Let G(n, c/n) and G r (n) be an n-node sparse random graph and a sparse random r-regular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest independent set in G(n, c/n) and G r (n). The asymptotic value of I(n, c)/n as n → ∞, can be computed using the Karp-Sipser algorithm when c ≤ e. For random cubic graphs, r = 3, it is only… (More)
In this paper we shall show that there exists a polynomial unimodal map f : [0, 1] → [0, 1] which is • non-renormalizable (therefore for each x from a residual set, ω(x) is equal to an interval), • for which ω(c) is a Cantor set and • for which ω(x) = ω(c) for Lebesgue almost all x. So the topological and the metric attractor of such a map do not coincide.… (More)
A sufficient geometrical condition for the existence of absolutely continuous invariant probability measures for S−unimodal maps will be discussed. The Lebesgue typical existence of such measures in the quadratic family will be a consequence.
We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the… (More)
We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the functional space, where we look for a global attractor. We consider the following bifurcation problem: Given a probability… (More)
BACKGROUND There are many pathological conditions with hepatic iron overload. Classical definite diagnostic methods of these disorders are invasive and based on a direct tissue biopsy material. For the last years the role of MR imaging in liver diagnostics has been increasing. MRI shows changes of liver intensity in patients with hepatic iron overload.… (More)
In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (2008). By analyzing-dimensional lattice-free sets, we prove that for every integer there exists a positive integer such that every facet-defining… (More)
BACKGROUND Cavernous hemangiomas are the most frequent neoplasms of the liver and in routine clinical practice they often need to be differentiated from malignant tumors and other benign focal lesions. The purpose of this study is to evaluate whether diagnostic accuracy of magnetic resonance imaging (MRI) of hepatic hemangiomas, showing atypical pattern on… (More)