Computer Sciences Commons^™

Optimizing Accuracy And Generalization In Numeric Classification Systems, M. D. Walters, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms that take training instances as input and produce a set of rules as output. The classifier systems focused on in this paper represent the knowledge they learn in the form of decision trees, and are built upon Quinlan's [ 1986] inductive algorithm ID3.

The ID3 algorithm suffers from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a continuous domain or from a domain with a large number of discrete values. A number of approaches have been developed for extending ID3 to handle …

The Identification And Processing Of Don't-Care Attribute Values In Id3 Decision Tree Construction, P. D. Dorr, D. C. St. Clair

Computer Science Technical Reports

ID3 is most successful when used with sets of training and testing data that contain no missing attribute values. Many times, however, real-world domains have attributes with missing values. Sometimes these attribute values may not be needed to classify an instance. Such attribute values are called don't-care attribute values. In other cases, the values are needed but are unavailable. These values are called unknown attribute values. This paper describes the difference between unknown and don't-care attribute values and discusses several ways of identifying don't-care attribute values in ID3. Numerical results are described which validate the practicality of these approaches.

Network Key Management In A Large Distributed Environment, J. J. Stapleton, D. C. St. Clair

Computer Science Technical Reports

The technique of using encryption for protecting information in a network environment involves managing encryption keys within that same network. In large distributed networks the goal of achieving a secure environment requires a secure method of performing network key management. Network security, system security, and application security by means of data encryption rely on encryption keys remaining secret.

Both international and domestic standards organizations such as the International Organization for Standardization (ISO), the American National Standards Institute (ANSI), and the National Institute of Standards and Technology (NIST) address the issues of encryption through various standards. However, these standards discuss methods …

Graph Theory Based Routing Algorithms, Bo Wu

Masters Theses

In this thesis, we study two VLSI layout problems.

We investigate the Minimum-Bend Single Row Routing Problem in which the objective function is to minimize the number of doglegs (or blends) per net. Our approach uses a graph theoretic representation in which an instance of the Single Row Routing Problem is represented by three graphs, an overlap graph, a containment graph and an interval graph. Using this graph representation, we develop three algorithms for minimum-bend single row routing problem.

We present a three-layer over-the-cell router (ICR-3) for the standard cell design style based on a new cell model which assumes …

Fractal (Reconstructive Analogue) Memory, David J. Stucki, Jordan B. Pollack

Mathematics Faculty Scholarship

This paper proposes a new approach to mental imagery that has the potential for resolving an old debate. We show that the methods by which fractals emerge from dynamical systems provide a natural computational framework for the relationship between the “deep” representations of long-term visual memory and the “surface” representations of the visual array, a distinction which was proposed by (Kosslyn, 1980). The concept of an iterated function system (IFS) as a highly compressed representation for a complex topological set of points in a metric space (Barnsley, 1988) is embedded in a connectionist model for mental imagery tasks. Two advantages …

Formation Of Clusters And Resolution Of Ordinal Attributes In Id3 Classification Trees, Chaman Sabharwal, Keith R. Hacke, Daniel C. St. Clair

Computer Science Faculty Research & Creative Works

Many learning systems have been designed to construct classification trees from a set of training examples. One of the most widely used approaches for constructing decision trees is the ID3 algorithm [Quinlan 1986]. Decision trees are ill-suited to handle attributes with ordinal values. Problems arise when a node representing an ordinal attribute has a branch for each value of the ordinal attribute in the training set. This is generally infeasible when the set of ordinal values is very large. Past approaches have sought to cluster large sets of ordinal values before the classification tree is constructed [Quinlan 1986; Lebowitz 1985; …

On Hamiltonian Line Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

Bounds On Constraint Weight Parameters Of Hopfield Networks For Stability Of Optimization Problem Solutions, Gursel Serpen

Electrical & Computer Engineering Theses & Dissertations

The purpose of the presented research is to study the convergence characteristics of Hopfield network dynamics. The relation between constraint weight parameter values and the stability of solutions of constraint satisfaction and optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. The dependency of solution stability on constraint weight parameter values is shown employing an abstract optimization problem. A theorem defining bounds on the constraint weight parameter magnitudes for solution stability of constraint satisfaction and optimization problems is proved. Simulation analysis on a set of optimization and constraint …

[Introduction To] The Vax Book: An Introduction, John R. Hubbard

Bookshelf

This book is an expansion of the book, A Gentle Introduction to the Vax System. The purpose of the book is to guide the novice, step-by-step, through the initial stages of learning to use the Digital Equipment Corporation's Vax computers, running under the VMS operating system (Version 5.0 or later). As a tutorial for beginners, this book assumes no previous experience with computers.

The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An error has been found in the cited paper; namely, Theorem 3.1 is false.

A Tale Of Two Mathematicians, Robert Brabenec

ACMS Conference Proceedings 1991

The goal of this paper is to identify some of the discoveries in mathematics during the period from 1820 to 1875 that have profoundly changed the nature of mathematics. To provide a context for this, the author compares some results of mathematics before the year 1820 with those present after 1875. And to humanize this, the author discusses the details of the life and times of two mathematicians, one who was active before 1820 and one who was active after 1875.

Cantor's Concept Of Infinity: Implications Of Infinity For Contingence, Bruce A. Hedman

ACMS Conference Proceedings 1991

Georg Cantor (1845-1918) was a devout Lutheran whose explicit Christian beliefs shaped his philosophy of science. Joseph Dauben has traced the impact Cantor's Christian convictions had on the development of transfinite set theory. In this paper I propose to examine how Cantor's transfinite set theory has contributed to an increasingly contingent world view in modern science. The contingence of scientific theories is not just a cautious tentativeness, but arises out of the actual state of the universe itself. The mathematical entities Cantor studied, transfinite numbers, he admitted were fraught with paradoxes. But he believed that they were grounded in a …

Using Mathematica To Teach Calculus, Russell W. Howell

ACMS Conference Proceedings 1991

For the past two years Westmont College has been one of the beta test sites for the calculus reform experiment being conducted at the University of Illinois under the direction of Jerry Uhl. Brown, Porta, and Uhl have created text which is integrated with Mathematica, a very powerful symbol manipulation, graphics, and number crunching software package produced by Wolfram Research, Inc. A preliminary version of this text has just been released [2]. We have used the Illinois materials for an honors course of incoming Freshmen with prior calculus experience. The purpose of this paper is to evaluate the curriculum and …

Reviving The Argument From Design: Detecting Design Through Small Probabilities, William A. Dembski

ACMS Conference Proceedings 1991

How small do probabilities of events have to get before we refuse to attribute those events to chance? Smallness of probability is itself not enough since events with extremely small probability occur all the time. But when such events are also prespecified, it becomes difficult to attribute their occurrence to chance. Typically we search for a causal account of how chance was offset. Lacking such a causal story, however, are we still justified in asserting that an extremely improbable prespecified event was not the result of chance? This question is relevant to such diverse areas as prophecy, miracles, parapsychology, gambling, …

Real Number Representations And The Distribution Of Following Segments, C.R. Rosentrater

ACMS Conference Proceedings 1991

No abstract provided.

Mathematical And Religious Knowledge In Nineteenth-Century England, Joan Richards

ACMS Conference Proceedings 1991

No abstract provided.

The Rigorous And The Natural In Eighteenth Century Mathematics, Joan Richards

ACMS Conference Proceedings 1991

No abstract provided.

Discrete Mathematics Versus Calculus - A Modern Day Extension Of The Formalist-Intuitionist Controversy, Marvin L. Johnson, Ph.D

ACMS Conference Proceedings 1991

No abstract provided.

Can Mathematical Methods Yield Theological Truth?, Jan De Koning

ACMS Conference Proceedings 1991

This paper discusses the negative impact mathematical methods in theology can have on the church by looking specifically at Arminius and Voetius, Dutch theologians living in the late sixteenth and early seventeenth century. Both Arminius and Voetius used mathematical methodology, although they came to different conclusions. I think their differences were due to their different worldviews, which in turn were fundamentally influenced by their upbringing. Both theologians, however, made the same mistake with their methodology and the church split because of that mistake.

How Has Christian Theology Furthered Mathematics?, Gene B. Chase

ACMS Conference Proceedings 1991

In revising my Bibliography of Christianity and Mathematics to include material prior to the 20th century, it is difficult to know what to include and what to exclude, since Christian presuppositions informed much scholarship in a vague, cultural sort of way. This paper is a first cut at attempting to narrow down candidates for that Bibliography by looking for specific ways in which Christian theology has furthered mathematics.

C. S. Lewis, George Macdonald, And Mathematics, David L. Neuhouser

ACMS Conference Proceedings 1991

This paper examines the influence and role of mathematics and mathematicians in the stories of George MacDonald and C. S. Lewis.

Introduction (1991), Robert Brabenec

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

Table Of Contents (1991), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

Schedule (1991), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.