Related papers: SPM Bulletin 2
We present a quantitative, data-driven machine learning approach to mitigate the problem of unpredictability of Computer Science Graduate School Admissions. In this paper, we discuss the possibility of a system which may help prospective…
The words ``Programming is the second literacy'' were coined more than 40 years ago but never came to life. This paper is one in the series of papers aimed at the analysis of mathematical requirements for a merge of school mathematics with…
This Resource Letter provides a guide to some of the the introductory and review literature in string theory. It is in no way complete, though it is intended to be of use to students at several levels. Owing to the nature of the subject,…
Spin, $s$ in quantum theory can assume only half odd integer or integer values. For a given $s$, there exist $n=2s+1$ states $|s,m\rangle$, $m=s,s-1,........,-s$. A statistical assembly of particles (like a beam or target employed in…
The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
This paper aims to justify the use of statistical mechanics tools in situations where the system is out of equilibrium and jammed. Specifically, we derive a Boltzmann equation for a jammed granular system and show that the Boltzmann's…
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
The first chapter serves as an introduction to the MSSM. I briefly review the model and explain why stops and sbottoms provide an interesting playground for exploring and testing this model. In the second chapter I discuss stop and sbottom…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
Search engines are the most important tools for web data acquisition. Web pages are crawled and indexed by search Engines. Users typically locate useful web pages by querying a search engine. One of the challenges in search engines…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
Spreadsheet engineering adapts the lessons of software engineering to spreadsheets, providing eight principles as a framework for organizing spreadsheet programming recommendations. Spreadsheets raise issues inadequately addressed by…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
CONTENTS: New reals: Can live with them, can live without them; Uniform almost everywhere domination; Heredity of tau-pseudocompactness; Understanding preservation theorems: omega^omega-bounding; Classification problems in continuum theory;…
We introduce factorize sum split product networks (FSPNs), a new class of probabilistic graphical models (PGMs). FSPNs are designed to overcome the drawbacks of existing PGMs in terms of estimation accuracy and inference efficiency.…
This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…
In the first part of this study (Paper I), we introduced the systematic improvement probability (SIP) as a tool to assess the level of improvement on absolute errors to be expected when switching between two computational chemistry methods.…
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…