Mathematics Commons^™

Integer Ratio Logarithm Based Edge Detection For Runway Hazard Detection, Sri Satya Vardhan Gogineni

Electrical & Computer Engineering Theses & Dissertations

As air traffic is growing in leaps and bounds every day, flying safe has been a major concern in day to day life. Aviation safety is always dependent on the performance of the pilot and air traffic controllers. The very involvement of human discretion introduces judgment as a component of a safe takeoff and landing. A convenient and immediate alternative would be the use of technology to alleviate the problem. Several algorithms have been developed to solve this problem. However, most computer vision algorithms leave the task of interpreting the end data unaddressed. Juggling the myriad tasks during landing and …

Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin

CMC Faculty Publications and Research

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.

On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a greater than or equal to 3. These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets.

Architecture And Implementation Of A Trust Model For Pervasive Applications, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Sailaja Bulusu, Mehrab Monjur

Mathematics, Statistics and Computer Science Faculty Research and Publications

Collaborative effort to share resources is a significant feature of pervasive computing environments. To achieve secure service discovery and sharing, and to distinguish between malevolent and benevolent entities, trust models must be defined. It is critical to estimate a device's initial trust value because of the transient nature of pervasive smart space; however, most of the prior research work on trust models for pervasive applications used the notion of constant initial trust assignment. In this paper, we design and implement a trust model called DIRT. We categorize services in different security levels and depending on the service requester's context information, …

Foundations And Interpretations Of Quantum Mechanics, Cory Johnson

Honors Theses

The first famous thought experiment of Einstein gives rise to his theories of relativity, the bedrock of modern astrophysics and cosmology. His second famous thought experiment begins the investigation into the foundations of quantum mechanics. It leads to a paradox, inspiring various 'no-go' theorems proven by Bell, Kochen, and Specker. Physicists and philosophers worldwide become increasingly dissatisfied with the probabilistic complementarity interpretation (Born-Bohr) and eventually offer their own accounts of the theory. By the end of the 20th century two alternative approaches stand out as the best candidates: Both the hidden variables interpretation (de Broglie-Bohm) and the many worlds interpretation …

Effects Of Context Of Natural And Artifactual Objects On Categorization, Linsey Walker

Honors Theses

Categorization of animals and vehicles in different contexts was investigated in three experiments using event related potentials (ERPs). The presence of a background and congruency of the background in relation to the object were both manipulated in order to determine the effects of context on visual processing. In Experiment 1, adults were presented with images of animals and vehicles in two conditions: situated in a congruent context (e.g. an animal in a field) and in the absence of a context (an animal in a white homogeneous background). In experiment 2, adults were presented with images of animals and vehicles in …

Cauchy’S Arm Lemma On A Growing Sphere, Zachary Abel, David Charlton, Sébastien Collette, Erik D. Demaine, Martin L. Demaine, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Godfried Toussaint

Computer Science: Faculty Publications

We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a comparison of three alternate proofs, to show the links between Toponogov's Comparison Theorem, Legendre's Theorem and Cauchy's Arm Lemma.

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

An Impregnable Lightweight Device Discovery (Ildd) Model For The Pervasive Computing Environment Of Enterprise Applications, Munirul H. Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

The worldwide use of handheld devices (personal digital assistants, cell phones, etc.) with wireless connectivity will reach 2.6 billion units this year and 4 billion by 2010. More specifically, these handheld devices have become an integral part of industrial applications. These devices form pervasive ad hoc wireless networks that aide in industry applications. However, pervasive computing is susceptible and vulnerable to malicious active and passive snoopers. This is due to the unavoidable interdevice dependency, as well as a common shared medium, very transitory connectivity, and the absence of a fixed trust infrastructure. In order to ensure security and privacy in …

Grid Vertex-Unfolding Orthogonal Polyhedra, Mirela Damian

Computer Science: Faculty Publications

No abstract provided.

A Class Of Convex Polyhedra With Few Edge Unfoldings, Alex Benton, Joseph O'Rourke

Computer Science: Faculty Publications

We construct a sequence of convex polyhedra on n vertices with the property that, as n -> infinity, the fraction of its edge unfoldings that avoid overlap approaches 0, and so the fraction that overlap approaches 1. Nevertheless, each does have (several) nonoverlapping edge unfoldings.

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader

Theses Digitization Project

The purpose of this project was to define the relationship and show how an important subset of spatial differential equations can be transformed into cellular automata. Contains source code.

Thermal Roots Of Correlation-Based Complexity, Philip Fraundorf

Physics Faculty Works

Bayesian maxent lets one integrate thermal physics and information theory points of view in the quantitative study of complex systems. Since net surprisal (a free energy analog for measuring “departures from expected”) allows one to place second law constraints on mutual information (a multimoment measure of correlations), it makes a quantitative case for the role of reversible thermalization in the natural history of invention, and suggests multiscale strategies to monitor standing crop as well. It prompts one to track evolved complexity starting from live astrophysically observed processes, rather than only from evidence of past events. Various gradients and boundaries that …

Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.

Pathos: Pervasive At Home Sleep Monitoring, Ian Obermiller, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Sleeping disorders affect a large percentage of the population, and many of them go undiagnosed each year because the method of diagnosis is to stay overnight at a sleep center. Because pervasive technologies have become so prevalent and affordable, sleep monitoring is no longer confined to a permanent installation, and can therefore be brought directly into the user home. We present a unique solution to the problem of home sleep monitoring that has the possibility to take the place of and expand on the data from a sleep center. PATHOS focuses not only on analyzing patterns during the night, but …

Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

A domination graph of a digraph D , dom(D)dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)]{u,v}∈E[dom(D)] whenever (u,z)∈A(D)(u,z)∈A(D) or (v,z)∈A(D)(v,z)∈A(D) for every other vertex z∈V(D)z∈V(D). The underlying graph of a digraph DD, UG(D)UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D)UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.

Molecular Targets Of 2,3,7,8-Tetrachlorodibenzo-P-Dioxin (Tcdd) Within The Zebrafish Ovary: Insights Into Tcdd-Induced Endocrine Disruption And Reproductive Toxicity, Tisha C. King Heiden, Craig Struble, Matthew L. Rise, Martin J. Hessner, Reinhold J. Hutz, Michael J. Carvan Iii

Mathematics, Statistics and Computer Science Faculty Research and Publications

TCDD is a reproductive toxicant and endocrine disruptor, yet the mechanisms by which it causes these reproductive alterations are not fully understood. In order to provide additional insight into the molecular mechanisms that underlie TCDD's reproductive toxicity, we assessed TCDD-induced transcriptional changes in the ovary as they relate to previously described impacts on serum estradiol concentrations and altered follicular development in zebrafish. In silico computational approaches were used to correlate candidate regulatory motifs with observed changes in gene expression. Our data suggest that TCDD inhibits follicle maturation via attenuated gonadotropin responsiveness and/or depressed estradiol biosynthesis, and that interference of estrogen-regulated …

Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or …

Set Linear Algebra And Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is comfortable working with it. It is with the passage of time, that we can think of set linear algebras as a paradigm shift from linear algebras. Here, the authors have also given the fuzzy parallels of these new classes of set linear algebras. This book abounds with examples to enable the reader to understand these new concepts easily. Laborious theorems and …

Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …

Unit Rectangle Visibility Graphs, Alice M. Dean, Joanna A. Ellis-Monaghan, Sarah J. Hamilton, Greta Pangborn

Mathematics, Statistics and Computer Science Faculty Research and Publications

Over the past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph G is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate …

Reed-Solomon Codes Construction & Decoding, Samuel J. Parsons

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Band Unfoldings And Prismatoids: A Counterexample, Joseph O'Rourke

Computer Science: Faculty Publications

This note shows that the hope expressed in [ADL+07]--that the new algorithm for edge-unfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap--cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, with the property that every placement of the prismatoid top face overlaps with the band unfolding.

A Nifty Tool For Studying Program And System Behaviors: Nifty Tools, Pete Sanderson, Kenneth Vollmar

Mathematics Faculty Scholarship

MARS is an integrated development environment (IDE) and simulator for MIPS assembly language programming. New features enable MARS to be a useful tool for discovery and experimentation even in courses that do not involve assembly language programming.

How Geometer’S Sketchpad Improves Student Learning, William George Awe

Mathematics Graduate Theses

This study investigated whether dynamic software improves learning and reviews different types of dynamic software. The study then narrows its focus to one type of dynamic software, Geometer’s Sketchpad and studies how Geometer’s Sketchpad, in itself, improves student learning. The researcher identified what dynamic software is, the importance of dynamic software and different types of dynamic software. The researcher also identifies how dynamic software is utilized in schools and researches how to improve the use of dynamic software in schools. Dynamic software, and Geometer’s Sketchpad, In particular, was found to improve learning across grade levels and with different levels of …

A Software-Based Trust Framework For Distributed Industrial Management Systems, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Steve Wolfe

Mathematics, Statistics and Computer Science Faculty Research and Publications

One of the major problems in industrial security management is that most organizations or enterprises do not provide adequate guidelines or well-defined policy with respect to trust management, and trust is still an afterthought in most security engineering projects. With the increase of handheld devices, managers of business organizations tend to use handheld devices to access the information systems. However, the connection or access to an information system requires appropriate level of trust. In this paper, we present a flexible, manageable, and configurable software-based trust framework for the handheld devices of mangers to access distributed information systems. The presented framework …

Unfolding Restricted Convex Caps, Joseph O'Rourke

Computer Science: Faculty Publications

This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap’s faces are quadrilaterals, with vertices over an underlying integer lattice, and such that the cap convexity is "radially monotone," a type of smoothness constraint. Extensions of Cauchy’s arm lemma are used in the proof of non-overlap.

Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …

Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman

ACMS Conference Proceedings 2007

Many mathematics instructors at the college level are looking for a curricular option that has the potential to serve a number of different constituencies. It could be to encourage more students to take math courses, or to give worthwhile options to students who need to take math but who are not ready for calculus (or its sequence). On the other hand, one may wish to add a new course for majors outside of the typical offerings, or even to prepare students for undergraduate research. The mathematics of voting and choice is ideally suited to meet all these needs in the …