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Articles 1  30 of 26096
FullText Articles in Physical Sciences and Mathematics
New Examples Of SelfDual NearExtremal Ternary Codes Of Length 48 Derived From 2(47,23,11) Designs, Sanja Rukavina, Vladimir Tonchev
New Examples Of SelfDual NearExtremal Ternary Codes Of Length 48 Derived From 2(47,23,11) Designs, Sanja Rukavina, Vladimir Tonchev
Michigan Tech Publications, Part 2
In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of selfdual nearextremal ternary codes of length 48 for 145 distinct values of the number A12 of codewords of minimum weight 12, and raised the question about the existence of codes for other values of A12. In this note, we use symmetric 2(47,23,11) designs with an automorphism group of order 6 to construct selfdual nearextremal ternary codes of length 48 for 150 new values of A12.
Ramanujan Type Congruences For Quotients Of Klein Forms, Timothy Huber, Nathaniel Mayes, Jeffery Opoku, Dongxi Ye
Ramanujan Type Congruences For Quotients Of Klein Forms, Timothy Huber, Nathaniel Mayes, Jeffery Opoku, Dongxi Ye
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this work, Ramanujan type congruences modulo powers of primes p≥5 are derived for a general class of products that are modular forms of level p. These products are constructed in terms of Klein forms and subsume generating functions for tcore partitions known to satisfy Ramanujan type congruences for p=5,7,11. The vectors of exponents corresponding to products that are modular forms for Γ1(p) are subsets of bounded polytopes with explicit parameterizations. This allows for the derivation of a complete list of products that are modular forms for Γ1(p) of weights 1≤k≤5 for primes 5≤p≤19 and whose Fourier coefficients …
My Experience As An It Data Intern, Annajo V. Vonseth
My Experience As An It Data Intern, Annajo V. Vonseth
Research & Creative Achievement Day
This poster presentation is focused on my internship as an IT Data Intern with B’nai B’rith Youth Organization (BBYO). I was able to use the skills already learned through courses here at WSU to help project and produce highend reports. Additionally, I was incharge of the creation of the survey all the way to creating the PowerPoint presentation with the results. I will also discuss how Microsoft Suites played a huge role in my daytoday work, from large, complex data sets to cleaning and refining old data, I will be discussing the skills I learned during my time as an …
Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz
Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz
Research & Creative Achievement Day
Companies often are curious about their employee performance. But how, exactly, do they analyze this? As a Data Analytics Intern for Xcel Energy, I was in charge of doing just this. This poster will walk you through the methods used to analyze and model employee performance, as well as the results found and the different ways managers at Xcel Energy used them
Data Analytics Internship At Fastenal, Jacob J. Haines
Data Analytics Internship At Fastenal, Jacob J. Haines
Research & Creative Achievement Day
The poster will present the results from an analysis of Fastenal's customer base to find characteristics among them that serve as useful predictors of their spending habits. This will allow Fastenal to create more accurate control groups when assessing the effectiveness of various marketing initiatives. This poster acts as the communication of capstone experience outcomes which is required for Data Science majors in addition to the capstone experience.
Hgs3 The Influence Of A Tandem Cycling Program In The Community On Physical And Functional Health, Therapeutic Bonds, And Quality Of Life For Individuals And Care Partners Coping With Parkinson’S Disease, Leila Djerdjour, Jennifer L. Trilk
Hgs3 The Influence Of A Tandem Cycling Program In The Community On Physical And Functional Health, Therapeutic Bonds, And Quality Of Life For Individuals And Care Partners Coping With Parkinson’S Disease, Leila Djerdjour, Jennifer L. Trilk
SC Upstate Research Symposium
Purpose Statement: Several studies have shown that aerobic exercise can have a positive impact on alleviating symptoms experienced by individuals with Parkinson's disease (PD). Despite this evidence, the potential benefits of exercise for both PD patients and their care partners (PD dyad) remain unexplored. This research project investigates the effectiveness, therapeutic collaborations, and physical outcomes of a virtual reality (VR) tandem cycling program specifically designed for PD dyads.
Methods: Following approval from the Prisma Health Institutional Review Board, individuals with PD were identified and screened by clinical neurologists. The pretesting measures for PD dyads (N=9) included emotional and cognitive status …
VariableOrder Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, Yixuan Wu, Yanzhi Zhang
VariableOrder Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, Yixuan Wu, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
The variableorder fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variableorder Laplacian (Δ) α (x) / 2 with 0 < α (x) ≤ 2, which will also be referred as the variableorder fractional Laplacian if α(x) is strictly less than 2. We present a class of hypergeometric functions whose variableorder Laplacian can be analytically expressed. Building on these analytical results, we design the meshfree methods based on globally supported radial basis functions (RBFs), including Gaussian, generalized inverse multiquadric, and Besseltype RBFs, to approximate the variableorder Laplacian (Δ) α (x) / 2. Our meshfree methods integrate the advantages of both pseudodifferential and hypersingular integral forms of the variableorder fractional Laplacian, and thus avoid numerically approximating the hypersingular integral. Moreover, our methods are simple and flexible of domain geometry, and their computer implementation remains the same for any dimension d ≥ 1. Compared to finite difference methods, our methods can achieve a desired accuracy with much fewer points. This fact makes our method much attractive for problems involving variableorder fractional Laplacian where the number of points required is a critical cost. We then apply our method to study solution behaviors of variableorder fractional PDEs arising in different fields, including transition of waves between classical and fractional media, and coexistence of anomalous and normal diffusion in both diffusion equation and the Allen–Cahn equation. These results would provide insights for further understanding and applications of variableorder fractional derivatives.
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine
Honors Program Theses and Research Projects
Stochastic ordering of probability distributions holds various practical applications. However, in realworld scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …
How Difficult Is It To Comprehend A Program That Has Significant Repetitions: FuzzyRelated Explanations Of Empirical Results, Christian Servin, Olga Kosheleva, Vladik Kreinovich
How Difficult Is It To Comprehend A Program That Has Significant Repetitions: FuzzyRelated Explanations Of Empirical Results, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In teaching computing and in gauging the programmers' productivity, it is important to property estimate how much time it will take to comprehend a program. There are techniques for estimating this time, but these techniques do not take into account that some program segments are similar, and this similarity decreases the time needed to comprehend the second segment. Recently, experiments were performed to describe this decrease. These experiments found an empirical formula for the corresponding decrease. In this paper, we use fuzzyrelated ideas to provide commonsensebased theoretical explanation for this empirical formula.
Mcfadden's Discrete Choice And Softmax Under Interval (And Other) Uncertainty: Revisited, Bartlomiej Jacek Kubica, Olga Kosheleva, Vladik Kreinovich
Mcfadden's Discrete Choice And Softmax Under Interval (And Other) Uncertainty: Revisited, Bartlomiej Jacek Kubica, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Studies of how people actually make decisions have led to an empirical formula that predicts the probability of different decisions based on the utilities of different alternatives. This formula is known as McFadden's formula, after a Nobel prize winning economist who discovered it. A similar formula  known as softmax  describes the probability that the classification predicted by a deep neural network is correct, based on the neural network's degrees of confidence in the object belonging to each class. In practice, we usually do not know the exact values of the utilities  or of the degrees of confidence. …
Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva, Vladik Kreinovich
Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many computational situations  in particular, in computations under interval or fuzzy uncertainty  it is convenient to approximate a function by a polynomial. Usually, a polynomial is represented by coefficients at its monomials. However, in many cases, it turns out more efficient to represent a general polynomial by using a different basis  of socalled Bernstein polynomials. In this paper, we provide a new explanation for the computational efficiency of this basis.
Somewhat Surprisingly, (Subjective) Fuzzy Technique Can Help To Better Combine Measurement Results And Expert Estimates Into A Model With Guaranteed Accuracy: Digital Twins And Beyond, Niklas Winnewisser, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Somewhat Surprisingly, (Subjective) Fuzzy Technique Can Help To Better Combine Measurement Results And Expert Estimates Into A Model With Guaranteed Accuracy: Digital Twins And Beyond, Niklas Winnewisser, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To understand how different factors and different control strategies will affect a system  be it a plant, an airplane, etc.  it is desirable to form an accurate digital model of this system. Such models are known as digital twins. To make a digital twin as accurate as possible, it is desirable to incorporate all available knowledge of the system into this model. In many cases, a significant part of this knowledge comes in terms of expert statements, statements that are often formulated by using imprecise ("fuzzy") words from natural language such as "small", "very possible", etc. To translate …
How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid TizpazNiari, Olga Kosheleva, Vladik Kreinovich
How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid TizpazNiari, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In general, in statistics, the most widely used way to describe the difference between different elements of a sample if by using standard deviation. This characteristic has a nice property of being decomposable: e.g., to compute the mean and standard deviation of the income overall the whole US, it is sufficient to compute the number of people, mean, and standard deviation over each state; this statebystate information is sufficient to uniquely reconstruct the overall standard deviation. However, e.g., for gauging income inequality, standard deviation is not very adequate: it provides too much weight to outliers like billionaires, and thus, does …
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that there is a  somewhat unexpected  common trend behind several seemingly unrelated historic transitions: from Aristotelian physics to modern (Newton's) approach, from crisp sets (such as intervals) to fuzzy sets, and from traditional neural networks, with closetostepfunction sigmoid activation functions to modern successful deep neural networks that use a completely different ReLU activation function. In all these cases, the main idea of the corresponding transition can be explained, in mathematical terms, as going from the first order to second order differential equations.
How To Make A Decision Under Interval Uncertainty If We Do Not Know The Utility Function, Jeffrey Escamilla, Vladik Kreinovich
How To Make A Decision Under Interval Uncertainty If We Do Not Know The Utility Function, Jeffrey Escamilla, Vladik Kreinovich
Departmental Technical Reports (CS)
Decision theory describes how to make decisions, in particular, how to make decisions under interval uncertainty. However, this theory's recommendations assume that we know the utility function  a function that describes the decision maker's preferences. Sometimes, we can make a recommendation even when we do not know the utility function. In this paper, we provide a complete description of all such cases.
Paradox Of Causality And Paradoxes Of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel MikiSilva, Olga Kosheleva, Vladik Kreinovich
Paradox Of Causality And Paradoxes Of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel MikiSilva, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Logical paradoxes show that human reasoning is not always fully captured by the traditional 2valued logic, that this logic's extensions  such as multivalued logics  are needed. Because of this, the study of paradoxes is important for research on multivalued logics. In this paper, we focus on paradoxes of set theory. Specifically, we show their analogy with the known paradox of causality, and we use this analogy to come up with similar settheoretic paradoxes.
Number Representation With Varying Number Of Bits, Anuradha Choudhury, Md Ahsanul Haque, Saeefa Rubaiyet Nowmi, Ahmed Ann Noor Ryen, Sabrina Saika, Vladik Kreinovich
Number Representation With Varying Number Of Bits, Anuradha Choudhury, Md Ahsanul Haque, Saeefa Rubaiyet Nowmi, Ahmed Ann Noor Ryen, Sabrina Saika, Vladik Kreinovich
Departmental Technical Reports (CS)
In a computer, usually, all real numbers are stored by using the same number of bits: usually, 8 bytes, i.e., 64 bits. This amount of bits enables us to represent numbers with high accuracy  up to 19 decimal digits. However, in most cases  whether we process measurement results or whether we process expertgenerated membership degrees  we do not need that accuracy, so most bits are wasted. To save space, it is therefore reasonable to consider representations with varying number of bits. This would save space used for representing numbers themselves, but we would also need to store …
Data Fusion Is More Complex Than Data Processing: A Proof, Robert Alvarez, Salvador Ruiz, Martine Ceberio, Vladik Kreinovich
Data Fusion Is More Complex Than Data Processing: A Proof, Robert Alvarez, Salvador Ruiz, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Empirical data shows that, in general, data fusion takes more computation time than data processing. In this paper, we provide a proof that data fusion is indeed more complex than data processing.
How To Fairly Allocate Safety Benefits Of SelfDriving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich
How To Fairly Allocate Safety Benefits Of SelfDriving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we describe how to fairly allocated safety benefits of selfdriving cars between drivers and pedestrians  so as to minimize the overall harm.
Using Known Relation Between Quantities To Make Measurements More Accurate And More Reliable, Niklas Winnewisser, Felix Mett, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Using Known Relation Between Quantities To Make Measurements More Accurate And More Reliable, Niklas Winnewisser, Felix Mett, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Most of our knowledge comes, ultimately, from measurements and from processing measurement results. In this, metrology is very valuable: it teaches us how to gauge the accuracy of the measurement results and of the results of data processing, and how to calibrate the measuring instruments so as to reach the maximum accuracy. However, traditional metrology mostly concentrates on individual measurements. In practice, often, there are also relations between the current values of different quantities. For example, there is usually an known upper bound on the difference between the values of the same quantity at close moments of time or at …
Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar AlmEldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. AbdelRaouf Ibrahim Dr. Eng.
Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar AlmEldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. AbdelRaouf Ibrahim Dr. Eng.
Journal of Engineering Research
Recently, premixed combustion has dominated the field of combustion research worldwide. The current work is a review that addresses the effects of design and operating regimes on the combustion and emission characteristics of premixed turbulent flames. The study accounts for recent developments aimed at overcoming combustor operability issues that influence emissions and flame stability. Various experimental setups have been utilized in investigations, with results pertaining to performance and emissions concerning premixed turbulent flames. Thus, the objective of this paper is to provide a comprehensive review of the effects of swirl vane angles and equivalence fuelair ratios for tests conducted both …
Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, Heather Moore
Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, Heather Moore
University Honors Theses
This thesis presents a surprising result that the difference in a certain sums of constant rotations by the golden mean approaches exactly 1/5. Specifically, we focus on the Birkhoff sums of these rotations, with the number of terms equal to squared Fibonacci numbers. The proof relies on the properties of continued fraction approximants, Vajda's identity and the explicit formula for the Fibonacci numbers.
Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo BenAri, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro
Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo BenAri, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro
Journal of Stochastic Analysis
No abstract provided.
The Basel Problem And Summing Rational Functions Over Integers, Pranjal Jain
The Basel Problem And Summing Rational Functions Over Integers, Pranjal Jain
RoseHulman Undergraduate Mathematics Journal
We provide a general method to evaluate convergent sums of the form ∑_{k∈Z} R(k) where R is a rational function with complex coefficients. The method is entirely elementary and does not require any calculus beyond some standard limits and convergence criteria. It is inspired by a geometric solution to the famous Basel Problem given by Wästlund (2010), so we begin by demonstrating the method on the Basel Problem to serve as a pilot application. We conclude by applying our ideas to prove Euler’s factorisation for sin x which he originally used to solve the Basel Problem.
Understanding Waveguides In Resonance, Pieter Johannes Daniel Vandenberge
Understanding Waveguides In Resonance, Pieter Johannes Daniel Vandenberge
Dissertations and Theses
Several important classes of modern optical waveguides, including antiresonant reflecting and photonic bandgap fibers, make use of geometries that guide energy in low refractive index material, a property that makes them of significant interest in numerous applications, notably including highpower delivery and guidance. These waveguides frequently exhibit resonance phenomena, in which their ability to propagate an input signal is sharply curtailed at particular operating frequencies. In this work we detail new advances in understanding these resonance effects and their implications for numerical modeling of these structures.
Part 1 focuses on the fields of slab waveguides, relatively simple structures for which …
Wang Tilings In Arbitrary Dimensions, Ian Tassin
Wang Tilings In Arbitrary Dimensions, Ian Tassin
RoseHulman Undergraduate Mathematics Journal
This paper makes a new observation about arbitrary dimensional Wang Tilings,
demonstrating that any d dimensional tile set that can tile periodically along d − 1 axes must be able to tile periodically along all axes.
This work also summarizes work on Wang Tiles up to the present day, including
definitions for various aspects of Wang Tilings such as periodicity and the validity of a tiling. Additionally, we extend the familiar 2D definitions for Wang Tiles and associated properties into arbitrary dimensional spaces. While there has been previous discussion of arbitrary dimensional Wang Tiles in other works, it has been …
Algorithmic Design And Computational Modeling Using Dynamic Spectrum Allocation Techniques To Optimize Bandwidth Management In Wireless Communication Systems, Ankit Walishetti
Algorithmic Design And Computational Modeling Using Dynamic Spectrum Allocation Techniques To Optimize Bandwidth Management In Wireless Communication Systems, Ankit Walishetti
Distinguished Student Work
This study aims to address the pressing need for efficient spectrum management methodologies in wireless communication systems by developing innovative sorting and allocation algorithms. Leveraging Dynamic Spectrum Allocation (DSA) techniques, this research devises strategies to optimize the utilization of bandwidth within existing spectrum space, ultimately reducing the need for network infrastructure expansion.
Ensuring thorough coverage of DSA techniques, 5 distinct transmitter sorting algorithms were programmed and tested across 8 performance metrics designed to measure specific capabilities. For consistency, a single bandwidth allocation program was designed to ‘pack’ transmitters starting from the left endpoint of the spectrum space. Progressively varying the …
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Turkish Journal of Mathematics
Let H be a supersolvable Hall π subgroup of a finite group G. We prove that G has a normal π complement if and only if H controls Gfusion in H.
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Turkish Journal of Mathematics
This paper is devoted to defining the delayed analogue of the MittagLeffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.
Qualitative Results For A Generalized 2Component CamassaHolm System With Weak Dissipation Term, Nurhan Dündar
Qualitative Results For A Generalized 2Component CamassaHolm System With Weak Dissipation Term, Nurhan Dündar
Turkish Journal of Mathematics
Our main aim in the current study is to examine the mathematical properties of a generalized 2component CamassaHolm system with a weakly dissipative term. Firstly, we acquire the theorem of wellposedness in locally for the generalized system with weak dissipation. Then, we demonstrate that this system can reveal the blowup phenomenon. Finally, we acquire the theorem of global existence utilizing a method of the Lyapunov function.