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.

Assignment of Putative Functions to Membrane "Hypothetical Proteins" from the Trypanosoma cruzi Genome

Protozoan parasites cause thousands of deaths each year in developing countries. The genome projects of these parasites opened a new era in the identification of therapeutic targets. However, the putative function could be predicted for fewer than half of the protein-coding genes. In this work, all Trypanosoma cruzi proteins containing predicted transmembrane spans were processed through an automated computational routine and further analyzed in order to assign the most probable function. The analysis consisted of dissecting the whole predicted protein in different regions. More than 5,000 sequences were processed, and the predicted biological functions were grouped into 19 categories according to the hits obtained after analysis. One focus of interest, due to the scarce information available on trypanosomatids, is the proteins involved in signal-transduction processes. In the present work, we identified 54 proteins belonging to this group, which were individually analyzed. The results show that by means of a simple pipeline it was possible to attribute probable functions to sequences annotated as coding for "hypothetical proteins.'' Also, we successfully identified the majority of candidates participating in the signal-transduction pathways in T. cruzi.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Expression of the P2X(2) receptor in different classes of ileum myenteric neurons in the female obese ob/ob mouse

AIM: To examine whether the ob/ob mouse model of obesity is accompanied by enteric nervous system abnormalities such as altered motility. METHODS: The study examined the distribution of the P2X(2) receptor (P2X(2)R) in myenteric neurons of female ob/ob mice. Specifically, we used immunohistochemistry to analyze the co-expression of the P2X(2)R with neuronal nitric oxide synthase (nNOS), choline acetyltransferase (ChAT), and calretinin (CalR) in neurons of the small intestine myenteric plexus in ob/ob and control female mice. In these sections, we used scanning confocal microscopy to analyze the co-localization of these markers as well as the neuronal density (cm(2)) and area profile (mu m(2)) of P2X(2)R-positive neurons. In addition, enteric neurons were labeled using the nicotinamide adenine dinucleotide (NADH) diaphorase method and analyzed with light microscopy as an alternate means by which to analyze neuronal density and area. RESULTS: In the present study, we observed a 29.6% increase in the body weight of the ob/ob animals (OG) compared to the control group (CG). In addition, the average small intestine area was increased by approximately 29.6% in the OG compared to the CG. Immunoreactivity (IR) for the P2X(2)R, nNOS, ChAT and CaIR was detectable in the myenteric plexus, as well as in the smooth muscle, in both groups. This IR appeared to be mainly cytoplasmic and was also associated with the cell membrane of the myenteric plexus neurons, where it outlined the neuronal cell bodies and their processes. P2X(2)R-IR was observed to co-localize 100% with that for nNOS, ChAT and CaIR in neurons of both groups. In the ob/ob group, however, we observed that the neuronal density (neuron/cm(2)) of P2X(2)R-IR cells was increased by 62% compared to CG, while that of NOS-IR and ChAT-IR neurons was reduced by 49% and 57%, respectively, compared to control mice. The neuronal density of CaIR-IR neurons was not different between the groups. Morphometric studies further demonstrated that the cell body profile area (mu m(2)) of nNOS-IR, ChAT-IR and CaIR-IR neurons was increased by 34%, 20% and 55%, respectively, in the OG compared to controls. Staining for NADH diaphorase activity is widely used to detect alterations in the enteric nervous system; however, our qualitative examination of NADH-diaphorase positive neurons in the nnyenteric ganglia revealed an overall similarity between the two groups. CONCLUSION: We demonstrate increases in P2X(2)R expression and alterations in nNOS, ChAT and CaIR IR in ileal myenteric neurons of female ob/ob mice compared to wild-type controls. (c) 2012 Baishideng. All rights reserved.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Local inflammatory events induced by Bothrops atrox snake venom and the release of distinct classes of inflammatory mediators

Bothrops atrox is responsible for most accidents involving snakes in the Brazilian Amazon and its venom induces serious systemic and local effects. The local effects are not neutralized effectively by commercial antivenoms, resulting in serious sequelae in individuals bitten by this species. This study investigates the local inflammatory events induced in mice by B. atrox venom (Bay), such as vascular permeability, leukocyte influx and the release of important inflammatory mediators such as cytokines, eicosanoids and the chemokine CCL-2, at the injection site. The effect of Bay on cyclooxygenase (COX-1 and COX-2) expression was also investigated. The results showed that intraperitoneal (i.p.) injection of BaV promoted a rapid and significant increase in vascular permeability, which reached a peak 1 h after venom administration. Furthermore, BaV caused leukocyte infiltration into the peritoneal cavity between 1 and 8 h after i.p. injection, with mononuclear leukocytes (MNs) predominating in the first 4 h, and polymorphonuclear leukocytes (PMNs) in the last 4 h. Increased protein expression of COX-2, but not of COX-1, was detected in leukocytes recruited in the first and fourth hours after injection of BaV. The venom caused the release of eicosanoids PGD(2), PGE(2), TXA(2) and LTB4, cytokines TNF-alpha, IL-6, IL-10 and IL-12p70, but not IFN-gamma, and chemokine CCL-2 at different times. The results show that Bay is able to induce an early increase in vascular permeability and a leukocyte influx to the injection site consisting mainly of MNs initially and PMNs during the later stages. These phenomena are associated with the production of cytokines, the chemokine CCL-2 and eicosanoids derived from COX-1 and COX-2. (c) 2012 Elsevier Ltd. All rights reserved.

Molecular Characterization and Physical Mapping of Two Classes of 5S rDNA in the Genomes of Gymnotus sylvius and G. inaequilabiatus (Gymnotiformes, Gymnotidae)

The nucleotide sequences of the 5S rRNA multigene family and their distribution across the karyotypes in 2 species of Gymnotiformes, genus Gymnotus (G. sylvius and G. inaequilabiatus) were investigated by means of fluorescence in situ hybridization (FISH). The results showed the existence of 2 distinct classes of 5S rDNA sequences in both species: class I and class II. A high conservative pattern of the codifying region of the 5S rRNA gene was identified, contrasting with significant alterations detected in the nontranscribed spacer (NTS). The presence of TATA-like sequences along the NTS of both species was an expected occurrence, since such sequences have been associated with the regulation of the gene expression. FISH using 5S rDNA class I and class II probes revealed that both gene classes were collocated in the same chromosome pair in the genome of G. sylvius, while in that of G. inaequilabiatus, class II appeared more disperse than class I. Copyright (C) 2012 S. Karger AG, Basel

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Hypoellipticity in spaces of ultradistributions-Study of a model case

In this work we study C (a)-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hormander's condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.

Ontology for Data Representation in the Production of Cotton Fiber in Brazil

An important feature in computer systems developed for the agricultural sector is to satisfy the heterogeneity of data generated in different processes. Most problems related with this heterogeneity arise from the lack of standard for different computing solutions proposed. An efficient solution for that is to create a single standard for data exchange. The study on the actual process involved in cotton production was based on a research developed by the Brazilian Agricultural Research Corporation (EMBRAPA) that reports all phases as a result of the compilation of several theoretical and practical researches related to cotton crop. The proposition of a standard starts with the identification of the most important classes of data involved in the process, and includes an ontology that is the systematization of concepts related to the production of cotton fiber and results in a set of classes, relations, functions and instances. The results are used as a reference for the development of computational tools, transforming implicit knowledge into applications that support the knowledge described. This research is based on data from the Midwest of Brazil. The choice of the cotton process as a study case comes from the fact that Brazil is one of the major players and there are several improvements required for system integration in this segment.