A theorem of McCann [15] shows that for any two absolutely continuous probability measures on Rd there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that density estimation can be recast in terms of transformations. In particular, one can fix any absolutely continuous probability measure, call it P, and t...

Problem: Determine the complex structure of the stable manifolds of f . It is not hard to see, using f(W s p ) = W s fp, that W s p is a monotone union of balls, and this in turn implies [Br] that it is diffeomorphic to real Euclidean space. Moreover, by the contracting nature of the dynamics, one sees that the Kobayashi pseudometric of W s p vanishes identically. However, when dim(W s p ) ≥ 3,...

Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose fidelity based valid measure purity monotone establish relationship between them. This formulation is extended to correlation relative measurement. We have also studied the role weak measurement on purity.

In this paper we consider the following covering problem. Given a set S of n points in d-dimensional space, d 2, nd two axis-parallel boxes that together cover the set S such that the measure of the largest box is minimized, where the measure is a monotone function of the box. We present a simple algorithm for nding boxes in O(n log n + n d?1) time and O(n) space.

For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent [Formula: see text] holds shy set in measure-theoretic sense. This exhibits admit no observable chaos, notion of which was formulated by L.S. Young. We further such phenomenon chaos is robust under text]-perturbation systems.

We revise the geometric measure of entanglement (GME). The revised geometric measure of entanglement (RGME) is an entanglement monotone. Some useful inequalities about RGME are deduced. As the RGME’s application, the twoparameter class of states in 2⊗ n quantum system, the two particles high dimensional maximally entangled mixed state, the isotropic state including n-particle d-level case and t...

We give an algorithm that learns any monotone Boolean function f : {−1, 1}n → {−1, 1}to any constant accuracy, under the uniform distribution, in time polynomial in n and in thedecision tree size of f. This is the first algorithm that can learn arbitrary monotone Booleanfunctions to high accuracy, using random examples only, in time polynomial in a reasonablemeasure of the c...

in this paper, some recent results established by marin borcut [m. borcut, tripled fixed point theorems for monotone mappings in partially ordered metric spaces, carpathian j. math. 28, 2 (2012), 207--214] and [m. borcut, tripled coincidence theorems for monotone mappings in partially ordered metric spaces, creat. math. inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207--214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...