(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' 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[ 114880, 3011]*) (*NotebookOutlinePosition[ 115525, 3033]*) (* CellTagsIndexPosition[ 115481, 3029]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["The Gessel-Viennot Algorithm for size 2", "Subtitle"], Cell[CellGroupData[{ Cell["\<\ Notebook 2: Some faults with the form of the calculations have been repaired \ or clarified. \ \>", "Section"], Cell["\<\ Here I have created a plot of the results of the Gessel-Viennot algorithm for \ small separations for particular choices of the long-term behavior.\ \>", "Text"], Cell["Separations (initial condition)", "Text"], Cell["\<\ So I will space out two parallel paths and start them with one N up and N \ right of the other, and see how this affects the entropy.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(size\ = \ 500;\)\), "\[IndentingNewLine]", \(\(slope\ = \ 0.5;\)\), "\[IndentingNewLine]", \(\(maxPosn\ = \ 100;\)\)}], "Input"], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(slope\\)\\\" is similar to existing symbol \ \\\"\\!\\(slopes\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message"] }, Open ]], Cell["\<\ Appropriate starting positions are N up and N right of the start.\ \>", "Text"], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(data\ = \ Table[N[If[ Binomial[size, Floor[\ slope\ size]]\ Binomial[size, \ Floor[slope\ size]] - Binomial[size, \ Floor[slope\ size\ ] - \ startPosn]\ Binomial[size\ , Floor[\ slope\ size]\ + \ startPosn] < 0, 0, \(1\/size\) Log[Binomial[size, Floor[\ slope\ size]]\ Binomial[size, \ Floor[slope\ size]] - Binomial[size, \ Floor[slope\ size] - startPosn]\ Binomial[size, Floor[\ slope\ size]\ + \ startPosn]]]], {startPosn, \ 0, \ maxPosn}];\)\)\)], "Input"], Cell["\<\ Note well that these data points represent a diagonal separation of one LESS \ than the parameter, meaning that data[[2]] corresponds to an initial \ separation of one, et cetera. 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