Mathematics Commons^™

Multilocality And Fusion Rules On The Generalized Structure Functions In Two-Dimensional And Three-Dimensional Navier-Stokes Turbulence, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator “multilocality.” The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of …

Equivariant Formality Of Transversely Symplectic Foliations And Frobenius Manifolds, Yi Lin, Xiangdong Yang

Mathematical Sciences: Faculty Publications

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation whose basic cohomology satisfies the Hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic dδ-lemma in this setting. As an application, we show that there exists a natural Frobenius manifold structure on the equivariant basic cohomology of the given foliation. In particular, this result provides a class of new examples of dGBV-algebras whose cohomology carries a Frobenius manifold structure.

Lefschetz Contact Manifolds And Odd Dimensional Symplectic Geometry, Yi Lin

Mathematical Sciences: Faculty Publications

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology groups of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology groups of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for compact K-contact manifolds, which implies immediately that the two existing versions of Hard Lefschetz theorems are mathematically …

Noncrossing Partitions, Toggles, And Homomesies, David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, James Propp, Simon Rubinstein-Salzedo

Publications

We introduce n(n−1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average of f over the elements of a T -orbit is the same for all T -orbits. We can apply our method of proof more broadly to toggle operations back on the collection of independent sets …

The Ebb And Flow Of Official Calls In Water Polo, James Graham, John Mayberry

College of the Pacific Faculty Articles

Defensive fouls play an important role in elite men’s water polo generating over half of all goals. Despite their importance, little is known about the relationship between foul calling patterns and other game-state variables in the sport. Here we apply a sequence of hierarchical mixed logistic regression models on data from major tournaments in 2012–2014 to study such relationships and find a number of significant biases in foul calling rates. Offensive teams who are winning/tied are about 31% less likely to draw a defensive foul and 32% more likely to get called for an offensive foul than teams who are …

The Distribution Of The Number Of Clusters In The Arratia Flow, Vladimir Fomichov

Communications on Stochastic Analysis

No abstract provided.

Krawtchouk-Griffiths Systems I: Matrix Approach, Philip Feinsilver

Communications on Stochastic Analysis

No abstract provided.

Krawtchouk-Griffiths Systems Ii: As Bernoulli Systems, Philip Feinsilver

Communications on Stochastic Analysis

No abstract provided.

Ergodic Control Of Stochastic Navier-Stokes Equation With Lévy Noise, Manil T Mohan, Sivaguru S Sritharan

Communications on Stochastic Analysis

No abstract provided.

Exponential Convergence Of The Stochastic Micropolar And Magneto-Micropolar Fluid Systems, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.

A General Itô Formula For Adapted And Instantly Independent Stochastic Processes, Chii-Ruey Hwang, Hui-Hsiung Kuo, Kimiaki Saitô, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

Path Functionals Of A Class Of Lévy Insurance Risk Processes, Ekaterina T Kolkovska, Ehyter M Martin-González

Communications on Stochastic Analysis

No abstract provided.

Another Generalized Transmuted Family Of Distributions: Properties And Applications, Faton Merovci, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we …

Ultracoproduct Continua And Their Regular Subcontinua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We continue our study of ultracoproduct continua, focusing on the role played by the regular subcontinua—those subcontinua which are themselves ultracoproducts. Regular subcontinua help us in the analysis of intervals, composants, and noncut points of ultracoproduct continua. Also, by identifying two points when they are contained in the same regular subcontinua, we naturally generalize the partition of a standard subcontinuum of ℍ * into its layers.

On The Geometry Of The Rotating Liquid Drop, Ivailo M. Mladenov, John Oprea

Mathematics and Statistics Faculty Publications

Here we consider the problem of a fluid body rotating with a constant angular velocity and subjected to surface tension. Determining the equilibrium configuration of this system turns out to be equivalent to the geometrical problem of determining the surface of revolution with a prescribed mean curvature. In the simply connected case, the equilibrium surface can be parameterized explicitly via elliptic integrals of the first and second kind. Here, we present two such parameterizations of the drops and we use the second of them to study finer details of the drop surfaces such as the existence of closed geodesics.

Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman Iv

Mathematics and Statistics Faculty Publications and Presentations

A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G such that π(x)−x ≠ π(y) for all distinct x,y∈S. We refer to |S| as the size of π, and if S=G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, and what cycle types these permutations have.

It is known that conjugation by automorphisms of G forms a group action on the set of orthomorphisms of G. In this paper, we consider the …

Exploratory Modeling Of Tbi Data, Martin Zwick, Stephanie Kolakowsky-Hayner, Sadie Carney, Maya Balamane, Tracie Nettleton, D. Wright

Complex Systems Faculty Publications and Presentations

Most data analyses are confirmatory, but exploratory studies can find unexpected non-linear & many-variable interaction effects. The methodology of reconstructability analysis (RA) is explicitly designed for exploratory modeling. It analyzes both nominal and continuous (binned) variables, is easily interpretable, takes standard text input, is web-accessible, and is available for research use. This presentation reports some results of applying RA to data sets from Preece (auto accidents) and Wright (auto/motorcycle/bike accidents, hit pedestrians, and falls).

The Log-Logistic Weibull Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Susan Foya, Gayan Warahena-Liyanage, Shujiao Huang

Mathematical Sciences: Faculty Publications

In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This distribution contain the log-logistic Rayleigh (LLoGR), log-logistic exponential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators …

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.

The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong

Dissertations, Theses, and Capstone Projects

This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.

A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff

Math Theses

We survey vertex minimal graphs with prescribed automorphism group. Whenever possible, we also investigate the construction of such minimal graphs, confirm minimality, and prove a given graph has the correct automorphism group.

Hamiltonian Bifurcations In Schrodinger Trimers, Casayndra H. Basarab

Dissertations

The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic orbits whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of periodic orbits are discussed as a conserved …

Structural Exploration And Inference Of The Network, Ruihua Cheng

Dissertations

This dissertation consists of two parts. In the first part, a learning-based method for classification of online reviews that achieves better classification accuracy is extended. Automatic sentiment classification is becoming a popular and effective way to help online users or companies to process and make sense of customer reviews. The method combines two recent developments. First, valence shifters and individual opinion words are combined as bigrams to use in an ordinal margin classifier. Second, relational information between unigrams expressed in the form of a graph is used to constrain the parameters of the classifier. By combining these two components, it …

Numerical Simulations Of Dense Granular Systems With And Without Cohesive Effects, Lenka Kovalcinova

Dissertations

Granular materials are collections of objects ranging from sand grains that form sand piles or even sand castles to collections of large objects such as a group of meteors in outer space. The considered range of sizes of granular particles is such that the effect of thermal fluctuations is not relevant. However, the interaction between the particles may be very complex, involving inelasticity and friction, in addition to repulsive and possibly attractive interaction forces. These interactions that may be history dependent, make the systems that consist of a large number of particles complex to analyze and difficult to understand using …

Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu

Mathematical Sciences: Faculty Publications

In this study, we introduce a closed loop quotient controller into the three-dimensional Lorenz system. We then compute the equilibrium points and analyze their local stability. We use several examples to illustrate how cross-sections of the basins of attraction for the equilibrium points look for various parameter values. We then provided numerical evidence that with the controller, the controlled Lorenz system cannot exhibit chaos if the equilibrium points are locally stable.

Efficient High-Order Integral Equation Methods For The Heat Equation, Shaobo Wang

Dissertations

Efficient high-order integral equation methods have been developed for solving the boundary value problems of the heat equation with complex geometries in two and three dimensions. First of all, the classical heat potential theory is applied to convert such problems to Volterra integral equations of the second kind via the heat layer potentials. Some advantages of the integral formulation as compared with standard finite difference and finite element methods include reduction of the dimension of the problem by one, high order accuracy, unconditional stability, insensitivity to different geometries, and elimination of truncating the computational domain and the need of artificial …

Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the convergence rate is provably possible compared to either batched sampling or weighted sampling alone. We propose several computationally efficient schemes to approximate the optimal weights, and compute proposed sampling distributions explicitly for the least squares and hinge loss problems. We show both analytically and experimentally that substantial gains can be obtained

Bayesian Peer Calibration With Application To Alcohol Use, Miles Q. Ott, Joseph W. Hogan, Krista J. Gile, Crystal Linkletter, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Peers are often able to provide important additional information to supplement self-reported behavioral measures. The study motivating this work collected data on alcohol in a social network formed by college students living in a freshman dormitory. By using two imperfect sources of information (self-reported and peer-reported alcohol consumption), rather than solely self-reports or peer-reports, we are able to gain insight into alcohol consumption on both the population and the individual level, as well as information on the discrepancy of individual peer-reports. We develop a novel Bayesian comparative calibration model for continuous, count and binary outcomes that uses covariate information to …

On The Expression Of Higher Mathematics In American Sign Language, John Tabak

Journal of Interpretation

Abstract

The grammar and vocabulary of higher mathematics are different from the grammar and vocabulary of conversational English and conversational American Sign Language (ASL). Consequently, mathematical language presents interpreters with a unique set of challenges. This article characterizes those aspects of mathematical grammar that are peculiar to the subject. (A discussion of mathematical vocabulary and its expression in ASL can be found elsewhere (Tabak, 2014).) An increased awareness of the grammar of mathematical language will prove useful to those interpreters for the deaf and deaf mathematics professionals seeking to express higher mathematics in ASL.

In this article one will, for …

Invertibility Of Submatrices Of The Pascal Matrix And Birkhoff Interpolation, Scott N. Kersey

Mathematical Sciences: Faculty Publications

The infinite upper triangular Pascal matrix is T = [( j )i] for 0 ≤ i, j. It is easy to see that any leading principle square submatrix is triangular with determinant 1, hence invertible. In this paper, we investigate the invertibility of arbitrary square submatrices Tr, c comprised of rows r = [r0, … , rm ] and columns c = c0 , … , cm[] of T. We show that Tr, c is invertible r ≤ c i.e., ri ≤ ci for i = 0, …, m(), or equivalently, iff all diagonal entries are nonzero. To prove this …