Mathematics Commons^™

Realtime Event Detection In Sports Sensor Data With Machine Learning, Mallory Cashman

Honors Theses and Capstones

Machine learning models can be trained to classify time series based sports motion data, without reliance on assumptions about the capabilities of the users or sensors. This can be applied to predict the count of occurrences of an event in a time period. The experiment for this research uses lacrosse data, collected in partnership with SPAITR - a UNH undergraduate startup developing motion tracking devices for lacrosse. Decision Tree and Support Vector Machine (SVM) models are trained and perform with high success rates. These models improve upon previous work in human motion event detection and can be used a reference …

Rock Paintings, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Rock Paintings: Solutions For Fermi Questions, September 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

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

College of Graduate Studies: Theses & 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.

Boundedness Of Some Multi-Parameter Fiber-Wise Multiplier Operators, Frédéric Bernicot, Polona Durcik

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove L^p estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted paraproduct studied in [V. Kovač, Boundedness of the twisted paraproduct. Rev. Mat. Iberoam. 28 (2012), no. 4, 1143–1164.].

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.

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 …

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.

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), …

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 …

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.

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 …

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., …

Calculating Infinitesimal Generators, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.

Recursive And Viterbi Estimation For Semi-Markov Chains, Robert J. Elliott, W. P. Malcolm

Journal of Stochastic Analysis

No abstract provided.

The N-Dimensional Quadratic Heisenberg Algebra As A “Non–Commutative” Sl(2,C), Luigi Accardi, Andreas Boukas, Yun-Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Rough Paths And Regularization, André O. Gomes, Alberto Ohashi, Francesco Russo, Alan Teixeira

Journal of Stochastic Analysis

No abstract provided.

Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy

Colorado Mathematics Teacher

This article shares three questions and answers about mathematical modeling in the classroom from an April 2020 online conversation with participants of a CCTM webinar. We hope that the answers to these questions will motivate teachers to embrace the value of implementing math modeling tasks, help students see the math all around them in the world, and empower future professionals to reach for the mathematical tools in their pockets to make data-driven decisions.

Generalized Grassmann Algebras And Applications To Stochastic Processes, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we present the groundwork for an Itô/Malliavin stochastic calculus and Hida's white noise analysis in the context of a supersymmetry with Z₃-graded algebras. To this end, we establish a ternary Fock space and the corresponding strong algebra of stochastic distributions and present its application in the study of stochastic processes in this context.

Generalized Girsanov Transform Of Processes And Zakai Equation With Jumps, Masatoshi Fujisaki, Takashi Komatsu

Journal of Stochastic Analysis

No abstract provided.

On The Uniqueness Of Solutions To Martingale Problems For Diffusion Operators With Progressively Measurable Random Coefficients, Masaaki Tsuchiya

Journal of Stochastic Analysis

No abstract provided.

Particle Representation For The Solution Of The Filtering Problem. Application To The Error Expansion Of Filtering Discretizations, Dan Crisan, Thomas G. Kurtz, Salvador Ortiz-Latorre

Journal of Stochastic Analysis

No abstract provided.

An Anti-Symmetric Version Of Malliavin Calculus, Jirô Akahori, Tomo Matsusita, Yasufumi Nitta

Journal of Stochastic Analysis

No abstract provided.

Eulerian Walk And Dna Sequence Assembly, Yifan Zhu

Symposium of Student Scholars

Children like jigsaw puzzles, and the way to assemble the puzzle is by putting together pieces that match, one by one, till the puzzle is complete. DNA sequence assembly could be thought of as something similar: when a strand of DNA is passed into a particular “sequencing machine”, it gives a large number of short reads of the DNA sequence. This type of technology is called shotgun sequencing. These reads form the jigsaw pieces in the puzzle and one must put together these pieces in an intelligent way to obtain the original sequence. There is, however, a catch here; apriori, …

Transfer Of Regularity For Markov Semigroups By Using An Interpolation Technique, Vlad Bally, Lucia Caramellino

Journal of Stochastic Analysis

No abstract provided.