Physical Sciences and Mathematics Commons^™

A Survey On Varieties Generated By Small Semigroups And A Companion Website, João Araújo, João Pedro Araújo, Peter J. Cameron, Edmond W. H. Lee, Jorge Raminhos

Mathematics Faculty Articles

This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite model builders, SAT solvers, and GAP. This platform is a living guide to the literature. In addition, the first complete and justified list of identity bases for all varieties generated by a semigroup of order up to 4 is provided as supplementary material. The paper concludes with an extensive list of open problems.

Linking Mathematical Models And Trap Data To Infer The Proliferation, Abundance, And Control Of Aedes Aegypti, Jing Chen, Xi Huo, Andre B. B. Wilke, John C. Beier, Chalmers Vasquez, William Petrie, Robert Stephen Cantrell, Chris Cosner, Shigui Ruan

Mathematics Faculty Articles

Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this paper, we develop a deterministic mosquito population model, estimate model parameters by using local entomological and temperature data, and use the model to calibrate the mosquito trap data from 2017 to 2019. We further use the model to compare the Ae. aegypti population and evaluate the impact of rainfall intensity …

A Permanent Inequality For Positive Semidefinite Matrices, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this paper, we prove an inequality involving the permanent of a positive semidefinite matrix and its leading submatrices. We obtain a result in the similar spirit of Bapat-Sunder per-max conjecture.

123-Forcing Matrices, Richard A. Brualdi, Lei Cao

Mathematics Faculty Articles

A permutation σ of {1, 2,...,n} contains a 123-pattern provided it contains an increasing subsequence of length 3 and, otherwise, is 123-avoiding. In terms of the n × n permutation matrix P corresponding to σ, P contains a 123-pattern provided the 3 × 3 identity matrix I3 is a submatrix of P. If A is an n × n (0, 1)-matrix, then A is 123-forcing provided every permutation matrix P ≤ A contains a 123-pattern. The main purpose of this paper is to characterize such matrices A with the minimum number of 0’s.

Effectiveness And Safety Of Tranexamic Acid Use In Acute Traumatic Injury In The Prehospital And In-Hospital Settings: A Systematic Review And Meta-Analysis Of Randomized Controlled Trials, Scott Rowe, Amy Liu, Israel Zagales, Muhammad Awan, Radleigh Santos, Mark Mckenney, Adel Elkbuli

Mathematics Faculty Articles

Background and Objectives:

This systematic review and meta-analysis of randomized controlled trials (RCTs) aims to assess efficacy and safety of tranexamic acid (TXA) use in acute traumatic injuries.

Methods:

PubMed and Cochrane libraries were searched for relevant RCTs published between January 2011 and January 3, 2021. Cohen’s Q Test for heterogeneous effects was used to determine the appropriateness of fixed versus random effects models.

Results:

Twenty-two studies met inclusion criteria. Meta-analysis of relative risk of mortality between treatment and placebo groups in the in-hospital, and perioperative settings was not significant. However, the risk of mortality is significantly lower in the …

Inhibition Of Aminoglycoside 6’-N-Acetyltransferase Type Ib [Aac(6′)-Ib]: Structure-Activity Relationship Of Substituted Pyrrolidine Pentamine Derivatives As Inhibitors, Kenneth Rocha, Jesus Magallon, Craig Reeves, Kimberly Phan, Peter Vu, Crista L. Oakley-Havens, Stella Kwan, Maria S. Ramirez, Travis Lavoi, Haley Donow, Prem Chapagain, Radleigh Santos, Clemencia Pinilla, Marc A. Giulianotti, Marcelo E. Tolmasky

Mathematics Faculty Articles

The aminoglycoside 6′-N-acetyltransferase type Ib [AAC(6′)-Ib] is a common cause of resistance to amikacin and other aminoglycosides in Gram-negatives. Utilization of mixture-based combinatorial libraries and application of the positional scanning strategy identified an inhibitor of AAC(6′)-Ib. This inhibitor’s chemical structure consists of a pyrrolidine pentamine scaffold substituted at four locations (R1, R3, R4, and R5). The substituents are two S-phenyl (R1 and R4), an S-hydroxymethyl (R3), and a 3-phenylbutyl (R5) groups. Another location, R2, does not have a substitution, but it is named because its stereochemistry was modified in some compounds utilized in this study. Structure-activity …

Association Of Hypothermia With Increased Mortality Rate In Sars-Cov-2 Infection, Naaz Fatteh, Glen E. Sutherland, Radleigh Santos, Rita Zeidan, Alexandra P. Gastesi, Christopher D. Naranjo

Mathematics Faculty Articles

Objective

We observed patients to have variable temperatures. The objective of the study was to identify if hypothermia in a patient infected with SARS-CoV-2 is associated with a higher than expected mortality.

Methods

We reviewed 331 charts from patients hospitalized with SARS-CoV-2 between March 9 to April 20, 2020.

Results

The probability of death was 2.06 times higher for those with hypothermia than those without [95% C.I. (1.25, 3.38)]. In ventilated patients, there were 32 deaths. Of those, 75% had been hypothermic. In a prior review of 10,000 non-SARS-CoV-2 patients with sepsis, the mortality rate in patients with hypothermia was …

Second-Order Semi-Discretized Schemes For Solving Stochastic Quenching Models On Arbitrary Spatial Grids, Nina Garcia-Montoya, Julienne Kabre, Jorge E. Macías-Díaz, Qin Sheng

Mathematics Faculty Articles

Reaction-diffusion-advection equations provide precise interpretations for many important phenomena in complex interactions between natural and artificial systems. This paper studies second-order semi-discretizations for the numerical solution of reaction-diffusion-advection equations modeling quenching types of singularities occurring in numerous applications. Our investigations particularly focus at cases where nonuniform spatial grids are utilized. Detailed derivations and analysis are accomplished. Easy-to-use and highly effective second-order schemes are acquired. Computational experiments are presented to illustrate our results as well as to demonstrate the viability and capability of the new methods for solving singular quenching problems on arbitrary grid platforms.

Beryllium-Specific Cd4+ T Cells Induced By Chemokine Neoantigens Perpetuate Inflammation, Michael T. Falta, Jeremy C. Crawford, Alex N. Tinega, Laurie G. Landry, Frances Crawford, Douglas G. Mack, Allison K. Martin, Shaikh M. Atif, Li Li, Radleigh Santos, Maki Nakayama, John W. Kappler, Lisa A. Maier, Paul G. Thomas, Clemencia Pinilla, Andrew Fontenot

Mathematics Faculty Articles

Discovering dominant epitopes for T cells, particularly CD4⁺ T cells, in human immune-mediated diseases remains a significant challenge. Here, we used bronchoalveolar lavage (BAL) cells from HLA-DP2-expressing patients with chronic beryllium disease (CBD), a debilitating granulomatous lung disorder characterized by accumulations of beryllium (Be)-specific CD4⁺ T cells in the lung. We discovered lung resident CD4⁺ T cells that expressed a disease-specific public CDR3β T cell receptor motif and were specific to Be-modified self-peptides derived from C-C motif ligands 4 (CCL4) and 3 (CCL3). HLA-DP2-CCL/Be tetramer staining confirmed that these chemokine-derived peptides represented major antigenic targets in CBD. …

Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker

Mathematics Faculty Articles

We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete …

A Classification Of Hull Operators In Archimedean Lattice-Ordered Groups With Unit, Ricardo Enrique Carrera, Anthony W. Hager

Mathematics Faculty Articles

The category, or class of algebras, in the title is denoted by W. A hull operator (ho) in W is a reflection in the category consisting of W objects with only essential embeddings as morphisms. The proper class of all of these is hoW. The bounded monocoreflection in W is denoted B. We classify the ho’s by their interaction with B as follows. A “word” is a function w : hoW → W^W obtained as a finite composition of B and x a variable ranging in hoW. The set of these,“Word”, is in a natural …

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang

Mathematics Faculty Articles

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (C_rI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R₀ of COVID-19 to be 4.79(95% C_rI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R_c ≈ 0.32(95% C_rI …

Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao

Mathematics Faculty Articles

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.

A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.

A Short Note On Extreme Points Of Certain Polytopes, Lei Cao, Ariana Hall, Selcuk Koyuncu

Mathematics Faculty Articles

We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly substochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

Eigenvalue Continuity And Gersgorin's Theorem, Chi-Kwong Li, Fuzhen Zhang

Mathematics Faculty Articles

Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.

Inequalities For Permanents And Permanental Minors Of Row Substochastic Matrices, Zhi Chen, Jiawei Li, Lizhen Yang, Zelin Zhu, Lei Cao

Mathematics Faculty Articles

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

On The Linear Independence Of Finite Wavelet Systems Generated By Schwartz Functions Or Functions With Certain Behavior At Infinity, Abdelkrim Bourouihiya

Mathematics Faculty Articles

One of the motivations to state HRT conjecture on the linear independence of finite Gabor systems was the fact that there are linearly dependent Finite Wavelet Systems (FWS). Meanwhile, there are also many examples of linearly independent FWS, some of which are presented in this paper. We prove the linear independence of every three point FWS generated by a nonzero Schwartz function and with any number of points if the FWS is generated by a nonzero Schwartz function, for which the absolute value of the Fourier transform is decreasing at infinity. We also prove the linear independence of any FWS …

Centrosymmetric Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker

Mathematics Faculty Articles

We consider the convex set Γ_m,n of m×n stochastic matrices and the convex set Γ^π_m,n ⊂Γ_m,n of m×n centrosymmetric stochastic matrices (stochastic matrices that are symmetric under rotation by 180 degrees). For Γ_m,n, we demonstrate a Birkhoff theorem for its extreme points and create a basis from certain (0,1)-matrices. For Γ^π_m,n, we characterize its extreme points and create bases, whose construction depends on the parity of m, using our basis construction for stochastic matrices. For each of Γ_m,n and Γ^π_m,n, we further characterize their extreme …

A Note On Multilevel Toeplitz Matrices, Lei Cao, Selcuk Koyuncu

Mathematics Faculty Articles

Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary …

Non-Finitely Based Finite Involution Semigroups With Finitely Based Semigroup Reducts, Edmond W. H. Lee

Mathematics Faculty Articles

Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.

Neuroevolutional Methods For Decision Support Under Uncertainty, Nina Komleva, Olga Khlopkova, Matthew He

Mathematics Faculty Articles

The article presents a comparative analysis of the fundamental neuroevolutional methods, which are widely applied for the intellectualization of the decision making support systems under uncertainty. Based on this analysis the new neuroevolutionary method is introduced. It is intended to modify both the topology and the parameters of the neural network, and not to impose additional constraints on the individual. The results of the experimental evaluation of the performance of the methods based on the series of benchmark tasks of adaptive control, classification and restoration of damaged data are carried out. As criteria of the methods evaluation the number of …

Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

Mathematics Faculty Articles

Let Ω_n denote the convex polytope of all n x n doubly stochastic matrices, and ω_n denote the convex polytope of all n x n doubly substochastic matrices. For a matrix A ϵ ω_n, define the sub-defect of A to be the smallest integer k such that there exists an (n + k) x (n + k) doubly stochastic matrix containing A as a submatrix. Let ω_n,k denote the subset of ω_n which contains all doubly substochastic matrices with sub-defect k. For π a permutation of symmetric group of degree …

The Duals Of *-Operator Frames For End*A(H), Abdelkrim Bourouihiya, M. Rossafi, H. Labrigui, A. Touri

Mathematics Faculty Articles

Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of ∗-operator frames and we show their propreties obtained in Hilbert A-modules and we establish some results.

Rigid Linkages And Partial Zero Forcing, Daniella Ferrero, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Seth A. Meyer, Shahla Nasserasr, Bryan Shader

Mathematics Faculty Articles

Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown that spanning forcing paths of a zero forcing process form a spanning rigid linkage and thus a vital linkage. A related generalization of zero forcing that produces a rigid linkage via a coloring process is developed. One of the motivations for introducing zero forcing is to provide an upper bound on the maximum multiplicity of an eigenvalue among the real symmetric matrices described by a graph. Rigid linkages and a related …

Identification Of A Novel Polyamine Scaffold With Potent Efflux Pump Inhibition Activity Toward Multi-Drug Resistant Bacterial Pathogens, Renee Fleeman, Ginamarie Debevec, Kirsten Antonen, Jessie L. Adams, Radleigh Santos, Greg Welmaker, Richard A. Houghten, Marc Giulianotti, Lindsey N. Shaw

Mathematics Faculty Articles

We have previously reported the use of combinatorial chemistry to identify broad-spectrum antibacterial agents. Herein, we extend our analysis of this technology toward the discovery of anti-resistance molecules, focusing on efflux pump inhibitors. Using high-throughput screening against multi-drug resistant Pseudomonas aeruginosa, we identified a polyamine scaffold that demonstrated strong efflux pump inhibition without possessing antibacterial effects. We determined that these molecules were most effective with an amine functionality at R1 and benzene functionalities at R2 and R3. From a library of 188 compounds, we studied the properties of 5 lead agents in detail, observing a fivefold to eightfold decrease …

Methodological Approach To The Ex Vivo Expansion And Detection Of T. Cruzi-Specific T Cells From Chronic Chagas Disease Patients, Gonzalo R. Acevedo, Silvia A. Longhi, Alcinette Bunying, Nazila Sabri, Augusto Atienza, Maria P. Zago, Radleigh Santos, Valeria A. Judkowski, Clemencia Pinilla, Karina A. Gomez

Mathematics Faculty Articles

The discovery of T cell epitopes is essential not only for gaining knowledge about host response to infectious disease but also for the development of immune-intervention strategies. In Chagas disease, given the size and complexity of the Trypanosoma cruzi proteome and its interaction with the host’s immune system, the fine specificity of T cells has not been extensively studied yet, and this is particularly true for the CD4+ T cell compartment. The aim of the present work was to optimize a protocol for the generation of parasite-specific memory T cell lines, representative of their in vivo precursor populations and capable …

Calcium Transient Assays For Compound Screening With Human Ipsc-Derived Cardiomyocytes: Evaluating New Tools, Neil J. Daily, Radleigh Santos, Joseph Vecchi, Pinar Kemanli, Tetsuro Wakatsuki

Mathematics Faculty Articles

Calcium (Ca2+) plays a central role in regulating many biological processes in the cell from muscle contraction to neurotransmitter release. The need for reliable fluorescent calcium indicator dyes is of vast importance for studying many aspects of cell biology as well as screening compounds using phenotypic high throughput assays. We have assessed two of the latest generation of calcium indicator dyes, FLIPR Calcium 6 and Cal-520 AM for studying calcium transients (CaTs) in induced pluripotent stem cell (iPSC) -derived human cardiomyocytes. FLIPR Calcium 6 and Cal-520 dyes both displayed robust CaTs with a high signal-to-noise ratio (SNR) and were non-toxic …

Spectral Properties Of A Sequence Of Matrices Connected To Each Other Via Schur Complement And Arising In A Compartmental Model, Evan Haskell, Vehbi Emrah Paksoy

Mathematics Faculty Articles

We consider a sequence of real matrices An which is characterized by the rule that A_n−1 is the Schur complement in A_n of the (1,1) entry of A_n, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of A_n. In particular,we show that An has a unique positive eigenvalue λ_n and {λ_n} is a decreasing convergent sequence. We also study the stability of A_n for small n using the Routh-Hurwitz criterion.

Discovery Of An Enzyme And Substrate Selective Inhibitor Of Adam10 Using An Exosite-Binding Glycosylated Substrate, Franck Madoux, Daniela Dreymuller, Jean-Phillipe Pettiloud, Radleigh Santos, Christoph Becker-Pauly, Andreas Ludwig, Gregg B. Fields, Thomas Bannister, Timothy P. Spicer, Mare Cudic, Louis D. Scampavia, Dmitriy Minond

Mathematics Faculty Articles

ADAM10 and ADAM17 have been shown to contribute to the acquired drug resistance of HER2-positive breast cancer in response to trastuzumab. The majority of ADAM10 and ADAM17 inhibitor development has been focused on the discovery of compounds that bind the active site zinc, however, in recent years, there has been a shift from active site to secondary substrate binding site (exosite) inhibitor discovery in order to identify non-zinc-binding molecules. In the present work a glycosylated, exosite-binding substrate of ADAM10 and ADAM17 was utilized to screen 370,276 compounds from the MLPCN collection. As a result of this uHTS effort, a selective, …