Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Designing Novel Antitrypanosomal Agents from a Mixed Graph-Theoretical Substructural Approach

Chagas disease is nowadays the most serious parasitic health problem. This disease is caused by Trypanosoma cruzi. The great number of deaths and the insufficient effectiveness of drugs against this parasite have alarmed the scientific community worldwide. In an attempt to overcome this problem, a model for the design and prediction of new antitrypanosomal agents was obtained. This used a mixed approach, containing simple descriptors based on fragments and topological substructural molecular design descriptors. A data set was made up of 188 compounds, 99 of them characterized an antitrypanosomal activity and 88 compounds that belong to other pharmaceutical categories. The model showed sensitivity, specificity and accuracy values above 85%. Quantitative fragmental contributions were also calculated. Then, and to confirm the quality of the model, 15 structures of molecules tested as antitrypanosomal compounds (that we did not include in this study) were predicted, taking into account the information on the abovementioned calculated fragmental contributions. The model showed an accuracy of 100% which means that the ""in silico"" methodology developed by our team is promising for the rational design of new antitrypanosomal drugs. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 882-894. 2010

A multicommuted flow-system for spectrophotometric determination of tannin exploiting the Cu(I)/BCA complex formation

A flow system exploiting the multicommutation approach is proposed for spectrophotometric determination of tannin in beverages. The procedure is based on the reduction of Cu(II) in the presence of 4,4`-dicarboxy-2,2`-biquinoline, yielding a complex with maximum absorption at 558 nm. Calibration graph was linear (r=0.999) for tannic acid concentrations up to 5.00 mu mol L-1. The detection limit and coefficient of variation were estimated as 10 nmol L-1 (99.7% confidence level) and 1% (1.78 mu mol L-1 tannic acid, n=10), respectively. The sampling rate was 50 determinations per hour. The proposed procedure is more sensitive and selective than the official Folin-Denis method, also minimizing drastically waste generation. Recoveries within 91.8 and 115% were estimated for total tannin determination in tea and wine samples. (C) 2007 Elsevier B.V. All rights reserved.

Expedient, accurate methods for the determination of the degree of substitution of cellulose carboxylic esters: Application of UV-vis spectroscopy (dye solvatochromism) and FTIR

Two techniques, namely UV-vis- and FTIR spectroscopy, have been employed in order to calculate the degree of substitution (DS) of cellulose carboxylic esters, including acetates, CAs, butyrates, CBs, and hexanoates, CHs. Regarding UV-vis spectroscopy, we have employed a novel approach, based on measuring the dependence of lambda(max) of the intra-molecular charge-transfer bands of polarity probes adsorbed on DS of the ester films (solvatochromism). Additionally, we have revisited the use of FTIR for DS determination. Several methods have been used in order to plot Beer`s law graph, namely: Absorption of KBr pellets, pre-coated with CA: reflectance (DRIFTS) of CAs-KBr solid-solid mixtures with, or without the use of 1.4-dicyanobenzene as an internal reference; reflectance of KBr powder pre-coated with CA. The methods indicated are simple, fast, and accurate, requiring much less ester than the titration method. The probe method is independent of the experimental variables examined. (c) 2010 Published by Elsevier Ltd.

Novel Application of 2D and 3D-Similarity Searches To Identify Substrates among Cytochrome P450 2C9, 2D6, and 3A4

Cytochrome P450 (CYP450) is a class of enzymes where the substrate identification is particularly important to know. It would help medicinal chemists to design drugs with lower side effects due to drug-drug interactions and to extensive genetic polymorphism. Herein, we discuss the application of the 2D and 3D-similarity searches in identifying reference Structures with higher capacity to retrieve Substrates of three important CYP enzymes (CYP2C9, CYP2D6, and CYP3A4). On the basis of the complementarities of multiple reference structures selected by different similarity search methods, we proposed the fusion of their individual Tanimoto scores into a consensus Tanimoto score (T(consensus)). Using this new score, true positive rates of 63% (CYP2C9) and 81% (CYP2D6) were achieved with false positive rates of 4% for the CYP2C9-CYP2D6 data Set. Extended similarity searches were carried out oil a validation data set, and the results showed that by using the T(consensus) score, not only the area of a ROC graph increased, but also more substrates were recovered at the beginning of a ranked list.