(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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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The application was \ installed on a server maintained by UN-L Information Services, with the \ assistance of Donna Liss, Director of Campus-Wide Information Services ,and \ Linda Hunt ,Steve Hunt and Alex MacAuly from Wolfram Research Incorporated. \ The application links input from clients using a web browser [Netscape 2.2 or \ later] to a server-side implementation of ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0b2.\n\nThis system can be consider in \"alpha-test\" mode, but it \ already stands as a proof-of-concept test with significance for distance \ education. This system shows that students using a web browser with no \ special helper applications can access an interactive page and perform \ mathematical experiments in real time. The example of a genetic algorithm \ program was chosen because\na. genetic algorithms are currently a \ high-interest area in computer science;\nb. these kinds of experiment are not \ readily done with a graphing calculator.\n\nThe author has created a number \ of ", StyleBox["Mathematica", FontSlant->"Italic"], "-based simulations and is interested in making them available on the Web \ as interactive lessons without translating them into a different language, \ such as Java.\n\nOne possibility for use of the system is to provide a \ demonstration for students with real-time prompting from a teacher connected \ through a video conferencing system. After students step through the on-line \ version, they could download a ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook for extended experimentation on their home or school computer. \ This phase of the operation would, of course, require that they have the ", StyleBox["Mathematica", FontSlant->"Italic"], " application on their machine. Alternatively, the students could perform \ off-line experiments, including \"pencil-assisted cognition\" and then return \ to the on-line system to test out their ideas." }], "Text"], Cell[CellGroupData[{ Cell["Sparse rulers", "Subsubsection"], Cell[TextData[ "Sparse rulers [Golomb rulers] will measure all the consecutive integer \ lengths from 0 to a given number n, although the ruler has fewer than n \ marks. For example the ruler with marks at 0, 1, 4, and 6 will measure the \ lengths 2\[LongDash]the distance between 4 and 6\[LongDash]and the lengths 3, \ and 5 as well.\n\nApplications of sparse ruler theory include topics to \ engineering, physics and coding theory. For example, the spacing of radio \ telescopes, called a \"minimum base-line array\" [Dewdney, 1987] is based on \ the theory of sparse rulers. There is no known formula for finding the \ minimal sparse ruler for a given value n."], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Genetic algorithms", "Subsubsection"], Cell[TextData[{ "Genetic algorithms and, more generally genetic programming, operate by \ assigning fitness values to an evolving population of solutions. Considerable \ information on genetic algorithms is available as described in the ", StyleBox["References", FontWeight->"Bold"], " section.\n\nThe sparse ruler problem provides a simple demonstration of a \ genetic algorithm. The basic procedure is to take two \"parent\" rulers and \ combine segments of one ruler with segments of the second ruler, to produce a \ set of \"offspring\" rulers. The process is somewhat analogous to chromosomal \ crossing-over. The offspring rulers are evaluated for \"fitness,\" with the \ best two rulers selected to be the new parents. Sucessive generations of \ rulers tend to have greater fitness, that is, they come closer to being \ minimal sparse rulers.\n\nThe crossing-over process is supplemented by a \ \"mutation\" process, in which new values may spontaneously occur. Here is an \ example." }], "Text"], Cell[BoxData[ \(r1\ = \ {0, \ 1, \ 2, \ 12}; \nr2\ = \ {0, \ 3, \ 7, \ 12}; \ \n offSpring[{r1, \ r2}, \ 5] = \n{{0, 1, 2, 12}, {0, 1, 2, 3, 12}, {0, 7, 11, 12}, {0, 1, 4, 12}, {0, 1, 2, 7, 12}}\)], "Input"], Cell["\<\ Each time the offSpring function is called, a different set of new \ rulers is produced. In the above example, the parent rulers r1 and r2 \ produced the five offspring rulers shown.The value 4 in the ruler {0,1,4,12} \ is the result of the mutation function. Two of the offspring then form the \ parents for the next generation. The selection of the two new parents depends \ upon the definition of \"fitness.\" For the algorithm used in this example, \ the fitness function is defined as \ \>", "Text"], Cell[BoxData[ \(TraditionalForm \`\(fitness(s_) := \(\((p + 1)\) - Length[s]\)\/\(\((p + 2)\) - Length[span(s)]\); \)\)], "Input", AspectRatioFixed->True], Cell["\<\ The respective fitness values for the five rulers shown above \ are:\ \>", "Text"], Cell[BoxData[ \({1.125`, 1.33333333333333325`, 1.2857142857142858`, 1.2857142857142858`, 1.60000000000000008`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "The Web-based ", StyleBox["Mathematica", FontSlant->"Italic"], " application" }], "Subsubsection"], Cell[TextData[{ "The author uploaded a ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0 notebook to the appropriate directory, where it was converted to html \ format with appropriate cgi-bin programming The intention of the WRI \ developers is to have the conversion system fully automatic. At present, some \ features of the conversion and the interface are under construction.\n\nThe \ interface will allow a student with no prior knowledge of ", StyleBox["Mathematica", FontSlant->"Italic"], " syntax a chance to perform experiments with sparse rulers. For example, \ the student can\na. enter a ruler and automatically measure its fitness.\nb. \ enter two rulers and automatically generate offspring rulers.\nc. enter two \ rulers and automatically generate numerous generations with an associated \ graph that plots the evolving fitness of the generations. " }], "Text"], Cell["\<\ Figure 1 shows a typical window in the current version of the \ system. The student can accept the default ruler {0, 1, 3, 8, 12} or define a \ new ruler, with standard mouse-and-click editing. 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In the \ Web-based version, most of the explanatory text has been removed, leaving the \ basic functions and some default values for the student to experiment with. \ The question of design for a Web-based application is not a simple one. \ Should the text be read in hard-copy format prior to the exploration? Should \ an on-line window contain optional text, or perhaps some additional \ instructional material, such as a short video clip or animated tutorial? As \ previously mentioned, a real-time video conferencing window is also a \ possibility." }], "Text"], Cell[GraphicsData["PICT", "\<\ e4@0:00X0MD1V`0A0_l<0?ooool0:00002P0006K0001e@000000000100X0:00X 0MD1V`2J0000oh;V02P0:07E0I/00003000000180000B0000100400300D00000 0F`0G0000000:00X0MD1V`0X02P1e@6K00002H40084008h0000<0000PGooPGoo Sgoo00`00021Oon1Oon?Ool03000085ooh5oohmoo`0J0000PGooPGooWgooo00O 0GooOool01omOol06000085ooh5ooi]oo`007o]oo`007oeoo`1P0000/Gooo000 jWoo1@00001oogoo00000?9oo`@00000Ool00000mGooo000lGoo0@00003lOol1 00000>iooo`00=Yooo/00?Qoo`400000WWooo@0Ongoo000OoGoo07P0002bOol1 00000?ioo`400000jgoo0@00003^Ool4000007oo00000?Ioo`400000oWoo0@00 003bOol100000>Qoo`400000oWoo0@00003KOol100000?ioo`400000nGoo0@00 002KOol001okOol001omOol1=@000;=oo`400000nGooo@001WooOol00000Ool0 0000oWooo@0007ooo@0017oo000007ooOoom003nOoom0009Oomoo`00001oo`00 001oo`00003nOol100000?ioo`400000oWoo0`00001oogooo@00oWooo@0047oo Ool00000Oomoo`00001oo`00001oo`00001oo`00003nOol4000007oo00000?eo 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If students were expected to learn the details of the ", StyleBox["Mathematica", FontSlant->"Italic"], " code, then additional resources might be needed. For example, ", StyleBox["Mathematica", FontSlant->"Italic"], " contains an excellent Help Browser, as well as on-line help and error \ messages. Since the genetic algorithm includes many specially-defined \ functions, additional usage information can be built into the notebook.\n\n\ Returning to the notion of Web-based experimentation, an obvious advantage of \ this experimental system is the capability for hyper-links to other Web sites \ dealing with ", StyleBox["Mathematica", FontSlant->"Italic"], ", genetic algorithms, or special pages devoted to the sparse ruler \ problem. In addition, if the Web-based server weres being used in a credit \ course, then a list-serve could be linked to a discussion page. Special \ access privileges to students could allow them to upload their own notebooks \ to a subdirectory, from which point the notebooks would be automatically \ converted to html documents for exploration by other members of the class." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["References", "Subsubsection"]], "Subsubsection"], Cell[TextData[{ "Holland, John H. ", StyleBox["Adaptation in Natural and Artificial Systems", FontSlant->"Italic"], ". MIT Press. (1992).\n\nKauffman, Stuart A. ", StyleBox["The Origins of Order", FontSlant->"Italic"], ". Oxford Press. (1993).\n\nKoza, John R. ", StyleBox["Genetic Programming", FontSlant->"Italic"], ". MIT Press. (1992)." }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["\<\ To try the server: http://crc-sybase.unl.edu/cgi-bin/Notebooks\ \>", "Subsubsection"], Cell[GraphicsData["PICT", "\<\ 1?H000000Ad1N00A0_l<0?ooool000000000005h00017@000000000N00402P00 00017@5h09X0003oQO`04`020C01P@0000@0000004P000180000400P00<02000 000003BL0000000C0081<05j0000004M0GP0000BP@210840P@210840P@2108@0 02CnA09EA3>10840R03nA09EA3>10840R03nA09EA3>10840R000:PHR8S_o0@00mol9 003oo`00ool00_o 0@00mol5003oo`00e?o^0?iE14AEE@3on`01o`3ho`40oh40lP3jo`400?go003f o`400=3o0@00oOl00?Ko0@00m_l1003[o`400?Oo1@00ool00=CokP01/05EI_iE 0D@0nOl00?So0021on[ooP3no`00o_om0?koo@3nooh0oOon0?goo@3noo`0oOom 0?ko0@00noon0?ko003nood0o_om0?koo@3noo`0oOom0?goo@3no`D00?oo003k o`T00?oo003oo`00o_om0?ko2@00ool00?oo003nood0o_l4003o003Xo`5EI_iE 0D@0nOl00?So0021on[ooP3no`00o_om0?koo@3nooh0oOon0?goo@3noo`0oOom 0?ko0@00noon0?ko003nood0o_om0?koo@3noo`0oOom0?goo@3no`D00?oo003k 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