Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polynomial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high.

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

Reconstruction of spatiotemporal capture data by means of orthogonal functions: the case of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic

[EN] The information provided by the International Commission for the Conservation of Atlantic Tunas (ICCAT) on captures of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic has a number of limitations, such as gaps in the statistics for certain fleets and the level of spatiotemporal detail at which catches are reported. As a result, the quality of these data and their effectiveness for providing management advice is limited. In order to reconstruct missing spatiotemporal data of catches, the present study uses Data INterpolating Empirical Orthogonal Functions (DINEOF), a technique for missing data reconstruction, applied here for the first time to fisheries data. DINEOF is based on an Empirical Orthogonal Functions decomposition performed with a Lanczos method. DINEOF was tested with different amounts of missing data, intentionally removing values from 3.4% to 95.2% of data loss, and then compared with the same data set with no missing data. These validation analyses show that DINEOF is a reliable methodological approach of data reconstruction for the purposes of fishery management advice, even when the amount of missing data is very high.

Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Exact Algorithms for Different Classes of Vehicle Routing Problems

We deal with five problems arising in the field of logistics: the Asymmetric TSP (ATSP), the TSP with Time Windows (TSPTW), the VRP with Time Windows (VRPTW), the Multi-Trip VRP (MTVRP), and the Two-Echelon Capacitated VRP (2E-CVRP). The ATSP requires finding a lest-cost Hamiltonian tour in a digraph. We survey models and classical relaxations, and describe the most effective exact algorithms from the literature. A survey and analysis of the polynomial formulations is provided. The considered algorithms and formulations are experimentally compared on benchmark instances. The TSPTW requires finding, in a weighted digraph, a least-cost Hamiltonian tour visiting each vertex within a given time window. We propose a new exact method, based on new tour relaxations and dynamic programming. Computational results on benchmark instances show that the proposed algorithm outperforms the state-of-the-art exact methods. In the VRPTW, a fleet of identical capacitated vehicles located at a depot must be optimally routed to supply customers with known demands and time window constraints. Different column generation bounding procedures and an exact algorithm are developed. The new exact method closed four of the five open Solomon instances. The MTVRP is the problem of optimally routing capacitated vehicles located at a depot to supply customers without exceeding maximum driving time constraints. Two set-partitioning-like formulations of the problem are introduced. Lower bounds are derived and embedded into an exact solution method, that can solve benchmark instances with up to 120 customers. The 2E-CVRP requires designing the optimal routing plan to deliver goods from a depot to customers by using intermediate depots. The objective is to minimize the sum of routing and handling costs. A new mathematical formulation is introduced. Valid lower bounds and an exact method are derived. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.