Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two-dimensional metric continuum with a continuous median operator, for which there is no median-preserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negat...

In this paper, we characterize self-dual elements of a free distributive lattice with n generators by means of a median operation on this lattice. Hence, we obtain a constructive characterization of Sperner's families, for which H is equal to Tr H. We construct some infinite sequences of these families. These results generalize those of N. M. Rivi6re (J. Combinatorial Theory 5 (1968), 229-234) ...

We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity) which is satisfied by a random function and prove linear lower bounds on the size of PC refutations for a wide class of tautologies based on immune functions. As some applications of our techniques, we introduce modp Tseitin tautologies in th...

bstract. We present an order-statistics-based vector filter for the emoval of impulsive noise from color images. The filter preserves he edges and fine image details by switching between the identity no filtering) operation and the vector median filter operation based n the robust univariate median operator. Experiments on a diverse et of images and comparisons with state of the art filters sho...

2 Set up 1 2.1 R code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 cclust Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Prediction Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Print Function . . . . . . . . . . . . . . . . . . . . . . . . ...

Assume that Alice, Bob and Carol, each of whom privately holds a one-bit input, want to learn the value of the majority function of their inputs without revealing more of their own secret inputs than is necessary. In this paper, we show that such a secure majority computation can be done with a deck of real cards; specifically, the three players can learn only the majority of their inputs using...

We study a collective search process in which tentative proposals arrive sequentially and members of a committee decide whether to accept the current proposal or continue searching. The acceptance decision is made according to a (qualified) majority rule. We study which members have more impact on the decision, as well as the degree of randomness of the decision, as members get patient. When pr...

In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the statistical learning context, is still limited. In this study, within the statistical learning framework, we investigate correntropy based regression ...

We present a simple randomized construction of size O(n3) and depth 5:3logn+O(1) monotone circuits for the majority function on n variables. This result can be viewed as a reduction in the size and a partial derandomization of Valiant’s construction of an O(n5:3) monotone formula, [15]. On the other hand, compared with the deterministic monotone circuit obtained from the sorting network of Ajta...