Kentucky Junior Academy of Science

      2000 Symposium Abstracts

         
    COMPUTER SCIENCE & MATHEMATICS

    A rat digital electroencephalograph: A tool for studying epilepsy.  MARK J. GRUENTHAL, Math, Science and Technology Program, duPont Manual High School, 120 West Lee Street, Louisville, KY 40202.
         Brains consist of cells called neurons.  Neurons communicate by transmitting electrical currents.  A device called an EEG is used to record and analyze these currents.  EEGs are used mainly to detect epileptic seizures.  Much testing in the study of epilepsy takes place on rats.  Traditional EEGs use analog data that is displayed on scrolling paper.  The problems with this are that so much paper is used and that manual analysis of the traces must be done.  Through a process called analog to digital conversion, analog data can be transformed into digital data that can be stored by computer.  However, these technologies have only been implemented for human EEGs and at great cost.  The purpose of this project was to create a cost-efficient method for collecting digital EEG data on rats.  In order to do this, software was developed to input, save, and replay EEG data with a computer.  Testing was then done on rats to determine the effectiveness of the procedure.
     

    The Efficiency Level of Automated Attendance Compared to Manual Attendance, TRAVIS J. ACKERT, duPont Manual High School, 120 West Lee Street, Louisville, Kentucky 40208.
         The topic of the paper being research has to do with the efficiency of manual attendance and automatic school attendance systems.  There are many steps that go into the attendance process.  Some of the steps are gathering attendance, recording those who are or tardy, distributing attendance back to teachers, and reporting absences to parents.  Much wasted money is spent every year on employees and loss of time teaching that is needed can not be fulfilled.
         For the experiment an automatic attendance program was created and its efficiency was measured up to that of the current automatic system.  The cost, speed, and ease of use were all measured in the research.  It was found that the hypothesis was supported by the research.  Schools using the automated system would save more money and time than those with manual systems.
     

    Error Free Web Page Design.  MICHAEL L. BLACK, duPont Manual High School, 120 West Lee Street, Louisville, KY 40208.
         A program was written that was intended to eliminate common errors created by popular HTML design tools.  These errors include incorrect hyperlink addresses and incorrect directory structure.  The program treats each item in an HTML document as a object with properties.  A user would create these items, edit their properties, and adjust the order they would appear in an html document.  After doing so the program would read through the data for each object (stored in a two dimensional array) and use it to fill in blanks in pre-generated HTML code.  The program would also move all files to a single folder to prevent the document from having incorrect link addresses.  The program also does similar tasks with style sheet documents and framesets.  This software does eliminate errors caused by software, however cannot eliminate those caused by the user.
     

    Chaotic Encryption.  RYAN P. HATCH, MST, duPont Manual High School, 120 West Lee Street, Louisville, KY 40208.
         To encrypt messages with traditional methods, a stream of pseudorandom numbers must be generated to interact with the message according to the encryption algorithm.  This project looks into the possibility of using chaotic functions to provide such streams of random numbers, thereby providing integrity to the encryption key since the chaotic functions involved are very sensitive to changes in their initial conditions.  It is also very difficult to find the starting conditions of the chaotic function or to predict the next series of data from a previous series.  Special emphasis has been put on the practical aspect of building a working prototype encryption system on UNIX workstations.  The traditional secretly-distributed-key (SDK) approach incorporates a secret key that has to be transmitted via a secure channel to the destination.  A number of keys are used in a SDK system to mix with the message in various ways to form a product cipher with the desired properties.  This encryption system uses a new way to drive the key generation and coding/decoding schemes: chaotic functions.  The sensitivity to initial conditions is a useful property of such functions, in providing integrity to a single key.  One key will generate a properly decoded message; otherwise, the key will render the message into "garbage" only.  The computer programs written include their own software floating-point library, which extends the numeric precision of the system for reasons of safety and compatibility.

    Magic Grid Graphs.  MARY SUN, Mathematics Department, duPont Manual High School, 120 West Lee Street, Louisville, KY 40222.
         Let G(V,E) be a graph.  A labeling assignment, denoted by L:E{I, 2,..}, is an assignment to each edge of G by a positive integer.  Let L(e) denote the label of the edge e in this assignment L. The vertex sum at vertex u is defined
    L*(u) = S(u,r)eE(G) L(u,v).  A labeling assignment is magic with magic index w if the sum of the labels of all the edges incident to each vertex is W. If there exists a magic labeling assignment to G, then this labeled graph is a magic graph.
         The strength of a magic labeling assignment L, denoted by s(L), is the maximum of L(e) for e e E(G). If a graph can be labeled magically, then there will exist an infinite number of magic labeling assignments.  The set of all the magic assignments of G is denoted by M(G).  The magic strength of a graph G, denoted by m(G), is defined to be the minimum of s(L) for L e M(G).  If a graph is not magic, then m(G) is defined to be 0.
        New Theorem

      In grid PmXPm:
      1. is not a Magic Graph if m, n are both odd numbers.
      2. is a Magic Graph if m or n is an even number.
      3. m(G) = 1 if m = n = 2
      4. m(G) = 2 if (m = 2 and n > 2) or (n = 2 and m > 2)
      5. m(G) = 3 if m or n is even and > 2
    Framework for developing fast multi-scale adaptive wavelet-Galerkin simulations.  MATTHEW REECE, duPont Manual High School, 120 West Lee Street, Louisville, KY 40208.
         The Navier-Stokes equation for fluid flow is an extremely computationally intensive problem.  An adaptive algorithm based on wavelets at multiple scales offers advantages in ease of implementation and numerical efficiency over traditional methods of solving the Navier-Stokes equation.
         Traditionally wavelet-Galerkin methods have used representations of a function of the form f(x) = Skck fkJ (X), that is in terms of basis functions on a single scale. The multiscale form f(x) = SkckfkJo (X) + SkSJj=Jodkjyk j (x) is ideal for fast adaptive methods.  A new multiscale wavelet-Galerkin algorithm, combining the best features of these methods, is made feasible through an algorithm for finding the connection coefficients <ykj | Dxa| yk’j’> for wavelets at different scales.  The algorithm is further enhanced through the use of multiwavelets.  Multiwavelets, unlike scalar wavelets, can simultaneously satisfy conditions of orthogonality, vanishing moments, compact support, and symmetry.  A C++ library, which is highly portable and can be used with a variety of array libraries, allows rapid development of solvers for partial differential equations (PSEs).  The library was used to construct a solver for Burgers equation, a nonlinear one--dimensional PDE which exhibits shocks.  The results indicate that the library facilitates construction of PDE solvers which are fast and accurate.

      [Abstract Index]