Mathematics Commons^™

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 …

A Theoretical And Methodological Framework To Analyze Long Distance Pleasure Travel, Vijayaraghavan Sivaraman

USF Tampa Graduate Theses and Dissertations

The United States (US) witnessed remarkable growth in annual long distance travel over the past few decades. Over half of the long distance travel in the US is made for pleasure, including visiting friends and relatives (VFR) and leisure activities. This trend could continue with increased use of information and communication technologies for socialization, and enhanced mobility being achieved using fuel-efficient (electric/hybrid) and technology enhanced vehicles. Despite these developments, and recent interest to implement alternate mass transit options to serve this market, not much exists on the measurement, analysis and modeling of long distance pleasure travel in the U.S.

Statewide …

Closed Range Composition Operators On Hilbert Function Spaces, Pratibha Ghatage, Maria Tjani

Mathematics and Statistics Faculty Publications

We show that a Carleson measure satisfies the reverse Carleson condition if and only if its Berezin symbol is bounded below on the unit disk D. We provide new necessary and sufficient conditions for the composition operator to have closed range on the Bergman space. The pull-back measure of area measure on D plays an important role. We also give a new proof in the case of the Hardy space and conjecture a condition in the case of the Dirichlet space.

A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu

CMC Faculty Publications and Research

Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas

CMC Faculty Publications and Research

The Kaczmarz and Gauss-Seidel methods both solve a linear system Xβ=y by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between …

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

College of the Pacific Faculty Presentations

Have you ever been working in one area of math, and another area arises unexpectedly? While working on a problem in 2008, we inadvertently discovered some trigonometric identities. This talk will explain fusion algebras, which are relatively simple algebraic objects that demonstrate nice algebraic applications of linear algebra. Then we will see how trigonometry can arise in even this most algebraic of settings.

Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu

Mathematics Colloquium Series

This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with …

Sexually Dimorphic Gene Expression In The Lateral Eyes Of Euphilomedes Carcharodonta (Ostracoda, Pancrustacea), Andrea Sajuthi, Brenna Carrillo-Zazueta, Briana Hu, Anita Wang, Logan Brodnansky, John Mayberry, Ajna S. Rivera

College of the Pacific Faculty Articles

Background: The evolution and development of sexual dimorphism illuminates a central question in biology: How do similar genomes produce different phenotypes? In an XX/XO system especially the state of a sexually dimorphic trait is determined by differences in gene expression, as there are no additional genetic loci in either sex. Here, we examine the XX/XO ostracod crustacean species Euphilomedes carcharodonta. This species exhibits radical sexual dimorphism of their lateral eyes, females have only a tiny simple lateral eye while males have elaborate ommatidial eyes. Results: We find that males express three of nine eye-development gene homologs at significantly higher levels …

On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete

Mathematics Faculty Publications

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …

Molecular Network Control Through Boolean Canalization, David Murrugarra, Elena S. Dimitrova

Mathematics Faculty Publications

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges …

Science Is Helpful For Engineering Applications: A Theoretical Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical evidence shows that when engineering design uses scientific analysis, we usually get a much better performance that for the system designed by using a trial-and-error engineering approach. In this paper, we provide a quantitative explanation for this empirical observation.

Why The Range Of A Robust Statistic Under Interval Uncertainty Is Often Easier To Compute, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In statistical analysis, we usually use the observed sample values x₁, ..., x_n to compute the values of several statistics v(x₁, ..., x_n) -- such as sample mean, sample variance, etc. The usual formulas for these statistics implicitly assume that we know the exact values x₁, ..., x_n. In practice, the sample values X₁, ..., X_n come from measurements and are, thus, only approximations to the actual (unknown) values x₁, ..., x_n of the corresponding quantity. Often, the only information that we have …

Positive Consequences Of Negative Attitude: Game-Theoretic Analysis, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, the world would be a better place if all the people had positive attitude towards each other. It is known that this is not always the case: sometimes, the excess of positive attitude can lead to negative consequences. In this paper, we show that, vice versa, a reasonable amount of negative attitude can make life better for everyone. What is therefore needed is not the exclusive appearance of positive attitude, but rather a balance -- titled towards moderately positive attitude.

Maximum Entropy Approach Is Not As Arbitrary As It May Seem At First Glance, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we only have partial information about the probability distribution, i.e., when several different probability distributions are consistent with our knowledge, then it makes sense to select a distribution with the largest entropy. In particular, when we only know that the quantity is located within a certain interval -- and we have no information about the probability of different values within this intervals -- then it is reasonable to assume that all these values are equally probable, i.e., that we have a uniform distribution on this interval. The problem with this idea is that if we apply it to the …

Decision Making Under Interval (And More General) Uncertainty: Monetary Vs. Utility Approaches, Vladik Kreinovich

Departmental Technical Reports (CS)

In many situations, e.g., in financial and economic decision making, the decision results either in a money gain (or loss) and/or in the gain of goods that can be exchanged for money or for other goods. In such situations, interval uncertainty means that we do not know the exact amount of money that we will get for each possible decision, we only know lower and upper bounds on this amount. In this case, a natural idea is to assign a fair price to different alternatives, and then to use these fair prices to select the best alternative. In the talk, …

On The Importance Of Duality And Multi-Ality In Mathematics Education, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

For each mathematical object, there are usually several different equivalent representations: for example, a spatial object can be represented either in geometric terms, or by a function that describes its shape. The need for several representations comes from the fact that each of these representations is useful in solving some problems for which the use of other representations is less helpful. Thus, the more representations a student knows, the more capable this student is of solving mathematical problems. In this paper, we propose a general formal description of the corresponding notion of duality (and, more generally, "multi-ality"), and we explain …

From Equations To Tri-Quations And Multi-Quations, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, an equation A(x₁, ..., x_n)= B(x₁, ..., x_n) corresponds to the situation when we have two quantities A(x₁, ..., x_n) and B(x₁, ..., x_n) which are known to be equal, we know how each of these quantities depends on the unknown parameters x₁, ..., x_n, and we want to find the values of the unknowns x_i from this equality -- and from other similar equalities. In some practical situations, instead of two equal values, we have three …

2015: "Go With The Flow", Paul Nebres '16, Kushagra Gupta '16, Jason Chen '16, Noor Michael '16

Distinguished Student Work

In a famous incident in August 2010, a Chinese traffic jam stretched for over 100 kilometers and stranded drivers took over two weeks to get from one side to the other. Stemming from a routine lane closure for road maintenance, the traffic jam soon spiraled out of control, as cars piling up at the jam greatly outnumbered those leaving the other end. Sadly, in todays overpopulated world, these sorts of nightmare scenarios are only becoming more and more common, from chronic traffic jams in congested Chinese cities to Carmageddon in Los Angeles. For drivers, these extensive traffic jams can be …