Mathematics Commons^™

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 …

2015: "No Safety, Know Pain : Know Safety, No Pain", Brice Wang '16, Joy Qiu '16, Daniel Sohn '16, Angad Garg '16

Distinguished Student Work

In the world we live in today, many people live in urban or suburban areas. For this reason, residents of these metropolitan areas should be aware of the safety of the city they live in so they can take necessary precautions and educate youth about what actions are safe. In addition, judging the safety of a city allows the government of the city to analyze what factors and laws make other cities safer, and how they can replicate these conditions to make their city a safer place as well.

Waning Influence Of History: Why?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the past, history played an important role in education: students learned history of science, history of mathematics, etc. In the last decades, the influence of history has waned. In this paper, we provide a natural explanation for this waning.

Explaining Boris Pasternak's Observation That Complex Ideas Are Sometimes Easier To Understand, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Probably the most cited lines from the poetry of the Nobel-prize winning Russian writer Boris Pasternak contain the observation that complex ideas are sometimes easier to understand than simpler ones. This is not just a paradoxical poetic statement: many teachers have observed the same seemingly counter-intuitive phenomenon. In this paper, we provide a possible explanation for this phenomenon, by showing that indeed, many easier-to-describe mathematical models lead to more-difficult-to-solve mathematical problems.

Why The Graph Isomorphism Problem Is Easier Than Propositional Satisfiability: A Possible Qualitative Explanation, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

A recent result has shown that the graph isomorphism problem can be solved in quasi-polynomial time, while the general belief is that only exponential time algorithms are possible for propositional satisfiability. This is somewhat counter-intuitive, since for propositional satisfiability, we need to look for one of 2ⁿ options, while in graph isomorphism, we need to look for one of n! options, and n! is much larger than 2ⁿ. Our qualitative explanation for this counter-intuitive fact comes from the fact that, in general, a graph isomorphism problem has a unique solution -- in contrast to propositional satisfiability which, …

Skew Row-Strict Quasisymmetric Schur Functions, Sarah K. Mason, Elizabeth Niese

Mathematics Faculty Research

Mason and Remmel introduced a basis for quasisymmetric functions known as the row-strict quasisymmetric Schur functions. This basis is generated combinatorially by fillings of composition diagrams that are analogous to the row-strict tableaux that generate Schur functions. We introduce a modification known as Young row-strict quasisymmetric Schur functions, which are generated by row-strict Young composition fillings. After discussing basic combinatorial properties of these functions, we define a skew Young row-strict quasisymmetric Schur function using the Hopf algebra of quasisymmetric functions and then prove this is equivalent to a combinatorial description. We also provide a decomposition of the skew Young row-strict …

Audiovisual Processing Is Abnormal In Parkinson's Disease And Correlates With Freezing Of Gait And Disease Duration, Conor Fearon, John Butler, Louise Newman, Timothy Lynch, Richard B. Reilly

Articles

Background: Sensory and perceptual disturbances progress with disease duration in Parkinson’s disease (PD) and probably contribute to motor deficits such as bradykinesia and gait disturbances, including freezing of gait (FOG). Simple reaction time tests are ideal to explore sensory processing, as they require little cognitive processing. Multisensory integration is the ability of the brain to integrate sensory information from multiple modalities into a single coherent percept, which is crucial for complex motor tasks such as gait. 9 10 11 12 13 Objectives: The aims of this study were to: 1. Assess differences in unisensory (auditory and visual) and multisensory processing …

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

Tight Super-Edge-Graceful Labelings Of Trees And Their Applications, Alex Collins, Colton Magnant, Hua Wang

Mathematical Sciences: Faculty Publications

The concept of graceful labeling of graphs has been extensively studied. In 1994, Mitchem and Simoson introduced a stronger concept called super-edge-graceful labeling for some classes of graphs. Among many other interesting pioneering results, Mitchem and Simoson provided a simple but powerful recursive way of constructing super-edge-graceful trees of odd order. In this note, we present a stronger concept of “tight” super-edge-graceful labeling. Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels. This concept enables us to recursively construct tight super-edge-graceful trees of any order. As applications, we provide …

From Subcompact To Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

No abstract provided.

The Heart Failure Overweight/Obesity Survival Paradox : The Missing Sex Link, Amanda R. Vest, Yuping Wu, Roy Hachamovitch, James B. Young, Leslie Cho

Mathematics and Statistics Faculty Publications

Objectives: This study sought to determine whether body mass index (BMI) has a differential impact on survival for females versus males with advanced systolic heart failure (HF). Background: Females have a survival advantage in HF, the mechanisms of which are unclear. There is also a proposed “obesity survival paradox” in which excess adiposity promotes HF survival. Methods: We reviewed 3,811 patients with left ventricular ejection fraction ≤40% who had undergone cardiopulmonary exercise testing between 1995 and 2011. The endpoint was all-cause mortality. Multivariable analysis was performed using a Cox proportional hazards model. Because of the nonlinearity of BMI, a restricted …

Reversible Peg Solitaire On Graphs, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph G. If xyz forms a path in G and there are pegs on vertices x and y but not z, then a jump places a peg on z and removes the pegs from x and y. A graph is called solvable if, for some configuration of pegs occupying all but one vertex, some sequence of jumps leaves a single peg. We study the game of reversible peg …

Alternating Direction Implicit Method With Adaptive Grids For Modeling Chemotaxis In Dictyostelium Discoideum, Christopher F. Loomis

Theses and Dissertations

Dictyostelium discoideum (Dd) is a model organism, studied for reasons from cell movement to chemotaxis to human disease control. Creating a computer model of the life cycle of Dd has garnered great interest, one part of which is the Aggregation Stage, where thousands of amoeba gather together to form a slug. Chemotaxis is the mechanism through which this is accomplished. This thesis develops two- and three-dimensional alternating direction implicit code which solves the diffusion equation on an adaptive grid. The calculated values for both two and three dimensions are checked against the actual solution and error results are provided. Comparisons …