MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP equivalent terms given b...

We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grasmannian is viewed as a Poisson homogeneous space of the general linear group equipped wit...

For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is primarily of interest to show two things: First, it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool for computing the measure ...

Adaptation and self-organization are two main aspects of swarm mechanisms and collective intelligence. We adress here the global question of controlling the coordination of groups of mobile agents in order to achieve optimization processings. We study in this paper a simple case involving “logistic“ agents –whose internal decision is governed by a logistic map, that is a discrete parametrized q...

We present a structural attack on the DME cryptosystem with parameters ( 3 , 2 q ) . The recovers 10 of 12 coefficients first linear map. also show that, if those were known, rest private key can be efficiently obtained by solving systems quadratic equations just two variables.

in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

The notion of Misiurewicz maps has its origin from the paper [10] from 1981 by M. Misiurewicz. The (real) maps studied in this paper have, among other things, no sinks and the omega limit set ω(c) of every critical point c does not contain any critical point. In particular, in the quadratic family fa(x) = 1 − ax 2, where a ∈ (0, 2), a Misiurewicz map is a non-hyperbolic map where the critical p...

A combinatorial map is a topological model that can represent the subdivisions of space into cells and their adjacency relations in n dimensions. This data structure is increasingly used in image processing, but it still lacks tools for analysis. Our goal is to define new tools for combinatorial maps nD. We are particularly interested in the extraction of submaps in a database of maps. We defin...

Given a finite set T of maps on a finite ring R, we look at the finite simple graph G = (V,E) with vertex set V = R and edge set E = {(a, b) | ∃t ∈ T, b = t(a), and b 6= a}. An example is when R = Zn and T consists of a finite set of quadratic maps Ti(x) = x 2 + ai. Graphs defined like that have a surprisingly rich structure. This holds especially in an algebraic setup when T is generated by po...

1. Introduction. In 1844, a list of 11 open problems composed by Eisen-stein was published in Crelle's journal [7]. Among these problems, which are rather diverse in nature and precision, there are three that pertain to class groups of quadratic orders. Class groups of other orders were still unknown at that time, and Eisenstein's questions are couched in Gauss's language of quadratic forms. In...