A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, 2022 Marquette University Law School

#### A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell

*Marquette Law Review*

Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.

Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, 2022 University of South Carolina

#### Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor

*Senior Theses*

Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …

Superoscillating Sequences And Supershifts For Families Of Generalized Functions, 2022 Politecnico di Milano

#### Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by λ ∈ R. The frame in which we introduce such families is that of the evolution through Schrödinger equation (i∂/∂t−H (x))(ψ) = 0 (H (x) = −(∂2/∂x2)/2+V (x)), V being a suitable potential). If F = {(t, x) → ϕλ(t, x) ; λ ∈ R}, where ϕλ is evolved from the initial datum x → eiλx , F-supershifts will be of …

High School Student Perspective: My Njit Stem For Success Internship Experience, 2022 STEM for Success

#### High School Student Perspective: My Njit Stem For Success Internship Experience, Michael Mora

*STEM Month*

During the 2020-2021 school year, I was a senior at the Academy for Mathematics, Science, and Engineering (AMSE) in Rockaway, NJ. At AMSE, a STEM-focused four-year magnet high school program hosted at Morris Hills High School, participating in an extended internship senior year is a cornerstone of the learning process. Required to complete a STEM-related internship to graduate, Academy students are encouraged to seek out an internship they’re passionate about in a field of their choice. The internship, which must be conducted under the mentorship of an industry professional, must meet the New Jersey-approved standards for a work-based learning experience …

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, 2022 Università di Roma Tor Vergata, via Columbia 2, 00133 Roma, Italy

#### Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

*Journal of Stochastic Analysis*

No abstract provided.

Construction Of The Canonical Representation From A Noncanonical Representation, 2022 Saga University, Saga, 8408502, JAPAN

#### Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino

*Journal of Stochastic Analysis*

No abstract provided.

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, 2022 University of Nebraska - Lincoln

#### Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

*Honors Theses, University of Nebraska-Lincoln*

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, 2022 University of Toronto, Toronto, ON, M5S 2E4, Canada

#### New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, Alexander Ya. Kreinin, Vladimir V. Vinogradov

*Journal of Stochastic Analysis*

No abstract provided.

Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, 2022 Université d’Évry Val d’Essonne, Laboratoire de Mathématiques et Modélisation, 23 Bd. de France, F-91037 Évry Cedex, France

#### Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, Adrien Barrasso, Francesco Russo

*Journal of Stochastic Analysis*

No abstract provided.

Teiresias, Proportions, And Sexual Pleasure, 2022 National and Kapodistrian University of Athens

#### Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis

*Journal of Humanistic Mathematics*

In this short article, I claim that Teiresias, the blind prophet of Apollo, in order to answer the question of whether “*in sexual intercourse the woman had a larger share of pleasure than the man did*”, measured the abstract concept of sexual pleasure and acted as a present-day scholar. With the help of numerical, not geometrical, proportions, he ended up with the conclusion “*a man enjoyed one-tenth of the pleasure and a woman nine-tenths*”.

Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, 2022 Hofstra University, Hempstead, NY 11549, USA

#### Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, Majnu John, Yihren Wu

*Journal of Stochastic Analysis*

No abstract provided.

Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), 2022 Belmont University

#### Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), Andrew J. Miller

*Numeracy*

Author Jane E. Miller has brought her considerable experience writing and teaching about numerate communication to a new textbook, *Making Sense of Numbers. *Miller uses clear prose, timely and authentic examples, and thought-provoking exercises to educate the next generation of consumers and producers of data, students in introductory quantitative reasoning, research methods, or data analysis courses. While the textbook does not fit the mold of a "typical" quantitative literacy course, creative instructors may find ways to use it in innovative quantitative literacy, data literacy, or introductory data science courses.

The Zagreb Index Of Several Random Models, 2022 University of Pennsylvania, Philadelphia, PA 19104, USA

#### The Zagreb Index Of Several Random Models, Panpan Zhang

*Journal of Stochastic Analysis*

No abstract provided.

Batch Normalization Preconditioning For Neural Network Training, 2022 University of Kentucky

#### Batch Normalization Preconditioning For Neural Network Training, Susanna Luisa Gertrude Lange

*Theses and Dissertations--Mathematics*

Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this work, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during training. This is designed to improve the Hessian matrix of the loss …

Finding Optimal Cayley Map Embeddings Using Genetic Algorithms, 2022 Rollins College

#### Finding Optimal Cayley Map Embeddings Using Genetic Algorithms, Jacob Buckelew

*Honors Program Theses*

Genetic algorithms are a commonly used metaheuristic search method aimed at solving complex optimization problems in a variety of fields. These types of algorithms lend themselves to problems that can incorporate stochastic elements, which allows for a wider search across a search space. However, the nature of the genetic algorithm can often cause challenges regarding time-consumption. Although the genetic algorithm may be widely applicable to various domains, it is not guaranteed that the algorithm will outperform other traditional search methods in solving problems specific to particular domains. In this paper, we test the feasibility of genetic algorithms in solving a …

Results On The Generalized Covering Radius Of Error Correcting Codes, 2022 Claremont Colleges

#### Results On The Generalized Covering Radius Of Error Correcting Codes, Benjamin Langton

*HMC Senior Theses*

The recently proposed generalized covering radius is a fundamental property of error correcting codes. This quantity characterizes the trade off between time and space complexity of certain algorithms when a code is used in them. However, for the most part very little is known about the generalized covering radius. My thesis seeks to expand on this field in several ways. First, a new upper bound on this quantity is established and compared to previous bounds. Second, this bound is used to derive a new algorithm for finding codewords within the generalized covering radius of a given vector, and also to …

An Exploration Of Voting With Partial Orders, 2022 Harvey Mudd College

#### An Exploration Of Voting With Partial Orders, Mason Acevedo

*HMC Senior Theses*

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, 2022 Georgia Southern University

#### 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.

Local Finiteness And Automorphism Groups Of Low Complexity Subshifts, 2022 University of Denver

#### Local Finiteness And Automorphism Groups Of Low Complexity Subshifts, Ronnie Pavlov, Scott Schmieding

*Mathematics: Faculty Scholarship*

We prove that for any transitive subshift X with word complexity function c_{n}(X), if lim inf(log(c_{n}(X)/n)/(log log log n)) = 0, then the quotient group Aut(X, σ)/〈 σ〉 of the automorphism group of X by the subgroup generated by the shift σ is locally finite. We prove that significantly weaker upper bounds on c_{n}(X) imply the same conclusion if the gap conjecture from geometric group theory is true. Our proofs rely on a general upper bound for the number of automorphisms of X of range n in terms of word complexity, which may be …

Local-Global Results On Discrete Structures, 2022 University of Denver

#### Local-Global Results On Discrete Structures, Alexander Lewis Stevens

*Electronic Theses and Dissertations*

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …