Related papers: A simple characterization of tightness for convex …
A closed convex subset of a normed linear space is said to have the strong separation property if it can be strongly separated from every other disjoint closed and convex set by a closed hyperplane. In this paper we give some results on the…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
It is shown that (1) if a good set has finitely many related components, then they are full, (2) loops correspond one-to-one to extreme points of a convex set. Some other properties of good sets are discussed.
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random…
A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\Phi:X\to exp(X)$ such that $[x,y]\subset\Phi(x)\cup \Phi(y)$ for all $x,y\in X$. We prove that each convex subset of…
In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…
It is known that any open necklace with beads of $t$ types in which the number of beads of each type is divisible by $k$, can be partitioned by at most $(k-1)t$ cuts into intervals that can be distributed into $k$ collections, each…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
For a given element $f\in L^1$ and a convex cone $C\subset L^\infty$, $C\cap L^\infty_+=\{0\}$ we give necessary and sufficient conditions for the existence of an element $g\ge f$ lying in the polar of $C$. This polar is taken in…
This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand…
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…
We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…