Physical Sciences and Mathematics Commons^™

Continuous Semi-Supervised Nonnegative Matrix Factorization, Michael R. Lindstrom, Xiaofu Ding, Feng Liu, Anand Somayajula, Deanna Needell

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower rank. In certain applications it is desirable to extract topics and use them to predict quantitative outcomes. In this paper, we show Nonnegative Matrix Factorization can be combined with regression on a continuous response variable by minimizing a penalty function that adds a weighted regression error to a matrix factorization error. We show theoretically that as the weighting increases, the regression error in training …

Euler Archive Spotlight, Erik R. Tou

Euleriana

A survey of two translations posted to the Euler Archive in 2022.

Euler And The Duplication Formula For The Gamma-Function, Alexander Aycock

Euleriana

We show how the formulas in Euler’s paper "Variae considerationes circa series
hypergeometricas" [ 4] imply Legendre’s duplication formula for the Γ-function. This
paper can be seen as an Addendum to [2].

Euler Found The First Binary Digit Extraction Formula For Π In 1779, Nick Craig-Wood

Euleriana

In 1779 Euler discovered two formulas for π which can be used to calculate any binary digit of π without calculating the previous digits. Up until now it was believed that the first formula with the correct properties (known as a BBP-type formula) for this calculation was published by Bailey, Borwein and Plouffe in 1997.

Analytical Observations (Translation Of E326), Cynthia Huffman Ph.D.

Euleriana

Euler, in this publication with Eneström number E326, provides an induction fallacy which arises from analyzing a particular sequence. Euler wrote this work in 1763, one of only two papers he wrote on sequences and/or series in the 1760’s, out of a total of 79 papers on series during his career. His goal in E326 is to investigate the middle terms in the expansion of powers of quadratic trinomial expressions, beginning with the specific simple quadratic , before considering the general quadratic .

The induction fallacy shows up during the analysis of the simple case when Euler first finds an …

Euler's Anticipations, Christopher Goff, Erik Tou

Euleriana

Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!

Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez

Mathematics & Statistics ETDs

For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as …

Lacunary Eta Quotients With Identically Vanishing Coefficients, Timothy Huber, James Mclaughlin, Dongxi Ye

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

For |q|<1 >, define fi=∏∞n=1(1−qin) , and let (A(q),B(q)) be any of the pairs (f41,f81f22), (f41,f101f23), (f61,f42f21), (f61,f141f42), (f101,f62f21), (f141,f53f1),(f141,f82f21). For any such pair (A(q),B(q)) , define the sequences {a(n)} and {b(n)} to be the coefficients of qn of A(q) and B(q) , respectively. Then for each pair it is shown that a(n) vanishes if and only if b(n) vanishes. In each case, a criterion is given which states precisely when a(n)=b(n)=0 . Moreover, for the pairs (f261,f93f1) , (f261,f162f61) it is shown that a(n)=b(n)=0 if 12n+13 satisfies a criteria of Serre for a(n)=0 .

Regular Solutions To Elliptic Equations, Alfonso Castro, Jon T. Jacobsen

All HMC Faculty Publications and Research

A review of results and techniques on the existence of regular radial solutions to second order elliptic boundary value problems driven by linear and quasilinear operators is presented. Of particular interest are results where the solvability of a given elliptic problem can be analyzed by the relationship between the spectrum of the operator and the behavior of the nonlinearity near infinity and at zero. Energy arguments and Pohozaev type identities are used extensively in that analysis. An appendix with a proof of the contraction mapping principle best suited for using continuous dependence to ordinary differential equations on initial conditions is …

Hörmander’S L2 -Method, ∂-Problem And Polyanalytic Function Theory In One Complex Variable, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we consider the classical ∂-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the ∂-problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels.

Multi-Scale Hybridized Topic Modeling: A Pipeline For Analyzing Unstructured Text Datasets Via Topic Modeling, Keyi Cheng, Stefan Inzer, Adrian Leung, Xiaoxian Shen, Deanna Needell, Todd Presner, Michael Perlmutter, Michael R. Lindstrom, Joyce Chew

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We propose a multi-scale hybridized topic modeling method to find hidden topics from transcribed interviews more accurately and more efficiently than traditional topic modeling methods. Our multiscale hybridized topic modeling method (MSHTM) approaches data at different scales and performs topic modeling in a hierarchical way utilizing first a classical method, Nonnegative Matrix Factorization, and then a transformer-based method, BERTopic. It harnesses the strengths of both NMF and BERTopic. Our method can help researchers and the public better extract and interpret the interview information. Additionally, it provides insights for new indexing systems based on the topic level. We then deploy our …

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

UNO Student Research and Creative Activity Fair

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

Time Evolution Is A Source Of Bias In The Wolf Algorithm For Largest Lyapunov Exponents, Kolby Brink, Tyler Wiles, Nicholas Stergiou, Aaron Likens

UNO Student Research and Creative Activity Fair

Human movement is inherently variable by nature. One of the most common analytical tools for assessing movement variability is the largest Lyapunov exponent (LyE) which quantifies the rate of trajectory divergence or convergence in an n-dimensional state space. One popular method for assessing LyE is the Wolf algorithm. Many studies have investigated how Wolf’s calculation of the LyE changes due to sampling frequency, filtering, data normalization, and stride normalization. However, a surprisingly understudied parameter needed for LyE computation is evolution time. The purpose of this study is to investigate how the LyE changes as a function of evolution time …

On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.

Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh

LSU Doctoral Dissertations

In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …

Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Formal Conjugacy Growth In Graph Products I, Laura Ciobanu,, Susan Hermiller, Valentin Mercier

Department of Mathematics: Faculty Publications

In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.

On The Negative Order Loaded Modified Korteweg–De Vries Equation, Praveen Agarwal, Bakhrom Abdullaev, Iroda Baltaeva, Shoira Atanazarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this study, we establish the integration of the negative order loaded modified Korteweg-de Vries equation using the inverse scattering transform method. The main result is included in deriving the evolution equations for scattering data of the Dirac operator which is associated with the considered problem. Moreover, it was described the process of the construction of one-soliton solution of the negative order loaded modified Korteweg-de Vries equation.

On Generalizations Of The Upper Half Plane In A Multidimensional Complex Space, Bukharbay Kurbanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The paper considers an unbounded realization of a polydisk and a unit ball: the group of holomorphic automorphisms is described, and the Cauchy-Szego and Poisson kernels are calculated explicitly.

A Characterization Of Approximately Inner Automorphisms Of Aw*-Factor Of Type Ii1, Dmitriy Kim

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Approximately inner *-automorphisms of AW*-algebra of type II₁ are considered. Faithful normalized quasitraces of AW*-algebras are studied and the inequality connecting ||.||₁ and ||.||₂ norms generated by quasitrace is obtained. It is showed the characterization of approximately inner *-automorphisms of AW*-algebra of type II₁.

Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider self-adjoint 4x4 operator matrices A. For some special cases the alternative formulas for the calculating the quartic numerical range of 4x4 operator matrices A are derived. Using the obtained alternative formula for the quartic numerical range of A we estimate the lower and upper bound of A.

Inverse Source Problem For The Heat Equation On A Metric Star Graph With Integral Over-Determination Condition, Zarif Sobirov, Ariuxan Turemuratova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this work we investigated an initial boundary value problem for the heat equation on a metric star graph in Sobolev space. The existence and uniqueness of the generalized solution are proved with the classical functional method based on a priori estimates. Also, we considered the inverse source problem with the integral over-determination condition. We reduced the inverse problem to the operator-based equation and proved that the corresponding resolvent operator is well-defined.

Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, Oxunjon Ismoilov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we show that the negative-order Korteweg-de Vries equation with a self-consistent source can be solved by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with the potential associated with the solution of the negative order Korteweg-de Vries equation with a self-consistent source is determined. The results obtained make it possible to apply the method of the inverse scattering problem to solve the problem under consideration.

Epidemic Highs And Lows: A Stochastic Diffusion Model For Active Cases, Luis F. Gordillo, Priscilla E. Greenwood, Dana Strong

Mathematics and Statistics Faculty Publications

We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed without breaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of ‘attenuated Allee effect’ and a capacity factor is controlling the size of the process. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows …

Optimal Orientations Of Vertex-Multiplications Of Trees With Diameter 4, Willie Han Wah Wong, Eng Guan Tay

Theory and Applications of Graphs

Koh and Tay proved a fundamental classification of G vertex-multiplications into three classes ζ₀, ζ₁ and ζ₂. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class ζ₂. Of interest, G vertex-multiplications are extensions of complete n-partite graphs and Gutin characterised complete bipartite graphs with orientation number 3 (or 4 resp.) via an ingenious use of Sperner's theorem. In this paper, we investigate vertex-multiplications of trees with diameter 4 in ζ₀ (or ζ₁) and exhibit its intricate connections with …

Symmetric Functions Algebras I: Introduction And Basic Features, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

A Dialogue With Professor Ellen Veomett: The Intersections Of Mathematics & Gerrymandering, Ellen Veomett

SMC Community Engagement

No abstract provided.

Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson

Honors Theses

The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.

A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …

Random Variables With Overlapping Number And Weyl Algebras I, Ruma Dutta, Gabriela Popa, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Odds And Ends, Jimmie D. Lawson

Seminar on Continuity in Semilattices

No date.