New Examples Of Self-Dual Near-Extremal Ternary Codes Of Length 48 Derived From 2-(47,23,11) Designs, 2024 Faculty of Mathematics, University of Rijeka

#### New Examples Of Self-Dual Near-Extremal 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 self-dual near-extremal 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 self-dual near-extremal ternary codes of length 48 for 150 new values of A12.

Ramanujan Type Congruences For Quotients Of Klein Forms, 2024 The University of Texas Rio Grande Valley

#### 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 *t*-core 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 …

Data Analytics Internship At Fastenal, 2024 Winona State University

#### 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.

Using Data Visualizations To Analyze Employee Performance At Xcel Energy, 2024 Winona State University

#### 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

My Experience As An It Data Intern, 2024 Winona State University

#### 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 high-end reports. Additionally, I was in-charge 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 day-to-day 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 …

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, 2024 SUNY New Paltz

#### “Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

*Excelsior: Leadership in Teaching and Learning*

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Hgs-3 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, 2024 university of south carolina school of medicine greenville

#### Hgs-3 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 pre-testing measures for PD dyads (N=9) included emotional and cognitive status …

Variable-Order Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, 2024 Missouri University of Science and Technology

#### Variable-Order Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, Yixuan Wu, Yanzhi Zhang

*Mathematics and Statistics Faculty Research & Creative Works*

The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variable-order Laplacian (-Δ) α (x) / 2 with 0 < α (x) ≤ 2, which will also be referred as the variable-order fractional Laplacian if α(x) is strictly less than 2. We present a class of hypergeometric functions whose variable-order 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 Bessel-type RBFs, to approximate the variable-order Laplacian (-Δ) α (x) / 2. Our meshfree methods integrate the advantages of both pseudo-differential and hypersingular integral forms of the variable-order 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 variable-order fractional Laplacian where the number of points required is a critical cost. We then apply our method to study solution behaviors of variable-order 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 variable-order fractional derivatives.

How Difficult Is It To Comprehend A Program That Has Significant Repetitions: Fuzzy-Related Explanations Of Empirical Results, 2024 El Paso Community College

#### How Difficult Is It To Comprehend A Program That Has Significant Repetitions: Fuzzy-Related 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 fuzzy-related ideas to provide commonsense-based theoretical explanation for this empirical formula.

Mcfadden's Discrete Choice And Softmax Under Interval (And Other) Uncertainty: Revisited, 2024 Warsaw University of Life Sciences

#### 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, 2024 The University of Texas at El Paso

#### 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 so-called 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, 2024 Leibniz University Hannover

#### 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, 2024 The University of Texas at El Paso

#### How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid Tizpaz-Niari, 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 state-by-state 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?, 2024 El Paso Community College

#### 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 close-to-step-function 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, 2024 The University of Texas at El Paso

#### 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, 2024 The University of Texas at El Paso

#### Paradox Of Causality And Paradoxes Of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel Miki-Silva, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Logical paradoxes show that human reasoning is not always fully captured by the traditional 2-valued logic, that this logic's extensions -- such as multi-valued logics -- are needed. Because of this, the study of paradoxes is important for research on multi-valued 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 set-theoretic paradoxes.

Number Representation With Varying Number Of Bits, 2024 The University of Texas at El Paso

#### 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 expert-generated 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, 2024 The University of Texas at El Paso

#### 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 Self-Driving Cars, 2024 The University of Texas at El Paso

#### How To Fairly Allocate Safety Benefits Of Self-Driving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In this paper, we describe how to fairly allocated safety benefits of self-driving 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, 2024 Leibniz University Hannover

#### 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 …