Approximation Algorithms for <Emphasis Type="Italic">k</Emphasis>-hurdle Problems

The polynomial-time solvable k-hurdle problem is a natural generalization of the classical s-t minimum cut problem where we must select a minimum-cost subset S of the edges of a graph such that |p∩S|≥k for every s-t path p. In this paper, we describe a set of approximation algorithms for “k-hurdle” variants of the NP-hard multiway cut and multicut problems. For the k-hurdle multiway cut problem with r terminals, we give two results, the first being a pseudo-approximation algorithm that outputs a (k−1)-hurdle solution whose cost is at most that of an optimal solution for k hurdles. Secondly, we provide a 2(1-\frac1r)2(1-\frac{1}{r})-approximation algorithm based on rounding the solution of a linear program, for which we give a simple randomized half-integrality proof that works for both edge and vertex k-hurdle multiway cuts that generalizes the half-integrality results of Garg et al. for the vertex multiway cut problem. We also describe an approximation-preserving reduction from vertex cover as evidence that it may be difficult to achieve a better approximation ratio than 2(1-\frac1r)2(1-\frac{1}{r}). For the k-hurdle multicut problem in an n-vertex graph, we provide an algorithm that, for any constant ε>0, outputs a ⌈(1−ε)k⌉-hurdle solution of cost at most O(log n) times that of an optimal k-hurdle solution, and we obtain a 2-approximation algorithm for trees.     

The Interaction of Anti-DNA Antibodies with DNA: Evidence for Unconventional Binding Mechanisms

Antibodies to DNA (anti-DNA) are the serological hallmark of systemic lupus erythematosus, a prototypic autoimmune disease. These antibodies bind to conserved sites on single-stranded and double-stranded DNA and display variable region somatic mutations consistent with antigen selection. Nevertheless, the interaction of anti-DNA with DNA has unconventional features. Anti-DNA antibodies bind by a mechanism called monogamous bivalency, in which stable interaction requires contact of both Fab sites with determinants on the same extended DNA molecule; the size of this DNA can be hundreds to thousands of bases, especially in solid phase assays. This binding also requires the presence of the Fc portion of IgG, a binding mechanism known as Fc-dependent monogamous bivalency. As shown by the effects of ionic strength in association and dissociation assays, anti-DNA binding is primarily electrostatic. Like anti-DNA autoantibodies, anti-DNA antibodies that bind specifically to non-conserved sites on bacterial DNA, a type of anti-DNA found in otherwise healthy individuals, also interact by monogamous bivalency. The unconventional features of anti-DNA antibodies may reflect the highly charged and polymeric nature of DNA and the need for molecular rearrangements to facilitate monogamous bivalency; the Fc portion contributes to binding in an as yet unknown way.     

Color Cherenkov imaging of clinical radiation therapy

Color vision is used throughout medicine to interpret the health and status of tissue. Ionizing radiation used in radiation therapy produces broadband white lig...     

European research policy and bibliometric indicators, 1990�C2005

This paper describes and analyses the role played in the development of bibliometric indicators??and the use made of bibliometric indicators for policy purposes??by the European Commission??s Directorate-General Research in the period 1990?C2005.