Mathematics Commons^™

Mathematics And The Love Of God: An Introduction To The Thought Of Simone Weil, Scott Taylor

ACMS Conference Proceedings 2003

Simone Weil was the sister of Andre Weil, one of the twentieth century's foremost mathematicians. She is a widely read and creative writer on spiritual themes. She addressed mathematics extensively in her writings. This paper discusses her views of mathematics and beauty, her critiques of modern science, her views on truth, and her concept that mathematical ideas can serve as symbols of spiritual ideas.

Introduction (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

A Christian Perspective On Mathematics – History Of Mathematics And Study Guides, Johan Deklerk

ACMS Conference Proceedings 2003

This paper addresses two questions: (1) Will a study of the history of the subject serve any purpose in promoting a Christian perspective on mathematics? (2) Can the "science in context" approach be of further help in promoting such a perspective? The author answers both positively and provides specific examples of how he has done this in his own classes.

Table Of Contents (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

On The Nonembeddability And Crossing Numbers Of Some Kleinical Polyhedral Maps On The Torus, Adrian Riskin, Judy L. Klein

Mathematics

We designed and constructed a sundial for the purpose of observing the declination of the sun and thus marking solar seasonal variation. The 122 × 122 cm vertical sundial on the south-facing wall of our library has two unusual features: a nodus on the gnomon that casts a shadow of a point for marking the height of the sun and a large blank working space for students to mark the shadow of the nodus at different hours of the day and to connect the marks of 1 day in a line of declination. We discuss the design of a dial …

A Christian Perspective On Mathematics – History Of Mathematics And Study Guides, Johan Deklerk

ACMS Journal 2004

This paper addresses two questions: (1) Will a study of the history of the subject serve any purpose in promoting a Christian perspective on mathematics? (2) Can the "science in context" approach be of further help in promoting such a perspective? The author answers both positively and provides specific examples of how he has done this in his own classes.

Creationism – A Viable Philosophy Of Mathematics, Jonathan Zderad

ACMS Journal 2004

In this paper, the author addresses two classical questions of the philosophy of mathematics: What, if any, of mathematics exists in the objective sense? How do humans know that our knowledge of mathematics is correct? He argues that the Christian doctrine of God as creator provides a basis for answering these questions. He also provides a critique of eight widely discussed philosophies of mathematics.

Mathematics And The Love Of God: An Introduction To The Thought Of Simone Weil, Scott Taylor

ACMS Journal 2004

Simone Weil was the sister of Andre Weil, one of the twentieth century's foremost mathematicians. She is a widely read and creative writer on spiritual themes. She addressed mathematics extensively in her writings. This paper discusses her views of mathematics and beauty, her critiques of modern science, her views on truth, and her concept that mathematical ideas can serve as symbols of spiritual ideas.

Stone Coalgebras, Clemens Kupke, Alexander Kurz, Yde Venema

Engineering Faculty Articles and Research

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. …

Sedimentological And Plant Taphonomic Evaluation Of The Early Middle Devonian Trout Valley Formation, Jonathan Allen

Honors Theses

The Trout Valley Formation of Emsian-Eifelian age, outcropped in Baxter State Park, Maine, consists offluvial and coastal deposits preserving early land plants. Massive, crudely bedded conglomerate represents deposits of proximal braided channels on an alluvial fan complex. Lithic sandstone bodies in channel-form geometries represent deposits of river channels draining the Acadian highlands whereas associated siltstones represent overbank deposits, intertidal flats, and tidal channels. Localized lenticular quartz arenites represent nearshore shelf bar deposits that were storm influenced. The majority of plant assemblages preserved mainly in siltstone lithologies are allochthonous and parautochthonous, with only one autochthonous assemblage identified in the sequence. Plant …

Computational Geometry Column 44, Joseph O'Rourke

Computer Science: Faculty Publications

The open problem of whether or not every pair of equal-area polygons has a hinged dissection is discussed.

Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen

Mathematics & Statistics Faculty Publications

We report our results in classifying protein matrix-assisted laser desorption/ionizationtime of flight mass spectra obtained from serum samples into diseased and healthy groups. We discuss in detail five of the steps in preprocessing the mass spectral data for biomarker discovery, as well as our criterion for choosing a small set of peaks for classifying the samples. Cross-validation studies with four selected proteins yielded misclassification rates in the 10-15% range for all the classification methods. Three of these proteins or protein fragments are down-regulated and one up-regulated in lung cancer, the disease under consideration in this data set. When cross-validation studies …

Partitioning Regular Polygons Into Circular Pieces I: Convex Partitions, Mirela Damian, Joseph O'Rourke

Computer Science: Faculty Publications

We explore an instance of the question of partitioning a polygon into pieces, each of which is as “circular” as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. The problem is rich even for partitioning regular polygons into convex pieces, the focus of this paper. We show that the optimal (most circular) partition for an equilateral triangle has an infinite number of pieces, with the lower bound approachable to any accuracy desired by a …

On The Development Of The Intersection Of A Plane With A Polytope, Joseph O'Rourke

Computer Science: Faculty Publications

Define a “slice” curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex “openings” of a planar convex chain.

Computational Geometry Column 43, Joseph O'Rourke

Computer Science: Faculty Publications

The concept of pointed pseudo-triangulations is defined and a few of its applications described.

Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution of a question posed by Biedl, Lubiw, and Sun [BLS99].

Communicator-In-Chief: Presidential Use Of Television Past, Present, And Future, Jenna Wasson

Honors Theses

This thesis seeks to determine how television has changed as a communication medium for presidents over the past half century. An evaluation of the evolving ways presidents use television to communicate with and to build support from the American people has been conducted. Presidential communication strategies have been identified by drawing primarily from primary sources written by presidents and White House staff. Television technology and the television audience have changed over the years. Presidents have taken a more pro-active, aggressive role in their efforts to harness television for their own purposes. Why have these changes occurred? What impact have these …

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …

Self-Similarity In Network Traffic, Francisco Chinchilla

Honors Theses

It is critical to properly understand the nature of network traffic in order to effectively design models describing network behavior. These models are usually used to simulate network traffic, which in turn are used to construct congestion control techniques, perform capacity planning studies, and/or evaluate the behavior of new protocols. Using the wrong models could lead to potentially serious problems such as delayed packet transmissions or an increase in packet drop rates.

Traditionally, packet arrivals were assumed to follow a Poisson arrival process. Although Poisson processes have several properties that make them easy to work with, they do not accurately …

L-Arginine Uptake And Metabolism Following In Vivo Silica Exposure In Rat Lungs, Leif D. Nelin, Gary S. Krenz, Louis G. Chicoine, Christopher A. Dawson, Ralph M. Schapira

Mathematics, Statistics and Computer Science Faculty Research and Publications

Pulmonary inflammation increases nitric oxide (NO) production via inducible nitric oxide synthase (iNOS). This study was performed to determine some of the factors that affect the availability of the NOS substrate, L-arginine (L-arg), in the intact lung subjected to silica-induced inflammation. Nitrate production, as an index of NO production, was significantly greater in silica-exposed lungs (53.5 ± 12.1 nmol/90 min) compared with controls (22.5 ±5.1 nmol/90 min, P < 0.05). This was accompanied by greater (P< 0.0001) 90-min [³H]L-arg uptake (62 ± 3% control, 82 ± 1% silica), a significantly (P < 0.005) increased permeability-surface area product for L-arg(0.28 ± 0.05 ml/min control, 0.63 ± 0.07 ml/min silica), and asignificantly (P < 0.001) increased urea production (1.16 ± 0.08µmol/90 min control, 1.77 ± 0.06 µmol/90 min silica). There was no difference in eNOS protein between groups and eNOS mRNA was not detectable in either group, whereas silica exposure resulted in the appearance of both iNOS protein and mRNA. Silica exposure increased CAT-1 and CAT-2 mRNA ~ 8-fold compared with controls. We conclude that the increase in NO production in silica-exposed lungs was associated with increased L-arg uptake from the vasculature, presumably resulting from increased CAT-1 and CAT-2, and by increased L-arg metabolism via arginase.

Enumerating Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke

Computer Science: Faculty Publications

We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are, roughly: exponentially many, or nondenumerably infinite.

Medical Inference System On Arthritis Using Fuzzy Relational Theory, Chee Kau Lim

Student Works (2000-2009)

Fuzzy relational theory is a branch in the study of fuzzy sets theory. According to this theory, mapping among two sets can be carried out in four ways, which arc represented by circle product, sub-triangular product, super-triangular product and square product. Each of these products can be abstracted into inference structures. which is useful in designing the inference engine of an expert system. Based on the revised version [DeBaets and Kerre 1993. Hallam and Yew l998a] of fuzzy relational theory. a series of 18 inference structures, namely sub-K inference structures (denoted as Kt to Kl8) are constructed. Based on these …

Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.

Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …

The Evolution Of Cell Colonies In Volvocacean Algae : Investigation By Theoretical Analysis And Computer Simulation., Frank Noe

Theses

This thesis presents a mathematical analysis and computational simulation which is used to investigate the evolution of cell colonies. The evolutionary transition from unicellular to cell colony form is a prerequesite for multicellular life as it exists abundantly on earth. This transition has occured numerous times independently so that we expect a high selective advantage to be associated with it. The photosynthetic green algae order Volvocaceae is an appropriate set of model organisms for the study of the evolution of cell colonies since it comprises living unicellular organisms, cell colonies, and multicellular organisms of different shapes, sizes and levels of …

[Introduction To] Data Structures With Java: A Laboratory Approach, Joe Kent, Lewis Barnett Iii

Bookshelf

This book is designed to present the key topics in the second course for computer science students using the Java programming language. For convenience, we cover exceptions and file operations in Java, although this may have been covered in the first course. We also cover material on the binary representation of data and Java's bitwise operations, with applications.These are topics needed for computer organization an operating systems courses.

Geometric Integrators For Hamiltonian Pdes, Dmitry Karpeev

Computer Science Theses & Dissertations

We consider methods for systematic construction of algorithms for a class of time-dependent PDEs with Hamiltonian structure. These systems possess phase space geometry and constants of the motion that need to be preserved by the integration algorithm to reflect the qualitative features of the system.

We exploit the structure of Hamiltonian systems, in particular their variational formulation based on a Lagrangian, and the dual covariant formulation, to expose the geometric features of the system that have natural analogs when discretized. We emphasize the local space-time approach to the constructions, making them amenable to parallelization and preconditioning using domain decomposition methods, …

Preface, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.