Pii: S0166-0934(01)00389-5

Pii: S0014-5793(97)00389-x

New complexities for BRCA1 and BRCA2

A large number of diverse functions have been attributed to the BRCA1 and BRCA2 breast cancer susceptibility genes. Here we review recent progress in the field.

Measures on monotone properties of graphs

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.

Conway's problem for three-word sets

We prove two results on commutation of languages. First, we show that the maximal language commuting with a three-element language, i.e. its centralizer, is rational, thus giving an a5rmative answer to a special case of a problem proposed by Conway in 1971. Second, we characterize all languages commuting with a three-element code. The characterization is similar to the one proved by Bergman for...

Shattering a set of objects in 2d

In this paper, we propose an algorithm for shattering a set of disjoint line segments of arbitrary length and orientation placed arbitrarily on a 2D plane. The time and space complexities of our algorithm are O(n2) and O(n) respectively. It is an improvement of the O(nlogn) time algorithm proposed in [5]. A minor modi cation of this algorithm applies when objects are simple polygons, keeping th...