Computer Sciences Commons^™

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 …

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.

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.

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. …

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.

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 …

Preface, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

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.

[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.

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 …

Vertex-Unfoldings Of Simplicial Manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, Joseph O'Rourke

Computer Science: Faculty Publications

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.

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, …

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.

Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that, in all dimensions d ≥ 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of “moves.” These results contrast to those known for d = 2, where trees can “lock,” and for d = 3, where open and closed chains can lock.

Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke

Computer Science: Faculty Publications

A compendium of thirty previously published open problems in computational geometry is presented.

What Mathematical Paradoxes Teach Us About Paradoxes In Christianity, Paul Bialek

ACMS Conference Proceedings 2001

In Christian academic circles, we talk about the integration of our faith and learning. That is, we seek to discover and develop connections between our Christian faith and our particular discipline. This is notoriously difficult when the discipline is mathematics. I have found that asking myself these three questions has helped me to integrate my Christian faith with mathematics, although they could be applied to any discipline: (1) How does the fact that I am a Christian affect the way I view mathematics? (2) How does the fact that I am a mathematician affect the way I view Christianity? (3) …

Three Problems From Number Theory, Robert Brabenec

ACMS Conference Proceedings 2001

This paper discusses the experiences of Wheaton College mathematics and computer science department colloquium as they explored open-ended problems.

The Soviet Concept Of The Correlation Of Forces, James Bradley

ACMS Conference Proceedings 2001

This paper takes a look at the Soviet Union’s accumulation of nuclear weapons during the Cold War and what mathematical strategy they employed to make their choices.

Gravitational Acceleration In Hades, Andrew Simoson

ACMS Conference Proceedings 2001

Does acceleration due to gravity increase or decrease upon descending from Earth’s surface? The answer—as we show—depends on one’s model for Earth’s density. For our Earth, gravity increases before it collapses to zero at Earth center.

Theism & Mathematical Realism, John Byl

ACMS Conference Proceedings 2001

This paper examines connections between theism and mathematical realism. Mathematical realism, which offers the best account of mathematics, strongly supports theism. Theism, in turn, supports mathematical realism. Theism readily explains the intricate relations between mathematics, matter, and mind. The attributes of the biblical God provide justification for classical mathematics.

Mathematics Memory Verses: Weekly Devotionals For Math Class, Mark Colgan

ACMS Conference Proceedings 2001

Each Monday during the semester I start class with a short devotional on a verse that relates in some way to mathematics. After three weeks I choose one of the three at random for students to write out on their quiz for a possible bonus point. This encourages students to practice memorizing Scripture and it gives us the opportunity to discuss biblical principles that relate to some of the topics we are studying in the course.

I would like to share some of the Bible verses and weekly devotionals I have used in my mathematics classes. These can be organized …

Parables For Mathematicians: With Good News For Curved Beings, Ashley Reiter Ahlin

ACMS Conference Proceedings 2001

Because we often lack the language for talking about such deep matters, the things of God can be hard to understand or talk about. The things that we do see and know were made by the same God of whom we speak. Thus, they are reflections of His nature, purposes, and ways and can help us to think and take about Him. This presentation expresses a parable using the language of math.

On Periodic Points On Maps Of Trees And The Expansive Property, Fred Worth

ACMS Conference Proceedings 2001

In this paper, we consider the expansive property (A homeomorphism, f, of a metric space, X, onto itself is called expansive if there is a positive number, ε, such that if x and y are distinct points of X, then there exists an integer, n = n(x,y), such that d(f n(x), f n(y)) > ε. It should be noted that n may be negative.) and how it relates to shift homeomorphisms of a tree with a single, surjective bonding map. We also consider some results regarding the periodicity of points in self-maps of trees.

Why Natural Selection Can't Design Anything, William A. Dembski

ACMS Conference Proceedings 2001

In The Fifth Miracle Paul Davies suggests that any laws capable of explaining the origin of life must be radically different from scientific laws known to date? The problem, as he sees it, with currently known scientific laws, like the laws of chemistry and physics, is that they cannot explain the key feature of life that needs to be explained. That feature is specified complexity. Life is both complex and specified. The basic institution here is straightforward. Davies rightly notes, laws (that is, necessities of nature) can explain specification but not complexity. Once life (or more generally some self-replicator) …