Mathematics Commons^™

A Pebbling Game On Powers Of Paths, Garth Isaak, Matthew Prudente, Joseph M. Marcinik Iii

Communications on Number Theory and Combinatorial Theory

Two Player Graph Pebbling is an extension of graph pebbling. Players Mover and Defender use pebbling moves, the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex, to win. If a specified vertex has a pebble on it, then Mover wins. If a specified vertex is pebble-free and there are no more valid pebbling moves, then Defender wins. The Two-Player Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement of m pebbles and for any specified vertex, Mover can win. We specify the …

Graded Geometry And Generalized Reduction, Henrique Bursztyn, Alberto S. Cattaneo, Rajan Amit Mehta, Marco Zambon

Mathematics Sciences: Faculty Publications

We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out graded symplectic reduction, both in the coisotropic and hamiltonian settings. Specializing the latter to the exact case, we recover in a systematic way the reduction schemes of Bursztyn-Cavalcanti-Gualtieri.

Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya

Mathematics and Statistics Faculty Research & Creative Works

In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.

Vallée-Poussin Theorem For Equations With Caputo Fractional Derivative, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the functional differential equation (^CD_a^α+x)(t) + ^mΣ_i=0 (T_ix(ⁱ))(t) = f(t); t 2 [a; b]; with Caputo fractional derivative ^CD_a^α+ is studied. The operators Ti act from the space of continuous to the space of essentially bounded functions. They can be operators with deviations (delayed and advanced), integral operators and their various linear combinations and superpositions. Such equations could appear in various applications and in the study of systems of, for example, two fractional differential equations, when one of the components can be …

(R1986) Neutrosophic Soft Contra E-Continuous Maps, Contra E-Irresolute Maps And Application Using Distance Measure, P. Revathi, K. Chitirakala, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, δ-continuous maps, δ- semi continuous maps, δ-pre continuous maps and e∗ continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance …

Modeling And A Domain Decomposition Method With Finite Element Discretization For Coupled Dual-Porosity Flow And Navier–Stokes Flow, Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We First Propose and Analyze a Steady State Dual-Porosity-Navier–Stokes Model, Which Describes Both Dual-Porosity Flow and Free Flow (Governed by Navier–Stokes Equation) Coupled through Four Interface Conditions, Including the Beavers–Joseph Interface Condition. Then We Propose a Domain Decomposition Method for Efficiently Solving Such a Large Complex System. Robin Boundary Conditions Are Used to Decouple the Dual-Porosity Equations from the Navier–Stokes Equations in the Coupled System. based on the Two Decoupled Sub-Problems, a Parallel Robin-Robin Domain Decomposition Method is Constructed and Then Discretized by Finite Elements. We Analyze the Convergence of the Domain Decomposition Method with the Finite …

Which Activation Function Works Best For Training Artificial Pancreas: Empirical Fact And Its Theoretical Explanation, Lehel Dénes-Fazakas, Lásló Szilágyi, György Eigner, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most effective ways to help patients at the dangerous levels of diabetes is an artificial pancreas, a device that constantly monitors the patient's blood sugar level and injects insulin based on this level. Patient's reaction to insulin is highly individualized, so the artificial pancreas needs to be trained on each patient. It turns out that the best training results are attained when instead of the usual ReLU neurons, we use their minor modification known as Exponential Linear Units (ELU). In this paper, we provide a theoretical explanation for the empirically observed effectiveness of ELUs.

Dialogs Re-Enacted Across Languages, Version 2, Nigel G. Ward, Jonathan E. Avila, Emilia Rivas, Divette Marco

Departmental Technical Reports (CS)

To support machine learning of cross-language prosodic mappings and other ways to improve speech-to-speech translation, we present a protocol for collecting closely matched pairs of utterances across languages, a description of the resulting data collection and its public release, and some observations and musings. This report is intended for:

• people using this corpus
• people extending this corpus
• people designing similar collections of bilingual dialog data.

Change Notes. This version supersedes UTEP-CS-22-108. There is some new information and numerous clarifications, mostly arising from our experiences diversifying our corpus and helping a vendor to use this protocol.

(R1957) Some Types Of Continuous Function Via N-Neutrosophic Crisp Topological Spaces, A. Vadivel, C. John Sundar

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this article is to introduced a new type of continuous functions such as N-neutrosophic crisp gamma continuous and weakly N-neutrosophic crisp gamma continuous functions in a N-neutrosophic crisp topological space and also discuss a relation between them in a N-neutrosophic crisp topological spaces. We also investigate some of their properties in N-neutrosophic crisp gamma continuous function via N-neutrosophic crisp topological spaces. Further, a contra part of continuity called N-neutrosophic crisp gamma-contra continuous map in a N-neutrosophic crisp topology is also initiated. Finally, an application based on neutrosophic score function of medical diagnosis is examined with graphical representation.

(R1997) Distance Measures Of Complex Fermatean Fuzzy Number And Their Application To Multi-Criteria Decision-Making Problem, V. Chinnadurai, S. Thayalan, A. Bobin

Applications and Applied Mathematics: An International Journal (AAM)

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a …

(R2026) Special Smarandache Ruled Surfaces According To Flc Frame In E^3, Süleyman Şenyurt, Kebire Hilal Ayvacı, Davut Canlı

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as TD₂, TD₁ ve D₂D₁ Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled …

Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata

Mathematics and Statistics Faculty Research & Creative Works

We Consider the One-Dimensional Nonlinear Schrödinger Equation with an Attractive Delta Potential and Mass-Supercritical Nonlinearity. This Equation Admits a One-Parameter Family of Solitary Wave Solutions in Both the Focusing and Defocusing Cases. We Establish Asymptotic Stability for All Solitary Waves Satisfying a Suitable Spectral Condition, Namely, that the Linearized Operator Around the Solitary Wave Has a Two-Dimensional Generalized Kernel and No Other Eigenvalues or Resonances. in Particular, We Extend Our Previous Result [35] Beyond the Regime of Small Solitary Waves and Extend the Results of [19, 29] from Orbital to Asymptotic Stability for a Suitable Family of Solitary Waves.

Natural Color Interpretation Of Interval-Valued Fuzzy Degrees, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Intuitively, interval-values fuzzy degrees are more adequate for representing expert uncertainty than the traditional [0,1]-based ones. Indeed, the very need for fuzzy degrees comes from the fact that experts often cannot describe their opinion not in terms of precise numbers, but by using imprecise ("fuzzy") words from natural language like "small". In such situations, it is strange to expect the same expert to be able to provide an exact number describing his/her degree of certainty; it is more natural to ask this expert to mark the whole interval (or even, more generally, a fuzzy set of possible degrees). In spite …

Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar

Departmental Technical Reports (CS)

Many thousands years ago, our primitive ancestors did not have the ability to reason logically and to perform logical inference. This ability appeared later. A natural question is: was this appearance inevitable -- or was this a lucky incident that could have been missed? In this paper, we use fuzzy techniques to provide a possible answer to this question. Our answer is: yes, the appearance of logical inference in inevitable.

Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main limitations of many current AI-based decision-making systems is that they do not provide any understandable explanations of how they came up with the produced decision. Taking into account that these systems are not perfect, that their decisions are sometimes far from good, the absence of an explanation makes it difficult to separate good decisions from suspicious ones. Because of this, many researchers are working on making AI explainable. In some applications areas -- e.g., in chess -- practitioners get an impression that there is a limit to understandability, that some decisions remain inhuman -- not explainable. …

Why Fuzzy Control Is Often More Robust (And Smoother): A Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, practitioners use easier-to-compute fuzzy control to approximate the more-difficult-co-compute optimal control. As expected, for many characteristics, this approximate control is slightly worse than the optimal control it approximates, However, with respect to robustness or smoothness, the approximating fuzzy control is often better than the original one. In this paper, we provide a theoretical explanation for this somewhat mysterious empirical phenomenon.

(R1977) On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3-Space, Emad Solouma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E₁³ using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.

Exploring The Genotypic And Phenotypic Differences Distinguishing Lactobacillus Jensenii And Lactobacillus Mulieris, Adriana Ene, Swarnali Banerjee, Alan J. Wolfe, Catherine Putonti

Mathematics and Statistics: Faculty Publications and Other Works

Lactobacillus crispatus, Lactobacillus gasseri, Lactobacillus iners, and Lactobacillus jensenii are dominant species of the urogenital microbiota. Prior studies suggest that these Lactobacillus species play a significant role in the urobiome of healthy females. In our prior genomic analysis of all publicly available L. jensenii and Lactobacillus mulieris genomes at the time (n = 43), we identified genes unique to these two closely related species. This motivated our further exploration here into their genotypic differences as well as into their phenotypic differences. First, we expanded genome sequence representatives of both species to 61 strains, including publicly available …

On Colorings And Orientations Of Signed Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.

Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical problems, the most effective classification techniques are based on deep learning. In this approach, once the neural network generates values corresponding to different classes, these values are transformed into probabilities by using the softmax formula. Researchers tried other transformation, but they did not work as well as softmax. A natural question is: why is softmax so effective? In this paper, we provide a possible explanation for this effectiveness: namely, we prove that softmax is the only consistent approach to probability-based classification. In precise terms, it is the only approach for which two reasonable probability-based ideas -- Least …

Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

A reasonable way to make AI results explainable is to approximate the corresponding deep-learning-generated function by a simple expression formed by fuzzy operations. Experiments on real data show that out of all easy-to-compute fuzzy operations, the best approximation is attained if we use an operation a + b − 0.5 ( limited to the interval [0,1]$. In this paper, we provide a possible theoretical explanation for this empirical result.

Discrete Polylogarithm Functions, Tom Cuchta, Dallas Freeman

Mathematics Faculty Research

We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series.

Hospital-Acquired Pressure Injuries In Adults With Prone Positioning Using Manual Method Versus Specialty Bed: A Retrospective Comparison Cohort Study, Jacqueline M. Demellow, Harbir Dhillon, Mouchumi Bhattacharyya, Daniel Pacitto, Teri M. Kozik

Pacific Faculty Work

Purpose: The purpose of this study was to compare the incidence of hospital-acquired pressure injuries (HAPIs) in patients with acute respiratory distress syndrome (ARDS) and placed in a prone position manually or using a specialty bed designed to facilitate prone positioning. A secondary aim was to compare mortality rates between these groups. Design: Retrospective review of electronic medical records. SUBJECTS AND SETTING: The sample comprised 160 patients with ARDS managed by prone positioning. Their mean age was 61.08 years (SD = 12.73); 58% (n = 96) were male. The study setting was a 355-bed community hospital in the Western United …

Production Functions Of Ncaa Men And Women Water Polo Matches, Joey Gullikson, Lewis R. Gale, John Mayberry, Lara Killick, John Kim

College of the Pacific Faculty Articles

Previous research has adapted the use of economic production functions to estimate the scoring production of teams in professional sports. Most of these studies have focused on professional male team sports, most notably, US baseball, basketball, and association football. This study adds to the literature by utilizing a new and distinctive data set of shooting statistics from 88 men’s and 38 women’s NCAA water polo contests to estimate production functions for United States’ collegiate water polo games and identify the most important variables for predicting margin of victory in such competitions. The results show that shots on goal, average shot …

Representations From Group Actions On Words And Matrices, Joel T. Anderson

Master's Theses

We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.

Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis, Jackie Driscoll

Master's Theses

Pluripotent stem cells have been observed to segregate into Turing-like patterns during the early stages of Dox-inducible hiPSC differentiation. In this thesis, we de- velop a tool to quantify the tortuosity in the patterns formed by colonies of pluripo- tent stem cells using methods from topological data analysis. We use clustering techniques and the mapper algorithm to create simplicial complexes representing samples of cells and detail a method of evaluating the tortuosity of these complexes. We use the resulting persistence landscapes and their associated norms to evaluate experimental data and simulated data from an agent based model. This thesis finds …

(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …

(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …

(R2050) Dual Quaternion Matrices And Matlab Applications, Kemal Gökhan Nalbant, Salim Yüce

Applications and Applied Mathematics: An International Journal (AAM)

There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given. The originality of our research, the set of dual quaternion matrix we studied, will be defined for the first time in this study, and its properties will be given. Moreover, this study is critical because it is an applied study related to dual quaternion matrices. It will be easier to solve examples with large matrix sizes with MATLAB. People who use different …

Engaging Students With High-Stakes Problems, Deepak Basyal

Mathematics and Statistics

Engaging students in meaningful mathematics problem-solving is the intention of many education stakeholders around the world. Research suggests that the implementation of high-stakes problems in mathematics teaching is one way to strengthen students’ conceptual understanding. Many carefully crafted open-ended problems constitute high-stakes problems, and proper use of such problems in teaching and learning not only encourages learners’ flexible thinking but also helps detect their misconceptions. However, what is less practiced and understood is: how exactly one should aim to implement such problems in a classroom setting. Teaching pre-service middle school teachers for a few years using high-stakes (mostly open-ended problems) …