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2016

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Articles 241 - 270 of 1329

Full-Text Articles in Mathematics

Fast Cycles Detecting In Non-Linear Discrete Systems, Dmitriy Dmitrishin, Elena Franzheva, Alexander M. Stokolos Aug 2016

Fast Cycles Detecting In Non-Linear Discrete Systems, Dmitriy Dmitrishin, Elena Franzheva, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of detecting T-cycles. Some numerical simulations are presented.

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Prediction And Optimal Scheduling Of Advertisements In Linear Television, Mark J. Panaggio, Pak-Wing Fok, Ghan S. Bhatt, Simon Burhoe, Michael Capps, Christina J. Edholm, Fadoua El Moustaid, Tegan Emerson, Star-Lena Estock, Nathan Gold, Ryan Halabi, Madelyn Houser, Peter R. Kramer, Hsuan-Wei Lee, Qingxia Li, Weiqiang Li, Dan Lu, Yuzhou Qian, Louis F. Rossi, Deborah Shutt, Vicky Chuqiao Yang, Yingxiang Zhou Aug 2016

Prediction And Optimal Scheduling Of Advertisements In Linear Television, Mark J. Panaggio, Pak-Wing Fok, Ghan S. Bhatt, Simon Burhoe, Michael Capps, Christina J. Edholm, Fadoua El Moustaid, Tegan Emerson, Star-Lena Estock, Nathan Gold, Ryan Halabi, Madelyn Houser, Peter R. Kramer, Hsuan-Wei Lee, Qingxia Li, Weiqiang Li, Dan Lu, Yuzhou Qian, Louis F. Rossi, Deborah Shutt, Vicky Chuqiao Yang, Yingxiang Zhou

Mathematical Sciences Faculty Research

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of "impressions" in the target demographic. However, because the number of impressions for a given program is not known a priori and because …

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Improved Compressive Sensing Of Natural Scenes Using Localized Random Sampling, Victor J. Barranca, G. Kovačič, D. Zhou, D. Cai Aug 2016

Improved Compressive Sensing Of Natural Scenes Using Localized Random Sampling, Victor J. Barranca, G. Kovačič, D. Zhou, D. Cai

Mathematics & Statistics Faculty Works

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized …

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Determinantal Representations Of Semihyperbolic Polynomials, Greg Knese Aug 2016

Determinantal Representations Of Semihyperbolic Polynomials, Greg Knese

Mathematics Faculty Research

We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representation for hyperbolic polynomials to the class of semihyperbolic polynomials, a strictly larger class, as shown by an example. We also prove that certain hyperbolic polynomials affine in two out of four variables divide a determinantal polynomial. The proofs are based on work related to polynomials with no zeros on the bidisk and tridisk.

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Quantum Dynamics, Entropy And Quantum Versions Of Maxwell’S Demon, Paul Bracken Aug 2016

Quantum Dynamics, Entropy And Quantum Versions Of Maxwell’S Demon, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Several subjects which reside in the overlap area of quantum mechanics, statistical physics and thermodynamics are investigated in depth. This collection of subjects shares a common domain which is referred to as Maxwell’s demon. The classical version of this idea is introduced, and then, the contribution made by Szilard to the subject is presented. Several demons are considered, and it is shown that to best understand this area, quantum mechanics and the role information plays in it must be appreciated deeply.

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Expert Elicitation On The Uncertainties Associated With Chronic Wasting Disease, Michael G. Tyshenko, Tamer Oraby, Shalu Darshan, Margit Westphal, Maxine C. Croteau, Willy Aspinall, Susie Elsaadany, Daniel Krewski, Neil Cashman Aug 2016

Expert Elicitation On The Uncertainties Associated With Chronic Wasting Disease, Michael G. Tyshenko, Tamer Oraby, Shalu Darshan, Margit Westphal, Maxine C. Croteau, Willy Aspinall, Susie Elsaadany, Daniel Krewski, Neil Cashman

School of Mathematical & Statistical Sciences Faculty Publications

A high degree of uncertainty exists for chronic wasting disease (CWD) transmission factors in farmed and wild cervids. Evaluating the factors is important as it helps to inform future risk management strategies. Expert opinion is often used to assist decision making in a number of health, science, and technology domains where data may be sparse or missing. Using the "Classical Model" of elicitation, a group of experts was asked to estimate the most likely values for several risk factors affecting CWD transmission. The formalized expert elicitation helped structure the issues and hence provide a rational basis for estimating some transmission …

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On The Geodesic Centers Of Polygonal Domains, Haitao Wang Aug 2016

On The Geodesic Centers Of Polygonal Domains, Haitao Wang

Computer Science Faculty and Staff Publications

In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain P of n vertices. We give a necessary condition for a point being a geodesic center. We show that there is at most one geodesic center among all points of P that have topologically-equivalent shortest path maps. This implies that the total number of geodesic centers is bounded by the size of the shortest path map equivalence decomposition of P, which is known to be O(n^{10}). One key observation is a pi-range property on shortest path lengths when points are moving. With these observations, …

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From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos Aug 2016

From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered.

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Tolerant Compressed Sensing With Partially Coherent Sensing Matrices, Tobias Birnbaum, Yonina C. Eldar, Deanna Needell Aug 2016

Tolerant Compressed Sensing With Partially Coherent Sensing Matrices, Tobias Birnbaum, Yonina C. Eldar, Deanna Needell

CMC Faculty Publications and Research

We consider compressed sensing (CS) using partially coherent sensing matrices. Most of CS theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications, such as signal detection, motion detection and radar. Moreover, in these applications it is often not necessary to know the support of the signal exactly, but instead small errors in the support and signal are tolerable. In this paper, we focus on d-tolerant recovery, in which support set reconstructions are considered accurate when their locations match the true …

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Gender Representation On Journal Editorial Boards In The Mathematical Sciences, Chad M. Topaz, Shilad Sen Aug 2016

Gender Representation On Journal Editorial Boards In The Mathematical Sciences, Chad M. Topaz, Shilad Sen

Faculty Publications

No abstract provided.

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Generalizing The Gsvd, Mark Gockenbach Aug 2016

Generalizing The Gsvd, Mark Gockenbach

Department of Mathematical Sciences Publications

The generalized singular value decomposition (GSVD) of a pair of matrices is the natural tool for certain problems defined on Euclidean space, such as certain weighted least-squares problems, the result of applying Tikhonov regularization to such problems (sometimes called regularization with seminorms), and equality-constrained least-squares problems. There is an extension of the GSVD to pairs of bounded linear operators defined on Hilbert space that turns out to be a natural representation for analyzing the same problems in the infinite-dimensional setting.

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A Practical Study Of Longitudinal Reference Based Compressed Sensing For Mri, Samuel Birns, Bohyun Kim, Stephanie Ku, Kevin Stangl, Deanna Needell Aug 2016

A Practical Study Of Longitudinal Reference Based Compressed Sensing For Mri, Samuel Birns, Bohyun Kim, Stephanie Ku, Kevin Stangl, Deanna Needell

CMC Faculty Publications and Research

Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS significantly speeds up scan time by requiring far fewer measurements than standard MRI techniques. Such a reduction in sampling time leads to less power consumption, less need for patient sedation, and more accurate images. This accuracy increase is especially pronounced in pediatric MRI where patients have trouble being still for long scan periods. Although such gains are already significant, even further improvements can be …

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Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng Aug 2016

Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when p; t > 1, q; s > 0 and λ; μ > (N - 2)2=4, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When λ; μ > 0, p; t > 1 and q; s > 0, we show that any radial positive solution is decreasing in r.

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Survival Analysis In A Clinical Setting, Yunzhao Liu Aug 2016

Survival Analysis In A Clinical Setting, Yunzhao Liu

Arts & Sciences Graduate Student Theses and Dissertations

With the fast paced advancement of modern medicine, cancer treatments have improved greatly over the past few decades; however, the overall survival rate has not improved for head neck squamous cell carcinoma (HNSCC). Traditionally, the general affected population of HNSCC was male over 50-60 years of age, whom have had history of alcohol and tobacco use. Conversely, in the recent decades, HNSCC has exhibited significant rise in younger patients, largely due to the increase in human papillomavirus (HPV) infection among young adults. Generally, HPV as the most prevalent sexually transmitted disease, consisted of strains that do not cause harm to …

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Freedom Through Inquiry, Francis Su Aug 2016

Freedom Through Inquiry, Francis Su

All HMC Faculty Publications and Research

I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.

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Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski Aug 2016

Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski

Dissertations and Theses

An orthomorphism, π, of a group, (G, +), is a permutation of G with the property that the map x → -x + π(x) is also a permutation. In this paper, we consider orthomorphisms of the additive group of binary n-tuples, Zn2. We use known orthomorphism preserving functions to prove a uniformity in the cycle types of orthomorphisms that extend certain partial orthomorphisms, and prove that extensions of particular sizes of partial orthomorphisms exist. Further, in studying the action of conjugating orthomorphisms by automorphisms, we find several symmetries within the orbits and stabilizers of this action, and …

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Limiting Forms Of Iterated Circular Convolutions Of Planar Polygons, Boyan Kostadinov Aug 2016

Limiting Forms Of Iterated Circular Convolutions Of Planar Polygons, Boyan Kostadinov

Publications and Research

We consider a complex representation of an arbitrary planar polygon P centered at the origin. Let P(1) be the normalized polygon obtained from P by connecting the midpoints of its sides and normalizing the complex vector of vertex coordinates. We say that P(1) is a normalized average of P. We identify this averaging process with a special case of a circular convolution. We show that if the convolution is repeated many times, then for a large class of polygons the vertices of the limiting polygon lie either on an ellipse or on a star-shaped polygon. We derive a complete and …

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Incorporating Exponential Functions Into An Optimal Control Model For A Chronic Wound, Peter Agaba Aug 2016

Incorporating Exponential Functions Into An Optimal Control Model For A Chronic Wound, Peter Agaba

Mahurin Honors College Capstone Experience/Thesis Projects

A chronic wound is a wound that does not heal in an orderly manner and on time. In this project, we simulate different ways of minimizing the time of therapy using exponential functions. The analysis in this research project focuses on treating chronic wounds using both mathematical and biological models. These models primarily focus on the amount of oxygen supplied to the wound using both hyperbaric and topical oxygen therapies. This amount should be optimal since too much oxygen is toxic to the body, and can potentially lead to death. The goal is to minimize the time spent in therapies …

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A Classification Of The Intersections Between Regions And Their Topical Transitions, Kathleen Bell Aug 2016

A Classification Of The Intersections Between Regions And Their Topical Transitions, Kathleen Bell

Mahurin Honors College Capstone Experience/Thesis Projects

As two topological regions are morphed and translated, how does their intersection change? Previous research has been done on static configurations with planar spatial regions. I expand upon this research to include dynamically changing regions and intersections. I examine what forms of intersection are possible, and what transitions are directly possible, while considering such variables as the connectedness of the regions.

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Clawpack: Building An Open Source Ecosystem For Solving Hyperbolic Pdes, Donna Calhoun Aug 2016

Clawpack: Building An Open Source Ecosystem For Solving Hyperbolic Pdes, Donna Calhoun

Mathematics Faculty Publications and Presentations

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a …

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Modeling Zombie Outbreaks: A Problem-Based Approach To Improving Mathematics One Brain At A Time, Matthew Lewis, James A. Powell Aug 2016

Modeling Zombie Outbreaks: A Problem-Based Approach To Improving Mathematics One Brain At A Time, Matthew Lewis, James A. Powell

Mathematics and Statistics Faculty Publications

A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans vs. Zombies moderated tag game played on the USU campus. We discuss the project in the context of an undergraduate differential equations course and discuss how the project is launched. We highlight examples of students mathematical models along with their verbal and written responses as well as discussing assessment and student learning. Results are discussed in the context …

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Improving Proof-Writing With Reading Guides, Mike Janssen Aug 2016

Improving Proof-Writing With Reading Guides, Mike Janssen

Faculty Work Comprehensive List

One of the barriers in the transition to advanced mathematics is that the proofs and ideas in even the best mathematics texts must be read more carefully than many students are accustomed to. Yet in order to learn to write proofs well, one must learn how to read proofs well. Borrowing an idea from Lewis Ludwig, I flipped my introduction to proofs (discrete structures) course in Spring 2016 with the use of reading guides. Each day, students were responsible for reading a section of the text and completing a worksheet that highlighted the main points, asked students to create their …

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Projective Geometry Hidden Inside: Can You Spot It?, Tom Clark Aug 2016

Projective Geometry Hidden Inside: Can You Spot It?, Tom Clark

Faculty Work Comprehensive List

In this talk Dr. Clark shared about a Math Teachers’ Circle session he recently ran centered around the children’s game Spot it! This game has some very interesting mathematics behind it and naturally begs to be explored with inquiry. He described the way he led teachers to ask questions about the game, the way the teachers then explored the topic, and the mathematics behind it all.

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Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri Aug 2016

Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri

Master of Science in Computer Science Theses

Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of parallel …

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Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings Aug 2016

Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings

Department of Mathematics Faculty Scholarship and Creative Works

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high- dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a …

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Using In Situ Liquid Single Photon Ionization Mass Spectrometry (Spi-Ms) To Probe Lithium Polysulfide Electrolyte In Motion, Aala M. Al Hasan, Jiachao Yu, Juan Yao, Vijayakumar Murugesan, Manjula Nandasiri, Xiao-Ying Yu Aug 2016

Using In Situ Liquid Single Photon Ionization Mass Spectrometry (Spi-Ms) To Probe Lithium Polysulfide Electrolyte In Motion, Aala M. Al Hasan, Jiachao Yu, Juan Yao, Vijayakumar Murugesan, Manjula Nandasiri, Xiao-Ying Yu

STAR Program Research Presentations

The solid-liquid (s-l) interface is the most common interface encountered in electrochemical systems. The s-l interface has wide applications in energy storage, catalysis, and material sciences. In situ studies of chemical reactions taking place on the s-l interfaces can further our understanding of electron transfer and link to real-world device functions under challenging conditions. Direct probing of the solid electrode and liquid electrolyte interface has been realized using a vacuum compatible electrochemical microfluidic reactor, system for analysis at the liquid vacuum interface (SALVI) with time-of-flight secondary ion mass spectrometry (ToF-SIMS). Most recently, the electrochemical version of SALVI was integrated to …

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Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska Aug 2016

Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska

Mathematics and Statistics Faculty Research & Creative Works

This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.

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Connecting Models Of Configuration Spaces: From Double Loops To Strings, Jason M. Lucas Aug 2016

Connecting Models Of Configuration Spaces: From Double Loops To Strings, Jason M. Lucas

Open Access Dissertations

Foundational to the subject of operad theory is the notion of an En operad, that is, an operad that is quasi-isomorphic to the operad of little n-cubes Cn. They are central to the study of iterated loop spaces, and the specific case of n = 2 is key in the solution of the Deligne Conjecture. In this paper we examine the connection between two E 2 operads, namely the little 2-cubes operad C 2 itself and the operad of spineless cacti. To this end, we construct a new suboperad of C2, which we name the operad of tethered …

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Size Variables In Audit Fee Models: An Examination Of The Effects Of Alternative Mathematical Transformations, Charles Cullinan, Hui Du, Xiaochuan Zheng Aug 2016

Size Variables In Audit Fee Models: An Examination Of The Effects Of Alternative Mathematical Transformations, Charles Cullinan, Hui Du, Xiaochuan Zheng

Accounting Department Faculty Journal Articles

We consider the mathematical transformations used for assets of different valuation complexity in audit fee models. These mathematical transformations (such as logs and square roots) relate to the non-linear relationship between client size and audit fees. We use closed-end mutual fund audits to examine this question because virtually all fund assets are reported at fair value. We find that more complexly valued assets are less likely to follow the traditional log transformation because the presence of these assets has a stronger relationship with audit fees that is not fully captured by the coefficient on the logged variable alone. The significance …

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An Update On A Few Permanent Conjectures, Fuzhen Zhang Aug 2016

An Update On A Few Permanent Conjectures, Fuzhen Zhang

Mathematics Faculty Articles

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise a few new questions for future study. (†conjectures have been recently settled negatively.)

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