Mathematics Commons^™

Signal Processing With Neural Networks, Pero Smrzlic

Masters Theses

In this study, we introduce the Adaptive Back Propagation (ABP) learning algorithm, computationally superior to the standard Back Propagation. The ABP is based on the new activation function, with its corresponding adaptive learning parameter. By using the combination of computer simulations and analysis in the domain of activation function, the Method of One Hidden layer was developed for the effective utilization of units in one-hidden layer networks. A parallel version of the ABP was designed and implemented on a nCUBE-2 supercomputer with 128 processors.

The simulation results suggested a strong correlation between frequency of signals and the role of hidden …

Dynamic Id3: A Symbolic Learning Algorithm For Many-Valued Attribute Domains, Roger Gallion, Chaman Sabharwal, Daniel C. St. Clair, William E. Bond

Computer Science Faculty Research & Creative Works

Quinlan's ID3 machine learning algorithm induces classification trees (rules) from a set of training examples. The algorithm is extremely effective when training examples are composed of attributes whose values are taken from small discrete domains. The classification accuracy of ID3-produced trees on domains whose attributes are many-valued tends to be marginal due to the large number of possible values which may be associated with each attribute. Attempts to solve this problem by a priori grouping of attribute values into distinct subsets has met with limited success. The dynamic ID3 algorithm improves the performance of ID3 on this type of problem …

Georg Cantor And The Battle For Transfinite Set Theory, Joseph Dauben

ACMS Journal 2004

Georg Cantor is well known as the founder of transfinite set theory. Equally celebrated, however, are the obstacles he faced in trying to win acceptance for his seemingly unorthodox views, his acrimonious differences with Leopold Kronecker and his unfortunate but progressively debilitating nervous breakdowns that some authors have linked directly to his many problems with set theory. Above all, Cantor's justification of set theory was all the more urgent because of Kronecker's critical denunciation of Cantor's mathematics. In tracing the evolution of Cantorian set theory, it is necessary to examine the opposition it met, and evaluate the technical, philosophical, psychological, …

On Extremal Nonsupereulerian Graphs With Clique Number M, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

On The Edge Arboricity Of A Random Graph, P. A. Catlin, Zhi-Hong Chen, E. M. Palmer

Scholarship and Professional Work - LAS

No abstract provided.

On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia

Complex Systems Faculty Publications and Presentations

To achieve reduced training time and improved generalization with artificial neural networks (ANN, or NN), it is important to use a reduced complexity NN structure. A "problem" is defined by constraints among the variables describing it. If knowledge about these constraints could be obtained a priori, this could be used to reduce the complexity of the ANN before training it. Systems theory literature contains methods for determining and representing structural aspects of constrained data (these methods are herein called GSM, general systems method). The suggestion here is to use the GSM model of the given data as a pattern for …

Pseudobases In Direct Powers Of An Algebra, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A subset P of an abstract algebra A is a pseudobasis if every function from P into A extends uniquely to an endomorphism on A. A is called K-free has a pseudobasis of cardinality K; A is minimally free if A has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the 1-free groups are always abelian, and are precisely the additive groups of E-rings.) Our interest here is in the existence of pseudobases in direct powers A^I of an algebra A. On the positive side, if A is a rigid …

An Animation System For Shift Reduce Parsers, M. S. Mandl, T. J. Sager, D. C. St. Clair

Computer Science Technical Reports

This paper presents the design and implementation of the Parse Display Utility (POU) system. This system introduces a mechanism to augment traditional methods of exploring parsing theory by providing a PRESENTATION scheme which allows a user to view the operation of a shift-reduce parser.

The overall operation of the tool revolves around an LALR (LookAhead LR) parser/parser generator and is managed by a Graphical User-Interface (GUI) developed using Borland's Turbo Vision product. The GUI allows access to a facility which draws derivation trees in Turbo Pascal graphics. This parse tree facility utilizes an algorithm which can easily be ported to …

The Management Of Replicated Data, Hsueh-Chi Shih, C. Y. Ho, S. Alptekin

Computer Science Technical Reports

Data replication, which has the benefits of improving system availability and read performance, proved to be indispensable to many database applications. In a replicated database, the one-copy serializability of transaction executions can be ensured by employing a replica control mechanism on top of the traditional concurrency control mechanism. This work contains two replica control algorithms and a read-only transaction processing algorithm. Both replica control algorithms handle multiple site, communication and partitioning failures. The replica control algorithms achieve read operation efficiency by always translating a logical read operation into one local physical read operation and by taking advantage of the locality …

Effects Of Nonsymmetric Release Times On Rate Monotonic Scheduling, R. G. Karl, T. L. Lo, D. C. St. Clair

Computer Science Technical Reports

This paper discusses problems associated with scheduling periodic tasks in a hard, real-time processing or computing environment using a static-priority, preemptive-resume operating system . The scheduling problems associated with a task set containing a single periodic task which has two fixed release periods of unequal length are examined. Some real-world applications may require task release times which are periodic, but whose tasking periods are not symmetric. A scheduling algorithm for task sets with a single nonsymmetric task has been developed for staticpriority, preemptive-resume operating systems. The nonsymmetric scheduling algorithm is based on the rate monotonic scheduling algorithm which assigns higher …

Design Of Backpropagation Neural Network Architectures Using A Decision Tree Classifier, B. M. Van Horn, D. C. St. Clair

Computer Science Technical Reports

The backpropagation neural network algorithm is a popular machine learning methodology. One difficulty with using the algorithm is that the network architecture must be designed before learning can occur. This includes deciding the number of layers, the number of nodes in each layer, and the number of connections. Traditionally this problem is solved by heuristics gained by an expert through experience.

This paper presents an algorithm for using ID3 decision trees to design the network architecture. Previous approaches rely on binary decision trees. The proposed technique utilizes n-ary trees. These trees are easier to understand, are better suited for continuous-valued …

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 …

On Hamiltonian Line Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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; …

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.