Mathematics Commons^™

Factors Associated With Microalbuminuria In Type 2 Diabetes Patients In Nan Hospital, Thailand, Chuanchom Tepsukon, Timothy O'Brien

Mathematics and Statistics: Faculty Publications and Other Works

Objective: To determine risk factors associated with microalbuminuria in type 2 diabetes patients.

Method: This retrospective study was performed on 198 patients with type 2 diabetes attending the diabetes clinic at Nan Hospital in Northern Thailand. Basic information (i.e., gender, age, weight, body mass index) of patients and factors associated with microalbuminuria [i.e., fasting blood sugar, hemoglobin A1C (HbA1C), low-density lipoprotein, blood pressure, urine microalbuminuria, serum creatinine, foot problem, eye problem] were investigated. Comparisons of mean were performed using the Student’s t-tests, and comparisons of proportions using the chi-square tests. Binary logistic regression and odds ratio analyses were performed to …

Quantization Dimension For Gibbs-Like Measures On Cookie-Cutter Sets, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper using the Banach limit we have determined a Gibbs-like measure μ h supported by a cookie-cutter set E which is generated by a single cookie-cutter mapping f . For such a measure μ h and r ∈ ( 0 , + ∞ ) we have shown that there exists a unique κ r ∈ ( 0 , + ∞ ) such that κ r is the quantization dimension function of the probability measure μ h , and we established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to …

Block Kaczmarz Method With Inequalities, Jonathan Briskman, Deanna Needell

CMC Faculty Publications and Research

The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell and Tropp provided an analysis of a block version of the method for systems of linear equations. This paper considers the use of a block type method for systems of mixed equalities and inequalities, bridging these two bodies of work. We show that utilizing a matrix paving over the equalities of the system can lead to significantly improved convergence, and prove a linear convergence rate as …

Counting Edge-Kempe-Equivalence Classes For 3-Edge-Colored Cubic Graphs, Sarah-Marie Belcastro, Ruth Haas

Mathematics Sciences: Faculty Publications

Two edge colorings of a graph are edge-Kempe equivalent if one can be obtained from the other by a series of edge-Kempe switches. This work gives some results for the number of edge-Kempe equivalence classes for cubic graphs. In particular we show every 2-connected planar bipartite cubic graph has exactly one edge-Kempe equivalence class. Additionally, we exhibit infinite families of nonplanar bipartite cubic graphs with a range of numbers of edge-Kempe equivalence classes. Techniques are developed that will be useful for analyzing other classes of graphs as well.

Stochastic Modeling And Analysis Of Energy Commodity Spot Price Processes, Olusegun Michael Otunuga

USF Tampa Graduate Theses and Dissertations

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand

expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues.

The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of …

Topological Data Analysis Of Properties Of Four-Regular Rigid Vertex Graphs, Grant Mcneil Conine

USF Tampa Graduate Theses and Dissertations

Homologous DNA recombination and rearrangement has been modeled with a class of four-regular rigid vertex graphs called assembly graphs which can also be represented by double occurrence words. Various invariants have been suggested for these graphs, some based on the structure of the graphs, and some biologically motivated.

In this thesis we use a novel method of data analysis based on a technique known as partial-clustering analysis and an algorithm known as Mapper to examine the relationships between these invariants. We introduce some of the basic machinery of topological data analysis, including the construction of simplicial complexes on a data …

Connecting Galois Representations With Cohomology, Joseph Allen Adams

Theses and Dissertations

In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 …

Work In Progress: Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Mathematics is intrinsic to engineering and as such plays an integral role in the education of engineers. New challenges are being faced in higher education particularly in the areas of student motivation, engagement and attainment. As a result mathematics is often the focus of engineering education research. Traditional methods of delivery such as lectures and tutorials need to evolve to counter these challenges with new pedagogical approaches explored including the use of new technologies. Today’s students are immersed in an increasingly technological world and are willing to adapt to new technological advances. This paper describes a study being undertaken in …

Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke

Theses and Dissertations

We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.

A Modified Weighted Holm Procedure For Multiple Comparisons, Jared Ray Wolf

Student Theses and Dissertations

Multiplicity is a well established notion in statistics that arises when simultaneously testing n &ge2 individual hypotheses. To combat this issue, over time, numerous multiple comparison procedures have been developed. Such methods are relied upon heavily in confirmatory clinical trials, both in dose-finding and multiple-endpoint scenarios. The proposed procedure is a hybrid between the data-driven Weighted Holm procedure and the Fallback procedure which relies heavily on the a priori ordering of the hypotheses based on weights. Strong control of the familywise error rate is proven. Both general and previous clinical examples are performed utilizing this new method while comparing the …

New Approaches To Parameter Estimation And Structural Discrimination For Stationary Time Series, Ashton Erwin

Student Theses and Dissertations

This thesis gives a comprehensive report of my research in time series analysis from fall 2010 to spring 2014. It is comprised of two main efforts: interval estimation for a first-order autoregressive parameter and new tests for discriminating between the autocovariance structures of stationary time series. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them.

Energy Driven Pattern Formation In Planar Dipole-Dipole Systems In The Presence Of Weak Noise, Jaron P. Kent-Dobias '14, Andrew Bernoff

All HMC Faculty Publications and Research

We study pattern formation in planar fluid systems driven by intermolecular cohesion (which manifests as a line tension) and dipole-dipole repulsion which are observed in physical systems including ferrofluids in Hele-Shaw cells and Langmuir layers. When the dipolar repulsion is sufficiently strong, domains undergo forked branching reminiscent of viscous fingering. A known difficulty with these models is that the energy associated with dipole-dipole interactions is singular at small distances. Following previous work, we demonstrate how to ameliorate this singularity and show that in the macroscopic limit, only the relative scale of the microscopic details of a system are relevant, and …

Continuous Everywhere But Differentiable Nowhere Functions, Delong Li

Student Theses and Dissertations

In this thesis, we consider a classical problem in real analysis: the construction of continuous but differentiable nowhere functions. This problem has a long history in mathematics starting with Weierstrass's first example in 1872. We use an approach developed by Kiesswetter in 1966 and find the generalized Kiesswetter's functions. We establish a criterion for such generalizations and show how such functions can be understood geometrically.

Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt

Theses and Dissertations

Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is …

Two-Part Reconstruction With Noisy-Sudocodes, Yanting Ma, Dror Baron, Deanna Needell

CMC Faculty Publications and Research

We develop a two-part reconstruction framework for signal recovery in compressed sensing (CS), where a fast algorithm is applied to provide partial recovery in Part 1, and a CS algorithm is applied to complete the residual problem in Part 2. Partitioning the reconstruction process into two complementary parts provides a natural trade-off between runtime and reconstruction quality. To exploit the advantages of the two-part framework, we propose a Noisy-Sudocodes algorithm that performs two-part reconstruction of sparse signals in the presence of measurement noise. Specifically, we design a fast algorithm for Part 1 of Noisy-Sudocodes that identifies the zero coefficients of …

Cytokine Production But Lack Of Proliferation In Peripheral Blood Mononuclear Cells From Chronic Chagas' Disease Cardiomyopathy Patients In Response To T. Cruzi Ribosomal P Proteins, Silvia A. Longhi, Augusto Atienza, Graciela Perez Prados, Alcinette Buying, Virginia Balouz, Carlos A. Buscaglia, Radleigh Santos, Laura M. Tasso, Ricardo Bonato, Pablo Chiale, Clemencia Pinilla, Valeria A. Judkowski, Karina A. Gomez

Mathematics Faculty Articles

Background

Trypanosoma cruzi ribosomal P proteins, P2β and P0, induce high levels of antibodies in patients with chronic Chagas' disease Cardiomyopathy (CCC). It is well known that these antibodies alter the beating rate of cardiomyocytes and provoke apoptosis by their interaction with β1-adrenergic and M2-muscarinic cardiac receptors. Based on these findings, we decided to study the cellular immune response to these proteins in CCC patients compared to non-infected individuals.

Methodology/Principal findings

We evaluated proliferation, presence of surface activation markers and cytokine production in peripheral blood mononuclear cells (PBMC) stimulated with P2β, the C-terminal portion of P0 (CP0) proteins and T. …

The Asymptotic Dirichlet Problems On Manifolds With Unbounded Negative Curvature, Ran Ji

Dissertations, Theses, and Capstone Projects

Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable if the curvature satisfies the condition $-C e^{(2-\eta)r(x)} \leq K_M(x)\leq -1$ with $\eta>0$. We give an analytical proof of the same statement. In addition, using this new approach we are able to establish two boundary Harnack inequalities under the curvature condition $-C e^{(2/3-\eta)r(x)} \leq K_M(x)\leq -1$ with $\eta>0$. This implies that there is a natural homeomorphism between the Martin boundary and the geometric boundary of $M$. As far as we know, this is the first result of this kind under unbounded curvature …

Exploring Platform (Semi)Groups For Non-Commutative Key-Exchange Protocols, Ha Lam

Dissertations, Theses, and Capstone Projects

In this work, my advisor Delaram Kahrobaei, our collaborator David Garber, and I explore polycyclic groups generated from number fields as platform for the AAG key-exchange protocol. This is done by implementing four different variations of the length-based attack, one of the major attacks for AAG, and submitting polycyclic groups to all four variations with a variety of tests. We note that this is the first time all four variations of the length-based attack are compared side by side. We conclude that high Hirsch length polycyclic groups generated from number fields are suitable for the AAG key-exchange protocol.

Delaram Kahrobaei …

Stable Commutator Length In Amalgamated Free Products, Timothy Susse

Dissertations, Theses, and Capstone Projects

We show that stable commutator length is rational on free products of free Abelian groups amalgamated over Z^k, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. We then use the combinatorics of this algorithm to prove that for a word w in the (p, q)-torus knot complement, scl(w) is quasirational in p and q. Finally, we analyze central …

Asymptotic Invariants And Flatness Of Local Endomorphisms, Nikita Miasnikov

Dissertations, Theses, and Capstone Projects

For a local endomorphism of a noetherian local ring we introduce 3 asymptotic invariants one of which we call entropy. We use this notion of entropy to extend numerical conditions in Kunz' regularity criterion to every contracting endomorphism of a noetherian local ring, and to give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity. We also show that every finite endomorphism of a complete noetherian local ring of equal characteristic can be lifted to a finite endomorphism of a complete regular local ring. The local ring of an algebraic or analytic variety at a point fixed by a finite …