Computer Sciences Commons^™

On The Noninterpolation Of Polyhedral Maps, Adrian Riskin, D.W. Barnette

Mathematics

In this paper we show that if attention is restricted to polyhedral embeddings of graphs, no theorem analogous to the Duke interpolation theorem for 2-cell embeddings is true. We also give two interesting classes of graphs: (i) a class in which the members have polyhedral embeddings in the torus and also in orientable manifolds of arbitrarily high genus, (ii) and another in which the members have polyhedral embeddings in the projective plane and also in orientable and nonorientable manifolds of arbitrarily low Euler characteristic.

Linear Codes And Error-Correction, Karen Brown

Presidential Scholars Theses (1990 – 2006)

The process of encoding information for transmission from one source to another is a vital process in many areas of science and technology. Whenever coded information is sent, there arises a certain possibility that an error will occur, either during transmission or in decoding. Therefore, it is imperative to develop methods to detect and correct errors in a code. The study of coding theory is a "new" area of mathematics which is relatively undeveloped.

This paper focuses on the properties of linear codes -and their corresponding methods of error-correction. To simplify the issue, only binary block codes are studied; hence …

A Run-Time Decision Procedure For Responsive Computing Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences will occur if the logical and physical specifications of the system are not met. In this paper, we present a logic, Interval Temporal Logic (ITL), to specify responsive systems and give decision procedures to verify properties of the system at run-time as follows. First, we collect, during execution, events occurring in the system to represent a distributed computation. Next, we specify properties of the system using ITL formulas. Finally, we apply the decision procedures to determine satisfaction of the formulas. Thus, …

Constructing An Interval Temporal Logic For Real-Time Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A real-time system is one that involves control of one or more physical devices with essential timing requirements. Examples of these systems are command and control systems, process control systems, flight control systems, and the space shuttle avionics systems. The characteristics of these systems are that severe consequences will occur if the logical and physical timing specifications of the systems are not met.

Formal specification and verification are among the techniques to achieve reliable software for real-time systems, in which testing may be impossible or too dangerous to perform. This paper presents a modal logic, Interval Temporal , built upon …

Optimizing Communication Routing In Parallel Computer Architectures, Nikolaos T. Liolios

Masters Theses

This thesis is a research effort to improve on existing algorithms for processor placement and routing on hypercube and 2d-transputer parallel architectures that perform communications through message propagation. Given a set of processors N, randomly distributed on the parallel computer network, the problem is to find an optimal communication routing that minimizes the number of required links and intermediate processors. It was concluded that the spanning tree is the best starting heuristic for the routing problem. For hypercubes an algorithm was developed that outperforms all algorithms in the literature. For 2d-transputers the method of overlap maximization used in VLSI routing, …

A Conjectured Paradigm Shift In 21st Century Mathematics Pedagogy, Paul Isihara

ACMS Conference Proceedings 1993

With greater and greater capacity for automated content delivery, the role of teachers may shift increasingly to providing the human touch in pedagogy such as love for students.

A New Look At An Old 3:16 An Acms Devotional, Russell W. Howell

ACMS Conference Proceedings 1993

This paper examines John 3:16 in the bible by examining the language and cultural backgrounds of the verse.

Knuth's (1, 2, 1) Unstacking, Paul J. Zwier

ACMS Conference Proceedings 1993

This presentation is dedicated to Donald Knuth who has proposed many interesting and challenging problems in the Problems Section of The American Mathematical Monthly. The problem considered ist hat proposed by Barry Hayes, Knuth, and Carlos Subi (E3267 [1988,456]). The published solution, due to Albert Nijenhuis, just recently appeared in the March 1993 Monthly, pages 292-294.

The problem is as follows. Suppose that we are given n piles of blocks; the i-th pile having ai blocks, i = 1, 2, …, n. Dismantle the piles by choosing a pile having 2 or more blocks, removing …

Paper Abstracts, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Using Maple To Teach Calculus, Ken Rietz

ACMS Conference Proceedings 1993

No abstract provided.

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

ACMS Conference Proceedings 1993

No abstract provided.

Introduction (1993), Russell Howell

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Using Matlab And Mathematica In Numerical Analysis, John H. Matthews

ACMS Conference Proceedings 1993

No abstract provided.

Abraham Robinson (1918-1974): The Man And The Mathematics, Joseph W. Dauben

ACMS Conference Proceedings 1993

No abstract provided.

Infinity And The Absolute: Insights Into Our World, Our Faith, And Ourselves, Tim Pennings

ACMS Conference Proceedings 1993

No abstract provided.

Devotional Reflections, Jonathan Leech

ACMS Conference Proceedings 1993

No abstract provided.

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

ACMS Conference Proceedings 1993

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, …

Table Of Contents (1993), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Schedule (1993), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

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 …

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 …

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 …

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 …