In 1982 (see [1]) Imre Bárány observed that some of the classical theorems in convexity admit interesting and mysterious generalizations which he called “colorful theorems”. For example, the Colorful Helly Theorem says that if a family (repetitions of the same sets are allowed) of compact convex sets in Rk is colored (properly) with k+1 colors and it has the property that any choice of k+1 diff...

Apex predators play important roles in ecosystem functioning and, where they coexist, intraguild interactions can have profound effects on trophic relationships. Interactions between range from predation and competition to facilitation through scavenging opportunities. Despite the increased availability of fine-scale GPS data, determinants outcomes encounters apex remain understudied. We used s...

This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the problem networks, we start with distribution set of nodes that needs to be “transported” target accounting network topology. We exploit specific structure problem, characterized by computation implicit gradient steps, and formulate an based on discretized flows. As result, our...

A new source of attraction between similarly charged colloidal particles in ordered suspensions is considered. The attractive force is due to the correlation between the fluctuating displacements of the colloidal particles from their equilibrium positions in the colloid crystal lattice. The effective charge of a particle, the eigenfrequency and the energy of attraction are calculated on the bas...