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. …
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 …
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 …
Festival Of Research Abstracts, Spring 2024,
2024
Wright State University
Festival Of Research Abstracts, Spring 2024, College Of Science And Mathematics, Wright State University
Festival of Research
The collection of abstracts accepted for the Spring 2024 Festival of Research hosted by the Wright State University College of Science and Mathematics.
2-Accessibility Of The Lucas Numbers/Fibonacci Like Sequences/Wythoff Array,
2024
Louisiana Tech University
2-Accessibility Of The Lucas Numbers/Fibonacci Like Sequences/Wythoff Array, Cameron Lejeune
Mathematics Senior Capstone Papers
In this project we will be delving into the combinatorics side of mathematics, with basic a graph theory idea such as set coloring. It will be a continuation of a question formed by the works of Bruce M. Landman, and Aaron Robertson, ”3-Accessibility of the Fibonacci Numbers.” They were able to prove the Fibonacci Numbers to be 2-Accessible, and while they did not supply the induction proof, we were able to construct and provide a proof. This project will use their lemmas and propositions to attempt to prove 2-Accessibility of the Lucas Numbers, Fibonacci-like sequences, and the Zeckendorf-Wythoff Array.
Can Compiled Player War Predict Mlb Team Win Percentage?,
2024
Louisiana Tech University
Can Compiled Player War Predict Mlb Team Win Percentage?, Thomas Hertel
Mathematics Senior Capstone Papers
The baseball statistic Wins Above Replacement (WAR) is a complex yet effective metric for approximating the contribution of a player to his team through representing how many more wins his team ought to earn than with a AAAA player in his stead. The intent of this paper is to test whether the accumulation of player’s WAR can be extended to satisfy another discipline of SABRmetrics, i.e. predicting an entire team’s future performance, through modeling the sum’s correspondence (or lack thereof) to wins. If WAR is shown to extend in this way then franchise front offices could feasibly isolate it as …
Using Multiple Regression Analysis To Determine The Strength Of Certain Factors On Student Absenteeism,
2024
Louisiana Tech University
Using Multiple Regression Analysis To Determine The Strength Of Certain Factors On Student Absenteeism, Emmitt Antwine
Mathematics Senior Capstone Papers
During the 2015-16 academic year, approximately 16% of the student population—exceeding 7 million students—were absent from school for 15 days or more. The escalation in chronic absenteeism is influenced by various factors, including poor health conditions, nonstandard work schedules of parents, socioeconomic disadvantages, changes in household compositions, frequent residential relocation, and substantial family responsibilities. Previous research on student absenteeism has examined the negative impacts that chronic absenteeism has had on students in diverse communities such as racial minorities, students with disabilities, and English Language Learners communities. We utilized information obtained from the U.S. Department of Education’s Civil Rights Data Collection …
An Exploration Of The Sums Of Two Squares And Pentagonal Numbers,
2024
Louisiana Tech University
An Exploration Of The Sums Of Two Squares And Pentagonal Numbers, Jacob Von Tress
Mathematics Senior Capstone Papers
In the field of number theory, square numbers are very significant, and finding the sums of square numbers is a topic of certain interest to mathematicians. The most immediate application for adding together two square numbers is to identify Pythagorean triples. However, apart from seeking sums of two squares that are squares themselves, interesting patterns emerge that have fascinated number theorists for decades. Particularly, the distribution of a number’s divisors can explicitly determine how many ways that number can be written as a sum of two squares. Furthermore, pentagonal numbers, similar to square numbers, can be visualized by drawing a …
Matroids Stemming From The Maximal Relaxation Of Graphic Matroids,
2024
Louisiana Tech University
Matroids Stemming From The Maximal Relaxation Of Graphic Matroids, Landen Nguyen
Mathematics Senior Capstone Papers
This research explores the base perspective for maximal relaxation of graphic matroids. We begin by covering the required knowledge of graph theory and the basics of matroid theory required to conduct this research such as definitions of matroids up to the definitions of relaxation, hyperplanes, and uniform matroids. We then analyze the conjecture in matroids obtained from simple connected graphs.
Four Colorful Methods For Finding The Chromatic Polynomial,
2024
Louisiana Tech University
Four Colorful Methods For Finding The Chromatic Polynomial, Emerson Statom
Mathematics Senior Capstone Papers
Mathematicians apply algebraic graph theory to address and interpret problems arising out of data structures and optimization. For example, graph coloring problems have intrigued mathematicians and computer scientists alike. The chromatic polynomial was created to help solve such problems. This research aims to create a greater understanding of the underlying structures behind chromatic polynomials by analyzing the algebraic, deletion-contraction, and color partition methods. Each method has differing applications, but by viewing them all together, this research hopes to show the depth of this most interesting subject in a condensed manner.
Factors That Contribute To Completing Gateway Math Course At Southern University,
2024
Louisiana Tech University
Factors That Contribute To Completing Gateway Math Course At Southern University, Emma Colvin
Mathematics Senior Capstone Papers
At Southern University in Shreveport, Louisiana, there are several pathways students can take to complete the institution’s required Gateway Math Courses (GMC). The GMC consists of Math 133, Math 135, and Math 136. Currently, there is a significantly low passing rate for these courses potentially due to several factors such as the student’s math ACT score, the student’s age, whether or not the student took optional developmental math courses beforehand, and whether or not the student took these courses online or in person.
Congruences Of The Sums Of The First Rp Fibonacci Numbers,
2024
Louisiana Tech University
Congruences Of The Sums Of The First Rp Fibonacci Numbers, Tyler Warzynak
Mathematics Senior Capstone Papers
This paper serves as an extension/application of a method detailed by Chang et. al. in two separate papers which worked with sums modulo p for combinatorial sequences, positive integers r, and prime numbers p. Using a known formula, the Fibonacci numbers were converted into a sum of binomial coefficients to apply the aforementioned method. A hypothesis was formed using computational methods, where a pattern was observed to hold for the first 50,000 prime numbers. This claim was then proven following the methodology from Chang et. al. using properties of Laurent polynomials, definitions and theorems related to the Fibonacci numbers, and …
Abstract Measures On Totally Ordered Sets,
2024
Louisiana Tech University
Abstract Measures On Totally Ordered Sets, Gregory Whitehurst
Mathematics Senior Capstone Papers
Two specific notions of integration were the motivation of this paper: Riemann-Stieltjes and Lebesgue-Stieltjes integration. The question that arose from these notions was the idea of generalization. How can Stieltjes integration be generalized to an arbitrary measure? The buildup to this question requires a beautiful combination of measure theory and order theory to deliver a measure on totally ordered sets that provide structure for a potential generalization. This paper shows that the set of chains in a totally ordered set is a σ-algebra and defines cumulative cardinality measure on (X, Σ) in an attempt to give insight on the structure …
Does The ”Freshman 15” Exist?,
2024
Louisiana Tech University
Does The ”Freshman 15” Exist?, Peyton Albritton
Mathematics Senior Capstone Papers
This experiment was performed to determine whether the environmental changes of adapting from high school to college impact a student’s weight. Using a Google form, we collected data from 58 college students in two Psychology 102 classes, with ages ranging from seventeen to twenty-two. The students were asked a series of questions regarding their age and gender, as well as their eating, sleeping, and activity habit changes. Data was analyzed using hypothesis testing and a t-test.
Injuries On Artificial Turf Vs. Natural Grass In The Nfl,
2024
Louisiana Tech University
Injuries On Artificial Turf Vs. Natural Grass In The Nfl, Robert Emory
Mathematics Senior Capstone Papers
The purpose of this research is to determine if artificial turf causes more injuries than natural grass. By referencing different statistics from a sample of games from the 2023 National Football League season. Out of the ten games sampled, five were played on natural grass and five were played on artificial turf. We ran the data collected from these games through two different regression analysis models that output p-values to show what truly caused the injuries. Our model uses a player’s position, height, weight, age, and snap counts along with the field surface type to see how if an injury …
Comparison Of Linear Control Techniques For The Underactuated Nonlinear Quadcopter System,
2024
Louisiana Tech University
Comparison Of Linear Control Techniques For The Underactuated Nonlinear Quadcopter System, Ian Golsby
Mathematics Senior Capstone Papers
Uncrewed Aerial Vehicles (UAVs) are a prevalent technology in many fields. They must be lightweight, efficient, and stable in order to carry out their objectives or support a payload. The control system that maintains a UAV’s attitude directly contributes to the stability and efficiency of the UAV, and more efficient UAVs can be made more lightweight by reducing battery size. Because the UAV has only four degrees of control (one per motor) but requires twelve dimensions to describe its orientation and position over time, it is considered an under-actuated nonlinear complex system. In this study, we compare various linear control …
