Related papers: Extreme Points and Large Contests

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…

Inspired in the theorem of Krein-Milamn, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite dimensional case, giving a geometric description of all…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…

We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…

We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring…

Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…

In finite problems comprising objects, situations, and an object- and situation-contingent payoff function, we study the comparative statics of the set of undominated objects, meaning those for which there exists no mixture over objects…

This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…

In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure…

This paper investigates applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for characterisation of systems with transitive competition when mutations deviate from Gibbs…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry…

In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…