Keywords: Monotone measure Atom Weak null-additivity Regularity Sugeno integral Choquet integral a b s t r a c t In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by...

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.

In this paper, we investigate Egoroff's theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff's theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff's theorem for non-additive measure is formulated in full generality.

In this paper, we extend monotone monomials as large itemsets in association rule mining to monotone DNF formulas. First, we introduce not only the minimum support but also the maximum overlap, which is a new measure how much all pairs of two monomials in a monotone DNF formula commonly cover data. Next, we design the algorithm dnf cover to extract coverings as monotone DNF formulas satisfying ...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Matrix monotone functions and relative modular operators are used. The origin is the relative entropy and the f -divergence, monotone metrics, covariance and the χ2 divergence are the most important particular cases. The extension of the monotone metric to two variables is a new concept.

It is proved that there is a monotone function in AC(0) 4 which requires exponential size monotone perceptrons of depth 3. This solves the monotone version of a problem which, in the general case, would imply an oracle separation of PPPH.

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms. keywords: Non Monotone, Lineal Search, Trust Region.

In this paper we study the lower bounds problem for monotone circuits. The main goal is to extend and simplify the well known method of approximations proposed by A. Razborov in 1985. The main result is the following combi-natorial criterion for the monotone circuit complexity: a monotone Boolean

This paper gives the first correlation bounds under product distributions (including the uniform distribution) against the class mNC of poly(n)-size O(log n)-depth monotone circuits. Our main theorem, proved using the pathset complexity framework recently introduced in [56], shows that the average-case k-CYCLE problem (on Erdős-Rényi random graphs with an appropriate edge density) is 12 + 1 pol...