Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

Candidate Genes for Chromosomes 6 and 10: Quantitative Trait Loci for Age-Related Retinal Degeneration in Mice

Purpose: In a previous study, several quantitative trait loci (QTL) that influence age-related degeneration (ageRD) were identified in a cross between the albino strains B6(Cg)-Tyr(c-2J)/J (B6a) and BALB/cByJ (C). The Chromosome (Chr) 6 and Chr 10 QTL were the strongest and most highly significant loci and both involved B6a protective alleles. The QTL were responsible for 21% and 9% of the variance in phenotypes, respectively. We focused on these two QTL to identify candidate genes. Methods: DNA microarrays were used for the two mouse strains at four and eight months of age to identify genes that are differentially regulated and map to either QTL. Gene Ontology (GO) analysis of the differentially expressed genes was performed to identify possible processes and pathways associated with ageRD. To identify additional candidates, database analyses (Positional Medline or PosMed) were used. Based on differential expression, PosMed, and the presence of reported polymorphisms, five genes per QTL were selected for further study by sequencing analysis and qRT-PCR. Tumor necrosis factor, alpha-induced protein 3 (Tnfaip3; on a C57BL/6J (B6) background) was phenotypically tested. Single nucleotide polymorphisms (SNPs) flanking this gene were correlated with outer nuclear layer thickness (ONL), and eight-month-old Tnfaip3(+/-) mice were tested for ageRD. Results: Polymorphisms were found in the coding regions of eight genes. Changes in gene expression were identified by qRT-PCR for Hexokinase 2 (Hk2) and Docking protein 1 (Dok1) at four months and for Dok1 and Tnfaip3 at eight months. Tnfaip3 was selected for phenotypic testing due to differential expression and the presence of two nonsynonymous mutations. However, when ONL thickness was compared in eight-month-old congenic Tnfaip3(+/-) and Tnfaip3(+/+) mice, no differences were found, suggesting that Tnfaip3 is not the quantitative trait gene (QTG) for the Chr 10 QTL. The GO analysis revealed that GO terms associated with stress and cell remodeling are overrepresented in the ageRD-sensitive C strain compared with the B6a strain with age (eight months). In the ageRD-resistant B6a strain, compared with the C strain, GO terms associated with antioxidant response and the regulation of blood vessel size are overrepresented with age. Conclusions: The analyses of differentially expressed genes and the PosMed database yielded candidate genes for the Chr 6 and Chr 10 QTL. HtrA serine peptidase 2 (Htra2), Dok1, and Tnfaip3 were deemed most promising because of their known roles in apoptosis and our finding of nonsynonymous substitutions between B6a and C strains. While Tnfaip3 was excluded as the QTG for the Chr 10 QTL, Dok1 and Htra2 remain good candidates for the Chr 6 QTL. Finally, the GO term analysis further supports the general hypothesis that oxidative stress is involved in ageRD

Domain wall interacting with a black hole: A new example of critical phenomena

We study a simple system that comprises all main features of critical gravitational collapse, originally discovered by Choptuik and discussed in many subsequent publications. These features include universality of phenomena, mass-scaling relations, self-similarity, symmetry between super-critical and sub-critical solutions, etc. The system we consider is a stationary membrane (representing a domain wall) in a static gravitational field of a black hole. For a membrane that spreads to infinity, the induced 2+1 geometry is asymptotically flat. Besides solutions with Minkowski topology there exists also solutions with the induced metric and topology of a 2+1 dimensional black hole. By changing boundary conditions at infinity, one finds that there is a transition between these two families. This transition is critical and it possesses all the above-mentioned properties of critical gravitational collapse. It is remarkable that characteristics of this transition can be obtained analytically. In particular, we find exact analytical expressions for scaling exponents and wiggle-periods. Our results imply that black hole formation as a critical phenomenon is far more general than one might expect.Comment: 23 pages, 5 postscript figures include

The moderating effect of brand orientation on inter-firm market orientation and performance

While prior research has shown that market and brand orientation are key contributors to successful business performance, research to date has not fully explored how inter firm collaboration for these two key orientations can enhance business performance. The purpose of the paper is to investigate the relationship between inter-firm market and performance; to test for the moderating role of brand orientation in that relationship. A total of 169 completed pairs of surveys were collected of small and medium enterprises operating internationally in a variety of industries in Switzerland. The results show that inter-firm market and brand orientation are two antecedents of marketing and financial performance. The impact of inter-firm market on marketing and financial performance is significant when the brand orientation is favorable. This study extends previous research by examining the moderating role of brand orientation on inter firm market orientation, which is important, especially for firms wanting to increase their brand reputation by entering into partnerships with other firms. Further research is indicated, to identify the key moderators of the driving force of inter-firm market in relation to business performance and the reason why maintaining a strong brand presence is important in the international marketplace

Adhesion between elastic solids with randomly rough surfaces: comparison of analytical theory with molecular dynamics simulations

The adhesive contact between elastic solids with randomly rough, self affine fractal surfaces is studied by molecular dynamics (MD) simulations. The interfacial binding energy obtained from the simulations of nominally flat and curved surfaces is compared with the predictions of the contact mechanics theory by Persson. Theoretical and simulation results agree rather well, and most of the differences observed can be attributed to finite size effects and to the long-range nature of the interaction between the atoms in the block and the substrate in the MD model, as compared to the analytical theory which is for an infinite system with interfacial contact interaction. For curved surfaces (JKR-type of problem) the effective interfacial energy exhibit a weak hysteresis which may be due to the influence of local irreversible detachment processes in the vicinity of the opening crack tip during pull-off.Comment: 6 pages, 6 figure

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Country-specific birth weight and length in type 1 diabetes high-risk HLA genotypes in combination with prenatal characteristics

Objective:To examine the relationship between high-risk human leukocyte antigen (HLA) genotypes for type 1 diabetes and birth size in combination with prenatal characteristics in different countries.Study Design:Four high-risk HLA genotypes were enrolled in the Environmental determinants of Diabetes in the Young study newborn babies from the general population in Finland, Germany, Sweden and the United States. Stepwise regression analyses were used to adjust for country, parental physical characteristics and environmental factors during pregnancy.Result:Regression analyses did not reveal differences in birth size between the four type 1 diabetes high-risk HLA genotypes. Compared with DQ 4/8 in each country, (1) DQ 2/2 children were heavier in the United States (P=0.028) mostly explained however, by parental weight; (2) DQ 2/8 (P=0.023) and DQ 8/8 (P=0.046) children were longer in Sweden independent of parents height and as well as (3) in the United States for DQ 2/8 (P=0.023), but again dependent on parental height.Conclusion:Children born with type 1 diabetes high-risk HLA genotypes have comparable birth size. Longitudinal follow-up of these children should reveal whether birth size differences between countries contribute to the risk for islet autoimmunity and type 1 diabetes.Journal of Perinatology advance online publication, 28 April 2011; doi:10.1038/jp.2011.26

P2X7 receptors induce degranulation in human mast cells.

Mast cells play important roles in host defence against pathogens, as well as being a key effector cell in diseases with an allergic basis such as asthma and an increasing list of other chronic inflammatory conditions. Mast cells initiate immune responses through the release of newly synthesised eicosanoids and the secretion of pre-formed mediators such as histamine which they store in specialised granules. Calcium plays a key role in regulating both the synthesis and secretion of mast-cell-derived mediators, with influx across the membrane, in particular, being necessary for degranulation. This raises the possibility that calcium influx through P2X receptors may lead to antigen-independent secretion of histamine and other granule-derived mediators from human mast cells. Here we show that activation of P2X7 receptors with both ATP and BzATP induces robust calcium rises in human mast cells and triggers their degranulation; both effects are blocked by the P2X7 antagonist AZ11645373, or the removal of calcium from the extracellular medium. Activation of P2X1 receptors with αβmeATP also induces calcium influx in human mast cells, which is significantly reduced by both PPADS and NF 449. P2X1 receptor activation, however, does not trigger degranulation. The results indicate that P2X7 receptors may play a significant role in contributing to the unwanted activation of mast cells in chronic inflammatory conditions where extracellular ATP levels are elevated