Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

BREAKING WAVES IN AN IDEAL QUARK GLUON PLASMA

We study the propagation of perturbations in the energy density in a quark gluon plasma. Expanding the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations we obtain a nonlinear differential equation called the breaking wave equation. We solve it numerically and follow the time-evolution of initially localized pulses. We find that, quite unexpectedly, these pulses live for a very long time (compared to the reaction time-scales) before breaking. In practice, they mimick the Korteweg-de Vries solitons. Their existence may have some observable consequences.

A model for the stabilization of atomic hydrogen centers in borate glasses

A previously proposed model describing the trapping site of the interstitial atomic hydrogen in borate glasses is analyzed. In this model the atomic hydrogen is stabilized at the centers of oxygen polygons belonging to B-O ring structures in the glass network by van der Waals forces. The previously reported atomic hydrogen isothermal decay experimental data are discussed in the light of this microscopic model. A coupled differential equation system of the observed decay kinetics was solved numerically using the Runge Kutta method. The experimental untrapping activation energy of 0.7 x 10(-19) J is in good agreement with the calculated results of dispersion interaction between the stabilized atomic hydrogen and the neighboring oxygen atoms at the vertices of hexagonal ring structures. (C) 2009 Elsevier B.V. All rights reserved.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Functional deficiencies of sulfite oxidase: Differential diagnoses in neonates presenting with intractable seizures and cystic encephalomalacia

Sulfite oxidase is a mitochondrial enzyme encoded by the SUOX gene and essential for the detoxification of sulfite which results mainly from the catabolism of sulfur-containing amino acids. Decreased activity of this enzyme can either be due to mutations in the SUOX gene or secondary to defects in the synthesis of its cofactor, the molybdenum cofactor. Defects in the synthesis of the molybdenum cofactor are caused by mutations in one of the genes MOCS1, MOCS2, MOCS3 and GEPH and result in combined deficiencies of the enzymes sulfite oxidase, xanthine dehydrogenase and aldehyde oxidase. Although present in many ethnic groups, isolated sulfite oxidase deficiency and molybdenum cofactor deficiency are rare inborn errors of metabolism, which makes awareness of key clinical and laboratory features of affected individuals crucial for early diagnosis. We report clinical, radiologic, biochemical and genetic data on a Brazilian and on a Turkish child with sulfite oxidase deficiency due to the isolated defect and impaired synthesis of the molybdenum cofactor, respectively. Both patients presented with early onset seizures and neurological deterioration. They showed no sulfite oxidase activity in fibroblasts and were homozygous for the mutations c.1136A>G in the SUOX gene and c.667insCGA in the MOCS1 gene, respectively. Widely available routine laboratory tests such as assessment of total homocysteine and uric acid are indicated in children with a clinical presentation resembling that of hypoxic ischemic encephalopathy and may help in obtaining a tentative diagnosis locally, which requires confirmation by specialized laboratories. (C) 2009 Published by Elsevier B.V.

ProbFAST: Probabilistic Functional Analysis System Tool

Background: The post-genomic era has brought new challenges regarding the understanding of the organization and function of the human genome. Many of these challenges are centered on the meaning of differential gene regulation under distinct biological conditions and can be performed by analyzing the Multiple Differential Expression (MDE) of genes associated with normal and abnormal biological processes. Currently MDE analyses are limited to usual methods of differential expression initially designed for paired analysis. Results: We proposed a web platform named ProbFAST for MDE analysis which uses Bayesian inference to identify key genes that are intuitively prioritized by means of probabilities. A simulated study revealed that our method gives a better performance when compared to other approaches and when applied to public expression data, we demonstrated its flexibility to obtain relevant genes biologically associated with normal and abnormal biological processes. Conclusions: ProbFAST is a free accessible web-based application that enables MDE analysis on a global scale. It offers an efficient methodological approach for MDE analysis of a set of genes that are turned on and off related to functional information during the evolution of a tumor or tissue differentiation. ProbFAST server can be accessed at http://gdm.fmrp.usp.br/probfast.

Differential regulation of PGC-1 alpha expression in rat liver and skeletal muscle in response to voluntary running

Background: The beneficial actions of exercise training on lipid, glucose and energy metabolism and insulin sensitivity appear to be in part mediated by PGC-1 alpha. Previous studies have shown that spontaneously exercised rats show at rest enhanced responsiveness to exogenous insulin, lower plasma insulin levels and increased skeletal muscle insulin sensitivity. This study was initiated to examine the functional interaction between exercise-induced modulation of skeletal muscle and liver PGC-1 alpha protein expression, whole body insulin sensitivity, and circulating FFA levels as a measure of whole body fatty acid (lipid) metabolism. Methods: Two groups of male Wistar rats (2 Mo of age, 188.82 +/- 2.77 g BW) were used in this study. One group consisted of control rats placed in standard laboratory cages. Exercising rats were housed individually in cages equipped with running wheels and allowed to run at their own pace for 5 weeks. At the end of exercise training, insulin sensitivity was evaluated by comparing steady-state plasma glucose (SSPG) concentrations at constant plasma insulin levels attained during the continuous infusion of glucose and insulin to each experimental group. Subsequently, soleus and plantaris muscle and liver samples were collected and quantified for PGC-1 alpha protein expression by Western blotting. Collected blood samples were analyzed for glucose, insulin and FFA concentrations. Results: Rats housed in the exercise wheel cages demonstrated almost linear increases in running activity with advancing time reaching to maximum value around 4 weeks. On an average, the rats ran a mean (Mean +/- SE) of 4.102 +/- 0.747 km/day and consumed significantly more food as compared to sedentary controls (P < 0.001) in order to meet their increased caloric requirement. Mean plasma insulin (P < 0.001) and FFA (P < 0.006) concentrations were lower in the exercise-trained rats as compared to sedentary controls. Mean steady state plasma insulin (SSPI) and glucose (SSPG) concentrations were not significantly different in sedentary control rats as compared to exercise-trained animals. Plantaris PGC-1 alpha protein expression increased significantly from a 1.11 +/- 0.12 in the sedentary rats to 1.74 +/- 0.09 in exercising rats (P < 0.001). However, exercise had no effect on PGC-1 alpha protein content in either soleus muscle or liver tissue. These results indicate that exercise training selectively up regulates the PGC-1 alpha protein expression in high-oxidative fast skeletal muscle type such as plantaris muscle. Conclusion: These data suggest that PGC-1 alpha most likely plays a restricted role in exercise-mediated improvements in insulin resistance (sensitivity) and lowering of circulating FFA levels.

Differential expression of genes in salivary glands of male Rhipicephalus (Boophilus)microplus in response to infection with Anaplasma marginale

Background: Bovine anaplasmosis, caused by the rickettsial tick-borne pathogen Anaplasma marginale (Rickettsiales: Anaplasmataceae), is vectored by Rhipicephalus (Boophilus) microplus in many tropical and subtropical regions of the world. A. marginale undergoes a complex developmental cycle in ticks which results in infection of salivary glands from where the pathogen is transmitted to cattle. In previous studies, we reported modification of gene expression in Dermacentor variabilis and cultured Ixodes scapularis tick cells in response to infection with A. marginale. In these studies, we extended these findings by use of a functional genomics approach to identify genes differentially expressed in R. microplus male salivary glands in response to A. marginale infection. Additionally, a R. microplus-derived cell line, BME26, was used for the first time to also study tick cell gene expression in response to A. marginale infection. Results: Suppression subtractive hybridization libraries were constructed from infected and uninfected ticks and used to identify genes differentially expressed in male R. microplus salivary glands infected with A. marginale. A total of 279 ESTs were identified as candidate differentially expressed genes. Of these, five genes encoding for putative histamine-binding protein (22Hbp), von Willebrand factor (94Will), flagelliform silk protein (100Silk), Kunitz-like protease inhibitor precursor (108Kunz) and proline-rich protein BstNI subfamily 3 precursor (7BstNI3) were confirmed by real-time RT-PCR to be down-regulated in tick salivary glands infected with A. marginale. The impact of selected tick genes on A. marginale infections in tick salivary glands and BME26 cells was characterized by RNA interference. Silencing of the gene encoding for putative flagelliform silk protein (100Silk) resulted in reduced A. marginale infection in both tick salivary glands and cultured BME26 cells, while silencing of the gene encoding for subolesin (4D8) significantly reduced infection only in cultured BME26 cells. The knockdown of the gene encoding for putative metallothionein (93 Meth), significantly up-regulated in infected cultured BME26 cells, resulted in higher A. marginale infection levels in tick cells. Conclusions: Characterization of differential gene expression in salivary glands of R. microplus in response to A. marginale infection expands our understanding of the molecular mechanisms at the tick-pathogen interface. Functional studies suggested that differentially expressed genes encoding for subolesin, putative von Willebrand factor and flagelliform silk protein could play a role in A. marginale infection and multiplication in ticks. These tick genes found to be functionally relevant for tick-pathogen interactions will likely be candidates for development of vaccines designed for control of both ticks and tick-borne pathogens.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

GEVREY SOLVABILITY AND GEVREY REGULARITY IN DIFFERENTIAL COMPLEXES ASSOCIATED TO LOCALLY INTEGRABLE STRUCTURES

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition (P).

Monoamine oxidase inhibitory activities of indolylalkaloid toxins from the venom of the colonial spider Parawixia bistriata: Functional characterization of PwTX-I

Colonial spiders evolved a differential prey-capture behaviour in concert with their venom chemistry, which may be a source of novel drugs. Some highly active tetrahydro-beta-carboline (TH beta C) toxins were recently isolated from the venom of the colonial spider Parawixia bistriata; the spiders use these toxins as part of their chemical arsenal to kill and/or paralyze preys. The major TH beta C compound isolated from this venom was identified as 6-hydroxytrypargine, also known as PwTX-I. Most natural compounds of animal origin occur in low abundance, and the natural abundance of PwTX-I is insufficient for complete functional characterization. Thus, PwTx-I was synthesized using a Pictet-Spengler condensation strategy, and the stereoisomers of the synthetic toxin were separated by chiral chromatography. The fraction of venom containing a mixture of three natural TH beta C toxins and enantiomers of PwTx-I were analyzed for inhibition of monoamine oxidase (MAO)-A and -B and for toxicity to insects. We reveal that the mixture of the natural TH beta C toxins, as well as the enantiomers of PwTx-I, were non-competitive inhibitors of MAO-A and MAO-B and caused potent paralysis of honeybees. The (-)-PwTX-I enantiomer is 2-fold more potent than the (+)-PwTX-I enantiomer in the assays performed. (C) 2009 Elsevier Ltd. All rights reserved.

Differential display and suppression subtractive hybridization analysis of the pulp of ripening banana

The fruit of banana undergoes several important physico-chemical changes during ripening. Analysis of gene expression would permit identification of important genes and regulatory elements involved in this process. Therefore, transcript profiling of preclimacteric and climacteric fruit was performed using differential display and Suppression subtractive hybridization. Our analyses resulted in the isolation of 12 differentially expressed cDNAs, which were confirmed by dot-blots and northern blots. Among the sequences identified were sequences homologous to plant aquaporins, adenine nucleotide translocator, immunophilin, legumin-like proteins, deoxyguanosine kinase and omega-3 fatty acid desaturase. Some of these cDNAs correspond to newly isolated genes involved in changes related to the respiratory climacteric, or stress-defense responses. Functional characterization of ripening-associated genes could provide information useful in controlling biochemical pathways that would have an impact on banana quality and shelf life. (C) 2009 Elsevier B.V. All rights reserved.