Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers.,
2025
Dakota Wesleyan University
Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers., Michael T. Catalano
Numeracy
Tom Chivers’ Everything is Predictable: How Bayesian Statistics Explain Our World, is an interesting and wide-ranging narrative on Bayesian thinking, its history, and its applicability to both our everyday lives and the pursuit of scientific truth. Although appropriate for the non-expert, afficionados and teachers of quantitative literacy should find the plethora of examples, links to psychology as it applies to how people reason about probabilities, and even Chivers’ philosophical musings informative and thought-provoking.
Operator Information Quantities Of Semigroups Associated With Functions Of The Number Operator,
2025
Department of Mathematics, Meijo University
Operator Information Quantities Of Semigroups Associated With Functions Of The Number Operator, Ryo Inayoshi, Kimiaki Saito
Journal of Stochastic Analysis
In this paper, we present recent developments on the operator information quantity acting on white noise functionals. In particular, we give a stochastic expression of the operator information quantity of a semigroup generated by some function of the number operator through a white noise delta distribution centered at an infinite dimensional Ornstein-Uhlenbeck process.
Frieze Symmetry Patterns Of Pennsylvania German Fraktur,
2025
Dickinson College
Frieze Symmetry Patterns Of Pennsylvania German Fraktur, Lorelei Koss
LASER Journal
Fraktur is an American folk art developed by German-speaking communities in Pennsylvania, New Jersey, Ohio, Virginia, Maryland, and North Carolina during the 18th and 19th centuries. This art form features ornate calligraphy combined with illustrations of flowers, birds, angels, and geometric border designs. It was often used for birth and baptismal certificates, religious texts, educational materials, and public notices. Fraktur commonly incorporates frieze pattern designs. Artistic designs based on frieze patterns appear across a wide range of cultures, and research has shown that cultural groups tend to favor certain types of frieze patterns. This paper investigates which types of frieze …
An Elementary Approach To The Probability Distribution Of The Product Of Multiple Random Variables,
2025
Tianjin University, Tianjin
An Elementary Approach To The Probability Distribution Of The Product Of Multiple Random Variables, Suwen Tian
Rose-Hulman Undergraduate Mathematics Journal
Abstract There arenindependent identically distributed (i.i.d.) uniform random variables defined as ξ1,ξ2,…,ξn, valued in interval [0,k](k>0), and there is a constantmvalued in interval (0,kn). We study the distribution of the product of these random numbers and prove a formula calculating Pr(∏i=1nξi≤m). Interestingly, we find that the result is exactly the sum of the firstnterms in the Taylor series expansion of the function exp(x) with x=nlnk-lnm. Through considering the corresponding probability density function, we make an extension of the formula calculating Pr(∏i=1nξi≤m) to any positive realn, and the extended formula can be written in a …
Exploring The Exceptional Extreme Rays Of The Copositive Cone,
2025
Northern Michigan University
Exploring The Exceptional Extreme Rays Of The Copositive Cone, Trent Holmgren
All NMU Master's Theses
In this paper we will look at the exceptional extreme rays of COP^5 and COP^6 and identify if they are exposed or nonexposed. We start with some necessary background material on copositive matrices and cones. Then we construct two algorithms to see if a matrix is exposed or nonexposed.
Machine Learning: Neural Networking With Relu And Optimization,
2025
University of Denver
Machine Learning: Neural Networking With Relu And Optimization, Aidan Redmond Brownell
Undergraduate Theses, Capstones, and Recitals
At its core, learning is an algorithmic process: it begins with input data, undergoes a series of transformations or computations, and yields an output intended to solve a specific task. This output is then compared against a target or desired result, and the internal mechanisms are updated based on how well the output aligns with expectations. While this feedback-driven process occurs almost effortlessly in humans, it is a far more structured, deliberate, and computationally intensive undertaking for machines.
Basic Theory And Implementations Of Quantum Error Correction,
2025
University of Denver
Basic Theory And Implementations Of Quantum Error Correction, Derek Rodriguez
Undergraduate Theses, Capstones, and Recitals
The introduction of quantum computing has presented algorithmic solutions to computationally difficult challenges that are far more efficient than those of classical computers. These algorithms leverage the properties of quantum mechanics to manipulate the quantum properties of subatomic particles, requiring immense precision and stability. Current quantum hardware, however, is too noisy and introduces too many errors for these algorithms to be useful in practice, necessitating the use of error correction algorithms. This field survey seeks to introduce various principles of quantum mechanics relevant to quantum computing and quantum error correction (QEC), detail the implementation and motivations of a basic QEC …
A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting,
2025
Portland State University
A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting, Takeshi Stormer
University Honors Theses
Fuzzy mathematics looks to incorporate the vagueness that exists within the real world, specifically regarding imprecise classes, or non-numerical information expressed as "linguistic" variables. Since most traditional mathematical theories do not have the ability to be applied with the exactness that is otherwise seen in mathematics. As such, there had been many applications of fuzzy mathematics throughout many different fields of mathematics, including that of forecasting. By exploring the fundamentals of fuzzy mathematics, including fuzzy sets, operations of fuzzy sets, the surface level introduction to fuzzy logic, fuzzy relations, operations of fuzzy relations, and fuzzy time-series, this work looks to …
On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications,
2025
Chuo University
On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications, Takahiko Fujita, Naohiro Yoshida
Journal of Stochastic Analysis
In this note, some applications of excursions associated with a certain local time of simple symmetric random walks are presented. Specifically, the excursions are applied to calculate some probability distributions of interest regarding the random walks. Furthermore, a solution of the Skorokhod embedding problem for random walks is obtained through the excursions.
Tilings In The 3 Dimensional Lattice With L-Tetrominoes,
2025
Florida State University
Tilings In The 3 Dimensional Lattice With L-Tetrominoes, Ian N. Bridges
Rose-Hulman Undergraduate Mathematics Journal
We consider three dimensional L-tetrominoes. We show that there exists at least one way to tile every three dimensional rectangle whose side lengths are at least $3$ and area is congruent to $1 \pmod 4$ such that one square goes untiled. In addition, we show that every three dimensional rectangle is tileable provided one side has length at least $2$ and the other is a multiple of $4$.
Banach Algebras And The Gelfand Theory Of Group Algebras On Locally Compact Abelian Groups,
2025
California Polytechnic State University, San Luis Obispo
Banach Algebras And The Gelfand Theory Of Group Algebras On Locally Compact Abelian Groups, James Gabriel Bonvanie
Master's Theses
A Banach algebra is a complex algebra that is simultaneously a Banach space in which the norm is submultiplicative. Notably, $L^1(\mathbb{R})$ with the convolutional product is an Abelian, non-unital Banach algebra that admits an approximate identity. We rectify $L^1(\mathbb{R})$ lacking a unit via the unitization $L^1(\mathbb{R})\times\mathbb{C}$ with identity $(0,1)$. Unitization opens the discussion to the spectrum $\sigma(x)$ of a Banach algebra element, in which the spectrum is a nonempty, compact subset of the complex plane. The spectrum of an Abelian Banach algebra is fully characterized with multiplicative linear functionals, and we prove that the Fourier transform is the unique multiplicative …
A Novel Closed Monoidal Structure On The Nucleus Of A Profunctor,
2025
CUNY Graduate Center
A Novel Closed Monoidal Structure On The Nucleus Of A Profunctor, Samantha K. Jarvis
Dissertations, Theses, and Capstone Projects
We describe a novel closed monoidal structure on the nucleus of a profunctor enriched over a posetal category, a distinguished subcategory of the category of presheaves given by the invariant part of an adjunction induced by the profunctor. Our structure is motivated by a connection to a notion of type given by orthogonality. For specific examples, we consider the two-element enriching category {0,1} and the reals.
The Jacod-Yor Theorem For Sigma Martingales And The Second Fundamental,
2025
University of South Africa, University of Finance and Administration Prague
The Jacod-Yor Theorem For Sigma Martingales And The Second Fundamental, Moritz Sohns
Journal of Stochastic Analysis
In this paper, we prove the Jacod-Yor Theorem for sigma martingales, a class of processes that generalize local martingales and play a pivotal role in financial mathematics. While the Jacod-Yor Theorem has been extensively studied for L2-martingales, martingales, and local martingales, no prior version exists for sigma martingales. Our result establishes the connection between sigma martingales and their martingale representation properties, addressing a critical gap in the literature. As an application, we prove the Second Fundamental Theorem of Asset Pricing for markets where price processes are modeled as sigma martingales.
Similarity Metrics, Metrics, And Conditionally Negative Definite Functions,
2025
Chapman University
Similarity Metrics, Metrics, And Conditionally Negative Definite Functions, Daniel Alpay, Liora Mayats-Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give an example of a similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Analyticity, Superoscillations And Supershifts In Several Variables,
2025
Politecnico di Milano
Analyticity, Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing their highest Fourier component. A different way of thinking about superoscillations consists in realizing that it is possible to reproduce the exponential function far away from the origin by only knowing its value in a countable set of points near the origin. By using this perspective, one can extend the idea of superoscillations to functions that are not a sum of exponential functions, namely to the notion of supershift. The study …
Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions,
2025
Texas A&M International University
Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr
Theses and Dissertations
A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. …
Statistics - What Does My Data Say About Me?,
2025
Chapman University
Statistics - What Does My Data Say About Me?, Taylor Gadsden-Deterville
Student Scholar Symposium Abstracts and Posters
For my Introduction to Statistics Class, I have been tasked with collecting unique, personal data to give insight into my daily routine. I decided to record nine different outcomes (two qualitative and seven quantitative). On February 6, 2025, I began with a blank Excel sheet, and so far, I have 57 full days of data collected. I will continue monitoring my findings for the remainder of the Spring 2025 Semester. Per my project instructions, I must include tables and graphs for my qualitative and quantitative outcomes. So far, I have collected daily quantitative data on my screen time (Instagram and …
A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring,
2025
Texas A&M International University
A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring, Jesus A. Mendiola Herrera
Theses and Dissertations
In 1890, David Hilbert published a set of notes on what now constitutes one of the bases of Commutative Algebra; his work would eventually influence the efforts of mathematicians like Ernst Kunz. In 1969, Ernst Kunz introduced a particular mapping regarding modules of regular local rings. His goal was to characterize Noetherian local rings of prime characteristic by computing the length of the composition series under Frobenius power transformations. In this thesis, the focus will be on stating the initial steps on finding the coefficients of the Hilbert-Kunz function of the normal affine semigroup ring of the form R = …
On The Hexgame,
2025
Rose-Hulman Institute of Technology
On The Hexgame, Corwin Jones
Mathematical Sciences Technical Reports (MSTR)
The SOMA Cube has been studied by mathematicians for a number of decades, but so far methods for solving three-dimensional space-filling puzzles like the SOMA cube remain numerical; we do not have a means to predict the number of solutions to SOMA-like puzzles. We present a two-dimensional puzzle that shares certain features of the SOMA Cube, with the hope that it will be a more convenient object of study for future research into space-filling/space-covering puzzles.
Analysis And Mathematical Recomposition Of The Art Of The Fugue,
2025
Montclair State University
Analysis And Mathematical Recomposition Of The Art Of The Fugue, Joshua Cellar
Theses, Dissertations and Culminating Projects
The Art of the Fugue is a collection of 18 fugues and cannons written by Johann Sebastian Bach in the 1700s. Each piece starts with a single theme which is transformed, developed and mixed in fascinating mathematical combinations resulting in a distinctive musical style. In this paper, we use the method introduced in [7] to analyze 14 pieces from The Art of the Fugue. We focus on the variation of motifs from one piece to another as well as the complexities of mathematical transformations present throughout the entire collection. We also demonstrate how using maps of transformations and the rules …
