The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ Rd and a gauge body B ⊂ Rd such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z), uB(L,Z), pB(L,Z), lB(L,Z)) given that Z ∩L = ∅, where Z is a Boolean model, dB(L...

A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ̄ and χ, respectively. A mixed hypergraph is called uniquely colo...

Biocontrol, or Biological Control, can be defined as the use of natural organisms, or genetically modified, genes or gene products, to reduce the effects of undesirable organisms to favour organisms useful to human, such as crops, trees, animals and beneficial microorganisms. This strategy of control is ecologicaly clean and compatible with different models of agriculture: organic, biological a...

This document contains several corrections and remarks for the Dynamic Cooperative Cleaners problem and for the CLEAN and SWEEP cleaning protocols, which were presented in previous works [1, 2].

We consider ancestry labeling schemes: Given a rooted tree T , assign a binary string (label) to each node, such that given the labels of any two nodes, one can determine whether the first is an ancestor of the second in T . Recently, Fraigniaud and Korman [STOC’10] showed that such labels can be assigned using log n+O(log log n) bits per label, solving a long standing open question and matchin...

We prove that if X is a Grassmannian of type A, then the Schubert basis (small) quantum cohomology ring QH(X) only homogeneous deformation ordinary multiplies with non-negative structure constants. This implies (three point, genus zero) Gromov-Witten invariants are uniquely determined by Witten's presentation and fact they non-negative. conjecture same true for any flag variety = G/P simply lac...