Abstract We study the minimization of a rank-one quadratic with indicators and show that underlying set function obtained by projecting out continuous variables is supermodular. Although supermodular is, in general, difficult, specific for can be minimized linear time. convex hull epigraph from inequalities lifting them into nonlinear original space variables. Explicit forms convex-hull descrip...

The main usage of supermodular functions is to cross out tight sets, that is to use only the following important property. The intersection and the union of two sets with a maximal function value also have maximal function value. But for this purpose we do not need the full strength of supermodularity, some weaker concept suffices. We introduce here a new property, the so called λsupermodularit...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. Therefore we also show that for an...

The forward estimation problem for stationary and ergodic time series {X n } ∞ n=0 taking values from a finite alphabet X is to estimate the probability that X n+1 = x based on the observations X i , 0 ≤ i ≤ n without prior knowledge of the distribution of the process {X n }. We present a simple procedure g n which is evaluated on the data)| → 0 almost surely for a subclass of all stationary an...

In the present study, we construct a new matrix which call quasi-Cesaro and is generalization of ordinary Cesaro matrix, introduce $BK$-spaces $C^q_k$ $C^q_{\infty}$ as domain $C^q$ in spaces $\ell_k$ $\ell_{\infty},$ respectively. Furthermore, exhibit some topological properties inclusion relations related to these newly defined spaces. We determine basis space obtain Köthe duals $C^q_{\infty}...

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing results on increasing differences and supermodularit...

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex coneH of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are eq...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...