Related papers: Helly's Theorem--A Very Early Introduction

This is the first in a series of papers that analyze college student beliefs in realms where common astronomy misconceptions are prevalent. Data was collected through administration of an inventory distributed at the end of an introductory…

We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed R\'enyi mutual…

We introduce and study a new class of $\eps$-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how $\eps$-convex…

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in…

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

Age structure is incorporated in many types of epidemic model. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of…

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent…

Statistics students need to develop the capacity to make sense of the staggering amount of information collected in our increasingly data-centered world. Data science is an important part of modern statistics, but our introductory and…

This two-part paper presents a new approach to predictive analysis for social processes. In Part I, we begin by identifying a class of social processes which are simultaneously important in applications and difficult to predict using…

Hierarchical multi-label classification (HMLC) is essential for modeling complex label dependencies in remote sensing. Existing methods, however, struggle with multi-path hierarchies where instances belong to multiple branches, and they…

The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose…

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous…

This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…

Absenteeism of elementary school children has been shown to be effective in the early detection of an incoming influenza epidemic within a given population. This paper introduces DESA, an R package designed to: 1) model an epidemic using…

The modeling theory of instruction is widely applied and highly successful in high-school instruction, and seldom in university physics. One reason is lack of familiarity with models in the physics classroom. Ongoing curriculum development…

There has been much recent interest in modelling epidemics on networks, particularly in the presence of substantial clustering. Here, we develop pairwise methods to answer questions that are often addressed using epidemic models, in…

Stewards of social science data face a fundamental tension. On one hand, they want to make their data accessible to as many researchers as possible to facilitate new discoveries. At the same time, they want to restrict access to their data…