Other Mathematics Commons^™

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

An Integration Of Art And Mathematics, Henry Jaakola

Undergraduate Honors Theses

Mathematics and art are seemingly unrelated fields, requiring different skills and mindsets. Indeed, these disciplines may be difficult to understand for those not immersed in the field. Through art, math can be more relatable and understandable, and with math, art can be imbued with a different kind of order and structure. This project explores the intersection and integration of math and art, and culminates in a physical interdisciplinary product. Using the Padovan Sequence of numbers as a theoretical basis, two artworks are created with different media and designs, yielding unique results. Through these pieces, the order and beauty of number …

Rock Paintings, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

Electronic Theses and Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Equitable Coloring Of Complete Tripartitle Graphs, Maxwell Vlam, Bailey Orehosky, Dominic Ditizio

Capstone Showcase

In this paper, we prove the Equitable Coloring Conjecture for variations of complete tripartite graphs with graphs K_n,n,n, K_n,n,2n, K_n,n,n+2, and K_n,n+2,n+4.

Lie-Derivations Of Three-Dimensional Non-Lie Leibniz Algebras, Emily H. Belanger

Rose-Hulman Undergraduate Mathematics Journal

The concept of Lie-derivation was recently introduced as a generalization of the notion of derivations for non-Lie Leibniz algebras. In this project, we determine the Lie algebras of Lie-derivations of all three-dimensional non-Lie Leibniz algebras. As a result of our calculations, we make conjectures on the basis of the Lie algebra of derivations of Lie-solvable non-Lie Leibniz algebras.

An Intrinsic Proof Of An Extension Of Itô’S Isometry For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

An Algorithm For Biobjective Mixed Integer Quadratic Programs, Pubudu Jayasekara Merenchige

All Dissertations

Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. Thus, in this work, we develop a branch and bound (BB) algorithm for solving biobjective mixed-integer quadratic programs (BOMIQPs). An algorithm of this type does not exist in the literature.

The algorithm relies on five fundamental components of the BB scheme: calculating an initial set of efficient solutions with associated Pareto points, solving node problems, fathoming, branching, and set dominance. Considering the properties of the Pareto set of …

Decisive Neutrality, Restricted Decisive Neutrality, And Split Decisive Neutrality On Median Semilattices And Median Graphs., Ulf Högnäs

Electronic Theses and Dissertations

Consensus functions on finite median semilattices and finite median graphs are studied from an axiomatic point of view. We start with a new axiomatic characterization of majority rule on a large class of median semilattices we call sufficient. A key axiom in this result is the restricted decisive neutrality condition. This condition is a restricted version of the more well-known axiom of decisive neutrality given in [4]. Our theorem is an extension of the main result given in [7]. Another main result is a complete characterization of the class of consensus on a finite median semilattice that satisfies the axioms …

Symmetric Representations Of Finite Groups And Related Topics, Connie Corona

Electronic Theses, Projects, and Dissertations

In this thesis, we have presented our discovery of original symmetric presentations of a number of non-abelian simple groups, including several sporatic groups, linear groups, and classical groups.

We have constructed, using our technique of double coset enumeration, J2, M₁₂, J₁, PSU(3, 3):2, M₁₁, A₁₀, S(4,3), M₂₂:2, PSL(3, 4), S₆, 2:S₅, 2:PSL(3, 4) as homomorphic images of the involutory progenitors 2^*32:(2⁵:A₅), 2^*110: PSL(2, 11), 2^*5:A₅, 3^*4:D₈, 2^*110:PSL(2, 11), …

Measure And Integration, Jeonghwan Lee

Electronic Theses, Projects, and Dissertations

Measure and Integral are important when dealing with abstract spaces such as function spaces and probability spaces. This thesis will cover Lebesgue Measure and Lebesgue integral. The Lebesgue integral is a generalized theory of Riemann integral learned in mathematics. The Riemann integral is centered on the domain of the function, but the Lebesgue integral is different in that it is centered on the range of the function, and uses the basic concept of analysis. Measure and integral have widely applied not only to mathematics but also to other fields.

Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Covariant Ergodic Quantum Markov Semigroups Via Systems Of Imprimitivity, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

De Finetti’S Theorem In Categorical Probability, Tobias Fritz, Tomáš Gonda, Paolo Perrone

Journal of Stochastic Analysis

No abstract provided.

Splitting-Up Technique And Cubic Spline Approximations For Solving Modified Coupled Burgers' Equations, Anwar Abdulla Bassaif

Hadhramout University Journal of Natural & Applied Sciences

In this paper, a finite difference scheme based on the splitting-up technique and cubic spline approximations is developed for solving modified coupled Burgers' equations. The accuracy and stability of the scheme have been analyzed. It is found that the scheme is of first-order accuracy in time and second-order accuracy in space direction and is unconditionally stable. The numerical results are obtained with severe/moderate gradients in the initial and boundary conditions and the steady state solutions are plotted for different values of given parameters. It is concluded that the resulting scheme produces satisfactory results, even in the case of very severe …

A Clark-Ocone Type Formula Via Itô Calculus And Its Application To Finance, Takuji Arai, Ryoichi Suzuki

Journal of Stochastic Analysis

No abstract provided.

Algorithmic Correspondence For Relevance Logics, Bunched Implication Logics, And Relation Algebras Via An Implementation Of The Algorithm Pearl, Willem Conradie, Valentin Goranko, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

The non-deterministic algorithmic procedure PEARL (acronym for ‘Propositional variables Elimination Algorithm for Relevance Logic’) has been recently developed for computing first-order equivalents of formulas of the language of relevance logics LR in terms of the standard Routley-Meyer relational semantics. It succeeds on a large class of axioms of relevance logics, including all so called inductive formulas. In the present work we re-interpret PEARL from an algebraic perspective, with its rewrite rules seen as manipulating quasi-inequalities interpreted over Urquhart’s relevant algebras, and report on its recent Python implementation. We also show that all formulae on which PEARL succeeds are canonical, i.e., …

Unary-Determined Distributive ℓ -Magmas And Bunched Implication Algebras, Natanael Alpay, Peter Jipsen, Melissa Sugimoto

Mathematics, Physics, and Computer Science Faculty Articles and Research

A distributive lattice-ordered magma (dℓ-magma) (A,∧,∨,⋅) is a distributive lattice with a binary operation ⋅ that preserves joins in both arguments, and when ⋅ is associative then (A,∨,⋅) is an idempotent semiring. A dℓ-magma with a top ⊤ is unary-determined if x⋅y=(x⋅⊤∧y)∨(x∧⊤⋅y). These algebras are term-equivalent to a subvariety of distributive lattices with ⊤ and two join-preserving unary operations p, q. We obtain simple conditions on p, q such that x⋅y=(px∧y)∨(x∧qy) is associative, commutative, idempotent and/or has an identity element. This generalizes previous results on the structure of doubly idempotent semirings and, in the case when the …