相关论文: Hoeffding's inequality in game-theoretic probabili…

We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give a affirmative answer to the analogue in this setting of a famous conjecture of…

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…

We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of…

This article presents a new game semantics for Martin-L\"of type theory (MLTT), in which each game is equipped with selected isomorphism strategies that represent (computational) proofs for (intensional) equality between strategies on the…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game---a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically…

Fairness of machine learning algorithms has been of increasing interest. In order to suppress or eliminate discrimination in prediction, various notions as well as approaches have been proposed to impose fairness. Given a notion of…

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in positive integers inspired by the classical proof of the…

This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using…

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

Many fundamental problems in extremal combinatorics are equivalent to proving certain polynomial inequalities in graph homomorphism densities. In 2011, a breakthrough result by Hatami and Norine showed that it is undecidable to verify…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

The relations between Bell's inequality and quantum probability trees are explained against the background offered by the concept of a quantum probability tree built in others works. It is shown that f we use a concept of probability tree…

We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both…

In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.