Mathematics Commons^™

Spectral Clustering: An Empirical Study Of Approximation Algorithms And Its Application To The Attrition Problem, B. Cung, T Jin, J. Ramirez, A. Thompson, C. Boutsidis, Deanna Needell

CMC Faculty Publications and Research

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation …

Immunoglobulins Against Tyrosine-Nitrated Epitopes In Coronary Artery Disease, Leonor Thomson, Margarita Tenopoulou, Richard Lightfoot, Epida Tsika, Ioannis Parastatidis, Marissa Martinez, Todd M. Greco, Paschalis Thomas Doulias, Yuping Wu, W.H. Wilson Tang, Stanley L. Hazen, Harry Ischiropoulos

Mathematics and Statistics Faculty Publications

Background—Several lines of evidence support a pathophysiological role of immunity in atherosclerosis. Tyrosine-nitrated proteins, a footprint of oxygen- and nitrogen-derived oxidants generated by cells of the immune system, are enriched in atheromatous lesions and in circulation of patients with coronary artery disease (CAD). However, the consequences of possible immune reactions triggered by the presence of nitrated proteins in subjects with clinically documented atherosclerosis have not been explored. Methods and Results—Specific immunoglobulins that recognize 3-nitrotyrosine epitopes were identified in human lesions, as well as in circulation of patients with CAD. The levels of circulating immunoglobulins against 3-nitrotyrosine epitopes were quantified in …

Variational Methods And Critical Point Theory, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera

Mathematics and System Engineering Faculty Publications

[No abstract provided]

Numerical Solutions Of Elliptic Inverse Problems Via The Equation Error Method, Mohammad F. Al-Jamal

Dissertations, Master's Theses and Master's Reports - Open

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be …

Radar Signal Delay In The Dvali-Gabadadze-Porrati Gravity In The Vicinity Of The Sun, Ioannis Haranas, Omiros Ragos, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use the space time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects we derive expressions for the signal time delays in the vicinity of the sun, and for various angles of the signal approach. We use the corresponding numerical value for the parameter r₀ to be equal to 5 Mpc, and from that we calculate that the time contribution due to DGP correction to the metric is proportional to b^{3/2 …}

Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Forbidden Symmetries, Frank A. Farris

Mathematics and Computer Science

The purpose of this paper is to show that an effort to construct functions known not to exist may on occasion produce interesting frauds. Our method produces a family of Harald Bohr's quasiperiodic functions, which may well remind readers of the quasicrystals that have been much in the news since Daniel Shechtman won the Nobel Prize in Chemistry in 2011.

Elementary Orbifold Differential Topology, Joseph E. Borzellino, Victor Brunsden

Mathematics

Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sardʼs theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold …

Weak Covering Properties And Infinite Games, L. Babinkostova, B. A. Pansera, M. Scheepers

Mathematics Faculty Publications and Presentations

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use generic extensions by Cohen reals to illustrate the necessity of some of the hypotheses in our theorems.

Clinical And Genetic Association Of Serum Paraoxonase And Arylesterase Activities With Cardiovascular Risk, W.H. Wilson Tang, Jaana Hartiala, Yiying Fan, Yuping Wu, Alexandre F.R. Stewart, Jeanette Erdmann, Sekar Kathiresan, Cardiogram Consortium, Lerner Research Institute, Robert Roberts, Ruth Mcpherson, Hooman Allayee, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Objective—Diminished serum paraoxonase and arylesterase activities (measures of paraoxonase-1 [PON-1] function) in humans have been linked to heightened systemic oxidative stress and atherosclerosis risk. The clinical prognostic use of measuring distinct PON-1 activities has not been established, and the genetic determinants of PON-1 activities are not known. Methods and Results—We established analytically robust high-throughput assays for serum paraoxonase and arylesterase activities and measured these in 3668 stable subjects undergoing elective coronary angiography without acute coronary syndrome and were prospectively followed for major adverse cardiovascular events (MACE= death, myocardial infarction, stroke) over 3 years. Low serum arylesterase and paraoxonase activities were …

Prognostic Role Of Pulmonary Arterial Capacitance In Advanced Heart Failure, Matthias Dupont, Wilfried Mullens, Hadi N. Skouri, Zuheir Abrahams, Yuping Wu, David O. Taylor, Randall C. Starling, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

Background—Right ventricular (RV) dysfunction frequently occurs and independently prognosticates in left-sided heart failure. It is not clear which RV afterload measure has the greatest impact on RV function and prognosis. We examined the determinants, prognostic role, and response to treatment of pulmonary arterial capacitance (PAC, ratio of stroke volume over pulmonary pulse pressure), in relation to pulmonary vascular resistance (PVR) in heart failure. Methods and Results—We reviewed 724 consecutive patients with heart failure who underwent right heart catheterization between 2000 and 2005. Changes in PAC were explored in an independent cohort of 75 subjects treated for acute decompensated heart failure. …

G-Cimp Status Prediction Of Glioblastoma Samples Using Mrna Expression Data, Mehmet Baysan, Serdar Bozdag, Margaret C. Cam, Svetlana Kotliarova, Susie Ahn, Jennifer Walling, Jonathan K. Killian, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma Multiforme (GBM) is a tumor with high mortality and no known cure. The dramatic molecular and clinical heterogeneity seen in this tumor has led to attempts to define genetically similar subgroups of GBM with the hope of developing tumor specific therapies targeted to the unique biology within each of these subgroups. Recently, a subset of relatively favorable prognosis GBMs has been identified. These glioma CpG island methylator phenotype, or G-CIMP tumors, have distinct genomic copy number aberrations, DNA methylation patterns, and (mRNA) expression profiles compared to other GBMs. While the standard method for identifying G-CIMP tumors is based on …

Self-Assembled Nanoparticle Antiglare Coatings, Khalid Askar, Blayne M. Phillips, Xuan Dou, Juan Lopez, Carl Smith, Bin Jiang, Peng Jiang

Mathematics and Statistics Faculty Publications and Presentations

Here we report a simple and scalable bottom-up technology for assembling close-packed nanoparticle monolayers on both sides of a glass substrate as high-quality antiglare coatings. Optical measurements show that monolayer coatings consisting of 110 nm silica nanoparticles can significantly reduce optical reflectance and enhance specular transmittance of the glass substrate for a broad range of visible wavelengths. Both experiments and numerical simulations reveal that the antiglare properties of the self-assembled colloidal monolayers are significantly affected by the size of the colloidal particles.

G-Strands, Darryl Holm, Rossen Ivanov, James Percival

Articles

A G-strand is a map g(t,s): RxR --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. The SO(3)-strand is the G-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3)_K-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the SO(3) …

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.

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). …

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?