We consider the problem of augmenting a graph with n vertices embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present an exact algorithm for the cases when the input graph is a path that runs in O(n log n) time. We also present an algorithm that computes a (1 + ε)approximation in O(n+1/ε) time for paths in R, where d is a...

In the Intervalizing Colored Graphs problem, one must decide for a given graph G = (V,E) with a proper vertex coloring of G whether G is the subgraph of a properly colored interval graph. For the case that the number of colors k is xed, we give an exact algorithm that uses O∗(2n/log (n)) time for all > 0. We also give an O∗(2n) algorithm for the case that the number of colors k is not xed.

The 2012 Albert Lasker Special Achievement Award in Medical Science will be shared by Donald Brown and Tom Maniatis for their scientific work leading to the purification and study of single genes by physical and molecular biological methodologies. Brown and Maniatis are also recognized for their extraordinary commitment and generosity in promoting the careers of young scientists. The impact of ...

this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.

We investigate distality and existence of distal expansions in valued fields related structures. In particular, we characterize a large class ordered abelian groups, provide an Ax-Kochen-Eršov-style characterization for henselian fields, demonstrate that certain e.g., the differential field logarithmic-exponential transseries, are distal. As new tool analyzing employ relative quantifier elimina...

Presented are exactly integrable models with pure radiation in R2 gravity a cosmological constant related to wave-like Shapovalov spacetimes type II. Spatially homogeneous of were considered. The obtained solutions belong spaces III according the Bianchi classification and N Petrov classification. For under consideration, exact for equations motion test particles Hamilton–Jacobi formalism. mode...

2014 We formulate a conjecture concerning the critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) which generalize a recent one stated for planar lattices. The present conjecture is verified within satisfactory accuracy (exactly in some cases) for all the lattices or arrays whose critical points are known. Its use leads to the prediction of : a) a considerabl...

Abstract. While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and th...

A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a saddle point approximation is more accurate, becoming, in some cases asymptotically exact as the transformations are iterated. The formalism provides a simplified...

The measurability by means of continuous measurements, of an observable A(t0), at an instant, and of a time averaged observable, Ā = 1/T ∫ A(t)dt, is examined for linear and in particular for non-linear quantum mechanical systems. We argue that only when the exact (non-perturbative) solution is known, an exact measurement may be possible. A perturbative approach is shown to fail in the non-line...