Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

The leptospiral antigen Lp49 is a two-domain protein with putative protein binding function

Pathogenic Leptospira is the etiological agent of leptospirosis, a life-threatening disease that affects populations worldwide. Currently available vaccines have limited effectiveness and therapeutic interventions are complicated by the difficulty in making an early diagnosis of leptospirosis. The genome of Leptospira interrogans was recently sequenced and comparative genomic analysis contributed to the identification of surface antigens, potential candidates for development of new vaccines and serodiagnosis. Lp49 is a membrane-associated protein recognized by antibodies present in sera from early and convalescent phases of leptospirosis patients. Its crystal structure was determined by single-wavelength anomalous diffraction using selenomethionine-labelled crystals and refined at 2.0 angstrom resolution. Lp49 is composed of two domains and belongs to the all-beta-proteins class. The N-terminal domain folds in an immunoglobulin-like beta-sandwich structure, whereas the C-terminal domain presents a seven-bladed beta-propeller fold. Structural analysis of Lp49 indicates putative protein-protein binding sites, suggesting a role in Leptospira-host interaction. This is the first crystal structure of a leptospiral antigen described to date. (C) 2008 Elsevier Inc. All rights reserved.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

A New Class of Non Negative Distributions Generated by Symmetric Distributions

In this article, we study a new class of non negative distributions generated by the symmetric distributions around zero. For the special case of the distribution generated using the normal distribution, properties like moments generating function, stochastic representation, reliability connections, and inference aspects using methods of moments and maximum likelihood are studied. Moreover, a real data set is analyzed, illustrating the fact that good fits can result.

Wavelet regression with correlated errors on a piecewise Holder class

This paper generalizes the methodology of Cat and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Holder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case. (c) 2008 Elsevier B.V. All rights reserved.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

Novel insights for dihydroorotate dehydrogenase class 1A inhibitors discovery

The enzyme dihydroorotate dehydrogenase (DHODH) has been suggested as a promising target for the design of trypanocidal agents. We report here the discovery of novel inhibitors of Trypanosoma cruzi DHODH identified by a combination of virtual screening and ITC methods. Monitoring of the enzymatic reaction in the presence of selected ligands together with structural information obtained from X-ray crystallography analysis have allowed the identification and validation of a novel site of interaction (S2 site). This has provided important structural insights for the rational design of T cruzi and Leishmania major DHODH inhibitors. The most potent compound (1) in the investigated series inhibits TcDHODH enzyme with K(i)(app) value of 19.28 mu M and possesses a ligand efficiency of 0.54 kcal mol(-1) per non-H atom. The compounds described in this work are promising hits for further development. (C) 2010 Elsevier Masson SAS. All rights reserved.