相关论文: Matroid bingo
The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are…
We study periodic linear trajectories in the double pentagon and periodic billiard trajectories in the regular pentagon.
Mutual imitation games among artificial birds are studied. By employing a variety of mappings and game rules, the evolution to the edge between chaos and windows is universally confirmed. Some other general features are observed, including…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
In this paper we investigate the distribution of zeros of Boubaker polynomials.
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the…
We give a beautiful explicit example of a convex plane curve such that the outer billiard has a given finite number of invariant curves. Moreover, the dynamics on these curves is a standard shift. This example can be considered as an outer…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of…
We introduce a notion of palindromicity of a natural number which is independent of the base. We study the existence and density of palindromic and multiple palindromic numbers, and we raise several related questions.
Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…
We give the asymptotic growth of the number of primitive periodic trajectories of a two dimensional dispersive billiard, when we prescribe their number of bounces on one of the obstacles.
Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…
We study combinatorial games under mis\`ere convention. Several sets of games have been considered earlier to better understand the behaviour of mis\`ere games. We here connect several of these sets. In particular, we prove that comparison…
We initiate the study of the natural multiplayer generalization of the classic continuous Colonel Blotto game. The two-player Blotto game, introduced by Borel as a model of resource competition across $n$ simultaneous fronts, has been…