Physical Sciences and Mathematics Commons^™

Symmetric Integer Matrices Having Integer Eigenvalues, Lei Cao, Selcuk Koyuncu

Mathematics Faculty Articles

We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.

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.)

Finite Involution Semigroups With Infinite Irredundant Bases Of Identities, Edmond W. H. Lee

Mathematics Faculty Articles

A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis for the algebra. The first known examples of finite involution semigroups with infinite irredundant bases are exhibited. These involution semigroups satisfy several counterintuitive properties: their semigroup reducts do not have irredundant bases, they share reducts with some other finitely based involution semigroups, and they are direct products of finitely based involution semigroups.

Identification Of Protein Palmitoylation Inhibitors From A Scaffold Ranking Library, Laura D. Hamel, Brian J. Lenhart, David A. Mitchell, Radleigh Santos, Marc A. Giulianotti, Robert J. Deschenes

Mathematics Faculty Articles

The addition of palmitoyl moieties to proteins regulates their membrane targeting, subcellular localization, and stability. Dysregulation of the enzymes which catalyzed the palmitoyl addition and/or the substrates of these enzymes have been linked to cancer, cardiovascular, and neurological disorders, implying these enzymes and substrates are valid targets for pharmaceutical intervention. However, current chemical modulators of zDHHC PAT enzymes lack specificity and affinity, underscoring the need for screening campaigns to identify new specific, high affinity modulators. This report describes a mixture based screening approach to identify inhibitors of Erf2 activity. Erf2 is the Saccharomyces cerevisiae PAT responsible for catalyzing the palmitoylation …

Decomposition Of Finite Schmidt Rank Bounded Operators On The Tensor Product Of Separable Hilbert Spaces, Abdelkrim Bourouihiya

Mathematics Faculty Articles

Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are reflected by the operators involved in its Schmidt decomposition. These properties include compactness of FSR bounded operators and convergence of sequences whose terms are FSR bounded operators.

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 …

Investigating The Role Of The Host Multidrug Resistance Associated Protein Transporter Family In Burkholderia Cepacia Complex Pathogenicity Using A Caenorhabditis Elegans Infection Model, Pietro Tedesco, Marco Visone, Ermenegilda Parrilli, Maria Luisa Tutino, Elena Perrin, Isabel Maida, Renato Fani, Francesco Ballestriero, Radleigh Santos, Clemencia Pinilla, Elia Di Schiavi, George Tegos, Donatella De Pascale

Mathematics Faculty Articles

This study investigated the relationship between host efflux system of the non-vertebrate nematode Caenorhabditis elegans and Burkholderia cepacia complex (Bcc) strain virulence. This is the first comprehensive effort to profile host-transporters within the context of Bcc infection. With this aim, two different toxicity tests were performed: a slow killing assay that monitors mortality of the host by intestinal colonization and a fast killing assay that assesses production of toxins. A Virulence Ranking scheme was defined, that expressed the toxicity of the Bcc panel members, based on the percentage of surviving worms. According to this ranking the 18 Bcc strains were …

Modeling The Geographic Spread Of Rabies In China, Jing Chen, Lan Zou, Shigui Ruan

Mathematics Faculty Articles

Abstract

In order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans, in which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed, infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The existence of the disease-free equilibrium is discussed, the basic reproduction number is calculated, and the effect of moving rates of dogs between …

Antigen Discovery For The Identification Of Vaccine Candidates And Biomarkers Using A T Cell Driven Approach In Combination With Positional Scanning Peptide Libraries, Valeria A. Judkowski, Radleigh Santos, Gonzalo R. Acevedo, Marc Giulianotti, Jon R. Appel, Silvia A. Longhi, Karina A. Gomez, Clemencia Pinilla

Mathematics Faculty Articles

The prevention and treatment of infectious diseases is highly dependent on the availability of reliable diagnostic tests and protective or therapeutic vaccines. There also exists an urgent need to develop reliable biomarkers to monitor treatment success and to predict disease progression from asymptomatic to symptomatic disease in several disease scenarios. The elucidation of the disease-relevant antigens that elicit the protective immune responses is critical and required for the development of biomarkers, diagnostics, and vaccines. However; one of the main obstacles to the study of antigen specificity in human T cells is their low frequency in PBMC samples. To overcome this …

Improvement Of Ifng Elispot Performance Following Overnight Resting Of Frozen Pbmc Samples Confirmed Through Rigorous Statistical Analysis, Radleigh Santos, Alcinette Bunying, Nazila Sabri, John Yu, Anthony Gringeri, James Bender, Sylvia Janetzki, Clemencia Pinilla, Valeria A. Judkowski

Mathematics Faculty Articles

Immune monitoring of functional responses is a fundamental parameter to establish correlates of protection in clinical trials evaluating vaccines and therapies to boost antigen-specific responses. The IFNg ELISPOT assay is a well-standardized and validated method for the determination of functional IFNg-producing T-cells in peripheral blood mononuclear cells (PBMC); however, its performance greatly depends on the quality and integrity of the cryopreserved PBMC. Here, we investigate the effect of overnight (ON) resting of the PBMC on the detection of CD8-restricted peptide-specific responses by IFNg ELISPOT. The study used PBMC from healthy donors to evaluate the CD8 T-cell response to five pooled …

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. …

Inequalities Of Generalized Matrix Functions Via Tensor Products, Vehbi Emrah Paksoy, Ramazan Turkmen, Fuzhen Zhang

Mathematics Faculty Articles

By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtained.

Identification Of Tetrapeptides From A Mixture Based Positional Scanning Library That Can Restore Nm Full Agonist Function Of The L106p, I69t, I102s, A219v, C271y, And C271r Human Melanocortin-4 Polymorphic Receptors (Hmc4rs), Erica M. Haslach, Huisuo Huang, Marvin Dirain, Ginamarie Debevec, Phaedra Geer, Radleigh Santos, Marc Giulianotti, Clemencia Pinilla, Jon R. Appel, Skye R. Doering, Michael A. Walters, Richard A. Houghten, Carrie Haskell-Luevano

Mathematics Faculty Articles

Human obesity has been linked to genetic factors and single nucleotide polymorphisms (SNPs). Melanocortin-4 receptor (MC4R) SNPs have been associated with up to 6% frequency in morbidly obese children and adults. A potential therapy for individuals possessing such genetic modifications is the identification of molecules that can restore proper receptor signaling and function. These compounds could serve as personalized medications improving quality of life issues as well as alleviating diseases symptoms associated with obesity including type 2 diabetes. Several hMC4 SNP receptors have been pharmacologically characterized in vitro to have a decreased, or a lack of response, to endogenous agonists …

Identification Of Beryllium-Dependent Peptides Recognized By Cd4+ T Cells In Chronic Beryllium Disease, Michael T. Falta, Clemencia Pinilla, Douglas G. Mack, Alex N. Tinega, Francis Crawford, Marc Giulianotti, Radleigh Santos, Gina M. Clayton, Yuxiao Wang, Xuewu Zhang, Lisa A. Maier, Philippa Marrack, John W. Kappler, Andrew P. Fontenot

Mathematics Faculty Articles

Chronic beryllium disease (CBD) is a granulomatous disorder characterized by an influx of beryllium (Be)-specific CD4+ T cells into the lung. The vast majority of these T cells recognize Be in an HLA-DP–restricted manner, and peptide is required for T cell recognition. However, the peptides that stimulate Be-specific T cells are unknown. Using positional scanning libraries and fibroblasts expressing HLA-DP2, the most prevalent HLA-DP molecule linked to disease, we identified mimotopes and endogenous self-peptides that bind to MHCII and Be, forming a complex recognized by pathogenic CD4+ T cells in CBD. These peptides possess aspartic and glutamic acid residues at …

The Mathematics Of A Successful Deconvolution: A Quantitative Assessment Of Mixture-Based Combinatorial Libraries Screened Against Two Formylpeptide Receptors, Radleigh Santos, Jon R. Appel, Marc Giulianotti, Bruce S. Edwards, Larry A. Sklar, Richard A. Houghten, Clemencia Pinilla

Mathematics Faculty Articles

In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further …

On The Null Space Structure Associated With Trees And Cycles, Shaun M. Fallat, Shahla Nasserasr

Mathematics Faculty Articles

In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in the case of trees, and seems to represent a unifying theory within the context of the support of the null space. We extend this idea and apply it to describe the null vectors and corresponding nullities of certain symmetric matrices associated with cycles

Complex Dynamics In Predator-Prey Models With Nonmonotonic Functional Response And Seasonal Harvesting, Jicai Huang, Jing Chen, Yijun Gong, Weipeng Zhang

Mathematics Faculty Articles

In this paper we study the complex dynamics of predator-prey systems with nonmonotonic functional response and harvesting. When the harvesting is constant-yield for prey, it is shown that various kinds of bifurcations, such as saddle-node bifurcation, degenerate Hopf bifurcation, and Bogdanov-Takens bifurcation, occur in the model as parameters vary. The existence of two limit cycles and a homoclinic loop is established by numerical simulations. When the harvesting is seasonal for both species, sufficient conditions for the existence of an asymptotically stable periodic solution and bifurcation of a stable periodic orbit into a stable invariant torus of the model are given. …

Convergence Analysis Of A Fully Discrete Family Of Iterated Deconvolution Methods For Turbulence Modeling With Time Relaxation, Iuliana Stanculescu, R. Ingram, N Mays, C. C. Manica

Mathematics Faculty Articles

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified) Tikhonov-Lavrentiev and (modified) Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.

Co-Adventurers In Discovery: Collaborative Research Between Undergraduate Students And Faculty, Rajeswari Murugan, Evan Haskell

Mathematics Faculty Articles

There are many opportunities available beyond the classroom for undergraduate students to engage in cutting-edge scholarship. Some of the opportunities include study abroad, internships, and independent study. We strongly suggest that students experience such programs. Independent study courses can serve not only to sharpen the student’s engagement skills with the open-ended questions of current research, but also to enhance his or her own relationship with faculty. In this article we share the experiences of a biology student and a mathematics faculty member coming together as co-adventurers learning from each other about the mechanisms and mathematics involved in cardiac arrhythmia through …

Gm-Csf Production Allows The Identification Of Immunoprevalent Antigens Recognized By Human Cd4+ T Cells Following Smallpox Vaccination, Valeria A. Judkowski, Alcinette Bunying, Feng Ge, Jon R. Appel, Kingyee Law, Atima Sharma, Claudia Raja-Gabaglia, Patricia Norori, Radleigh Santos, Marc Giulianotti, Mark K. Slifka, Daniel C. Douek, Barney S. Graham, Clemencia Pinilla

Mathematics Faculty Articles

The threat of bioterrorism with smallpox and the broad use of vaccinia vectors for other vaccines have led to the resurgence in the study of vaccinia immunological memory. The importance of the role of CD4+ T cells in the control of vaccinia infection is well known. However, more CD8+ than CD4+ T cell epitopes recognized by human subjects immunized with vaccinia virus have been reported. This could be, in part, due to the fact that most of the studies that have identified human CD4+ specific protein-derived fragments or peptides have used IFN-γ production to evaluate vaccinia specific T cell responses. …

Finite Basis Problem For 2-Testable Monoids, Edmond W. H. Lee

Mathematics Faculty Articles

A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.

On A Semigroup Variety Of György Pollák, Edmond W. H. Lee

Mathematics Faculty Articles

Let P be the variety of semigroups defined by the identity xyzx = x². By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains finitely many subvarieties, and the identities defining these varieties are described. Specifically, it is decidable when a finite set of identities defines a finitely generated subvariety …

Right Focal Boundary Value Problems For Difference Equations, Johnny Henderson, Xueyan Liu, Jeffrey W. Lyons, Jeffrey T. Neugebauer

Mathematics Faculty Articles

An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also Provided.

Classes Of Commutative Clean Rings, Wolf Iberkleid, Warren William Mcgovern

Mathematics Faculty Articles

Let A be a commutative ring with identity and I an ideal of A. A is said to be I-clean if for every element α∈A there is an idempotent e = e²∈A such that α−e is a unit and αe belongs to I. A filter of ideals, say F, of A is Noetherian if for each I∈F there is a finitely generated ideal J∈F such that J⊆I. We characterize I-clean rings for the ideals 0, n(A), J( …

Chebyshev Optimized Approximate Deconvolution Models Of Turbulence, Iuliana Stanculescu, William Layton

Mathematics Faculty Articles

If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ∗ϕ, the resulting system is not closed due to the filtered nonlinear termuu¯¯¯¯. An approximate deconvolution operator DD is a bounded linear operator which satisfies

u=D(u¯¯)+O(δα), Turn MathJaxon

where δδ is the filter width and α⩾2α⩾2. Using a deconvolution operator as an approximate filter inverse, yields the closure

uu¯¯¯¯=D(u¯¯)D(u¯¯)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+O(δα). Turn MathJaxon

The residual stress of this model (and related models) depends directly on the deconvolution error,u−D(u¯¯). This report derives deconvolution operators yielding an effective turbulence model, which minimize the deconvolution error for velocity fields with finite kinetic energy. …

Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson

Mathematics Faculty Articles

Under certain conditions, solutions of the nonlocal boundary value problem, y⁽ⁿ⁾ = f(x, y, y', ... , y^{(n- 1)}), y(x_i) = Y_i for 1 £ i £ n- 1, and y(x_n) - Σ^m_k=1 Υ_iy (n_i) = y _n, are differentiated with respect to boundary conditions, where a < X₁ < X₂ < · · · < X_n-1 < n₁ < · · · < n_m < X_n < b, r₁, ... , r_m, Y1, ... , Y_n ∈ R .

Boundary Data Smoothness For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Johnny Henderson, Britney Hopkins, Eugenie Kim, Jeffrey W. Lyons

Mathematics Faculty Articles

Under certain conditions, solutions of the boundary value problem y(n)=f(x,y,y′,…,y(n−1)), y(n)=f(x,y,y′,…,y(n−1)), y(i−1)(x1)=yiy(i−1)(x1)=yi for 1≤i≤n−11≤i≤n−1, and y(x2)−∑mi=1riy(ηi)=yny(x2)−∑i=1mriy(ηi)=yn, are differentiated with respect to boundary conditions, where a

Hua's Matrix Equality And Schur Complements, Chris Paige, George P. H. Styan, Bo-Ying Wang, Fuzhen Zhang

Mathematics Faculty Articles

The purpose of this paper is to revisit Hua's matrix equality (and inequality) through the Schur complement. We present Hua's original proof and two new proofs with some extensions of Hua's matrix equality and inequalities. The new proofs use a result concerning Shur complements and a generalization of Sylvester's law of inertia, each of which is useful in its own right.

Mirror Principle For Flag Manifolds, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern polynomial. This is necessary to obtain related cohomology valued series for given arbitrary vector bundle and multiplicative characteristic class. Moreover, this can be used as a valuable testing ground for the theories which associates quantum cohomologies and J functions of non-abelian quotient to abelian quotients via quantization

On The Complete Join Of Permutative Combinatorial Rees–Sushkevich Varieties, Edmond W. H. Lee

Mathematics Faculty Articles

A semigroup variety is a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees–Sushkevich varieties constitutes an incomplete lattice that does not contain the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally finite, non-finitely generated, and contains only finitely based subvarieties. The subvarieties of J are precisely the combinatorial Rees–Sushkevich varieties that do not contain a certain semigroup of order four.