Physical Sciences and Mathematics Commons^™

The Choice Of Prior Distribution For A Covariance Matrix In Multivariate Meta-Analysis: A Simulation Study, Sandra M. Hurtado Rua, Madhu Mazumdar, Robert L. Strawderman

Mathematics and Statistics Faculty Publications

Bayesian meta-analysis is an increasingly important component of clinical research, with multivariate meta-analysis a promising tool for studies with multiple endpoints. Model assumptions, including the choice of priors, are crucial aspects of multivariate Bayesian meta-analysis (MBMA) models. In a given model, two different prior distributions can lead to different inferences about a particular parameter. A simulation study was performed in which the impact of families of prior distributions for the covariance matrix of a multivariate normal random effects MBMA model was analyzed. Inferences about effect sizes were not particularly sensitive to prior choice, but the related covariance estimates were. A …

The Stationary Phase Method For Real Analytic Geometry, Domenico Napoletani, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove that the existence of isolated solutions of systems of equations of analytical functions on compact real domains in R^p, is equivalent to the convergence of the phase of a suitable complex valued integral I(h) for h→∞. As an application, we then use this result to prove that the problem of establishing the irrationality of the value of an analytic function F(x) at a point x₀ can be rephrased in terms of a similar phase convergence.

Concurrent Kleene Algebra With Tests And Branching Automata, Peter Jipsen, M. Andrew Moshier

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce concurrent Kleene algebra with tests (CKAT) as a combination of Kleene algebra with tests (KAT) of Kozen and Smith with concurrent Kleene algebras (CKA), introduced by Hoare, Möller, Struth and Wehrman. CKAT provides a relatively simple algebraic model for reasoning about semantics of concurrent programs. We generalize guarded strings to guarded series-parallel strings , or gsp-strings, to give a concrete language model for CKAT. Combining nondeterministic guarded automata of Kozen with branching automata of Lodaya and Weil one obtains a model for processing gsp-strings in parallel. To ensure that the model satisfies the weak exchange law (x‖y)(z‖w)≤(xz)‖(yw) of …

Geometric Auxetics, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.

Unique Pseudo-Expectations For C∗-Inclusions, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

Given an inclusion D⊆C of unital C ∗ -algebras (with common unit), a unital completely positive linear map Φ of C into the injective envelope I(D) of D which extends the inclusion of D into I(D) is a pseudo-expectation. Pseudo-expectations are generalizations of conditional expectations, but with the advantage that they always exist. The set PsExp(C,D) of all pseudo-expectations is a convex set, and when D is Abelian, we prove a Krein–Milman type theorem showing that PsExp(C,D) can be recovered from its set of extreme points. In general, PsExp(C,D) is not a singleton. However, there are large and natural classes …

The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni

MPP Published Research

The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …

Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.

Doctoral Theses

For univariate as well as finite dimensional multivariate data, there is an extensive literature on nonparametric statistical methods. One of the reasons for the popularity of nonparametric methods is that it is often difficult to justify the assumptions (e.g., Gaussian distribution of the data) made in the models used in parametric methods. Nonparametric procedures use more flexible models, which involve less assumptions. So, they are more robust against possible departures from the model assumptions, and are applicable to a wide variety of data. Nonparametric methods outperform their parametric competitors in many situations, where the assumptions required for the parametric methods …

Towards A Theory Of Recursive Function Complexity: Sigma Matrices And Inverse Complexity Measures, Bradford M. Fournier

University of New Orleans Theses and Dissertations

This paper develops a data structure based on preimage sets of functions on a finite set. This structure, called the sigma matrix, is shown to be particularly well-suited for exploring the structural characteristics of recursive functions relevant to investigations of complexity. The matrix is easy to compute by hand, defined for any finite function, reflects intrinsic properties of its generating function, and the map taking functions to sigma matrices admits a simple polynomial-time algorithm . Finally, we develop a flexible measure of preimage complexity using the aforementioned matrix. This measure naturally partitions all functions on a finite set by characteristics …

Optimizing A Game Of Chinese Checkers, Nicholas Fonseca

Honors Program Theses and Projects

Chinese Checkers is a multi-player strategy game in which game play can become surprising complex as the game progresses. In spite of this game's complexity, questions involving games with multiple players have received little research attention. This paper considers the three player case and discusses how to describe short games. By utilizing these tendencies for short games, a heuristic function can be defined which associates a player's possible move with a heuristic value. These heuristic values guide a search algorithm which searches through all the possible moves made in a game. To guide this discussion for three player games, the …

Speedups And Orbit Equivalence Of Finite Extensions Of Ergodic Zᵈ-Actions, Aimee S.A. Johnson, D. M. Mcclendon

Mathematics & Statistics Faculty Works

We classify n-point extensions of ergodic Zᵈ-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Zᵈ-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Zᵈ-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgroups of the symmetric group on n elements.

Postural Responses To Perturbations Of The Vestibular System During Walking In Healthy Young And Older Adults, Jung Hung Chien

Theses & Dissertations

It has been shown that approximate one-third of US adults aged 40 years and older (69 million US citizens) have some type of vestibular problems. These declining abilities of the vestibular system affect quality of life. Difficulties in performing daily activities (dressing, bathing, getting in and out of the bed and etc.) have been highly correlated to loss of balance due to vestibular disorders. The exact number of people affected by vestibular disorders is still difficult to quantify. This might be because symptoms are difficult to describe and differences exist in the qualifying criteria within and across studies. Thus, it …

A Critical Analysis Of Random Response Techniques, Emanuel Zanzerkia

Honors Program Theses and Projects

In order to understand and make informed decision on sensitive topics such as domestic violence and drug use, interviews have been used to collect data. However it is difficult to assess how truthful respondents are since they may not feel at ease revealing the truth to an interviewer. Surveyors of sensitive issues face the problem that respondents may be reluctant to answer truthfully since the respondent may feel pressured socially or may fear the repercussions of their truthful answer. Processes known as random response techniques have been introduced to allow interviewers the ability to extract information they need for a …

Method Of Lines Transpose: An Efficient A-Stable Solver For Wave Propagation, Matthew Causley, Andrew Christlieb, Eric Wolf

Mathematics Publications

Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOLT), and the resulting semi-discrete (i.e. continuous in space) boundary value problem. In [7], A-stable schemes of high order were derived, and in [9] a high order, fast O(N) spatial solver was derived, which is matrix-free and is based on dimensional-splitting. In this work, are interested in building a wave solver, and our main concern is the development of boundary conditions. We demonstrate all desired boundary conditions for a wave solver, including outflow …

Fast Methods For Variable-Coefficient Peridynamic And Non-Local Diffusion Models, Che Wang

Theses and Dissertations

In previous studies, scientists developed the classical solid mechanic theory. The model has been widely used in scientific research and practical production. The main assumption of the classical theory of solid mechanics is that all internal forces act through zero distance. Because of this assumption, the mathematical model always leads to partial differential equations, which meet with problems when describing the spontaneous formation of discontinuities and other singularities. A peridynamic model was proposed as a reformation of solid mechanics [40, 41, 43, 44, 45], which leads to a non-local framework that does not explicitly involve the notion of deformation gradients, …

A Survey Of The Kinetic Monte Carlo Algorithm As Applied To A Multicellular System, Michael Richard Laughlin

Theses and Dissertations

We explore the origins and implementation of the Kinetic Monte Carlo method on a system of cells suspended in a liquid media. The situation presented herein has applications in the emerging field of biofabrication, which may have lasting impacts in medical science. The theory behind the method is explained in detail, starting with its emergence in the 1960s, and two major improvements to the scaling of the method are presented, along with a restriction to a special case. Finally, we give the results of several simulations.

Modeling, Simulation, And Applications Of Fractional Partial Differential Equations, Wilson Cheung

Theses and Dissertations

The Black-Scholes model is commonly used to track the price of European options with respect to maturity in many financial markets. This model degenerates into a partial differential equation that relates the European-style option price to the underlying price and time of expiry. Black-Scholes assumes that underlying prices satisfy a geometric Brownian motion.

After the U.S. stock market crash of 1987, this assumption becomes inaccurate as it fails to represent the behavior of S&P 500 European vanilla option prices. Specifically, under the measure of moneyness, the volatility smirk does not flatten out and the resulting conditional return distribution does not …

The Definitions Of Three-Dimensional Landmarks On The Human Face: An Interdisciplinary View, Stanislav Katina, Kathryn Mcneil, Ashraf Ayoub, Brendan Guilfoyle, Balvinder Khambay, Paul Siebert, Federico Sukno, Mario Rojas, Liberty Vittert, John Waddington, Paul F. Whelan, Adrian W. Bowman

Publications

The analysis of shape is a key part of anatomical research and in the large majority of cases landmarks provide a standard starting point. However, while the technology of image capture has developed rapidly and in particular three-dimensional imaging is widely available, the definitions of anatomical landmarks remain rooted in their two-dimensional origins. In the important case of the human face, standard definitions often require careful orientation of the subject. This paper considers the definitions of facial landmarks from an interdisciplinary perspective, including biological and clinical motivations, issues associated with imaging and subsequent analysis, and the mathematical definition of surface …

Augmenting The Immersed Boundary Method With Radial Basis Functions (Rbfs) For The Modeling Of Platelets In Hemodynamic Flows, Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson

Mathematics Faculty Publications and Presentations

We present a new computational method by extending the Immersed Boundary (IB) method with a geometric model based on parametric Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications involving surface elasticity. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we test the convergence of our method and compare our method with the traditional IB method in terms of computational cost, maximum stable time-step size and volume loss. We …

Direct Phenotypic Screening In Mice: Identification Of Individual, Novel Antinociceptive Compounds From A Library Of 734 821 Pyrrolidine Bis-Piperazines, Richard A. Houghten, Michelle L. Ganno, Jay P. Mclaughlin, Colette T. Dooley, Shainnel O. Eans Torrey Pines Institute For Molecular Studies, Radleigh Santos, Travis Lavoi, Adel Nefzi, Greg Welmaker, Marc A. Giulianotti, Lawrence Toll

Mathematics Faculty Articles

The hypothesis in the current study is that the simultaneous direct in vivo testing of thousands to millions of systematically arranged mixture-based libraries will facilitate the identification of enhanced individual compounds. Individual compounds identified from such libraries may have increased specificity and decreased side effects early in the discovery phase. Testing began by screening ten diverse scaffolds as single mixtures (ranging from 17 340 to 4 879 681 compounds) for analgesia directly in the mouse tail withdrawal model. The “all X” mixture representing the library TPI-1954 was found to produce significant antinociception and lacked respiratory depression and hyperlocomotor effects using …

Finite Groups In Which Pronomality And 𝔉-Pronormality Coincide, Adolfo Ballester-Bolinches, James C. Beidleman, Arnold D. Feldman, Matthew F. Ragland

Mathematics Faculty Publications

For a formation 𝔉, a subgroup U of a finite group G is said to be 𝔉-pronormal in G if for each g ∈ G, there exists x ∈ ⟨U, U^g⟩ ^𝔉 such that U^x = U^g. If 𝔉 contains 𝔑, the formation of nilpotent groups, then every 𝔉-pronormal subgroup is pronormal and, in fact, 𝔑-pronormality is just classical pronormality. The main aim of this paper is to study classes of finite soluble groups in which pronormality and 𝔉-pronormality coincide.

Efficient High-Order Methods For Solving Fractional Differential Equations Of Order Α ∈ (0, 1) Using Fast Convolution And Applications In Wave Propagation, Matthew F. Causley, Peter G. Petropoulus

Mathematics Publications

In this work we develop a means to rapidly and accurately compute the Caputo fractional derivative of a function, using fast convolution. The key element to this approach is the compression of the fractional kernel into a sum of M decaying exponentials, where M is minimal. Specifically, after N time steps we find M= O (log N) leading to a scheme with O (N log N) complexity. We illustrate our method by solving the fractional differential equation representing the Kelvin-Voigt model of viscoelasticity, and the partial differential equations that model the propagation of electromagnetic pulses in the Cole-Cole model of …

Hypercube Unfoldings That Tile R3 And R2, Giovanna Diaz, Joseph O'Rourke

Computer Science: Faculty Publications

We show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a "dimension-descending tiler." We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane.

Comparison Theorems And Asymptotic Behavior Of Solutions Of Discrete Fractional Equations, Baoguo Jia, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

Consider the following n-th order nabla and delta fractional difference equations

rn r (a)x(t) = c(t)x(t), t 2 Na+1, x(a) > 0.

and

Va+v-1x(t) = c(t)x(t + v - 1), t 2 Na, x(a + n - 1) > 0

We establish comparison theorems by which we compare the solutions x(t) of (*) and (**) with the solutions of the equations rn r(a)x(t) = bx(t) and Dn a+v-1x(t) = bx(t + v -1), respectively, where b is a constant. We obtain four asymptotic results, one of them extends the recent result [F. M. Atici, P. W. Eloe, Rocky Mountain J. Math. 41(2011), …

Stochastic Optimal Control For Online Seller Under Reputational Mechanisms, Milan Bradonij', Matthew Causley, Albert Cohen

Mathematics Publications

In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller’s reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which …

The Minimum And Other Free Energies For Non-Linear Materials With Memory., John Murrough Golden

Articles

Expressions are obtained for free energies of materials with a certain type of non-linear constitutive relation. In particular, the minimum and related free energies are considered in some detail. Minimal states are defined for these materials, and it is shown that any free energy yielding a linear constitutive equation that is a functional of the minimal state has a counterpart in the non-linear case which is also a minimal state functional in this more general context. These results are explored for simple examples, including discrete spectrum materials.

Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy

Mathematics Colloquium Series

Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that can only be explained by the ultimate abstraction that is embedded in mathematics. In this talk, I will discuss the concept of curvature and argue how it explains the “unexplainable”. We will see how the curvature proves that the earth is rotating, how good the soap bubbles are at proving profound mathematical results, and if the two dimensional residents can determine the shape of their …

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton

S. Allen Broughton

This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of PSL₂(q). A quasi-platonic action of a group G on a closed Riemann S surface is a conformal action for which S/G is a sphere and S->S/G is branched over {0, 1,infinity}. The unit interval in S/G may be lifted to a dessin d'enfant D, an embedded bipartite graph in S. The dessin forms the edges and vertices of a tiling on S by dihedrally symmetric polygons, generalizing the idea of a …

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of PSL₂(q). A quasi-platonic action of a group G on a closed Riemann S surface is a conformal action for which S/G is a sphere and S->S/G is branched over {0, 1,infinity}. The unit interval in S/G may be lifted to a dessin d'enfant D, an embedded bipartite graph in S. The dessin forms the edges and vertices of a tiling on S by dihedrally symmetric polygons, generalizing the idea of a …

The Effects Of Prompted Tutoring On An Emporium Model Math Course, Juliette Michelle Young

Honors Theses

My research goal is to investigate how specific prompting of students would affect their involvement and progress in an emporium developmental math course. With the aim of increasing the students’ involvement and progress I tested a method that was in tended to increase students’ perceived connectedness with the classroom and promote the use of the available tutors and teachers. I monitored consenting students’ progress in the Spring 2015 courses and sent emails to students who met any one of three different criterion: (1) If the students time investment was below a threshold. (2) If the student’s mastery pace was less …

Canonoid And Poissonoid Transformations, Symmetries And Bihamiltonian Structures, Giovanni Rastelli, Manuele Santoprete

Mathematics Faculty Publications

We give a characterization of linear canonoid transformations on symplectic manifolds and we use it to generate biHamiltonian structures for some mechanical systems. Utilizing this characterization we also study the behavior of the harmonic oscillator under canonoid transformations. We present a description of canonoid transformations due to E.T. Whittaker, and we show that it leads, in a natural way, to the modern, coordinate-independent definition of canonoid transformations. We also generalize canonoid transformations to Poisson manifolds by introducing Poissonoid transformations. We give examples of such transformations for Euler’s equations of the rigid body (on so*(3) and so*(4)) and for an integrable …