How To Deal With High-Impact Low-Probability Events: Theoretical Explanation Of The Empirically Successful Fuzzy-Like Technique,
2025
The University of Texas at El Paso
How To Deal With High-Impact Low-Probability Events: Theoretical Explanation Of The Empirically Successful Fuzzy-Like Technique, Juan Ulloa, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When making decisions, it is important to take into account high-impact low-probability events. For such events, traditional probability-based approach -- which considers the product of the probability p that this event happens and the probability P that a randomly selected building will be destroyed -- often underestimates risks. Available data has lead to an empirical table that provides a more adequate risk estimate. Most of the entries in this table correspond to the fuzzy-like formula min(p,P). This paper explains this empirical result. Specifically, it explains both the effectiveness of the min formula -- and also explains deviations from this formula.
Möbius Transformations And Hyperbolic Geometry In The Upper Half-Plane,
2025
Western Kentucky University
Möbius Transformations And Hyperbolic Geometry In The Upper Half-Plane, Emma Bunch
Mahurin Honors College Capstone Experience/Thesis Projects
In this thesis, we discuss several properties of Möbius transformations and hyperbolic geometry, a type of non-Euclidean geometry, in the upper half-plane using tools of complex analysis. We begin with preliminaries for our work, comprising the stereographic projection, the representation of circles and lines in the complex plane, conformal maps, and a result on cross-products, which we include for further development. We proceed to Möbius transformations and discuss their properties, cross-ratios, and various mappings. We additionally provide useful calculations. Lastly, we conclude with the hyperbolic metric in the upper half-plane and explore hyperbolic distance, including its invariance under Möbius transformations. …
Gaps In Knowledge: Topological Insights Into The Structure Of Science,
2025
Macalester College
Gaps In Knowledge: Topological Insights Into The Structure Of Science, Gavin Engelstad
Mathematics, Statistics, and Computer Science Honors Projects
Understanding scientific development is essential to ascertaining the mechanisms leading us into the future. Building this understanding requires both methodological developments and empirical research. This thesis contributes in both aspects using a topological approach to examine scientific knowledge. The first section presents a new algorithm to find optimal cycle representatives for homological features in complex networks, a context for which we demonstrate existing algorithms can be inadequate. The second section applies a number of topological methods, including our cycle optimization algorithm, to data on individual scientific fields, demonstrating the value of topological approaches and highlighting new insights about how science …
Existence And Uniqueness Of The Solution Of A Traffic Flow Partial Differential Equation On Multi-Lane Freeways,
2025
Claremont Graduate University
Existence And Uniqueness Of The Solution Of A Traffic Flow Partial Differential Equation On Multi-Lane Freeways, Sina Zareian
CGU Theses & Dissertations
In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.
Diophantine Avoidance, Number Fields, And Quadratic Forms,
2025
Claremont Graduate University
Diophantine Avoidance, Number Fields, And Quadratic Forms, Sehun Jeong
CGU Theses & Dissertations
Diophantine avoidance has been studied by several authors in recent years. This term refers to effective results on existence of points of bounded size (where size is measured by norm or height, depending on the context) in a given algebraic set avoiding some specified subsets. The application of avoidance conditions allows to understand how ``well distributed" are points of bounded size in a given set. If it is possible to find them outside of some prescribed collection of subsets of the set in question, then it suggests that they are evenly distributed, in some appropriate sense. Our first result investigates …
Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks,
2025
Claremont Graduate University
Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks, John Kath
CGU Theses & Dissertations
This dissertation addresses the challenge of modeling complex geophysical systems by developing efficient surrogate models and scalable quantum algorithms. Our approaches provide uncertainty quantification, assessing confidence in estimates while accounting for subsurface heterogeneity. These innovations are designed to replace costly solvers with parsimonious emulators. In combination with multi-fidelity and quantum techniques, they make physics-informed modeling computationally feasible. One of our studies involves the use of Gaussian process regression to generate Bayesian predictions for gas transport in 3D discrete fracture networks. This provides accurate estimates while offering substantial savings over computationally intensive high-fidelity simulations. Additionally, we study multi-fidelity modeling through the …
Characterizations Of Stability Via Morse Limit Sets,
2025
Smith College
Characterizations Of Stability Via Morse Limit Sets, Jacob D. Garcia
Mathematics Sciences: Faculty Publications
Subgroup stability is a strong notion of quasiconvexity that generalizes convex cocompactness in a variety of settings. In this paper, we characterize stability of a subgroup by properties of its limit set on the Morse boundary. Given H < G, both finitely generated, H is stable exactly when all the limit points of H are conical, or equivalently when all the limit points of H are horospherical, as long as the limit set of H is a compact subset of the Morse boundary for G We also demonstrate an application of these results in the settings of the mapping class …
Topological Symmetry Groups Of The Generalized Petersen Graphs,
2025
Embry–Riddle Aeronautical University
Topological Symmetry Groups Of The Generalized Petersen Graphs, Angelynn Álvarez, Erica Flapan, Mark Hunnell, John Hutchens, Emille Lawrence, Paul Lewis, Candice Price, Ruth Vanderpool
Mathematics Sciences: Faculty Publications
The topological symmetry group TSG(Γ) of an embedded graph Γ in S3 is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of (S3,Γ). If we restrict to orientation-preserving homeomorphisms then we obtain the orientation-preserving topological symmetry group TSG+(Γ). In this paper, we determine all groups that can beTSG(Γ) or TSG+(Γ) for some embedding Γ of a generalized Petersen graph other than the exceptional graphs P(12,5) and P(24,5).
Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications,
2025
Wayne State University
Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications, Thi Dai Trang Nguyen
Wayne State University Dissertations
Optimization and optimal control have a wide range of applications across fields like engineering, biology, data science, and economics. This dissertation is devoted to advanced optimal control problems discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization, which are truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems, we use the method of discrete approximation while establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. This approach, married to advanced tools of variational analysis, enables this research to …
Examining Student Understanding Of Series Convergence Using Script Writing,
2025
University of Texas at Arlington
Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez
Mathematics Dissertations - Archive
This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …
Construction Techniques For Linear Realizations Of Multisets With Small Support,
2025
Emerson College
Construction Techniques For Linear Realizations Of Multisets With Small Support, M. A. Ollis
Emerson Authors, Researchers, & Creators
The Buratti-Horak Rosa Conjecture is a problem in graph theory asking when we can find a Hamiltonian path in the complete graph that has various properties to do with edge lengths. In this paper, we use constructive methods to show that the conjecture is true for various parameter sets where it was previously unknown.
Random Graph Models For Dual Graphs,
2025
Scripps College
Random Graph Models For Dual Graphs, Anne Friedman
Scripps Senior Theses
This paper aims to better characterize dual graphs derived from state districting maps by developing random graph models that replicate their structural properties. Dual graphs provide a simplified way to represent districting maps, making it computationally feasible to analyze their structure. These representations enable researchers, legislators, and courts to assess district compactness, detect signs of gerrymandering, and generate alternative districting plans. A deeper understanding of the structural patterns of these dual graphs can help researchers choose or design more effective algorithms for redistricting analysis. The random graph models developed in this study serve as testbeds for evaluating algorithmic approaches to …
Analyzing Patterns In Chicago Motor Vehicle Crashes Using Time-Series Techniques,
2025
Eastern Michigan University
Analyzing Patterns In Chicago Motor Vehicle Crashes Using Time-Series Techniques, Christina Trotta
Senior Honors Theses and Projects
This project explores time series forecasting of daily traffic crash rates in Chicago from 2018 to 2024, with a focus on understanding how past crash patterns and external conditions influence future risk. The primary research question asks: To what extent does yesterday’s crash rate help predict today’s? Using a combination of Holt-Winters exponential smoothing, Prophet forecasting, and SARIMAX models, we assess the role of autoregression, seasonality, and exogenous variables such as weather and roadway conditions. Daily crash data was cleaned, aggregated, and enriched with engineered features including holiday indicators, weather metrics from O’Hare and Midway airports, and binary flags for …
A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales,
2025
Missouri University of Science and Technology
A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we introduce a novel formulation of dynamic Hardy-type inequalities on a time scale, motivated by a recently established convexity approach in the Haar measure. The classical Hardy inequality is refined so that the classical Lebesgue-measure constant is replaced by the sharp constant 1. We obtain time-scale analogues on finite intervals with best constants, and, for nonincreasing and nondecreasing functions, reversed inequalities with explicit weights described by incomplete β-functions. To establish our results, we employ two distinct time scales and apply the chain rule, together with the substitution rule, the derivative of inverse functions, and Fubini's theorem for …
Self-Tor Persistence Of Modules Over Determinantal Rings,
2025
University of Texas at Arlington
Self-Tor Persistence Of Modules Over Determinantal Rings, Tatheer F. Ajani
Mathematics Dissertations - Archive
Tor-persistence is the claim that Tor of a module with itself is only zero if the module has finite projective dimension. Work done by Avramov, Iyengar, Nasseh, Sather-Wagstaff, and various other authors have proved Tor-persistence of modules over certain rings. In this work, we will prove Tor-persistence for certain modules over determinantal rings, specifically for the hypersurface defined by the determinant of a generic matrix. We will then give an explicit proof that Tor^R_2(M,M) is never zero, that Tor^R_1(M,M)=0, and due to the periodicity of the given free resolution, our result can be extended to the entire complex, showing that …
Hyper B-Ary Representations Of A Number,
2025
Missouri University of Science and Technology
Hyper B-Ary Representations Of A Number, Mingway Wang
Masters Theses
In this work, we summarize combinatorial, analytical, and computational properties of Stern's diatomic sequence, and do the same for a generalization of a combinatorial property of this sequence to higher bases. We then construct special ``bit conversion'' functions $g_{b}$ that allows us to find a semi-explicit formula for the generalized sequences. Lastly, we analyze some of the properties of these $g_{b}$ functions.
Generalizations Of Finiteness Conditions And Extension Monads In Algebras With Infinitely Many Or Infinitary Operations,
2025
Missouri University of Science and Technology
Generalizations Of Finiteness Conditions And Extension Monads In Algebras With Infinitely Many Or Infinitary Operations, Danielle Christienne Bowerman
Doctoral Dissertations
In this work, we extend the results of finiteness conditions and extension monads found in Insall from finitely many finitary operations to infinitely many finitary operations, as well as touching on infinitary operations. We also examine varieties of algebras, including the notion of strong varieties introduced in Insall, and common constructions of extension monads in varieties of algebras. We see that for finite collections of algebras of the same signature, the extension monad operation on a variety of algebras commutes with the direct product operation, and all retractions from an enlargement or extension monad are trivial. We also see that …
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians,
2025
Butler University
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer Lc Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha Jayesekere
Scholarship and Professional Work
Academic librarians do not engage with all disciplinary departments equally. Despite equal or even greater efforts, some departments are less responsive to librarian outreach. One such department is mathematics. To understand mathematics departments’ relationships with their academic librarians, three mathematics librarians created a 20-question survey that was disseminated to mathematics faculty, instructors, and instructional staff in the United States and Canada. Of the 188 survey participants, more than a third reported that they never engage with their librarians, approximately half only do so occasionally, and a mere eight percent of participants collaborated with librarians to provide information literacy instruction (IL) …
Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic,
2025
Northern Illinois University
Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic, David J. Buller
Faculty Books & Book Chapters
This book is a companion text for lectures on first-order logic and its elementary metatheory (used in Intermediate Logic at Northern Illinois University). It covers the basic concepts of set theory necessary for a mathematical development of first-order logic; develops a formal language of first-order logic; presents a classical Tarskian semantics for the language and the “semantic” conception of logical consequence; presents a Gentzenian proof system and the “syntactic” conception of logical consequence; develops a partial decision procedure for logical consequence in the language; demonstrates applications of the formal system to modeling deductive inference expressed in natural language; and extends …
Ms-Yolo: Infrared Object Detection For Edge Deployment Via Mobilenetv4 And Slideloss,
2025
Missouri University of Science and Technology
Ms-Yolo: Infrared Object Detection For Edge Deployment Via Mobilenetv4 And Slideloss, Jiali Zhang, Thomas S. White, Haoliang Zhang, Wenqing Hu, Donald C. Wunsch, Jian Liu
Mathematics and Statistics Faculty Research & Creative Works
Infrared imaging has emerged as a robust solution for urban object detection under low-light and adverse weather conditions, offering significant advantages over traditional visible-light cameras. However, challenges such as class imbalance, thermal noise, and computational constraints can significantly hinder model performance in practical settings. To address these issues, we evaluate multiple YOLO variants on the FLIR ADAS V2 dataset, ultimately selecting YOLOv8 as our baseline due to its balanced accuracy and efficiency. Building on this foundation, we present MS-YOLO (MobileNetv4 and SlideLoss based on YOLO), which replaces YOLOv8's CSPDarknet backbone with the more efficient MobileNetV4, reducing computational overhead by 1.5% …
