Mathematics Commons^™

High Prevalence Of Subclinical Atherosclerosis By Carotid Ultrasound Among Mexican Americans: Discordance With 10-Year Risk Assessment Using The Framingham Risk Score, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Anne R. Rentfro, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Background: Framingham risk scores (FRS) were validated in a mostly Caucasian population. Evaluation of subclinical atherosclerosis by carotid ultrasound may improve ascertainment of risk in nonwhite populations. This study aimed to evaluate carotid intima-media thickness (cIMT) and carotid plaquing among Mexican Americans, and to correlate these markers with coronary risk factors and the FRS.

Methods/results: Participants (n = 141) were drawn from the Cameron County Hispanic Cohort. Carotid artery ultrasound was performed and cIMT measured. Carotid plaque was defined as areas of thickening >50% of the thickness of the surrounding walls. Mean age was 53.1 ± 11.7 years (73.8% female). …

Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young

Mathematics Faculty Research

We prove generalizations of Loewner's results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone.

Hamilton Decompositions Of Certain 6-Regular Cayley Graphs On Abelian Groups With A Cyclic Subgroup Of Index Two, Erik E. Westlund

Faculty Articles

Alspach conjectured that every connected Cayley graph of even valency on a finite Abelian group is Hamilton-decomposable. Using some techniques of Liu, this article shows that if A is an Abelian group of even order with a generating set {a,b}, and A contains a subgroup of index two, generated by c, then the 6-regular Cayley graph is Hamilton-decomposable.

Existence Of A Positive Solution For A Right-Focal Dynamic Boundary Value Problem, Jeffrey Lyons

Mathematics Colloquium Series

This talk presents an application made from an extension of the Leggett-Williams fixed-point theorem—which requires neither of the functional boundaries to be invariant—to a second-order right focal dynamic boundary value problem on a time scale. To conclude, Lyons will provide a non-trivial example.

Essays On Voting And Auction Theory., Mridu Prabal Goswami Dr.

Doctoral Theses

No abstract provided.

An Optimal Lower Bound On The Communication Complexity Of Gap-Hamming-Distance, Amit Chakrabarti, Oded Regev

Dartmouth Scholarship

We prove an optimal Ω(n) lower bound on the randomized communication complex- ity of the much-studied gap-hamming-distance problem. As a consequence, we obtain essentially optimal multipass space lower bounds in the data stream model for a number of fundamental prob- lems, including the estimation of frequency moments. The gap-hamming-distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively. They are promised that the Hamming distance between x and y is either at least n/2 + √n or at most n, and their goal is to decide which of these is the case. Since …

Blackbox Reduction Of Some Cryptographic Constructions., Rishiraj Bhattacharyya Dr.

Doctoral Theses

No abstract provided.

Bio-Logic Builder: A Non-Technical Tool For Building Dynamical, Qualitative Models, Tomáš Helikar, Brian Kowal, Alex Madrahimov, Manish Shrestha, Jay Pedersen, Kahani Limbu, Ishwor Thapa, Thaine Rowley, Rahul Satalkar, Naomi Kochi, John Konvalina, Jim A. Rogers

Mathematics Faculty Publications

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many …

Quantum Locally Compact Metric Spaces, Frédéric Latrémolière

Mathematics Preprint Series

We introduce the notion of a quantum locally compact metric space, which is the noncommutative analogue of a locally compact metric space, and generalize to the non-unital setting the notion of quantum metric spaces introduced by Rieffel. We then provide several examples of such structures, including the Moyal plane, compact quantum metric spaces and locally compact metric spaces. This paper provides an answer to the question raised in the literature about the proper notion of a quantum metric space in the nonunital setup and offers important insights into noncommutative geometry for non compact quantum spaces.

Hannum Family (Sc 746), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 746. Ciphering book containing problems using the British pound system, which also contains accounts of John Hannum, Jr., and Richard Hannum, and writings of Penelope Hannum, Logan County, Kentucky. Also clippings, chiefly from newspapers of Russellville, Kentucky, 1820-1860.

Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov

Articles

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction uid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing in ationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.

Uniqueness Of Nonnegative Solutions For Semipositone Problems On Exterior Domains, Alfonso Castro, Lakshmi Sankar, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the problem

−Δu = λK(|x|)f(u), x∈Ω

u=0 if |x|=r₀

u→0 as |x|→∞,

where λ is a positive parameter, Δu = div(∇u)is the Laplacian of u, Ω = {x ∈ Rⁿ; n > 2,|x| > r₀}, K ∈ C¹([r₀,∞),(0,∞)) is such that lim r→∞ K(r) = 0 and f ∈ C¹([0,∞),R) is a concave function which is sublinear at ∞ and f(0) < 0. We establish the uniqueness of nonnegative radial solutions when λ is large.

Obtaining Estimators From Correlation Coefficients: The Correlation Estimation System And R, Rudy Gideon

Mathematical Sciences Faculty Publications

Correlation coefficients are generally viewed as summaries, causing them to be underutilized. Creating functions from them leads to their use in diverse areas of statistics. Because there are many correlation coefficients (see, for example, Gideon (2007)) this extension makes possible a very broad range of statistical estimators that rivals least squares. The whole area could be called a "Correlation Estimation System." This paper outlines some of the numerous possibilities for using the system and gives some illustrative examples. Detailed explanations are developed in earlier papers. The formulae to make possible both the estimation and some of the computer coding to …

A Tale Of Two Workshops: Two Workshops, Three Papers, New Ideas, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Ultrasonic Analysis Of Breast Tissue For Pathology Classification, Kristina Marie Sorensen

Undergraduate Honors Capstone Projects

Real time measurements may assist surgeons in obtaining negative or cancer free margins during lumpectomy to eliminate invasive re-excision. Previous findings show that high-frequency ultrasound can differentiate between a range of breast pathologies in surgical specimens. Two parameters, peak density and second-order spectral slope, are sensitive to histopathology. Our objective was to determine the mechanism linking high-frequency ultrasound to histology. The hypothesis is that ultrasound sensitivity is a function of the microscopic heterogeneity (and thus histology) of the tissue. Ultrasonic results from breast specimens were used to construct a multivariate analysis of the parameters that permitted differentiation of normal, adipose, …

The Awards Project: Promoting Good Practices In Award Selection, Betty Mayfield, Francis Su

All HMC Faculty Publications and Research

Every year the MAA honors many members of our community with a wide variety of prizes, awards, and certificates for excellence in teaching, writing, scholarship, and service (see maa.org/awards). The winners exemplify our ideals as an association; consequently, they are often viewed as role models and leaders. So it is important to ask: Do these awards, as a whole, reflect the outstanding contributions of the breadth of association membership?

Assessing The Structure Of Binghamton University's Emerging Leaders Program, Tyler D. Lenga

MPA Capstone Projects 2006 - 2015

The Emerging leaders Program (ELP) is a multi-faced student leadership program coordinated through Binghamton University's Office of New Student Programs and sponsored by the Division of Student Affairs. This capstone project was designed to assess the effectiveness of the 'leadership team" component of the ELP, as well as identify areas of improvement. The leadership team component of the ELP plays a large role in the program achieving its desired outcomes. Therefore, the program has identified this component as an area needing further performance evaluation.

The Sense-Isomorphism Theoretical Image Voxel Estimation (Sense-Itive) Model For Reconstruction And Observing Statistical Properties Of Reconstruction Operators, Iain P. Bruce, M. Muge Karaman, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show …

On Lattices Of Varieties Of Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the …

Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc

Mathematics and Statistics Faculty Publications and Presentations

We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …