Related papers: Helly's Theorem--A Very Early Introduction
I give a short introduction to data ethics. I begin with some background information and societal context for data ethics. I then discuss data ethics in mathematical-science education and indicate some available course material. I briefly…
Statistics is running the risk of appearing irrelevant to today's undergraduate students. Today's undergraduate students are familiar with data science projects and they judge statistics against what they have seen. Statistics, especially…
One of the major views of privacy associates privacy with the control over information. This gives rise to the question how controllable privacy actually is. In this paper, we adapt certain formal methods of control theory and investigate…
In this paper, we present a variety of problems in the interface between combinatorics and geometry around the theorems of Helly, Radon, Carath\'eodory, and Tverberg. Through these problems we describe the fascinating area of Helly-type…
In Semi-Supervised Semi-Private (SP) learning, the learner has access to both public unlabelled and private labelled data. We propose a computationally efficient algorithm that, under mild assumptions on the data, provably achieves…
Although there are various ways to represent data patterns and models, visualization has been primarily taught in many data science courses for its efficiency. Such vision-dependent output may cause critical barriers against those who are…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national level. However, the epidemic models…
A large amount of information has been published to online social networks every day. Individual privacy-related information is also possibly disclosed unconsciously by the end-users. Identifying privacy-related data and protecting the…
Leakage of data from publicly available Machine Learning (ML) models is an area of growing significance as commercial and government applications of ML can draw on multiple sources of data, potentially including users' and clients'…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
The epidemiology has recently witnessed great advances based on computational models. Its scope and impact are getting wider thanks to the new data sources feeding analytical frameworks and models. Besides traditional variables considered…
We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Since social interactions have been shown to lead to symmetric clusters, we propose here that symmetries play a key role in epidemic modeling. Mathematical models on d-ary tree graphs were recently shown to be particularly effective for…
As Large Language Models (LLMs) become integral to scientific workflows, concerns over the confidentiality and ethical handling of confidential data have emerged. This paper explores data exposure risks through LLM-powered scientific tools,…
Research in epidemiology often focusses on designing interventions that result in the number of infected individuals asymptotically approaching zero, without considering that this number may peak at high values during transients. Recent…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
These are lecture notes for a minicourse on group actions on injective spaces and Helly graphs, given at the CRM Montreal in June 2023. We review the basics of injective metric spaces and Helly graphs, emphasizing the parallel between the…