Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and…
We present an algorithm that takes a discrete random variable $X$ and a number $m$ and computes a random variable whose support (set of possible outcomes) is of size at most $m$ and whose Kolmogorov distance from $X$ is minimal. In addition…
We have recently passed the 75th anniversary of one of the most important results in solar and space physics: Hannes Alfv\'en's discovery of Alfv\'en waves and the Alfv\'en speed. To celebrate the anniversary, this article recounts some…
In this paper we consider Montevideo's liberal progressive atmosphere towards the end of the nineteenth century and, within it, the trajectory of young science student Enrique Loedel Palumbo. We discuss some of his activities in Argentina,…
In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic sets as part of his solution of Shub's entropy conjecture for $C^\infty$ maps. The statement was further refined by Gromov, producing what is now known as the…
This paper is devoted to the extension of the regret lower bound beyond ergodic Markov decision processes (MDPs) in the problem dependent setting. While the regret lower bound for ergodic MDPs is well-known and reached by tractable…
Both resources in the natural environment and concepts in a semantic space are distributed "patchily", with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have…
In 1965 Adler, Konheim and McAndrew defined the topological entropy for continuous self-maps of compact spaces. Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is…
Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas.…
We report on the first results of experiments to measure the recombination rate of hydrogen on surfaces of astrophysical interest. Our measurements give lower values for the recombination efficiency (sticking probability S x probability of…
The theory of elliptic pairs, as investigated in a paper by Castravet, Laface, Tevelev, and Ugaglia, provides useful conditions to determine polyhedrality of the pseudo-effective cone, which give rise to interesting arithmetic questions…
This paper traces the early history of the Aharonov-Bohm effect. It appears to have been `discovered' at least three times to my knowledge before the defining paper of Aharonov and Bohm appeared in 1959. The first hint of the effect appears…
We two had year-long research leaves in Japan, working together fulltime with several Japanese plus Tony De Groot back in Livermore and Harald Posch in Vienna. We summarize a few of the high spots from that very productive year ( 1989-1990…
The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…
The game-theoretic version of Kolmogorov's strong law of large numbers says that Skeptic has a strategy forcing the statement of the law in a game of prediction involving Reality, Forecaster, and Skeptic. This note describes a simple…
We have carried out a coordinated experimental and theoretical study of single-electron traps based on submicron aluminum islands and aluminum oxide tunnel junctions. The results of geometrical modeling using a modified version of MIT's…
Invited Talk presented at the First Arctic Workshop on Particle Physics, Saariselkae, August 1994 and at the Workshop on Elementary Particles and Quantum Field Theory, Moscow, September 1994
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
In the symmetric rendezvous search game played on Kn (the completely connected graph on n vertices) two players are initially placed at two distinct vertices (called locations). The game is played in discrete steps and at each step each…