On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Predicting the connectivity of primate cortical networks from topological and spatial node properties

Abstract Background The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked together, in an attempt to recover the original network structure. Results Inferring primate cortical connectivity from the properties of the nodes, remarkably good reconstructions of the global network organization could be obtained, with the topological features allowing slightly superior accuracy to the spatial ones. Analogous reconstruction attempts for the C. elegans neuronal network resulted in substantially poorer recovery, indicating that cortical area interconnections are relatively stronger related to the considered topological and spatial properties than neuronal projections in the nematode. Conclusion The close relationship between area-based features and global connectivity may hint on developmental rules and constraints for cortical networks. Particularly, differences between the predictions from topological and spatial properties, together with the poorer recovery resulting from spatial properties, indicate that the organization of cortical networks is not entirely determined by spatial constraints.

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Abstract Background A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it. Results We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. Conclusions The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.

Modularity and evolutionary constraints in a baculovirus gene regulatory network

Abstract Background The structure of regulatory networks remains an open question in our understanding of complex biological systems. Interactions during complete viral life cycles present unique opportunities to understand how host-parasite network take shape and behave. The Anticarsia gemmatalis multiple nucleopolyhedrovirus (AgMNPV) is a large double-stranded DNA virus, whose genome may encode for 152 open reading frames (ORFs). Here we present the analysis of the ordered cascade of the AgMNPV gene expression. Results We observed an earlier onset of the expression than previously reported for other baculoviruses, especially for genes involved in DNA replication. Most ORFs were expressed at higher levels in a more permissive host cell line. Genes with more than one copy in the genome had distinct expression profiles, which could indicate the acquisition of new functionalities. The transcription gene regulatory network (GRN) for 149 ORFs had a modular topology comprising five communities of highly interconnected nodes that separated key genes that are functionally related on different communities, possibly maximizing redundancy and GRN robustness by compartmentalization of important functions. Core conserved functions showed expression synchronicity, distinct GRN features and significantly less genetic diversity, consistent with evolutionary constraints imposed in key elements of biological systems. This reduced genetic diversity also had a positive correlation with the importance of the gene in our estimated GRN, supporting a relationship between phylogenetic data of baculovirus genes and network features inferred from expression data. We also observed that gene arrangement in overlapping transcripts was conserved among related baculoviruses, suggesting a principle of genome organization. Conclusions Albeit with a reduced number of nodes (149), the AgMNPV GRN had a topology and key characteristics similar to those observed in complex cellular organisms, which indicates that modularity may be a general feature of biological gene regulatory networks.

Different approaches for dealing with rare variants in family-based genetic studies: application of a Genetic Analysis Workshop 17 problem

Rare variants are becoming the new candidates in the search for genetic variants that predispose individuals to a phenotype of interest. Their low prevalence in a population requires the development of dedicated detection and analytical methods. A family-based approach could greatly enhance their detection and interpretation because rare variants are nearly family specific. In this report, we test several distinct approaches for analyzing the information provided by rare and common variants and how they can be effectively used to pinpoint putative candidate genes for follow-up studies. The analyses were performed on the mini-exome data set provided by Genetic Analysis Workshop 17. Eight approaches were tested, four using the trait’s heritability estimates and four using QTDT models. These methods had their sensitivity, specificity, and positive and negative predictive values compared in light of the simulation parameters. Our results highlight important limitations of current methods to deal with rare and common variants, all methods presented a reduced specificity and, consequently, prone to false positive associations. Methods analyzing common variants information showed an enhanced sensibility when compared to rare variants methods. Furthermore, our limited knowledge of the use of biological databases for gene annotations, possibly for use as covariates in regression models, imposes a barrier to further research.

The Brazilian Network for HIV-1 Genotyping External Quality Control Assurance Programme

The Brazilian network for genotyping is composed of 21 laboratories that perform and analyze genotyping tests for all HIV-infected patients within the public system, performing approximately 25,000 tests per year. We assessed the interlaboratory and intralaboratory reproducibility of genotyping systems by creating and implementing a local external quality control evaluation. Plasma samples from HIV-1-infected individuals (with low and intermediate viral loads) or RNA viral constructs with specific mutations were used. This evaluation included analyses of sensitivity and specificity of the tests based on qualitative and quantitative criteria, which scored laboratory performance on a 100-point system. Five evaluations were performed from 2003 to 2008, with 64% of laboratories scoring over 80 points in 2003, 81% doing so in 2005, 56% in 2006, 91% in 2007, and 90% in 2008 (Kruskal-Wallis, p = 0.003). Increased performance was aided by retraining laboratories that had specific deficiencies. The results emphasize the importance of investing in laboratory training and interpretation of DNA sequencing results, especially in developing countries where public (or scarce) resources are used to manage the AIDS epidemic.

Mapping virtual networks onto substrate networks

Network virtualization is a promising technique for building the Internet of the future since it enables the low cost introduction of new features into network elements. An open issue in such virtualization is how to effect an efficient mapping of virtual network elements onto those of the existing physical network, also called the substrate network. Mapping is an NP-hard problem and existing solutions ignore various real network characteristics in order to solve the problem in a reasonable time frame. This paper introduces new algorithms to solve this problem based on 0–1 integer linear programming, algorithms based on a whole new set of network parameters not taken into account by previous proposals. Approximative algorithms proposed here allow the mapping of virtual networks on large network substrates. Simulation experiments give evidence of the efficiency of the proposed algorithms.