Related papers: Helly's Theorem--A Very Early Introduction
\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical homological algebra. We use set-theoretic \emph{elementary…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
Introducing the Boltzmann distribution very early in a statistical thermodynamics course (in the spirit of Feynmann) has many didactic advantages, in particular that of easily deriving the Gibbs entropy formula. In this note, a short…
The simplest epidemiologic model composed by mutually exclusive compartments SIR (susceptible-infected-susceptible) is presented to describe a reality. From health concerns to situations related with marketing, informatics or even…
Ensuring the usefulness of electronic data sources while providing necessary privacy guarantees is an important unsolved problem. This problem drives the need for an overarching analytical framework that can quantify the safety of…
Researchers find weaknesses in current strategies for protecting privacy in large datasets. Many anonymized datasets are reidentifiable, and norms for offering data subjects notice and consent over emphasize individual responsibility. Based…
This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra:…
We propose a combinatorial framework to analyze quantitative Helly-type questions. Using this framework, we prove a Quantitative Fractional Helly Theorem with Fractional Helly Number 3d and a stability version of the Quantitative Helly…
Elementary particle physics is gradually implemented into science curricula at high school level. However, common presentations on educational, semi-technical or popular level contain or support severe misconceptions. We discuss in…
HELM Learning (Helping Everyone Learn More) is the first online peer-to-peer learning platform which allows students (typically middle-to-high school students) to teach classes and students (typically elementary-to-middle school students)…
We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I.Barany and its…
Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. The ubiquity and…
As the adoption of explainable AI (XAI) continues to expand, the urgency to address its privacy implications intensifies. Despite a growing corpus of research in AI privacy and explainability, there is little attention on privacy-preserving…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
The application of semiparametric efficient estimators, particularly those that leverage machine learning, is rapidly expanding within epidemiology and causal inference. This literature is increasingly invoking the Riesz representation…
In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical…
In the fields of statistics and unsupervised machine learning a fundamental and well-studied problem is anomaly detection. Anomalies are difficult to define, yet many algorithms have been proposed. Underlying the approaches is the nebulous…
Transfer learning has become a common solution to address training data scarcity in practice. It trains a specified student model by reusing or fine-tuning early layers of a well-trained teacher model that is usually publicly available.…
The proliferation of vast quantities of available datasets that are large and complex in nature has challenged universities to keep up with the demand for graduates trained in both the statistical and the computational set of skills…