Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e. g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Differential geometry of grassmannians and the Plucker map

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For 'hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the 'elliptic' case.

Identical sequence patterns in the ends of exons and introns of human protein-coding genes

Intron splicing is one of the most important steps involved in the maturation process of a pre-mRNA. Although the sequence profiles around the splice sites have been studied extensively, the levels of sequence identity between the exonic sequences preceding the donor sites and the intronic sequences preceding the acceptor sites has not been examined as thoroughly. In this study we investigated identity patterns between the last 15 nucleotides of the exonic sequence preceding the 5' splice site and the intronic sequence preceding the 3' splice site in a set of human protein-coding genes that do not exhibit intron retention. We found that almost 60% of consecutive exons and introns in human protein-coding genes share at least two identical nucleotides at their 3' ends and, on average, the sequence identity length is 2.47 nucleotides. Based on our findings we conclude that the 3' ends of exons and introns tend to have longer identical sequences within a gene than when being taken from different genes. Our results hold even if the pairs are non-consecutive in the transcription order. (C) 2012 Elsevier Ltd. All rights reserved.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Evaluating different methods of microarray data normalization

Abstract Background With the development of DNA hybridization microarray technologies, nowadays it is possible to simultaneously assess the expression levels of thousands to tens of thousands of genes. Quantitative comparison of microarrays uncovers distinct patterns of gene expression, which define different cellular phenotypes or cellular responses to drugs. Due to technical biases, normalization of the intensity levels is a pre-requisite to performing further statistical analyses. Therefore, choosing a suitable approach for normalization can be critical, deserving judicious consideration. Results Here, we considered three commonly used normalization approaches, namely: Loess, Splines and Wavelets, and two non-parametric regression methods, which have yet to be used for normalization, namely, the Kernel smoothing and Support Vector Regression. The results obtained were compared using artificial microarray data and benchmark studies. The results indicate that the Support Vector Regression is the most robust to outliers and that Kernel is the worst normalization technique, while no practical differences were observed between Loess, Splines and Wavelets. Conclusion In face of our results, the Support Vector Regression is favored for microarray normalization due to its superiority when compared to the other methods for its robustness in estimating the normalization curve.

Dillapiole as Antileishmanial Agent: Discovery, Cytotoxic Activity and Preliminary SAR Studies of Dillapiole Analogues

In this paper, the isolation of dillapiole (1) from Piper aduncum was reported as well as the semi-synthesis of two phenylpropanoid derivatives [di-hydrodillapiole (2), isodillapiole (3)], via reduction and isomerization reactions. Also, the compounds' molecular properties (structural, electronic, hydrophobic, and steric) were calculated and investigated to establish some preliminary structureactivity relationships (SAR). Compounds were evaluated for in vitro antileishmanial activity and cytotoxic effects on fibroblast cells. Compound 1 presented inhibitory activity against Leishmania amazonensis (IC50?=?69.3 mu M) and Leishmania brasiliensis (IC50?=?59.4 mu M) and induced cytotoxic effects on fibroblast cells mainly in high concentrations. Compounds 2 (IC50?=?99.9 mu M for L. amazonensis and IC50?=?90.5 mu M for L. braziliensis) and 3 (IC50?=?122.9 mu M for L. amazonensis and IC50?=?109.8 mu M for L. brasiliensis) were less active than dillapiole (1). Regarding the molecular properties, the conformational arrangement of the side chain, electronic features, and the hydrophilic/hydrophobic balance seem to be relevant for explaining the antileishmanial activity of dillapiole and its analogues.