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The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…

The rapid advancement of Large Language Models (LLMs) has significantly influenced various domains, leveraging their exceptional few-shot and zero-shot learning capabilities. In this work, we aim to explore and understand the LLMs-based…

While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study…

Large-Language Models (LLMs) are changing the way learners acquire knowledge outside the classroom setting. Previous studies have shown that LLMs seem effective in generating to short and simple questions in introductory CS courses using…

We revisit the solvable lattice models described by Andrews Baxter and Forrester and their generalizations. The expressions for the local state probabilities were shown to be related to characters of the minimal models. We recompute these…

This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…

We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…

In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend the method of Michel-Venkatesh to reduce the bounds…

We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose…

This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…

We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.

We establish results on the rationality of ratios of successive critical values of Langlands-Shahidi $L$-functions, as they appear in the constant term of the Eisenstein series associated with the exceptional group of type $G_2$ over a…

Randomized rounding is a standard method, based on the probabilistic method, for designing combinatorial approximation algorithms. In Raghavan's seminal paper introducing the method (1988), he writes: "The time taken to solve the linear…

We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.

A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…

Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last three decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various…

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

We revisit several entries from Ramanujan's notebooks which follow from more elementary arguments than a first glance may suggest. Our goal is to demystify these results through more accessible proofs, while also shining some light on the…