 .66332 m .3125 .66255 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .30037 .68057 m .30673 .67602 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .29984 .67997 m .30037 .68057 L p .33495 .64551 L .837 .99 .726 r F P s P p .002 w .32221 .66325 m .31654 .66332 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .32544 .66158 m .32221 .66325 L p .33495 .64551 L .548 .093 .123 r F P s P p .002 w .33495 .64551 m .32946 .65669 L .32544 .66158 L p .548 .093 .123 r F P s P p .002 w .3682 .66288 m .36534 .67089 L .33495 .64551 L p .568 .481 .716 r F P s P p .002 w .3663 .68207 m .36534 .67089 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .33952 .64835 m .34593 .6553 L .33495 .64551 L p 0 0 .524 r F P s P p .002 w .36677 .65649 m .3682 .66288 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .36342 .6485 m .36677 .65649 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .3596 .64533 m .36342 .6485 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .35151 .64379 m .3596 .64533 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .33529 .64396 m .33952 .64835 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .33039 .63898 m .33529 .64396 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .32903 .63777 m .33039 .63898 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .32985 .63912 m .32903 .63777 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .35374 .6635 m .34593 .6553 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .35659 .66666 m .35374 .6635 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .35873 .66918 m .35659 .66666 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .35731 .66791 m .35873 .66918 L p .33495 .64551 L 0 0 .524 r F P s P p .002 w .33495 .64551 m .35096 .66163 L .35731 .66791 L p 0 0 .524 r F P s P p .002 w .36392 .68526 m .3663 .68207 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .35963 .68685 m .36392 .68526 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .35582 .68365 m .35963 .68685 L p .33495 .64551 L .568 .481 .716 r F P s P p .002 w .33495 .64551 m .34869 .6725 L .35582 .68365 L p .568 .481 .716 r F P s P p .002 w .32358 .6871 m .32435 .69185 L p .33495 .64551 L .807 .672 .715 r F P s P p .002 w .33495 .64551 m .32604 .67432 L .32358 .6871 L p .807 .672 .715 r F P s P p .2 1 0 r 2 Mabswid .33591 .6446 m .34403 .63695 L s P p .2 1 0 r 2 Mabswid .36924 .58663 m .3591 .59064 L s P p .2 1 0 r 2 Mabswid .41857 .7237 m .41605 .72998 L s P p .2 1 0 r 2 Mabswid .41592 .74462 m .41503 .7516 L s P p .2 1 0 r 2 Mabswid .4168 .73765 m .41592 .74462 L s P p .2 1 0 r 2 Mabswid .37063 .6993 m .36246 .7065 L s P p .2 1 0 r 2 Mabswid .41768 .73068 m .4168 .73765 L s P p .2 1 0 r 2 Mabswid .41857 .7237 m .41768 .73068 L s P p .2 1 0 r 2 Mabswid .42661 .71697 m .41857 .7237 L s P p .2 1 0 r 2 Mabswid .4975 .86633 m .49309 .87464 L s P p .2 1 0 r 2 Mabswid .62947 .2017 m .6346 .20754 L s P p .2 1 0 r 2 Mabswid .50203 .829 m .49645 .83367 L s P p .2 1 0 r 2 Mabswid .35325 .62824 m .34403 .63695 L s P p .2 1 0 r 2 Mabswid .48308 .76691 m .47595 .77315 L s P p .002 w .52804 .88864 m .52891 .8907 L .51833 .89395 L p .572 .484 .716 r F P s P p .002 w .44732 .89102 m .44723 .89205 L .46051 .89192 L p .595 .185 .234 r F P s P p .2 1 0 r 2 Mabswid .37943 .58243 m .36924 .58663 L s P p .2 1 0 r 2 Mabswid .3789 .69186 m .37063 .6993 L s P p .2 1 0 r 2 Mabswid .43474 .70998 m .42661 .71697 L s P p .2 1 0 r 2 Mabswid .502 .85767 m .4975 .86633 L s P p .2 1 0 r 2 Mabswid .3626 .61937 m .35325 .62824 L s P p .2 1 0 r 2 Mabswid .6346 .20754 m .63978 .21344 L s P p .2 1 0 r 2 Mabswid .50763 .82397 m .50203 .829 L s P p .2 1 0 r 2 Mabswid .49028 .76036 m .48308 .76691 L s P p .2 1 0 r 2 Mabswid .38966 .57801 m .37943 .58243 L s P p .2 1 0 r 2 Mabswid .38727 .68419 m .3789 .69186 L s P p .2 1 0 r 2 Mabswid .372 .61045 m .3626 .61937 L s P p .2 1 0 r 2 Mabswid .44295 .70273 m .43474 .70998 L s P p 0 1 .1 r .0005 w .37232 .60063 Mdot P p .2 1 0 r 2 Mabswid .37664 .59499 m .37232 .60063 L s P p .2 1 0 r 2 Mabswid .50653 .84895 m .502 .85767 L s P p 0 1 .1 r .001 w .37664 .59499 Mdot P p .2 1 0 r 2 Mabswid .38098 .58934 m .37664 .59499 L s P p .002 w .48528 .87791 m .48662 .87933 L .49116 .88444 L p 0 0 .481 r F P s P p 0 1 .1 r .0015 w .38098 .58934 Mdot P p .2 1 0 r 2 Mabswid .38532 .58368 m .38098 .58934 L s P p .2 1 0 r 2 Mabswid .38154 .60138 m .372 .61045 L s P p 0 1 .1 r .002 w .38532 .58368 Mdot P p .2 1 0 r 2 Mabswid .38966 .57801 m .38532 .58368 L s P p .2 1 0 r 2 Mabswid .63978 .21344 m .64524 .21974 L s P p .2 1 0 r 2 Mabswid .49754 .75352 m .49028 .76036 L s P p .2 1 0 r 2 Mabswid .3957 .67646 m .38727 .68419 L s P p 0 1 .1 r .0005 w .37818 .60474 Mdot P p .2 1 0 r 2 Mabswid .38105 .59806 m .37818 .60474 L s P p 0 1 .1 r .001 w .38105 .59806 Mdot P p .2 1 0 r 2 Mabswid .38392 .59138 m .38105 .59806 L s P p 0 1 .1 r .0015 w .38392 .59138 Mdot P p .2 1 0 r 2 Mabswid .38679 .5847 m .38392 .59138 L s P p 0 1 .1 r .002 w .38679 .5847 Mdot P p .2 1 0 r 2 Mabswid .38966 .57801 m .38679 .5847 L s P p .2 1 0 r 2 Mabswid .39999 .57356 m .38966 .57801 L s P p .2 1 0 r 2 Mabswid .49113 .77241 m .489 .77868 L s P p .2 1 0 r 2 Mabswid .51326 .81857 m .50763 .82397 L s P p .2 1 0 r 2 Mabswid .45124 .69542 m .44295 .70273 L s P p .2 1 0 r 2 Mabswid .49326 .76612 m .49113 .77241 L s P p .2 1 0 r 2 Mabswid .51115 .83988 m .50653 .84895 L s P p .2 1 0 r 2 Mabswid .39121 .59218 m .38154 .60138 L s P p .2 1 0 r 2 Mabswid .4954 .75983 m .49326 .76612 L s P p .2 1 0 r 2 Mabswid .49594 .77454 m .49541 .78154 L s P p .2 1 0 r 2 Mabswid .49648 .76754 m .49594 .77454 L s P p .2 1 0 r 2 Mabswid .49754 .75352 m .4954 .75983 L s P p .2 1 0 r 2 Mabswid .49701 .76053 m .49648 .76754 L s P p .002 w .38893 .74877 m .38299 .75527 L p .41042 .71931 L .79 .97 .672 r F P s P p .002 w .39723 .73821 m .38893 .74877 L p .41042 .71931 L .79 .97 .672 r F P s P p .2 1 0 r 2 Mabswid .40424 .66849 m .3957 .67646 L s P p .2 1 0 r 2 Mabswid .49754 .75352 m .49701 .76053 L s P p .002 w .38299 .75527 m .37342 .7643 L p .41042 .71931 L .79 .97 .672 r F P s P p .2 1 0 r 2 Mabswid .50488 .74661 m .49754 .75352 L s P p .2 1 0 r 2 Mabswid .42005 .63293 m .41088 .63725 L s P p .2 1 0 r 2 Mabswid .41037 .5689 m .39999 .57356 L s P p .2 1 0 r 2 Mabswid .40094 .58292 m .39121 .59218 L s P p .2 1 0 r 2 Mabswid .64524 .21974 m .65099 .22641 L s P p .2 1 0 r 2 Mabswid .45961 .68786 m .45124 .69542 L s P p .2 1 0 r 2 Mabswid .51587 .83048 m .51115 .83988 L s P p .2 1 0 r 2 Mabswid .51895 .81311 m .51326 .81857 L s P p .002 w .44601 .75322 m .44061 .76688 L p .41042 .71931 L .811 .675 .714 r F P s P p .002 w .44477 .74519 m .44601 .75322 L p .41042 .71931 L .811 .675 .714 r F P s P p .002 w .4356 .73473 m .44477 .74519 L p .41042 .71931 L .811 .675 .714 r F P s P p .002 w .44061 .76688 m .43457 .77656 L p .41042 .71931 L .811 .675 .714 r F P s P p .002 w .43457 .77656 m .42056 .78391 L .41042 .71931 L p .811 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .41289 .66031 m .40424 .66849 L s P p .2 1 0 r 2 Mabswid .41081 .57354 m .40094 .58292 L s P p .002 w .37342 .7643 m .36676 .77011 L p .41042 .71931 L .79 .97 .672 r F P s P p .2 1 0 r 2 Mabswid .42081 .56403 m .41037 .5689 L s P p .2 1 0 r 2 Mabswid .51229 .7394 m .50488 .74661 L s P p .2 1 0 r 2 Mabswid .46809 .68005 m .45961 .68786 L s P p .2 1 0 r 2 Mabswid .42927 .62835 m .42005 .63293 L s P p .2 1 0 r 2 Mabswid .52062 .82101 m .51587 .83048 L s P p .002 w .40776 .79935 m .42056 .78391 L p .41042 .71931 L .811 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .65099 .22641 m .65679 .23316 L s P p .2 1 0 r 2 Mabswid .65099 .22641 m .65057 .2361 L s P p .2 1 0 r 2 Mabswid .65099 .22641 m .65737 .2261 L s P p .2 1 0 r 2 Mabswid .65099 .22641 m .6455 .23703 L s P p .2 1 0 r 2 Mabswid .65099 .22641 m .65798 .22412 L s P p .2 1 0 r 2 Mabswid .42081 .56403 m .41081 .57354 L s P p .2 1 0 r 2 Mabswid .52468 .80729 m .51895 .81311 L s P p .2 1 0 r 2 Mabswid .4216 .65206 m .41289 .66031 L s P p .2 1 0 r 2 Mabswid .65798 .22412 m .66499 .22181 L s P p 0 1 .1 r .028 w .65798 .22412 Mdot P p .002 w .36676 .77011 m .36236 .77194 L .41042 .71931 L p .79 .97 .672 r F P s P p .002 w .40038 .80105 m .40776 .79935 L p .41042 .71931 L .811 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .65737 .2261 m .66378 .22578 L s P p 0 1 .1 r .028 w .65737 .2261 Mdot P p .2 1 0 r 2 Mabswid .6455 .23703 m .64021 .24803 L s P p .2 1 0 r 2 Mabswid .42081 .56403 m .41856 .571 L s P p .2 1 0 r 2 Mabswid .42081 .56403 m .42071 .57112 L s P p .2 1 0 r 2 Mabswid .43087 .55448 m .42081 .56403 L s P p .2 1 0 r 2 Mabswid .66499 .22181 m .67202 .2195 L s P p 0 1 .1 r .021 w .66499 .22181 Mdot P p .2 1 0 r 2 Mabswid .47663 .67218 m .46809 .68005 L s P p .2 1 0 r 2 Mabswid .41856 .571 m .4163 .57797 L s P p 0 1 .1 r .008 w .41856 .571 Mdot P p .002 w .39234 .79872 m .40038 .80105 L p .41042 .71931 L .811 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .51978 .73189 m .51229 .7394 L s P p .2 1 0 r 2 Mabswid .52548 .81121 m .52062 .82101 L s P p .2 1 0 r 2 Mabswid .4163 .57797 m .41405 .58495 L s P p 0 1 .1 r .006 w .4163 .57797 Mdot P p .2 1 0 r 2 Mabswid .41405 .58495 m .41179 .59193 L s P p 0 1 .1 r .004 w .41405 .58495 Mdot P p 0 1 .1 r .002 w .41179 .59193 Mdot P p .2 1 0 r 2 Mabswid .42071 .57112 m .4206 .57822 L s P p 0 1 .1 r .008 w .42071 .57112 Mdot P p .2 1 0 r 2 Mabswid .43853 .62351 m .42927 .62835 L s P p .002 w .35666 .73921 m .36796 .74364 L .41042 .71931 L p .56 .114 .149 r F P s P p .002 w .35513 .73471 m .35666 .73921 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .35631 .72874 m .35513 .73471 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .36168 .72572 m .35631 .72874 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .37657 .72262 m .36168 .72572 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .37392 .75127 m .36796 .74364 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .35182 .78045 m .36236 .77194 L p .41042 .71931 L .79 .97 .672 r F P s P p .002 w .35107 .77974 m .35182 .78045 L p .41042 .71931 L .79 .97 .672 r F P s P p .002 w .35338 .77567 m .35107 .77974 L p .41042 .71931 L .79 .97 .672 r F P s P p .002 w .3595 .76898 m .35338 .77567 L p .41042 .71931 L .79 .97 .672 r F P s P p .002 w .41042 .71931 m .37543 .75308 L .3595 .76898 L p .79 .97 .672 r F P s P p .002 w .38103 .75274 m .37392 .75127 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .39088 .75263 m .38103 .75274 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .39628 .74947 m .39088 .75263 L p .41042 .71931 L .56 .114 .149 r F P s P p .002 w .41042 .71931 m .40256 .7402 L .39628 .74947 L p .56 .114 .149 r F P s P p .002 w .4698 .74504 m .46383 .75162 L p .49242 .71515 L .758 .952 .636 r F P s P p .002 w .46383 .75162 m .45445 .76075 L p .49242 .71515 L .758 .952 .636 r F P s P p .002 w .45445 .76075 m .45324 .76185 L p .49242 .71515 L .758 .952 .636 r F P s P p .49242 .71515 m .45324 .76185 L .46738 .74417 L .758 .952 .636 r F P p .002 w .46852 .75008 m .46342 .76368 L .45644 .75784 L p .567 .48 .716 r F P s P p .002 w .45644 .75784 m .41042 .71931 L p .4644 .7479 L .567 .48 .716 r F P s P p .4644 .7479 m .46852 .75008 L .45644 .75784 L .567 .48 .716 r F P p .002 w .46604 .73907 m .46723 .74436 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .46723 .74436 m .46852 .75008 L p .4644 .7479 L .567 .48 .716 r F P s P p .41042 .71931 m .46723 .74436 L .4644 .7479 L .567 .48 .716 r F P p .002 w .46502 .78286 m .46342 .76368 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .451 .76083 m .47689 .73227 L p .45165 .76228 L .758 .952 .636 r F P s P p .002 w .46081 .78822 m .46502 .78286 L p .41042 .71931 L .567 .48 .716 r F P s P p .46738 .74417 m .44801 .76662 L .47689 .73227 L .758 .952 .636 r F P p .002 w .45319 .7619 m .45198 .763 L p .45301 .76174 L .758 .952 .636 r F P s P p .46738 .74417 m .45319 .7619 L .45301 .76174 L .758 .952 .636 r F P p .002 w .45324 .76185 m .45319 .7619 L p .46738 .74417 L .758 .952 .636 r F P s P p .46738 .74417 m .45198 .763 L .45168 .76236 L .758 .952 .636 r F P p .002 w .45328 .79075 m .46081 .78822 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .44663 .78514 m .45328 .79075 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .41042 .71931 m .43423 .76583 L .44663 .78514 L p .567 .48 .716 r F P s P p .002 w .43399 .77705 m .44408 .76845 L p .451 .76083 L .758 .952 .636 r F P s P p .49242 .71515 m .45045 .75961 L .451 .76083 L .758 .952 .636 r F P p .45045 .75961 m .43399 .77705 L .451 .76083 L .758 .952 .636 r F P p .002 w .41042 .71931 m .4392 .74825 L .45026 .7592 L p 0 0 .527 r F P s P p .41042 .71931 m .45026 .7592 L .45026 .75919 L 0 0 .527 r F P p .41042 .71931 m .45026 .75919 L .45006 .75874 L 0 0 .527 r F P p .002 w .4335 .77632 m .43399 .77705 L p .49242 .71515 L .758 .952 .636 r F P s P p .002 w .45026 .7592 m .45085 .75978 L p .45026 .75919 L 0 0 .527 r F P s P p .41042 .71931 m .45006 .75874 L .44951 .75752 L 0 0 .527 r F P p .002 w .43608 .77219 m .4335 .77632 L p .45017 .759 L .758 .952 .636 r F P s P p .49242 .71515 m .44984 .75826 L .45017 .759 L .758 .952 .636 r F P p .44984 .75826 m .43608 .77219 L .45017 .759 L .758 .952 .636 r F P p .41042 .71931 m .44951 .75752 L .44536 .75282 L 0 0 .527 r F P p .002 w .44223 .76541 m .43608 .77219 L p .49242 .71515 L .758 .952 .636 r F P s P p .002 w .49242 .71515 m .45799 .74931 L .44223 .76541 L p .758 .952 .636 r F P s P p .002 w .4502 .7582 m .44942 .75733 L p .44951 .75752 L 0 0 .527 r F P s P p .002 w .44942 .75733 m .44536 .75282 L p .44951 .75752 L 0 0 .527 r F P s P p .002 w .45085 .75978 m .45363 .7623 L p .45006 .75874 L 0 0 .527 r F P s P p .45026 .75919 m .45085 .75978 L .45006 .75874 L 0 0 .527 r F P p .002 w .44801 .76662 m .44408 .76845 L .451 .76083 L p .758 .952 .636 r F P s P p .45165 .76228 m .44801 .76662 L .451 .76083 L .758 .952 .636 r F P p .002 w .47689 .73227 m .49242 .71515 L p .46738 .74417 L .758 .952 .636 r F P s P p .002 w .45363 .7623 m .4502 .7582 L p .44951 .75752 L 0 0 .527 r F P s P p .45006 .75874 m .45363 .7623 L .44951 .75752 L 0 0 .527 r F P p .002 w .45198 .763 m .44801 .76662 L p .45168 .76236 L .758 .952 .636 r F P s P p .002 w .4205 .72635 m .43155 .73834 L .41042 .71931 L p 0 0 .527 r F P s P p .002 w .46021 .72528 m .46604 .73907 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .45352 .71973 m .46021 .72528 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .43934 .71686 m .45352 .71973 L p .41042 .71931 L .567 .48 .716 r F P s P p .002 w .41298 .71857 m .4205 .72635 L p .41042 .71931 L 0 0 .527 r F P s P p .002 w .40419 .70965 m .41298 .71857 L p .41042 .71931 L 0 0 .527 r F P s P p .002 w .4016 .70733 m .40419 .70965 L p .41042 .71931 L 0 0 .527 r F P s P p .002 w .40254 .70921 m .4016 .70733 L p .41042 .71931 L 0 0 .527 r F P s P p .002 w .44536 .75282 m .43155 .73834 L p .41042 .71931 L 0 0 .527 r F P s P p .002 w .39105 .79064 m .39234 .79872 L p .41042 .71931 L .811 .675 .714 r F P s P p .002 w .41042 .71931 m .39526 .76874 L .39105 .79064 L p .811 .675 .714 r F P s P p .2 1 0 r 2 Mabswid .4115 .71706 m .41613 .70747 L s P p .2 1 0 r 2 Mabswid .65057 .2361 m .6504 .2462 L s P p .2 1 0 r 2 Mabswid .66378 .22578 m .67022 .22547 L s P p 0 1 .1 r .021 w .66378 .22578 Mdot P p 0 1 .1 r .0005 w .42322 .64689 Mdot P p .2 1 0 r 2 Mabswid .42704 .64107 m .42322 .64689 L s P p .2 1 0 r 2 Mabswid .4206 .57822 m .42049 .58534 L s P p 0 1 .1 r .006 w .4206 .57822 Mdot P p .2 1 0 r 2 Mabswid .65679 .23316 m .66288 .24028 L s P p .2 1 0 r 2 Mabswid .67202 .2195 m .67908 .21718 L s P p 0 1 .1 r .014 w .67202 .2195 Mdot P p .2 1 0 r 2 Mabswid .43043 .6436 m .4216 .65206 L s P p .2 1 0 r 2 Mabswid .42049 .58534 m .42038 .59246 L s P p 0 1 .1 r .004 w .42049 .58534 Mdot P p 0 1 .1 r .001 w .42704 .64107 Mdot P p .2 1 0 r 2 Mabswid .43086 .63523 m .42704 .64107 L s P p .2 1 0 r 2 Mabswid .44107 .54481 m .43087 .55448 L s P p .2 1 0 r 2 Mabswid .53045 .8011 m .52468 .80729 L s P p .2 1 0 r 2 Mabswid .64021 .24803 m .63512 .2594 L s P p 0 1 .1 r .002 w .42038 .59246 Mdot P p .2 1 0 r 2 Mabswid .67022 .22547 m .67669 .22515 L s P p 0 1 .1 r .014 w .67022 .22547 Mdot P p 0 1 .1 r .007 w .67908 .21718 Mdot P p .2 1 0 r 2 Mabswid .42201 .69545 m .41613 .70747 L s P p 0 1 .1 r .0015 w .43086 .63523 Mdot P p .2 1 0 r 2 Mabswid .43469 .62937 m .43086 .63523 L s P p .002 w .4784 .73432 m .4698 .74504 L p .49242 .71515 L .758 .952 .636 r F P s P p .2 1 0 r 2 Mabswid .53045 .8011 m .52548 .81121 L s P p .2 1 0 r 2 Mabswid .48527 .66407 m .47663 .67218 L s P p 0 1 .1 r .0005 w .42904 .65106 Mdot P p .2 1 0 r 2 Mabswid .43141 .64418 m .42904 .65106 L s P p 0 1 .1 r .002 w .43469 .62937 Mdot P p .2 1 0 r 2 Mabswid .43853 .62351 m .43469 .62937 L s P p 0 1 .1 r .001 w .43141 .64418 Mdot P p .2 1 0 r 2 Mabswid .43378 .63729 m .43141 .64418 L s P p 0 1 .1 r .0015 w .43378 .63729 Mdot P p .2 1 0 r 2 Mabswid .43616 .6304 m .43378 .63729 L s P p 0 1 .1 r .0025 w .53061 .82877 Mdot P p .2 1 0 r 2 Mabswid .53057 .82186 m .53061 .82877 L s P p .2 1 0 r 2 Mabswid .6504 .2462 m .65048 .25672 L s P p .2 1 0 r 2 Mabswid .50081 .62815 m .49146 .63264 L s P p 0 1 .1 r .002 w .43616 .6304 Mdot P p .2 1 0 r 2 Mabswid .43853 .62351 m .43616 .6304 L s P p .2 1 0 r 2 Mabswid .45142 .53504 m .44107 .54481 L s P p 0 1 .1 r .007 w .67669 .22515 Mdot P p .2 1 0 r 2 Mabswid .44788 .61863 m .43853 .62351 L s P p .2 1 0 r 2 Mabswid .43937 .63492 m .43043 .6436 L s P p 0 1 .1 r .005 w .53057 .82186 Mdot P p .2 1 0 r 2 Mabswid .53053 .81495 m .53057 .82186 L s P p .002 w .5278 .74953 m .52237 .76338 L p .49242 .71515 L .813 .678 .714 r F P s P p .002 w .52658 .7414 m .5278 .74953 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .63512 .2594 m .63001 .27084 L s P p .2 1 0 r 2 Mabswid .42806 .68326 m .42201 .69545 L s P p .002 w .51748 .73079 m .52658 .7414 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .5243 .72735 m .52733 .72432 L s P p 0 1 .1 r .0075 w .53053 .81495 Mdot P p .2 1 0 r 2 Mabswid .53049 .80803 m .53053 .81495 L s P p .002 w .52237 .76338 m .51633 .77317 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .51978 .73189 m .5243 .72735 L s P p .2 1 0 r 2 Mabswid .66288 .24028 m .66927 .24777 L s P p 0 1 .1 r .0025 w .53788 .82919 Mdot P p .2 1 0 r 2 Mabswid .53602 .82217 m .53788 .82919 L s P p 0 1 .1 r .01 w .53049 .80803 Mdot P p .2 1 0 r 2 Mabswid .53045 .8011 m .53049 .80803 L s P p 0 1 .1 r .005 w .53602 .82217 Mdot P p .2 1 0 r 2 Mabswid .53417 .81515 m .53602 .82217 L s P p .002 w .51633 .77317 m .50235 .78061 L .49242 .71515 L p .813 .678 .714 r F P s P p 0 1 .1 r .0075 w .53417 .81515 Mdot P p .2 1 0 r 2 Mabswid .53231 .80813 m .53417 .81515 L s P p 0 1 .1 r .01 w .53231 .80813 Mdot P p .2 1 0 r 2 Mabswid .53045 .8011 m .53231 .80813 L s P p .2 1 0 r 2 Mabswid .46182 .52522 m .45142 .53504 L s P p .2 1 0 r 2 Mabswid .53545 .79092 m .53045 .8011 L s P p .2 1 0 r 2 Mabswid .49402 .65571 m .48527 .66407 L s P p .2 1 0 r 2 Mabswid .43414 .67102 m .42806 .68326 L s P p .2 1 0 r 2 Mabswid .63001 .27084 m .62512 .28263 L s P p .2 1 0 r 2 Mabswid .52733 .72432 m .53497 .71645 L s P p .2 1 0 r 2 Mabswid .65048 .25672 m .65057 .26731 L s P p .2 1 0 r 2 Mabswid .44838 .62618 m .43937 .63492 L s P p .002 w .48955 .79625 m .50235 .78061 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .51021 .62338 m .50081 .62815 L s P p .2 1 0 r 2 Mabswid .47236 .51532 m .46182 .52522 L s P p .2 1 0 r 2 Mabswid .44039 .65863 m .43414 .67102 L s P p .2 1 0 r 2 Mabswid .45729 .61348 m .44788 .61863 L s P p .002 w .64649 .3871 m .6311 .40385 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .67015 .35679 m .64649 .3871 L p .71159 .2976 L .808 .979 .692 r F P s P p .2 1 0 r 2 Mabswid .66927 .24777 m .67571 .25533 L s P p .2 1 0 r 2 Mabswid .62512 .28263 m .62044 .29477 L s P p .002 w .6311 .40385 m .6081 .42429 L p .71159 .2976 L .808 .979 .692 r F P s P p .2 1 0 r 2 Mabswid .50283 .64729 m .49402 .65571 L s P p .002 w .48219 .79797 m .48955 .79625 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .44683 .64611 m .44039 .65863 L s P p .2 1 0 r 2 Mabswid .48304 .50533 m .47236 .51532 L s P p .2 1 0 r 2 Mabswid .4575 .61723 m .44838 .62618 L s P p .2 1 0 r 2 Mabswid .65057 .26731 m .65091 .27831 L s P p .002 w .47418 .7956 m .48219 .79797 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .61573 .30697 m .62044 .29477 L s P p .002 w .43957 .73523 m .45142 .7397 L .49242 .71515 L p .557 .108 .142 r F P s P p .002 w .43763 .73069 m .43957 .73523 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .43832 .72466 m .43763 .73069 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .44351 .72162 m .43832 .72466 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .45835 .71849 m .44351 .72162 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .45813 .7474 m .45142 .7397 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .46547 .74889 m .45813 .7474 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .47546 .74878 m .46547 .74889 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .48067 .74558 m .47546 .74878 L p .49242 .71515 L .557 .108 .142 r F P s P p .002 w .49242 .71515 m .47717 .76523 L .47292 .78741 L p .813 .678 .714 r F P s P p .002 w .49242 .71515 m .48625 .73623 L .48067 .74558 L p .557 .108 .142 r F P s P p .002 w .55229 .74627 m .54697 .76007 L .49242 .71515 L p .567 .481 .716 r F P s P p .002 w .50502 .72216 m .51619 .73432 L .49242 .71515 L p 0 .031 .576 r F P s P p .002 w .54976 .73512 m .55229 .74627 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .5438 .72115 m .54976 .73512 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .53691 .71553 m .5438 .72115 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .52229 .71263 m .53691 .71553 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .49719 .71428 m .50502 .72216 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .48793 .70527 m .49719 .71428 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .48501 .70293 m .48793 .70527 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .48543 .70486 m .48501 .70293 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .54856 .7795 m .54697 .76007 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .53044 .74898 m .51619 .73432 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .53525 .75444 m .53044 .74898 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .53848 .7586 m .53525 .75444 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .53536 .75606 m .53848 .7586 L p .49242 .71515 L 0 .031 .576 r F P s P p .002 w .49242 .71515 m .52291 .74441 L .53536 .75606 L p 0 .031 .576 r F P s P p .002 w .54419 .78493 m .54856 .7795 L p .49242 .71515 L .567 .481 .716 r F P s P p .002 w .53641 .78751 m .54419 .78493 L p .49242 .71515 L .567 .481 .716 r F P s P p .2 1 0 r 2 Mabswid .53545 .79092 m .53725 .78723 L s P p .002 w .52956 .78183 m .53641 .78751 L p .49242 .71515 L .567 .481 .716 r F P s P p .2 1 0 r 2 Mabswid .53601 .71535 m .5427 .70829 L s P p .002 w .49242 .71515 m .51683 .76227 L .52956 .78183 L p .567 .481 .716 r F P s P p .002 w .47292 .78741 m .47418 .7956 L p .49242 .71515 L .813 .678 .714 r F P s P p .2 1 0 r 2 Mabswid .49421 .71138 m .49813 .70317 L s P p .2 1 0 r 2 Mabswid .45329 .63354 m .44683 .64611 L s P p .2 1 0 r 2 Mabswid .51966 .61834 m .51021 .62338 L s P p .2 1 0 r 2 Mabswid .49378 .49529 m .48304 .50533 L s P p .2 1 0 r 2 Mabswid .46675 .60808 m .45729 .61348 L s P p 0 1 .1 r .0005 w .50438 .64215 Mdot P p .2 1 0 r 2 Mabswid .50819 .63621 m .50438 .64215 L s P p .002 w .79969 .39703 m .78588 .43283 L p .71159 .2976 L .818 .683 .714 r F P s P p .002 w .79687 .37516 m .79969 .39703 L p .71159 .2976 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .51176 .63863 m .50283 .64729 L s P p .2 1 0 r 2 Mabswid .67571 .25533 m .68244 .26326 L s P p .2 1 0 r 2 Mabswid .45993 .62086 m .45329 .63354 L s P p .2 1 0 r 2 Mabswid .46675 .60808 m .4575 .61723 L s P p 0 1 .1 r .001 w .50819 .63621 Mdot P p .2 1 0 r 2 Mabswid .512 .63027 m .50819 .63621 L s P p .2 1 0 r 2 Mabswid .61125 .3195 m .61573 .30697 L s P p .2 1 0 r 2 Mabswid .65091 .27831 m .65151 .28968 L s P p .2 1 0 r 2 Mabswid .50399 .691 m .49813 .70317 L s P p .002 w .77444 .34504 m .79687 .37516 L p .71159 .2976 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .50466 .48518 m .49378 .49529 L s P p .002 w .78588 .43283 m .77059 .45784 L p .71159 .2976 L .818 .683 .714 r F P s P p 0 1 .1 r .0015 w .512 .63027 Mdot P p .2 1 0 r 2 Mabswid .51583 .62431 m .512 .63027 L s P p .2 1 0 r 2 Mabswid .5505 .70005 m .5427 .70829 L s P p .2 1 0 r 2 Mabswid .46675 .60808 m .45993 .62086 L s P p 0 1 .1 r .0005 w .51043 .64632 Mdot P p .2 1 0 r 2 Mabswid .51274 .63933 m .51043 .64632 L s P p 0 1 .1 r .001 w .51274 .63933 Mdot P p .2 1 0 r 2 Mabswid .51504 .63234 m .51274 .63933 L s P p 0 1 .1 r .002 w .51583 .62431 Mdot P p .2 1 0 r 2 Mabswid .51966 .61834 m .51583 .62431 L s P p .2 1 0 r 2 Mabswid .54748 .76621 m .55108 .75879 L s P p 0 1 .1 r .0015 w .51504 .63234 Mdot P p .2 1 0 r 2 Mabswid .51735 .62534 m .51504 .63234 L s P p .2 1 0 r 2 Mabswid .60699 .33233 m .61125 .3195 L s P p 0 1 .1 r .002 w .51735 .62534 Mdot P p .2 1 0 r 2 Mabswid .51966 .61834 m .51735 .62534 L s P p .2 1 0 r 2 Mabswid .51002 .67865 m .50399 .691 L s P p .2 1 0 r 2 Mabswid .51569 .47501 m .50466 .48518 L s P p .2 1 0 r 2 Mabswid .52079 .62975 m .51176 .63863 L s P p .2 1 0 r 2 Mabswid .5292 .61325 m .51966 .61834 L s P p .2 1 0 r 2 Mabswid .46675 .60808 m .46716 .61542 L s P p .2 1 0 r 2 Mabswid .46675 .60808 m .46945 .61487 L s P p .2 1 0 r 2 Mabswid .4736 .59526 m .46675 .60808 L s P p .002 w .77059 .45784 m .73539 .47533 L .71159 .2976 L p .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .46716 .61542 m .46756 .62278 L s P p 0 1 .1 r .012 w .46716 .61542 Mdot P p .2 1 0 r 2 Mabswid .46945 .61487 m .47216 .62166 L s P p 0 1 .1 r .012 w .46945 .61487 Mdot P p .2 1 0 r 2 Mabswid .46756 .62278 m .46797 .63014 L s P p 0 1 .1 r .009 w .46756 .62278 Mdot P p .2 1 0 r 2 Mabswid .68244 .26326 m .68946 .27154 L s P p .2 1 0 r 2 Mabswid .46797 .63014 m .46838 .6375 L s P p 0 1 .1 r .006 w .46797 .63014 Mdot P p .2 1 0 r 2 Mabswid .48063 .58236 m .4736 .59526 L s P p .2 1 0 r 2 Mabswid .47216 .62166 m .47486 .62847 L s P p 0 1 .1 r .009 w .47216 .62166 Mdot P p .2 1 0 r 2 Mabswid .52676 .4648 m .51569 .47501 L s P p .2 1 0 r 2 Mabswid .51608 .66624 m .51002 .67865 L s P p .2 1 0 r 2 Mabswid .55839 .69154 m .5505 .70005 L s P p .2 1 0 r 2 Mabswid .55108 .75879 m .55648 .74765 L s P p .2 1 0 r 2 Mabswid .47486 .62847 m .47758 .6353 L s P p .002 w .6081 .42429 m .59251 .43658 L p .71159 .2976 L .808 .979 .692 r F P s P p .2 1 0 r 2 Mabswid .60271 .34523 m .60699 .33233 L s P p .2 1 0 r 2 Mabswid .65151 .28968 m .65211 .30113 L s P p .2 1 0 r 2 Mabswid .48786 .5694 m .48063 .58236 L s P p 0 1 .1 r .003 w .47758 .6353 Mdot P p .2 1 0 r 2 Mabswid .5299 .6208 m .52079 .62975 L s P p .2 1 0 r 2 Mabswid .53798 .45454 m .52676 .4648 L s P p .2 1 0 r 2 Mabswid .59866 .35841 m .60271 .34523 L s P p .2 1 0 r 2 Mabswid .5223 .65366 m .51608 .66624 L s P p .2 1 0 r 2 Mabswid .4951 .5564 m .48786 .5694 L s P p .2 1 0 r 2 Mabswid .65211 .30113 m .65298 .31296 L s P p .2 1 0 r 2 Mabswid .68946 .27154 m .69654 .27989 L s P p .2 1 0 r 2 Mabswid .56201 .73624 m .55648 .74765 L s P p .2 1 0 r 2 Mabswid .50252 .54337 m .4951 .5564 L s P p .2 1 0 r 2 Mabswid .54935 .44423 m .53798 .45454 L s P p .002 w .52171 .59606 m .51199 .6067 L p .55982 .5443 L .785 .968 .667 r F P s P p .002 w .53598 .57796 m .52171 .59606 L p .55982 .5443 L .785 .968 .667 r F P s P p .2 1 0 r 2 Mabswid .59483 .37187 m .59866 .35841 L s P p .2 1 0 r 2 Mabswid .56638 .68273 m .55839 .69154 L s P p .2 1 0 r 2 Mabswid .52869 .64094 m .5223 .65366 L s P p .2 1 0 r 2 Mabswid .51014 .53031 m .50252 .54337 L s P p .002 w .51199 .6067 m .49691 .62073 L p .55982 .5443 L .785 .968 .667 r F P s P p .2 1 0 r 2 Mabswid .5292 .61325 m .5388 .60789 L s P p .002 w .70272 .51513 m .73539 .47533 L p .71159 .2976 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .5299 .6208 m .53912 .61163 L s P p .002 w .56771 .79982 m .55923 .80931 L p .60173 .75762 L .684 .904 .557 r F P s P p .002 w .58037 .78464 m .56771 .79982 L p .60173 .75762 L .684 .904 .557 r F P s P p .2 1 0 r 2 Mabswid .56076 .43389 m .54935 .44423 L s P p .2 1 0 r 2 Mabswid .51777 .51723 m .51014 .53031 L s P p .2 1 0 r 2 Mabswid .65298 .31296 m .65411 .32513 L s P p .2 1 0 r 2 Mabswid .591 .38538 m .59483 .37187 L s P p .002 w .55923 .80931 m .54763 .82135 L .54855 .82009 L p .684 .904 .557 r F P s P p .54855 .82009 m .60173 .75762 L .55923 .80931 L .684 .904 .557 r F P p .2 1 0 r 2 Mabswid .53511 .62816 m .52869 .64094 L s P p .2 1 0 r 2 Mabswid .56757 .72476 m .56201 .73624 L s P p .2 1 0 r 2 Mabswid .52559 .50414 m .51777 .51723 L s P p .002 w .61683 .60294 m .60804 .62546 L p .55982 .5443 L .817 .681 .714 r F P s P p .002 w .61491 .58948 m .61683 .60294 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .69654 .27989 m .70392 .28858 L s P p .2 1 0 r 2 Mabswid .57231 .42352 m .56076 .43389 L s P p .2 1 0 r 2 Mabswid .53361 .49107 m .52559 .50414 L s P p .2 1 0 r 2 Mabswid .591 .38538 m .58739 .39914 L s P p .002 w .6003 .57154 m .61491 .58948 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .57443 .67386 m .56638 .68273 L s P p .002 w .60804 .62546 m .59826 .64132 L p .55982 .5443 L .817 .681 .714 r F P s P p .002 w .65117 .80643 m .64429 .8243 L .6418 .82355 L p .818 .683 .714 r F P s P p .6418 .82355 m .60173 .75762 L .65117 .80643 L .818 .683 .714 r F P p .002 w .64952 .7948 m .65117 .80643 L p .60173 .75762 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .53511 .62816 m .54169 .61526 L s P p .2 1 0 r 2 Mabswid .54163 .47798 m .53361 .49107 L s P p .002 w .63684 .77974 m .64952 .7948 L p .60173 .75762 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .54984 .46493 m .54163 .47798 L s P p .2 1 0 r 2 Mabswid .58402 .41313 m .57231 .42352 L s P p .002 w .6418 .82355 m .62632 .81891 L p .60173 .75762 L .818 .683 .714 r F P s P p .002 w .59826 .64132 m .57566 .65296 L .55982 .5443 L p .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .57327 .71303 m .56757 .72476 L s P p .2 1 0 r 2 Mabswid .55824 .45193 m .54984 .46493 L s P p .002 w .59251 .43658 m .58455 .43564 L .71159 .2976 L p .808 .979 .692 r F P s P p .2 1 0 r 2 Mabswid .58402 .41313 m .58739 .39914 L s P p .2 1 0 r 2 Mabswid .65411 .32513 m .65524 .33738 L s P p .002 w .68396 .51863 m .70272 .51513 L p .71159 .2976 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .56665 .43892 m .55824 .45193 L s P p .2 1 0 r 2 Mabswid .57524 .42598 m .56665 .43892 L s P p .2 1 0 r 2 Mabswid .58402 .41313 m .57524 .42598 L s P p .002 w .49691 .62073 m .48657 .62954 L p .55982 .5443 L .785 .968 .667 r F P s P p .2 1 0 r 2 Mabswid .54169 .61526 m .54846 .60224 L s P p .2 1 0 r 2 Mabswid .53912 .61163 m .54846 .60224 L s P p .2 1 0 r 2 Mabswid .5388 .60789 m .54846 .60224 L s P p .2 1 0 r 2 Mabswid .58402 .41313 m .58063 .42716 L s P p .2 1 0 r 2 Mabswid .58402 .41313 m .5874 .41873 L s P p .2 1 0 r 2 Mabswid .58402 .41313 m .58963 .41711 L s P p .2 1 0 r 2 Mabswid .54846 .60224 m .54901 .6097 L s P p .2 1 0 r 2 Mabswid .54846 .60224 m .55134 .60914 L s P p .2 1 0 r 2 Mabswid .54846 .60224 m .55524 .58918 L s P p .002 w .54855 .82009 m .55432 .81217 L p .60173 .75762 L .684 .904 .557 r F P s P p .2 1 0 r 2 Mabswid .65524 .33738 m .65664 .34996 L s P p .2 1 0 r 2 Mabswid .54901 .6097 m .54956 .61716 L s P p .2 1 0 r 2 Mabswid .5791 .70105 m .57327 .71303 L s P p .2 1 0 r 2 Mabswid .58063 .42716 m .57748 .4414 L s P p .2 1 0 r 2 Mabswid .54956 .61716 m .55011 .62463 L s P p .2 1 0 r 2 Mabswid .55134 .60914 m .55423 .61604 L s P p .2 1 0 r 2 Mabswid .5874 .41873 m .59079 .42436 L s P p .2 1 0 r 2 Mabswid .58963 .41711 m .59527 .42111 L s P p .002 w .62632 .81891 m .60991 .81398 L .60173 .75762 L p .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .55011 .62463 m .55066 .63211 L s P p .002 w .55487 .67823 m .57566 .65296 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .55524 .58918 m .55838 .58324 L s P p .2 1 0 r 2 Mabswid .55423 .61604 m .55693 .6225 L s P p .2 1 0 r 2 Mabswid .57633 .67173 m .58259 .66471 L s P p .2 1 0 r 2 Mabswid .57443 .67386 m .57633 .67173 L s P p .002 w .66352 .51105 m .68396 .51863 L p .71159 .2976 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .57748 .4414 m .57457 .45583 L s P p .2 1 0 r 2 Mabswid .59079 .42436 m .59244 .42708 L s P p .2 1 0 r 2 Mabswid .59527 .42111 m .59688 .42225 L s P p .2 1 0 r 2 Mabswid .57457 .45583 m .57165 .47029 L s P p .2 1 0 r 2 Mabswid .58497 .689 m .5791 .70105 L s P p .002 w .6426 .31437 m .66186 .31747 L .71159 .2976 L p .409 0 0 r F P s P p .002 w .62971 .31229 m .6426 .31437 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .60937 .30901 m .62971 .31229 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .59842 .30725 m .60937 .30901 L p .71159 .2976 L .409 0 0 r F P s P p .59842 .30725 m .71159 .2976 L .62213 .3034 L .409 0 0 r F P p .002 w .67858 .32017 m .66186 .31747 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .55966 .44765 m .55991 .45248 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .56935 .43216 m .5674 .43427 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .5674 .43427 m .55966 .44765 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .58582 .4143 m .56935 .43216 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .71159 .2976 m .62551 .37618 L p .58582 .4143 L .808 .979 .692 r F P s P p .002 w .6875 .32161 m .67858 .32017 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .55991 .45248 m .58455 .43564 L p .71159 .2976 L .808 .979 .692 r F P s P p .002 w .69896 .32345 m .6875 .32161 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .71159 .2976 m .67172 .42968 L .66043 .4888 L p .818 .683 .714 r F P s P p .002 w .70411 .32428 m .69896 .32345 L p .71159 .2976 L .409 0 0 r F P s P p .002 w .66043 .4888 m .66352 .51105 L p .71159 .2976 L .818 .683 .714 r F P s P p .002 w .71159 .2976 m .70842 .32498 L .70411 .32428 L p .409 0 0 r F P s P p .002 w .75276 .29859 m .7562 .30872 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .75133 .29438 m .75276 .29859 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .75019 .29101 m .75133 .29438 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .73208 .29207 m .74006 .30446 L .71159 .2976 L p 0 .281 .782 r F P s P p .002 w .72553 .28188 m .73208 .29207 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .71215 .26986 m .72179 .27606 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .72179 .27606 m .72553 .28188 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .70635 .26613 m .71215 .26986 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .70191 .26326 m .70635 .26613 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .75915 .31744 m .7655 .33613 L .71159 .2976 L p .573 .485 .716 r F P s P p .002 w .7562 .30872 m .75915 .31744 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .74566 .31317 m .74006 .30446 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .74827 .31722 m .74566 .31317 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .75129 .32191 m .74827 .31722 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .75254 .32386 m .75129 .32191 L p .71159 .2976 L 0 .281 .782 r F P s P p .002 w .71159 .2976 m .75354 .32542 L .75254 .32386 L p 0 .281 .782 r F P s P p .002 w .77447 .36256 m .7655 .33613 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .7818 .38417 m .77447 .36256 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .79644 .42732 m .7818 .38417 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .80648 .4569 m .79644 .42732 L p .71159 .2976 L .573 .485 .716 r F P s P p .002 w .71159 .2976 m .77901 .41989 L p .80648 .4569 L .573 .485 .716 r F P s P p .2 1 0 r 2 Mabswid .70392 .28858 m .71159 .2976 L s P p .2 1 0 r 2 Mabswid .6577 .35814 m .65831 .36286 L s P p .2 1 0 r 2 Mabswid .60009 .42453 m .60092 .42512 L s P p .2 1 0 r 2 Mabswid .59086 .65529 m .58259 .66471 L s P p .2 1 0 r 2 Mabswid .59459 .43064 m .59762 .43566 L s P p .2 1 0 r 2 Mabswid .60092 .42512 m .6066 .42915 L s P p 0 1 .1 r .009 w .60092 .42512 Mdot P p .002 w .59969 .81091 m .60991 .81398 L p .60173 .75762 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .57165 .47029 m .56896 .48491 L s P p .2 1 0 r 2 Mabswid .57346 .55516 m .5765 .54953 L s P p .002 w .48657 .62954 m .48052 .63107 L .55982 .5443 L p .785 .968 .667 r F P s P p .002 w .54291 .68078 m .55487 .67823 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .56896 .48491 m .5665 .49966 L s P p .002 w .55432 .81217 m .56047 .80374 L .60173 .75762 L p .684 .904 .557 r F P s P p 0 1 .1 r .0045 w .59762 .43566 Mdot P p 0 1 .1 r .0045 w .6066 .42915 Mdot P p .2 1 0 r 2 Mabswid .5765 .54953 m .58383 .53621 L s P p .2 1 0 r 2 Mabswid .59099 .67673 m .58497 .689 L s P p .2 1 0 r 2 Mabswid .65831 .36286 m .65998 .37583 L s P p .2 1 0 r 2 Mabswid .5665 .49966 m .56404 .51445 L s P p .002 w .59526 .80958 m .59969 .81091 L p .60173 .75762 L .818 .683 .714 r F P s P p .2 1 0 r 2 Mabswid .59135 .52286 m .58383 .53621 L s P p .002 w .52989 .67656 m .54291 .68078 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .56404 .51445 m .56182 .52933 L s P p .002 w .59036 .80811 m .59526 .80958 L p .60173 .75762 L .818 .683 .714 r F P s P p .002 w .54785 .77987 m .56881 .77964 L .60173 .75762 L p .56 .115 .15 r F P s P p .002 w .52795 .78009 m .54785 .77987 L p .60173 .75762 L .56 .115 .15 r F P s P p .52795 .78009 m .60173 .75762 L .52494 .77191 L .56 .115 .15 r F P p .002 w .53206 .76731 m .52494 .77191 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .55308 .7626 m .53206 .76731 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .56431 .79848 m .56047 .80374 L p .60173 .75762 L .684 .904 .557 r F P s P p .002 w .56598 .79619 m .56431 .79848 L p .60173 .75762 L .684 .904 .557 r F P s P p .002 w .56783 .79365 m .56598 .79619 L p .60173 .75762 L .684 .904 .557 r F P s P p .002 w .56857 .79263 m .56783 .79365 L p .60173 .75762 L .684 .904 .557 r F P s P p .002 w .60173 .75762 m .56915 .79183 L .56857 .79263 L p .684 .904 .557 r F P s P p .002 w .58178 .7795 m .56881 .77964 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .58738 .77943 m .58178 .7795 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .59358 .77937 m .58738 .77943 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .58839 .80752 m .59036 .80811 L p .60173 .75762 L .818 .683 .714 r F P s P p .002 w .60173 .75762 m .58685 .80706 L .58839 .80752 L p .818 .683 .714 r F P s P p .002 w .59606 .77934 m .59358 .77937 L p .60173 .75762 L .56 .115 .15 r F P s P p .002 w .60173 .75762 m .598 .77932 L .59606 .77934 L p .56 .115 .15 r F P s P p .002 w .66676 .79124 m .64971 .7967 L .60173 .75762 L p .567 .48 .716 r F P s P p .002 w .61852 .76639 m .62484 .77514 L .60173 .75762 L p 0 .063 .609 r F P s P p .002 w .68308 .78602 m .66676 .79124 L p .60173 .75762 L .567 .48 .716 r F P s P p .68308 .78602 m .60173 .75762 L .67784 .76699 L .567 .48 .716 r F P p .002 w .66764 .75878 m .67784 .76699 L p .60173 .75762 L .567 .48 .716 r F P s P p .002 w .61244 .75799 m .61852 .76639 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .64593 .75441 m .66764 .75878 L p .60173 .75762 L .567 .48 .716 r F P s P p .61244 .75799 m .60173 .75762 L .59875 .74463 L 0 .063 .609 r F P p .002 w .59393 .74103 m .59875 .74463 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .59354 .74348 m .59393 .74103 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .63922 .80006 m .64971 .7967 L p .60173 .75762 L .567 .48 .716 r F P s P p .002 w .62872 .7805 m .62484 .77514 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .63038 .7828 m .62872 .7805 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .63222 .78534 m .63038 .7828 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .63295 .78635 m .63222 .78534 L p .60173 .75762 L 0 .063 .609 r F P s P p .002 w .60173 .75762 m .63352 .78714 L .63295 .78635 L p 0 .063 .609 r F P s P p .002 w .63471 .8015 m .63922 .80006 L p .60173 .75762 L .567 .48 .716 r F P s P p .002 w .62973 .80309 m .63471 .8015 L p .60173 .75762 L .567 .48 .716 r F P s P p .002 w .62774 .80373 m .62973 .80309 L p .60173 .75762 L .567 .48 .716 r F P s P p .002 w .60173 .75762 m .62618 .80423 L .62774 .80373 L p .567 .48 .716 r F P s P p .2 1 0 r 2 Mabswid .60245 .74824 m .60281 .74353 L s P p .2 1 0 r 2 Mabswid .59888 .50947 m .59135 .52286 L s P p .002 w .47393 .57213 m .49403 .57831 L .55982 .5443 L p .506 .018 .033 r F P s P p .002 w .47044 .56585 m .47393 .57213 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .47124 .55756 m .47044 .56585 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .47966 .55337 m .47124 .55756 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .50396 .54902 m .47966 .55337 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .50588 .5891 m .49403 .57831 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .46422 .64369 m .48052 .63107 L p .55982 .5443 L .785 .968 .667 r F P s P p .002 w .46356 .64176 m .46422 .64369 L p .55982 .5443 L .785 .968 .667 r F P s P p .002 w .468 .63423 m .46356 .64176 L p .55982 .5443 L .785 .968 .667 r F P s P p .002 w .47821 .62307 m .468 .63423 L p .55982 .5443 L .785 .968 .667 r F P s P p .002 w .55982 .5443 m .5041 .59743 L .47821 .62307 L p .785 .968 .667 r F P s P p .002 w .51838 .59117 m .50588 .5891 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .53521 .59096 m .51838 .59117 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .54365 .58641 m .53521 .59096 L p .55982 .5443 L .506 .018 .033 r F P s P p .002 w .55982 .5443 m .53486 .62643 L .52786 .66296 L p .817 .681 .714 r F P s P p .002 w .55982 .5443 m .55198 .57328 L .54365 .58641 L p .506 .018 .033 r F P s P p .002 w .63957 .59753 m .62731 .6111 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .65837 .57442 m .63957 .59753 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .62731 .6111 m .62553 .61285 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .62553 .61285 m .61637 .62183 L p .62586 .61031 L .734 .938 .61 r F P s P p .69101 .53123 m .62553 .61285 L .62586 .61031 L .734 .938 .61 r F P p .002 w .63293 .6014 m .55982 .5443 L p .64583 .58549 L .566 .48 .716 r F P s P p .55982 .5443 m .62779 .59586 L .62733 .59204 L 0 .137 .677 r F P p .69101 .53123 m .62586 .61031 L .65488 .57432 L .734 .938 .61 r F P p .62586 .61031 m .61637 .62183 L .62589 .61008 L .734 .938 .61 r F P p .62586 .61031 m .62589 .61008 L .65488 .57432 L .734 .938 .61 r F P p .002 w .63738 .60488 m .63293 .6014 L p .63445 .60091 L .566 .48 .716 r F P s P p .63445 .60091 m .66051 .59252 L .63738 .60488 L .566 .48 .716 r F P p .002 w .66051 .59252 m .65139 .61582 L .63738 .60488 L p .566 .48 .716 r F P s P p .64583 .58549 m .66051 .59252 L .63293 .6014 L .566 .48 .716 r F P p .002 w .65394 .64813 m .65139 .61582 L p .63293 .6014 L .566 .48 .716 r F P s P p .55982 .5443 m .62285 .61383 L .63293 .6014 L .566 .48 .716 r F P p .62285 .61383 m .65394 .64813 L .63293 .6014 L .566 .48 .716 r F P p .002 w .55982 .5443 m .61234 .58842 L .62721 .60022 L p 0 .137 .677 r F P s P p .69101 .53123 m .65488 .57432 L .67188 .55336 L .734 .938 .61 r F P p .002 w .65631 .57403 m .66051 .59252 L p .55982 .5443 L .566 .48 .716 r F P s P p .002 w .64628 .55106 m .65631 .57403 L p .55982 .5443 L .566 .48 .716 r F P s P p .67188 .55336 m .62611 .60846 L .62645 .60591 L .734 .938 .61 r F P p .002 w .6465 .65738 m .65394 .64813 L p .55982 .5443 L .566 .48 .716 r F P s P p .002 w .63331 .66203 m .6465 .65738 L p .55982 .5443 L .566 .48 .716 r F P s P p .002 w .6218 .65291 m .63331 .66203 L p .55982 .5443 L .566 .48 .716 r F P s P p .65488 .57432 m .60899 .62907 L .67188 .55336 L .734 .938 .61 r F P p .65488 .57432 m .62589 .61008 L .62608 .60868 L .734 .938 .61 r F P p .002 w .55982 .5443 m .60049 .62107 L .6218 .65291 L p .566 .48 .716 r F P s P p .002 w .59663 .64041 m .59039 .64252 L .69101 .53123 L p .734 .938 .61 r F P s P p .55982 .5443 m .62721 .60022 L .62723 .60001 L 0 .137 .677 r F P p .55982 .5443 m .62723 .60001 L .62738 .59891 L 0 .137 .677 r F P p .002 w .57108 .65896 m .59039 .64252 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .62721 .60022 m .63433 .60587 L p .62723 .60001 L 0 .137 .677 r F P s P p .002 w .60899 .62907 m .59663 .64041 L p .62645 .60591 L .734 .938 .61 r F P s P p .62611 .60846 m .60899 .62907 L .62645 .60591 L .734 .938 .61 r F P p .002 w .61637 .62183 m .60899 .62907 L p .62608 .60868 L .734 .938 .61 r F P s P p .62589 .61008 m .61637 .62183 L .62608 .60868 L .734 .938 .61 r F P p .55982 .5443 m .62738 .59891 L .62779 .59586 L 0 .137 .677 r F P p .002 w .57096 .65658 m .57108 .65896 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .63433 .60587 m .64015 .60923 L p .62738 .59891 L 0 .137 .677 r F P s P p .62723 .60001 m .63433 .60587 L .62738 .59891 L 0 .137 .677 r F P p .002 w .62816 .59303 m .62733 .59204 L p .62779 .59586 L 0 .137 .677 r F P s P p .002 w .57738 .64694 m .57096 .65658 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .64015 .60923 m .63523 .6015 L p .62779 .59586 L 0 .137 .677 r F P s P p .62738 .59891 m .64015 .60923 L .62779 .59586 L 0 .137 .677 r F P p .002 w .59044 .6325 m .57738 .64694 L p .69101 .53123 L .734 .938 .61 r F P s P p .002 w .69101 .53123 m .62272 .59937 L .59044 .6325 L p .734 .938 .61 r F P s P p .002 w .63523 .6015 m .62816 .59303 L p .62779 .59586 L 0 .137 .677 r F P s P p .002 w .62733 .59204 m .60292 .56827 L p .55982 .5443 L 0 .137 .677 r F P s P p .002 w .58552 .56667 m .61275 .57462 L .61831 .57153 L p .496 .002 .014 r F P s P p .002 w .63466 .54212 m .64628 .55106 L p .55982 .5443 L .566 .48 .716 r F P s P p .002 w .61831 .57153 m .69101 .53123 L p .60236 .56101 L .496 .002 .014 r F P s P p .002 w .60292 .56827 m .55982 .5443 L p .5817 .54738 L 0 .137 .677 r F P s P p .002 w .58727 .55106 m .60292 .56827 L p .5817 .54738 L 0 .137 .677 r F P s P p .60236 .56101 m .58552 .56667 L .61831 .57153 L .496 .002 .014 r F P p .002 w .57949 .54804 m .5799 .55862 L p .59361 .55524 L .496 .002 .014 r F P s P p .002 w .60997 .53823 m .63466 .54212 L p .55982 .5443 L .566 .48 .716 r F P s P p .69101 .53123 m .5821 .54765 L .59361 .55524 L .496 .002 .014 r F P p .5821 .54765 m .57949 .54804 L .59361 .55524 L .496 .002 .014 r F P p .55982 .5443 m .56748 .538 L .5817 .54738 L 0 .137 .677 r F P p .002 w .58961 .54272 m .57949 .54804 L p .69101 .53123 L .496 .002 .014 r F P s P p .002 w .57082 .53526 m .58426 .54774 L p .5817 .54738 L 0 .137 .677 r F P s P p .56748 .538 m .57082 .53526 L .5817 .54738 L 0 .137 .677 r F P p .002 w .58426 .54774 m .58727 .55106 L p .5817 .54738 L 0 .137 .677 r F P s P p .002 w .55484 .52146 m .57082 .53526 L p .55982 .5443 L 0 .137 .677 r F P s P p .002 w .54957 .51864 m .55484 .52146 L p .55982 .5443 L 0 .137 .677 r F P s P p .002 w .54959 .5238 m .54957 .51864 L p .55982 .5443 L 0 .137 .677 r F P s P p .2 1 0 r 2 Mabswid .59086 .65529 m .59919 .64579 L s P p .002 w .52786 .66296 m .52989 .67656 L p .55982 .5443 L .817 .681 .714 r F P s P p .2 1 0 r 2 Mabswid .59715 .66424 m .59099 .67673 L s P p .2 1 0 r 2 Mabswid .65998 .37583 m .66192 .3891 L s P p .2 1 0 r 2 Mabswid .6066 .49607 m .59888 .50947 L s P p .2 1 0 r 2 Mabswid .60405 .72923 m .60281 .74353 L s P p .2 1 0 r 2 Mabswid .61449 .48268 m .6066 .49607 L s P p .002 w .62213 .3034 m .59602 .30686 L .59842 .30725 L p .409 0 0 r F P s P p .2 1 0 r 2 Mabswid .60547 .71476 m .60405 .72923 L s P p .2 1 0 r 2 Mabswid .6224 .46926 m .61449 .48268 L s P p .2 1 0 r 2 Mabswid .60628 .63759 m .60763 .63603 L s P p .2 1 0 r 2 Mabswid .59919 .64579 m .60628 .63759 L s P p .2 1 0 r 2 Mabswid .59754 .66344 m .60334 .65169 L s P p .2 1 0 r 2 Mabswid .59715 .66424 m .59754 .66344 L s P p .2 1 0 r 2 Mabswid .66192 .3891 m .66412 .40263 L s P p .2 1 0 r 2 Mabswid .63049 .45586 m .6224 .46926 L s P p .2 1 0 r 2 Mabswid .60689 .70025 m .60547 .71476 L s P p .002 w .77901 .41989 m .80785 .46093 L .80648 .4569 L p .573 .485 .716 r F P s P p .2 1 0 r 2 Mabswid .63049 .45586 m .63876 .44252 L s P p .2 1 0 r 2 Mabswid .63876 .44252 m .64703 .42915 L s P p .2 1 0 r 2 Mabswid .64703 .42915 m .65549 .41585 L s P p .2 1 0 r 2 Mabswid .60849 .68558 m .60689 .70025 L s P p .2 1 0 r 2 Mabswid .60334 .65169 m .60969 .63894 L s P p .2 1 0 r 2 Mabswid .65549 .41585 m .66412 .40263 L s P p .2 1 0 r 2 Mabswid .66412 .40263 m .66633 .41624 L s P p .2 1 0 r 2 Mabswid .65987 .41695 m .66412 .40263 L s P p .2 1 0 r 2 Mabswid .66412 .40263 m .67006 .4067 L s P p .2 1 0 r 2 Mabswid .66412 .40263 m .67171 .40469 L s P p .2 1 0 r 2 Mabswid .60763 .63603 m .61619 .62602 L s P p .2 1 0 r 2 Mabswid .61027 .67078 m .60849 .68558 L s P p .002 w .7615 .60631 m .75046 .63507 L p .69101 .53123 L .822 .686 .714 r F P s P p .002 w .75921 .58913 m .7615 .60631 L p .69101 .53123 L .822 .686 .714 r F P s P p .2 1 0 r 2 Mabswid .65584 .43145 m .65987 .41695 L s P p .2 1 0 r 2 Mabswid .67171 .40469 m .67932 .40675 L s P p 0 1 .1 r .022 w .67171 .40469 Mdot P p .2 1 0 r 2 Mabswid .67006 .4067 m .67603 .41078 L s P p 0 1 .1 r .022 w .67006 .4067 Mdot P p .2 1 0 r 2 Mabswid .61027 .67078 m .61205 .65596 L s P p .2 1 0 r 2 Mabswid .60969 .63894 m .61619 .62602 L s P p .002 w .7412 .56619 m .75921 .58913 L p .69101 .53123 L .822 .686 .714 r F P s P p .2 1 0 r 2 Mabswid .65202 .4461 m .65584 .43145 L s P p .002 w .75046 .63507 m .73823 .65535 L p .69101 .53123 L .822 .686 .714 r F P s P p .2 1 0 r 2 Mabswid .66633 .41624 m .6688 .43009 L s P p .2 1 0 r 2 Mabswid .61205 .65596 m .61402 .64103 L s P p .2 1 0 r 2 Mabswid .67932 .40675 m .68695 .40881 L s P p 0 1 .1 r .0165 w .67932 .40675 Mdot P p .2 1 0 r 2 Mabswid .64819 .46078 m .65202 .4461 L s P p .2 1 0 r 2 Mabswid .67603 .41078 m .68201 .41488 L s P p 0 1 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Evaluatable->False], Cell[328365, 13857, 14465, 746, 21, 8372, 666, "GraphicsData", "PostScript", "Graphics", Evaluatable->False] }, Closed]], Cell[342845, 14606, 914, 27, 46, "Info", Evaluatable->False] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[343820, 14640, 87, 2, 31, "Section", Evaluatable->False], Cell[343910, 14644, 401, 7, 78, "Text", Evaluatable->False], Cell[344314, 14653, 106405, 8369, 290, 83132, 8077, "GraphicsData", "PostScript", "Graphics", Evaluatable->False], Cell[450722, 23024, 236, 5, 44, "Info", Evaluatable->False] }, Closed]], Cell[CellGroupData[{ Cell[450995, 23034, 87, 2, 31, "Section", Evaluatable->False], Cell[451085, 23038, 517, 17, 66, "Text", Evaluatable->False], Cell[451605, 23057, 203, 4, 46, "Text", Evaluatable->False], Cell[451811, 23063, 230, 5, 46, "Text", Evaluatable->False], Cell[452044, 23070, 195, 4, 46, "Text", Evaluatable->False], Cell[452242, 23076, 191, 4, 46, "Text", Evaluatable->False] }, Closed]], Cell[CellGroupData[{ Cell[452470, 23085, 93, 2, 31, "Section", Evaluatable->False], Cell[452566, 23089, 247, 5, 110, "Text", Evaluatable->False] }, Closed]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)