Mathematics Commons^™

Ensuring The Satisfaction Of A Temporal Specification At Run-Time, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Mathematics and Statistics Faculty Research & Creative Works

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences can occur if the run-time behavior does not conform to the expected behavior or specifications. In this paper, we present a formal approach to ensure satisfaction of the specifications in the operational environment as follows. First we specify behavior of the systems using Interval Temporal Logic (ITL). Next we give algorithms for trace checking of programs in such systems. Finally, we present a fully distributed run-time evaluation system which causally orders the events of the system during its execution and checks …

Computing Χ² Values, John F. Dooley, Daniel C. St Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Textbooks and courses on numerical algorithms contain numerous examples which lead students to believe that the algorithm of choice for computing the zeros of a function f1994 is Newton's algorithm. In many of these courses little or no time is spent in providing students with "real world" experiences where Newton's method fails. The work presented in this paper describes a slow convergence problem encountered while trying to use Newton to estimate values for the 2 distributions. The problem occurred while the authors were trying to implement a well-known machine learning algorithm from the field of artificial intelligence. The function being …

Topologies Invariant Under A Group Action, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We study links between faithful group actions on a set and topologies on that set. In one direction, a group action has its invariant topologies (so we may regard members of the action to be homeomorphisms relative to those topologies); in the other direction, a topology has its preserving group actions (i.e., the subgroups of the homeomorphism group of the topology). This two-way passage allows us to discuss topological features of group actions as well as symmetry features of topologies.

A New Approach To Automatic Target Recognition Using Wavelet Transforms, Anitha Panapakkam, S. N. Balakrishnan, Daniel St. Clair

Computer Science Technical Reports

Automatic Target Recognition (ATR) systems have significant impact in defense applications. There is a continuing need to develop new and robust techniques to handle the increasingly complex ATR problem. The objectives of this thesis are two-fold. First a new technique to be used for ATR is developed and secondly an integrated ATR system to investigate and combine all subsystems is developed. In this thesis, we have developed a new technique for the feature extraction stage of ATR problem using wavelet transforms. Wavelet transforms have been one of the widely investigated areas of research in the past few years. The promising …

Creation And Simulation Of A Model For A Discrete Time Buffer System With Interrupted Poisson Arrivals And Uncorrelated Server Interruptions, Susanne Naegele-Jackson

Masters Theses & Specialist Projects

A mathematical model for a discrete-time buffer system with both arrival and server interruptions is developed. In this model fixed-size packets arrive at the buffer according to a Poisson distribution and are stored there until they can be transmitted over the output channel. Service times are constant and the buffer is assumed to be of infinite size. Both arrival stream as well as the service of the packets are subjected to random interruptions described by Bernoulli processes, where the interruption process of the Poisson input stream is uncorrelated to the interruptions of the output line. Expressions are derived for the …

Classification Characteristics Of Som And Art2, J. Aleshunas, D. St. Clair, W. Bond

Computer Science Technical Reports

Artificial neural network algorithms were originally designed to model human neural activities. They attempt to recreate the processes involved in such activities as learning, short term memory, and long term memory. Two widely used artificial neural network algorithms are the Self-Organizing Map (SOM) and the Adaptive Resonance Theory (ART2). Each was designed to simulate a particular biological neural activity. Both can be used as unsupervised data classifiers.

This paper compares performance characteristics of two unsupervised artificial neural network architectures; the SOM and the ART2 networks. The primary factors analyzed were classification accuracy, sensitivity to data noise, and sensitivity to the …

Classification Characteristics Of Som And Art2, J. J. Aleshunas, Daniel C. St. Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Artificial neural network algorithms were originally designed to model human neural activities. They attempt to recreate the processes involved in such activities as learning, short term memory, and long-term memory. Two widely used unsupervised artificial neural network algorithms are the Self-Organizing Map (SOM) and Adaptive Resonance Theory (ART2). Each was designed to simulate a particular biological neural activity. Both can be used as unsupervised data classifiers. This paper compares performance characteristics of two unsupervised artificial neural network architectures; the SOM and the ART2 networks. The primary factors analyzed were classification accuracy, sensitivity to data noise, and sensitivity of the algorithm …

Generating Indexing Functions Of Regularly Sparse Arrays For Array Compilers, Scott Thibault, Lenore Mullin, Matt Insall

Computer Science Technical Reports

There are many applications involving arrays that contain non-zero components in regular geometric partitions. These include triangular, diagonal, tridiagonal, banded, etc. When computing with this type of arrays, they are usually stored in a packed form and computations are performed with only the non-zero components. This packed form requires an indexing function that maps an index of the array to an index of the packed lexico-graphically stored array. This paper presents a method of describing regular partitions and of automatically generating an indexing function from that description. These methods enable an array compiler to compile array operations on these type …

Conjugating Polynomials On Finite Rings, M. Insall, L. Mullin, R. Wilkerson

Computer Science Technical Reports

No abstract provided.

Projective Plane Embeddings Of Polyhedral Pinched Maps, Adrian Riskin

Mathematics

We give various conditions on pinched-torus polyhedral maps which are necessary for their graphs to be embeddable in the projective plane. Our other main result is that even if the graph of a polyhedral map in the pinched torus is embeddable in a projective plane, the map induced by the embedding cannot be polyhedral, but must have all faces bounded by cycles. Finally, we give a class of examples of graphs which have polyhedral embeddings on the pinched torus and also on orientable surfaces of arbitrary high genus.

The Complexity Of Local Stratification, Peter Cholak, Howard A. Blair

College of Engineering and Computer Science - Former Departments, Centers, Institutes and Projects

The class of locally stratified logic programs is shown to be Π 1 1-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.

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