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Articles 1 - 30 of 32
Full-Text Articles in Mathematics
Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr
Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr
Rudolf Kaehr
Report for the EMBASSI Project
A Hierarchy Of Maps Between Compacta, Paul Bankston
A Hierarchy Of Maps Between Compacta, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …
Computational Geometry Column 36, Joseph O'Rourke
Computational Geometry Column 36, Joseph O'Rourke
Computer Science: Faculty Publications
Two results in "computational origami" are illustrated.
Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group
Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group
Computer Science: Faculty Publications
We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open.
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Mathematics, Statistics and Computer Science Faculty Research and Publications
A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5<HS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for …
Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko
Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko
Computer Science: Faculty Publications
Everett et al. [EHN96, EHN97] introduced several varieties of stabbing information for the lines determined by pairs of vertices of a simple polygon P, and established their relationships to vertex visibility and other combinatorial data. In the same spirit, we define the “zero-parity (ZP) stabbing information” to be a natural weakening of their “weak stabbing information,” retaining only the distinction among {zero, odd, even > 0} in the number of polygon edges stabbed. Whereas the weak stabbing information’s relation to visibility remains an open problem, we completely settle the analogous questions for zero parity information, with three results: (1) ZP information …
The Deconstruction Of Mathematics, David J. Stucki
The Deconstruction Of Mathematics, David J. Stucki
ACMS Conference Proceedings 1999
This paper is a criticism of Reuben Hersh's What is Mathematics, Really? and the humanist philosophy of mathematics.
Teaching Linear Algebra And Abstract Algebra With Two Way Video And Audio, Edward Reinke
Teaching Linear Algebra And Abstract Algebra With Two Way Video And Audio, Edward Reinke
ACMS Conference Proceedings 1999
An outline of a presentation discussing teaching two different algebra courses long-distance as well as in a classroom.
Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser
Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser
ACMS Conference Proceedings 1999
Although a Christian, an author, and a mathematician, Charles Letwidge Dodgson (better known as Lewis Carroll) wrote very few works in which these three aspects of his person was present. The only examples of him merging these interests are in Sylvie and Bruno and Sylvie and Bruno Concluded. This paper will explore what motivated him to make these works and whether or not they were successful.
Book Review - The Language Of Mathematics: Making The Invisible Visible By Kieth Devlin, Charles R. Hampton
Book Review - The Language Of Mathematics: Making The Invisible Visible By Kieth Devlin, Charles R. Hampton
ACMS Conference Proceedings 1999
Charles R. Hampton reviews The Language of Mathematics: Making the Invisible Visible. By Kieth Devlin. W. H. Freeman and Company, 1998
Book Review: Virtual Gods: The Seduction Of Power And Pleasure In Cyberspace, Jonathan R. Senning
Book Review: Virtual Gods: The Seduction Of Power And Pleasure In Cyberspace, Jonathan R. Senning
ACMS Conference Proceedings 1999
This paper is a review of Virtual Gods: The Seduction of Power and Pleasure in Cyberspace, edited by Tal Brooke, Harvest House Publishers, 1997.
Tracking The Trochoid On Safari, Andrew Simoson
Tracking The Trochoid On Safari, Andrew Simoson
ACMS Conference Proceedings 1999
While on sabbatical in Dar es Salaam in 1997–98, I was tasked to be the department’s seminar director and discovered that a dearth of speakers roam about in east Africa; so I opted to set up a lecture tour for myself to include Zambia, Zimbabwe, and Botswana as well as Tanzania—and spoke about the envelope of curves generated by a series of line segments obtained when two runners attached by an ideal bungee cord (the line segments) proceed about a circular track. Herein we describe life in east Africa and show that those envelopes are trochoids.
Revolutions In Mathematics (Book Review), Kevin Vander Meulen
Revolutions In Mathematics (Book Review), Kevin Vander Meulen
ACMS Conference Proceedings 1999
A review of Revolutions in Mathematics, edited by Donald Gillies, Clarendon Press, Oxford 1992.
A Mathematician At The Science And Theology Book Club, Greg Crow
A Mathematician At The Science And Theology Book Club, Greg Crow
ACMS Conference Proceedings 1999
This paper is a case study of the insights gained and the contributions made in a weekly Science and Theology Faculty Book Club. The contribution of other group members to the expansion of one’s general understanding of their fields is demonstrated in increased vocabulary, use of existing theoretical models, glimpses of the depth of their disciplines, and in the recognition of the need for humility. The mathematician may contribute by helping to clarify definitions, by applying basic ideas in their own and related fields, and only very rarely by bringing their own research to the table.
Book Review, David J. Stucki
Book Review, David J. Stucki
ACMS Conference Proceedings 1999
A book review of Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science by Alan Sokal and Jean Bricmont.
Preface (1999), Association Of Christians In The Mathematical Sciences
Preface (1999), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1999
Twelfth ACMS Conference on Mathematics from a Christian Perspective
Introduction (1999), Association Of Christians In The Mathematical Sciences
Introduction (1999), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1999
Twelfth ACMS Conference on Mathematics from a Christian Perspective
Table Of Contents (1999), Association Of Christians In The Mathematical Sciences
Table Of Contents (1999), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1999
Twelfth ACMS Conference on Mathematics from a Christian Perspective
Schedule (1999), Association Of Christians In The Mathematical Sciences
Schedule (1999), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1999
Twelfth ACMS Conference on Mathematics from a Christian Perspective
Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai
Connectivity Of Cycle Matroids And Bicircular Matroids, Zhi-Hong Chen, Kuang Ying-Qiang, Hong-Jian Lai
Scholarship and Professional Work - LAS
A unified approach to prove former connectivity results of Tutte, Cunningham, Inukai and Weinberg, Oxley and Wagner.
Designing An Integrated Environment For Artificial Intelligence, Andrew B. Ritger '99
Designing An Integrated Environment For Artificial Intelligence, Andrew B. Ritger '99
Honors Projects
The SHELLEY RESEARCH GROUP (part of the Illinois Wesleyan Intelligence Network on Knowledge -IWINK) has been in existence for several years, and has benefited immensely from various student contributors who have added such components as robotic arm control, cross platform networking, an artificially intelligent tic-tac-toe player, and an interactive teaching tool demonstrating the functionality of artificial neural networks. What is lacking, however, amidst these undergraduate contributions to the SHELLEY Project, is an effective means of integrating existing components into a single cohesive functional unit, let alone any easy means of making further contributions within a simple unified context. The focus …
Shout With The Largest Mob : Toward A Model For Primitive Communication In Mobile Automata, Rebecca A. Weber
Shout With The Largest Mob : Toward A Model For Primitive Communication In Mobile Automata, Rebecca A. Weber
Honors Theses
We consider the problem of simulating communication between independent, autonomous agents, or machines, using only local rules with no global control over the agents' behavior. First, we construct an algorithm by which the machines will avoid collisions with each other and with boundaries or obstacles. Noting that collision avoidance alone will not result in higher-level behavior, and with the goal of creating agents which would self-organize, we begin to develop a signalling system by which agents can communicate. This leads to a new method for modeling agent motion in the plane. Throughout, we are motivated by possible linkages between our …
An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha
An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha
Department of Math & Statistics Technical Report Series
We examine the codewords with best possible merit factor (minimum sum of squares of periodic autocorrelations) for a variety of lengths. Many different approaches were tried in an attempt to find construction methods for such codewords, or for codewords with good but non-optimal merit factors.
Prestructuring Neural Networks Via Extended Dependency Analysis With Application To Pattern Classification, George G. Lendaris, Thaddeus T. Shannon, Martin Zwick
Prestructuring Neural Networks Via Extended Dependency Analysis With Application To Pattern Classification, George G. Lendaris, Thaddeus T. Shannon, Martin Zwick
Systems Science Faculty Publications and Presentations
We consider the problem of matching domain-specific statistical structure to neural-network (NN) architecture. In past work we have considered this problem in the function approximation context; here we consider the pattern classification context. General Systems Methodology tools for finding problem-domain structure suffer exponential scaling of computation with respect to the number of variables considered. Therefore we introduce the use of Extended Dependency Analysis (EDA), which scales only polynomially in the number of variables, for the desired analysis. Based on EDA, we demonstrate a number of NN pre-structuring techniques applicable for building neural classifiers. An example is provided in which EDA …
Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan
Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan
Mathematics, Statistics and Computer Science Faculty Research and Publications
Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …
Even Subgraphs Of A Graph, Hong-Jian Lai, Zhi-Hong Chen
Even Subgraphs Of A Graph, Hong-Jian Lai, Zhi-Hong Chen
Scholarship and Professional Work - LAS
No abstract provided.
Locked And Unlocked Polygonal Chains In 3d, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Mark Overmars, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides
Locked And Unlocked Polygonal Chains In 3d, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Mark Overmars, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides
Computer Science: Faculty Publications
In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a …
Method For Identification Of Origins Of Replication And Genes Regulated By Dnaa In Bacteria, Olga G. Troyanskaya
Method For Identification Of Origins Of Replication And Genes Regulated By Dnaa In Bacteria, Olga G. Troyanskaya
Honors Theses
The study is focused on developing computer programs to identify origin of DNA replication based on analysis of total bacterial genomes, scoring regions for number of DnaA binding sites, AT content, DNA adenine methylase boxes, and integration host factors binding sites. The programs were tested on cyanobacterium Synechocystis, and several potential origins were identified. However, no one definite region could be located. Currently, software is being developed to analyze common motifs around the origins of all bacteria with known origins. Genes whose transcription could be regulated by DnaA were identified by searching for DnaA boxes preceding promoter regions.
Codes, Correlations And Power Control In Ofdm, James A. Davis, Jonathan Jedwab, Kenneth G. Paterson
Codes, Correlations And Power Control In Ofdm, James A. Davis, Jonathan Jedwab, Kenneth G. Paterson
Department of Math & Statistics Faculty Publications
Practical communications engineering is continually producing problems of interest to the coding theory community. A recent example is the power-control problem in Orthogonal Frequency Division Multiplexing (OFDM). We report recent work which gives a mathematical framework for generating solutions to this notorious problem that are suited to low-cost wireless applications. The key result is a connection between Golay complementary sequences and Reed-Muller codes. The former are almost ideal for OFDM transmissions because they have a very low peak-to-mean envelope power ratio (PMEPR), while the latter have efficient encoding and decoding algorithms and good error correction capability. This result is then …
(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz
(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz
Engineering Faculty Articles and Research
We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.