In addition to statistical graph properties (diameter, degree, clustering, ...), Kleinberg [7] showed that a small-world can also be seen as a graph in which the routing task can be efficiently and easily done in spite of a lack of global knowledge. More precisely, in a lattice network augmented by extra random edges (but not chosen uniformly), a short path of polylogarithmic expected length ca...

A graph homomorphism from a graph G to a graph H is a mapping h : V (G)→ V (H) such that h(u) ∼ h(v) if u ∼ v. Graph homomorphisms are well studied objects and, for suitable choices of eitherG orH, many classical graph properties can be formulated in terms of homomorphisms. For example the question of wether there exists a homomorphism from G to H = Kq is the same as asking wether G is q-colour...

It is well-known that the set of h -terms modulo &-convertibility is a semi-group with I as identity element and composition 0, defined by M 0 N = BMN, where B = hxyt . x(yz). In [6, pp. 167,168] the question is raised under what conditions an element in this semi-group has an inverse. DezanXiancaglini gave in [8] a characterization of (w.r.t. A&-calculus) invertible terms having a normal form ...

I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algori...

An interatomic potential model has been developed for molecular-dynamics simulations of TiO2 ~rutile! based on the formalism of Streitz and Mintmire @J. Adhes. Sci. Technol. 8, 853 ~1994!#, in which atomic charges vary dynamically according to the generalized electronegativity equalization principle. The present model potential reproduces the vibrational density of states, the pressure-dependen...

Given a graph G, the (graph theory) general position problem is to find the maximum number of vertices such that no three vertices lie on a common geodesic. This graph invariant is called the general position number (gpnumber for short) of G and denoted by gp(G). In this paper, the gp-number is determined for a large class of subgraphs of the infinite grid graph and for the infinite diagonal gr...

This paper shows that the core outcomes of the assignment game coincides with the set of fixed points of a certain function. The lattice property of the core, as well as its non-emptiness, are proved using Tarski’s fixed point

NTRU public key cryptosystem is well studied lattice-based Cryptosystem along with Ajtai-Dwork and GGH systems. Underlying NTRU is a hard mathematical problem of finding short vectors in a certain lattice. (Shamir 1997) presented a lattice-based attack by which he could find the original secret key or alternate key. Shamir concluded if one designs a variant of NTRU where the calculations involv...

A point set satisses the Steinhaus property if no matter how it is placed on a plane, it covers exactly one integer lattice point. Whether or not such a set exists, is an open problem. Beck has proved 1] that any bounded set satisfying the Steinhaus property is not Lebesgue measurable. We show that any such set (bounded or not) must have empty interior. As a corollary, we deduce that closed set...