Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…
The first half of the 20th century in the history of Russian mathematics is striking with a combination of dramaticism, sometimes a tragedy, and outstanding achievements. The paper is devoted to St. Petersburg-Leningrad Mathematical School.…
These notes were intended as support material for a minicourse on Anosov flows in the conference "Symplectic geometry and Anosov flows'' which took place in Heidelberg in July 2024 organized by Peter Albers, Jonathan Bowden and Agust\'in…
The purpose of this expository article is to revisit the notions of amenability and ergodicity, and to point out that they appear for topological groups that are not necessarily locally compact in articles by Bogolyubov (1939), Fomin…
Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov-Sinai entropy from the setting of amenable groups. Some parts…
Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation…
Goeman and Solari [Statist. Sci. 26 (2011) 584-597, arXiv:1208.2841] have addressed the interesting topic of multiple testing for exploratory research, and provided us with nice suggestions for exploratory analysis. They defined properties…
The notion of cobordism of singular maps was introduced around 1980 by A. Sz\H{u}cs and U. Koschorke independently. As an application, Sz\H{u}cs used it to compute cobordism groups of immersions and embeddings in dimensions where the…
We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur…
This paper realises the Khovanov homology of a link in the 3-sphere as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for…
In this informal report, I outline my research efforts, collaborations, and other experiences while participating in the Naval Research Laboratory (NRL)'s Advanced Graduate Research Program (AGRP), aka Sabbatical, from October 2008 through…
These lecture notes, which were designed for the Summer School "Heegaard-Floer Homology and Khovanov Homology" in Marseilles, 29th May - 2nd June, 2006, provide an elementary introduction to Khovanov homology. The intended audience is…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
In 1980 Kowal and Drake found that in December 1612 and January 1613 Galileo observed the planet Neptune. At that time, according to these authors, Galileo was able to measure angular separations with an accuracy of about 10 seconds of arc.…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
As well-known, transition probabilities of jump Markov processes satisfy Kolmogorov's backward and forward equations. In the seminal 1940 paper, William Feller investigated solutions of Kolmogorov's equations for jump Markov processes.…
The Kolmogorov-Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally-obtained datasets for regression…
The study of semifeasible algorithms was initiated by Selman's work a quarter of century ago [Sel79,Sel81,Sel82]. Informally put, this research stream studies the power of those sets L for which there is a deterministic (or in some cases,…
Conway and Ryba considered a table of bi-infinite Fibonacci sequences and discovered new interesting patterns. We extend their considerations to tables that are defined by the recurrence $X_{n+1}=dX_n+X_{n-1}$ for natural numbers $d$. In…
This paper addresses the growing concern of cascading extreme events, such as an extreme earthquake followed by a tsunami, by presenting a novel method for risk assessment focused on these domino effects. The proposed approach develops an…
Gelfand and Ponomarev [Functional Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous…