(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 59008, 1435]*) (*NotebookOutlinePosition[ 143340, 4294]*) (* CellTagsIndexPosition[ 143193, 4286]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ \[LightBulb]\[LightBulb]\[LightBulb] DYNAMO 2x2x2 \[LightBulb]\ \[LightBulb]\[LightBulb] Phase Diagrams for Evolutionary Dynamics\ \>", "Title", CellFrame->True, TextAlignment->Center, FontSize->32, FontColor->GrayLevel[1], Background->RGBColor[0, 0, 0.500008]], Cell[CellGroupData[{ Cell["User-defined Parameters", "Subtitle", CellDingbat->None], Cell["\<\ When you have finished specifying paramaters, click on the \ rightmost vertical bar and press Enter (or Shift-Enter) to run the program.\ \ \>", "Text", Evaluatable->False, FontFamily->"Palatino", FontSize->14], Cell[BoxData[ \(\(Off[General::spell1];\)\)], "Input", CellOpen->False, InitializationCell->True], Cell[CellGroupData[{ Cell[TextData[StyleBox["Choice of game", "Section"]], "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["Choose a normal form game here. ", "Text", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[ RowBox[{ RowBox[{"M1", "=", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\({0, 0, 0}\), \({1, 1, 0}\)}, {\({1, 0, 1}\), \({0, 1, 1}\)} }], "\[NegativeThinSpace]", ")"}]}], " ", ";", " ", RowBox[{"M2", "=", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\({0, 1, 1}\), \({1, 0, 1}\)}, {\({1, 1, 0}\), \({0, 0, 0}\)} }], "\[NegativeThinSpace]", ")"}]}], " ", ";"}]], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Nonlinear population games", FontSlant->"Italic"]], "SmallText"], Cell[TextData[{ "To choose a nonlinear game, set ", StyleBox["nonlineargame", FontWeight->"Bold"], " = 1 and define ", StyleBox["F1[x_,y_,z_]", FontWeight->"Bold"], " , ", StyleBox["F2[x_,y_,z_] and F3[x_,y_,z_]", FontWeight->"Bold"], " as you like. In doing so, the components of x should be entered as \ x[[1]], x[[2]], and the components of y and z should be entered similarly. \ The definitions of A[. , ] are used in the normal form case." }], "Text", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{\(nonlineargame\ = 0\ ;\), "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{\(A[1, 1]\), "=", RowBox[{"(", GridBox[{ {\(M1\[LeftDoubleBracket]1, 1, 1\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]1, 2, 1\[RightDoubleBracket]\)}, {\(M2\[LeftDoubleBracket]1, 1, 1\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]1, 2, 1\[RightDoubleBracket]\)} }], ")"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{\(A[1, 2]\), "=", RowBox[{"(", GridBox[{ {\(M1\[LeftDoubleBracket]2, 1, 1\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]2, 2, 1\[RightDoubleBracket]\)}, {\(M2\[LeftDoubleBracket]2, 1, 1\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]2, 2, 1\[RightDoubleBracket]\)} }], ")"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{\(A[2, 1]\), "=", RowBox[{"(", GridBox[{ {\(M1\[LeftDoubleBracket]1, 1, 2\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]2, 1, 2\[RightDoubleBracket]\)}, {\(M2\[LeftDoubleBracket]1, 1, 2\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]2, 1, 2\[RightDoubleBracket]\)} }], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{\(A[2, 2]\), "=", RowBox[{"(", GridBox[{ {\(M1\[LeftDoubleBracket]1, 2, 2\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]2, 2, 2\[RightDoubleBracket]\)}, {\(M2\[LeftDoubleBracket]1, 2, 2\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]2, 2, 2\[RightDoubleBracket]\)} }], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{\(A[3, 1]\), "=", RowBox[{"(", GridBox[{ {\(M1\[LeftDoubleBracket]1, 1, 3\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]1, 2, 3\[RightDoubleBracket]\)}, {\(M1\[LeftDoubleBracket]2, 1, 3\[RightDoubleBracket]\), \(M1\[LeftDoubleBracket]2, 2, 3\[RightDoubleBracket]\)} }], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{\(A[3, 2]\), "=", RowBox[{"(", GridBox[{ {\(M2\[LeftDoubleBracket]1, 1, 3\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]1, 2, 3\[RightDoubleBracket]\)}, {\(M2\[LeftDoubleBracket]2, 1, 3\[RightDoubleBracket]\), \(M2\[LeftDoubleBracket]2, 2, 3\[RightDoubleBracket]\)} }], ")"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", \(F1[x_, y_, z_]\ := \ {z . \((A[1, 1] . y\ )\), z . \((A[1, 2] . y\ )\)}; \ F2[x_, y_, z_]\ := {z . \((A[2, 1] . x\ )\), z . \((A[2, 2] . x\ )\)}\ ;\), "\[IndentingNewLine]", \(F3[x_, y_, z_] := \ {x . \((A[3, 1] . y\ )\), x . \((A[3, 2] . y\ )\)}\ ; \ F[x_, y_, z_] := {F1[x, y, z], F2[x, y, z], F3[x, y, z]}\ ;\)}], "Input"] }, Closed]], Cell["\<\ Give the strategies one-character names to be printed on the phase diagram. \ \ \>", "Text", FontFamily->"Palatino"], Cell[BoxData[{ \(\(strategy[1] = "\"\ ;\)\ \), "\[IndentingNewLine]", \(\(strategy[2] = "\"\ ;\)\ \), "\[IndentingNewLine]", \(\(strategy[3] = "\"\ ;\)\), "\[IndentingNewLine]", \(\(strategy[4] = "\"\ ;\)\), "\[IndentingNewLine]", \(\(strategy[5] = "\"\ ;\)\), "\[IndentingNewLine]", \(\(strategy[6] = "\"\ ;\)\)}], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Payoff-related definitions", FontSlant->"Italic"]], "SmallText"], Cell[BoxData[ \(Clear[Fbar]\ ; \ Clear[Fhat]\ ; \ \ Clear[Fhatplus]\ ;\)], "Input", InitializationCell->True], Cell["The population's average payoff", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fbar[1]\)[x_, y_, z_, F1_] := \[Sum]\+\(i = 1\)\%2 x\[LeftDoubleBracket] i\[RightDoubleBracket]\ \(F1[x, y, z]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fbar[2]\)[x_, y_, z_, F2_] := \ \[Sum]\+\(i = 1\)\%2 y\[LeftDoubleBracket] i\[RightDoubleBracket]\ \(F2[x, y, z]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fbar[3]\)[x_, y_, z_, F3_] := \ \[Sum]\+\(i = 1\)\%2 z\[LeftDoubleBracket] i\[RightDoubleBracket]\ \(F3[x, y, z]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\ ;\)\(\[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Excess payoff vector", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fhat[1]\)[x_, y_, z_, F1_] := F1[x, y, z]\ - \ \(Fbar[1]\)[x, y, z, F1]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhat[2]\)[x_, y_, z_, F2_] := F2[x, y, z]\ - \ \(Fbar[2]\)[x, y, z, F2]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhat[3]\)[x_, y_, z_, F3_] := F3[x, y, z]\ - \ \(Fbar[3]\)[x, y, z, F3]\ ;\)\(\[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Vector of positive parts of excess payoffs", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fhatplus[1]\)[x_, y_, z_, F1_] := \ {Max[ 0, \(\(Fhat[1]\)[x, y, z, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket]], Max[0, \(\(Fhat[1]\)[x, y, z, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket]]}\ ;\)\(\ \[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhatplus[2]\)[x_, y_, z_, F2_] := \ {Max[ 0, \(\(Fhat[2]\)[x, y, z, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket]], Max[0, \(\(Fhat[2]\)[x, y, z, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]]}\ ;\)\(\ \[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhatplus[3]\)[x_, y_, z_, F3_] := \ {Max[ 0, \(\(Fhat[3]\)[x, y, z, F3]\)\[LeftDoubleBracket]1\[RightDoubleBracket]], Max[0, \(\(Fhat[3]\)[x, y, z, F3]\)\[LeftDoubleBracket]2\[RightDoubleBracket]]}\ ;\)\(\ \[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Projected payoff vector", "Subsubsection"], Cell[BoxData[ \(\(PhiF[x_, y_, z_, F1_, F2_, F3_] := Flatten[{F1[x, y, z] - {1/2, 1/2} \(\[Sum]\+\(i = 1\)\%2\( F1[x, y, z]\)[\([i]\)]\), F2[x, y, z] - {1/2, 1/2} \(\[Sum]\+\(i = 1\)\%2\( F2[x, y, z]\)[\([i]\)]\), F3[x, y, z] - {1/2, 1/2} \(\[Sum]\+\(i = 1\)\%2\( F3[x, y, z]\)[\([i]\)]\)\ }, 1];\)\)], "Input", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Choice of dynamic", "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "To specify a dynamic, select the rhs of \"", StyleBox["Dynamic", FontWeight->"Bold"], " = (.)\" (excluding the semicolon), and then press the button \ corresponding to the dynamic you desire. Definitions of the dynamics can be \ found in the closed group at the end of this section.\nDetails: If you use \ Logit[\[Eta]] or ILogit[\[Eta]], be sure to enter a value for the noise \ parameter \[Eta] in the closed group below. Making \[Eta] very small \ generates close approximations of the best response dynamic. The definition \ of the projection dynamic is only correct on the interior of the simplex, so \ boundary trajectories of the projected payoff dynamic must be added by hand. \ ", " If you use Projection and if you are not using ", StyleBox["Mathematica", FontSlant->"Italic"], " version 5 or above, do not take initial condtions on the boundary. ", "EP (excess payoff dynamic), PC (pairwise comparison dynamic), ConvexComb, \ and Other must be specified in greater detail below." }], "Text", FontFamily->"Palatino"], Cell[CellGroupData[{ Cell["Noise level for the logit and i-logit dynamics", "SmallText"], Cell[BoxData[ \(\(\[Eta]\ = \ .01\ ;\)\)], "Input"] }, Closed]], Cell[BoxData[GridBox[{ { ButtonBox["Replicator"], ButtonBox[\(Logit[\[Eta]]\)], ButtonBox["BNN"], ButtonBox["PD"], ButtonBox["Projection"], ButtonBox["Combined"]}, { ButtonBox["MSReplicator"], ButtonBox[\(ILogit[\[Eta]]\)], ButtonBox["EP"], ButtonBox["PC"], "", ButtonBox["Other"]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]]], "Input", Active->True, Evaluatable->False], Cell[BoxData[ \(\(Dynamic = Replicator\ ;\)\)], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definition of combination of two dynamics", FontSlant->"Italic"]], "SmallText"], Cell["\<\ To define a combination of two dynamics, specify the two dynamics to be \ combined, the weights on the dynamics. 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z\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\(\( Fhatplus[3]\)[x, y, z, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\)}\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[BNN] = Nash\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Excess payoff dynamic", "Subsubsection", InitializationCell->True], Cell[TextData[{ "Here one specifies the vector field sigmatilde that defines an excess \ payoff dynamic. This definition should be stated in terms of the excess \ payoff vector Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,z,F", StyleBox["i", FontSlant->"Italic"], "], which is defined as Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,z,F", StyleBox["i", FontSlant->"Italic"], "] = F", StyleBox["i", FontSlant->"Italic"], "[x,y,z] - Fbar[", StyleBox["i", FontSlant->"Italic"], "][x,y,z,F", StyleBox["i", FontSlant->"Italic"], "], for each population ", StyleBox["i ", FontSlant->"Italic"], "= 1, 2,3. (", StyleBox["Mathematica", FontSlant->"Italic"], " subtracts the scalar from the vector correctly.) When computing rest \ points, the program assumes that sigmatilde is acute, so that the rest points \ of the dynamic are the Nash equilibria of the underlying game." }], "Text", InitializationCell->True, FontFamily->"Palatino"], Cell[BoxData[ \(\(sigmatilde[x_, y_, z_, F1_, F2_, F3_] := \ {\((Max[ 0, \(\(Fhat[1]\)[x, y, z, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket]])\)^2, \ \[IndentingNewLine]\((Max[ 0, \(\(Fhat[1]\)[x, y, z, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[2]\)[x, y, z, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[2]\)[x, y, z, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[3]\)[x, y, z, F3]\)\[LeftDoubleBracket]1\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[3]\)[x, y, z, F3]\)\[LeftDoubleBracket]2\[RightDoubleBracket]])\)^2};\)\ \)], "Input", InitializationCell->True], Cell[BoxData[ \(\(EP[x_, y_, z_, F1_, F2_, F3_] := {\(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]3\[RightDoubleBracket] - y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 3\)\%4\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]4\[RightDoubleBracket] - y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 3\)\%4\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]5\[RightDoubleBracket] - z\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 5\)\%6\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket]6\[RightDoubleBracket] - z\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 5\)\%6\( sigmatilde[x, y, z, F1, F2, F3]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\)}\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(RPCharacterization[EP] = Nash\ \ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True], Cell[BoxData[""], "Input", InitializationCell->True], Cell["Pairwise Difference Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[{ \(\(\(rho[1]\)[x_, y_, z_, F1_] := {{0, Max[\(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\), "\[IndentingNewLine]", \(\(\(rho[2]\)[x_, y_, z_, F2_] := {{0, Max[\(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}};\)\), "\[IndentingNewLine]", \(\(\(rho[3]\)[x_, y_, z_, F3_] := {{0, Max[\(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}};\)\)}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(PD[x_, y_, z_, F1_, F2_, F3_] := Join[Flatten[ Transpose[\(rho[1]\)[x, y, z, F1]] . \ x - {{x\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, x\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho[ 1]\)[x, y, z, F1] . {1, 1}], Flatten[Transpose[\(rho[2]\)[x, y, z, F2]] . \ y - {{y\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, y\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho[ 2]\)[x, y, z, F2] . {1, 1}], Flatten[Transpose[\(rho[3]\)[x, y, z, F3]] . \ z - {{z\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, z\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho[ 3]\)[x, y, z, F3] . {1, 1}]]\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[PD] = Nash\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Pairwise Comparison Dynamic", "Subsubsection", InitializationCell->True], Cell["\<\ Here one specifies the vector field rho1 that defines an excess payoff \ dynamic. \ \>", "Text", InitializationCell->True], Cell[BoxData[{ \(\(\(rho1[1]\)[x_, y_, z_, F1_] := {{0, Max[\(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\), "\[IndentingNewLine]", \(\(\(rho1[2]\)[x_, y_, z_, F2_] := {{0, Max[\(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}};\)\), "\[IndentingNewLine]", \(\(\(rho1[3]\)[x_, y_, z_, F3_] := {{0, Max[\(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}};\)\)}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(PC[x_, y_, z_, F1_, F2_, F3_] := Join[Flatten[ Transpose[\(rho1[1]\)[x, y, z, F1]] . \ x - {{x\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, x\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho1[ 1]\)[x, y, z, F1] . {1, 1}], Flatten[Transpose[\(rho1[2]\)[x, y, z, F2]] . \ y - {{y\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, y\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho1[ 2]\)[x, y, z, F2] . {1, 1}], Flatten[Transpose[\(rho1[3]\)[x, y, z, F3]] . \ z - {{z\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, z\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho1[ 3]\)[x, y, z, F3] . {1, 1}]]\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[PC] = Nash\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Projection Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(closetozero = 10^\((\(-7\))\)\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(Projection[x_, y_, z_, F1_, F2_, F3_] := {Evaluate[ If[x\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\), If[x\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\), \ \(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F1[x, y, z]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[x\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\), If[x\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\), \ \(F1[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F1[x, y, z]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[\((y\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\)\ \ , If[\((y\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\ \), \(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F2[x, y, z]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[\((y\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\)\ , If[\((y\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\ \)\ , \(F2[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F2[x, y, z]\)\[LeftDoubleBracket]j\[RightDoubleBracket])\ \))\), 0], 0]], Evaluate[ If[\((z\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\)\ \ , If[\((z\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\ \), \(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F3[x, y, z]\)\[LeftDoubleBracket]j\[RightDoubleBracket])\ \))\), 0], 0]], Evaluate[ If[\((z\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\)\ , If[\((z\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F3[x, y, z]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\ \)\ , \(F3[x, y, z]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F3[x, y, z]\)\[LeftDoubleBracket]j\[RightDoubleBracket])\ \))\), 0], 0]]\ }\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(RPCharacterization[Projection] = Nash\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Other", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["\<\ Define any other dynamic you want to use. When defining be sure you follow \ same style with previously defined dynamics. Otherwise, you may need to do \ major changes in the program.\ \>", "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(Other[x_, y_, z_, F1_, F2_, F3_] := {}\ ;\)\ \ \ \ \ \ \ \ \ \ \ \ (*\ to\ be\ defined\ here*) ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(RPCharacterization[Other] = Automatic\ \ ;\)\)], "Input", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Specification of solution trajectories", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Instructions for specification of solution trajectories", "SmallText"], Cell[TextData[{ StyleBox["data", FontWeight->"Bold"], " specfies the solution trajectories to be drawn. ex,: data= {{{ .989, \ .99, .99}, 20, {Thickness[.004], Hue[1]}},\n {{ .9905, .99, .99}, 20, \ {Thickness[.004] ,Hue[.65]}}}. The first entry in the example, {{ .989, .99, \ .99}, 20, {Thickness[.004], Hue[1]}} is for the first solution trajectory. \ The entry { .989, .99, .99} describes the initial condition of the \ solution. Each initial condition is entered as a list {x2, y2, z2} \ containing the weight placed on each population's second strategy. The \ entry 20 determines the time span over which which the differential \ equational will be solved, [0, 20]. Hue[1] determines in which color the \ solution trajectory will be drawn, in this case red. Any color command can be \ used, i.e. GrayLevel, Hue, RGBColor. This structure must be followed in order \ for the program run correctly (however you can take out or add graphics \ primitives like Dashing[{...}], Thickness in the last entry of each sol \ trajectory. i.e Hue[1], or {Thickness[.004], Hue[1]}, {Dashing[{.01,.03}], \ Thickness[.004], Hue[1]}, etc). If only one solution trajectory is needed, do \ not forget the outermost brackets, i.e. { {{.011, .989, .01, .99, .01, .99}, \ 20, {Thickness[.004], Hue[1]}} }. \n", StyleBox["Dotdata", FontWeight->"Bold"], " specifies dots to be drawn at rest points, etc. ex.: dotdata={{.01, {.7, \ .2, .3}, GrayLevel[.2]}, {...........}}. creates a spehere with radius .0, \ centered at {.3, .8, .7} and with color GrayLevel[.2 ]. The color that you \ will see is influenced by a number of factors. (Simulated illumination \ determines the shading of polygons in three\[Hyphen]dimensional pictures. The \ shading of a particular polygon is computed as a sum of contributions from \ point light sources, plus a contribution from ambient light. ) \n", StyleBox["ppoints", FontWeight->"Bold"], " determines the number of line segments used when drawing the solution \ trajectories. Increase its value if the trajectories have kinks. " }], "Text"] }, Closed]], Cell[BoxData[{ \(\(data = \ {{{ .5, .51, .5}, 24, {Thickness[ .005], Hue[1]}}, {{ .5, .5, .51}, 9, {Thickness[ .005], Hue[ .7]}}}\ ;\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(dotdata = {{ .01, { .5, .5, .5}, GrayLevel[ .2]}\ };\)\[IndentingNewLine]\), \ "\[IndentingNewLine]", \(\(ppoints = 1000\ ;\)\)}], "Input", ImageRegion->{{0, 1}, {0, 1}}, CellTags->"degisken"], Cell[TextData[{ "Specify the value of ", StyleBox["frontedge", FontWeight->"Bold"], " to determine whether edge LI or edge RI is in the foreground of the \ output. This choice determines the viewpoint used by ", StyleBox["Mathematica", FontSlant->"Italic"], " (", StyleBox["LIviewpoint ", FontWeight->"Bold"], "or ", StyleBox["RIviewpoint", FontWeight->"Bold"], ") as well as which edges of the cube are dashed. 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Sandholm and \ Emin Dokumaci \n\nmail:\t\t\tDepartment of Economics\n\t\t\tUniversity of \ Wisconsin\n\t\t\t1180 Observatory Drive\n\t\t\tMadison WI 53706\n\ne-mail:\t\t\ \twhs@ssc.wisc.edu\n\t\t\tedokumaci@wisc.edu\n\t\nwebsites:\t\t", ButtonBox["http://www.ssc.wisc.edu/~whs/", ButtonData:>{ URL[ "http://www.ssc.wisc.edu/~whs/"], None}, ButtonStyle->"Hyperlink"], "\n\t\t\t", ButtonBox["http://www.ssc.wisc.edu/~edokumac/", ButtonData:>{ URL[ "http://www.ssc.wisc.edu/~edokumac/"], None}, ButtonStyle->"Hyperlink"], "\n\t\t\nDynamo website:\t\t", ButtonBox["http://www.ssc.wisc.edu/~whs/dynamo", ButtonData:>{ URL[ "http://www.ssc.wisc.edu/~whs/dynamo"], None}, ButtonStyle->"Hyperlink"], "\n \nFinancial support from the National Science Foundation under Grant \ SES-0092145 is gratefully acknowledged." }], "Text", FontFamily->"Palatino"] }, Closed]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{46, 1600}, {0, 1002}}, AutoGeneratedPackage->Automatic, ScreenStyleEnvironment->"Working", WindowToolbars->{}, PrintAction->"PrintToNotebook", InitializationCellEvaluation->True, InitializationCellWarning->False, CellGrouping->Manual, WindowSize->{901, 648}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Title"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. 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"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "gridMathematica"->FormBox[ RowBox[ {"grid", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.17499999999999999, 0}, {0, 0}}]}], TextForm], "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.17499999999999999, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Verdana", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "SlideShow"]], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{60, Inherited}, {2, 10}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "gridMathematica"->FormBox[ RowBox[ {"grid", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.17499999999999999, 0}, {0, 0}}]}], TextForm], "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.17499999999999999, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsubsection", FontFamily->"Verdana", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "SlideShow"]], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{60, 10}, {7, 7}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "gridMathematica"->FormBox[ RowBox[ {"grid", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.17499999999999999, 0}, {0, 0}}]}], TextForm], "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> 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10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "SlideShow"]], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, TextJustification->0.5, Hyphenation->True, FontSize->7] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. Some attributes for these styles are actually set in FormatType Styles \ (in the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{66, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Mathematica", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["Input", "SlideShow"]], Cell[StyleData["Input", "Printout"], 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LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{66, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->11], Cell[StyleData["Output", "SlideShow"]], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, AutoStyleOptions->{"UnmatchedBracketStyle"->None}, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0.6, 0.100008, 0.100008]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Message", "SlideShow"]], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->7, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Print", "SlideShow"]], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->10], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "SlideShow"]], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0.269993, 0.308507, 0.6]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "SlideShow"]], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["FrameLabel"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["FrameLabel", "Presentation"], FontSize->12], Cell[StyleData["FrameLabel", "Condensed"], FontSize->9], Cell[StyleData["FrameLabel", "SlideShow"]], Cell[StyleData["FrameLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a \ cell exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["InlineFormula", "SlideShow"]], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["DisplayFormula", "SlideShow"]], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{60, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Program", "SlideShow"]], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Outline Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Outline1"], CellMargins->{{60, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, ParagraphIndent->-38, CounterIncrements->"Outline1", CounterAssignments->{{"Outline2", 0}, {"Outline3", 0}, {"Outline4", 0}}, FontSize->18, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>CapitalRomanNumeral}], Cell[StyleData["Outline1", "SlideShow"]], Cell[StyleData["Outline1", "Printout"], CounterBoxOptions->{CounterFunction:>CapitalRomanNumeral}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline2"], CellMargins->{{90, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, ParagraphIndent->-27, CounterIncrements->"Outline2", CounterAssignments->{{"Outline3", 0}, {"Outline4", 0}}, FontSize->15, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}], Cell[StyleData["Outline2", "SlideShow"]], Cell[StyleData["Outline2", "Printout"], CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline3"], CellMargins->{{120, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, ParagraphIndent->-21, CounterIncrements->"Outline3", CounterAssignments->{{"Outline4", 0}}, FontSize->12, CounterBoxOptions->{CounterFunction:>Identity}], Cell[StyleData["Outline3", "SlideShow"]], Cell[StyleData["Outline3", "Printout"], CounterBoxOptions->{CounterFunction:>Identity}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline4"], CellMargins->{{150, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, ParagraphIndent->-18, CounterIncrements->"Outline4", FontSize->10, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["Outline4", "SlideShow"]], Cell[StyleData["Outline4", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "SlideShow"]], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Condensed"], FontSize->11], Cell[StyleData["MainBookLink", "SlideShow"]], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "Condensed"], FontSize->11], Cell[StyleData["AddOnsLink", "SlideShow"]], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "SlideShow"]], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLinkText", "SlideShow"]], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "SlideShow"]], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "SlideShow"]], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "SlideShow"]], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "SlideShow"]], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "SlideShow"]], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, 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TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "SlideShow"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "SlideShow"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. 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For example, \ \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and \ parenthesis characters are displayed (typically by coloring them to make them \ stand out).\ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], FontSize->18], Cell[StyleData["MathCaption", "SlideShow"]], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{39, 0}, {0, 14}}, Hyphenation->True, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ObjectName"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["ObjectName", "Presentation"], FontSize->18], Cell[StyleData["ObjectName", "SlideShow"]], Cell[StyleData["ObjectName", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Usage"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Usage", "Presentation"], FontSize->18], Cell[StyleData["Usage", "SlideShow"]], Cell[StyleData["Usage", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Notes"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Notes", "Presentation"], FontSize->18], Cell[StyleData["Notes", "SlideShow"]], Cell[StyleData["Notes", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InlineOutput"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InlineOutput", "Presentation"], FontSize->18], Cell[StyleData["InlineOutput", "SlideShow"]], Cell[StyleData["InlineOutput", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Box"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["Box", "Presentation"], FontSize->18], Cell[StyleData["Box", "SlideShow"]], Cell[StyleData["Box", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DoubleBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->2, RowAlignments->Top}], Cell[StyleData["DoubleBox", "Presentation"], FontSize->18], Cell[StyleData["DoubleBox", "SlideShow"]], Cell[StyleData["DoubleBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["1ColumnBox", "SlideShow"]], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.31, 0.67}}], Cell[StyleData["2ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnBox", "SlideShow"]], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->9, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnEvenBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.46}], Cell[StyleData["2ColumnEvenBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnEvenBox", "SlideShow"]], Cell[StyleData["2ColumnEvenBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.35, ColumnAlignments->{Right, Left}}], Cell[StyleData["2ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnSmallBox", "SlideShow"]], Cell[StyleData["2ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.32}], Cell[StyleData["3ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnBox", "SlideShow"]], Cell[StyleData["3ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.24, ColumnAlignments->{Right, Center, Left}}], Cell[StyleData["3ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnSmallBox", "SlideShow"]], Cell[StyleData["3ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["4ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.13, 0.35, 0.13, 0.35}}], Cell[StyleData["4ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["4ColumnBox", "SlideShow"]], Cell[StyleData["4ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["5ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.202}], Cell[StyleData["5ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["5ColumnBox", "SlideShow"]], Cell[StyleData["5ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->9, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["6ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.12, 0.22, 0.12, 0.12, 0.22, 0.12}}], Cell[StyleData["6ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["6ColumnBox", "SlideShow"]], Cell[StyleData["6ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["FramedBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions->{RowSpacings->1.5, ColumnAlignments->{Left}}], Cell[StyleData["FramedBox", "Presentation"], FontSize->18], Cell[StyleData["FramedBox", "SlideShow"]], Cell[StyleData["FramedBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.4, 0.6}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox", "Presentation"], FontSize->18], Cell[StyleData["DefinitionBox", "SlideShow"]], Cell[StyleData["DefinitionBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[1]] }, 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