In this paper we prove new results about the extremal structure of paths in directed graphs. Say we are given a directed graph G = (V,E) on n nodes, a set of sources S ⊆ V of size |S| = n, and a subset P ⊆ S × V of pairs (s, t) where s ∈ S, of size O(n), such that for all pairs (s, t) ∈ P , there is a path from s to t. Our goal is to remove as many edges from G as possible while maintaining the...

It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G = (V,E): (1) an exact conflict constraint is an edge set C ⊆ E and a vertex v ∈ V such that C should not equal the set of incoming edges at v; (2...

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, so called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore we give and example where the Galois type itself does not have f...

We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Complex Multiplication. Furthermore, we demonstrate the efficiency of the algorithm in practice by giving practical running times. In addition, we present statistics on the number of cryptographically strong elliptic curves...

Recent theoretical a potential to signifi information-theoreti concerns, which we community that a s bits from a block o protected data. Even information bits can information-theoreti weak notion of secre ultimate secrecy ra namely one which b bridge the existing security, we present criterion. As in the formulation. The ex

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addit...

For a graph G, let 9(G) be the family of strong orientations of G, d(G) = min{d(D) / D t 9’ (G)} and p(G) = d(G) -d(G), where d(G) and d(D) are the diameters of G and D respectively. In this paper we show that p(G) = 0 if G is a Cartesian product of (I ) paths, and (2) paths and cycles, which satisfy some mild conditions.

We discuss two methods for generating cryptographically strong elliptic curves deened over nite prime elds. The advantages and disadvantages of these algorithms are discussed and a practical comparison of the algorithms is given.

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a penalized likelihood, where the penalty is a function of the minimum of the ratios of the scale parameters and the sample size. It is shown that the penalized max...

In this paper we study the local behavior of a solution to the Lamé system with Lipschitz coefficients in dimension n ≥ 2. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lamé system with Lipschitz coefficients...