Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

Symmetric Brownian motor

In this paper, we present a model of a symmetric Brownian motor which changes the sign of its velocity when the temperature gradient is inverted. The velocity, external work, and efficiency are studied as a function of the temperatures of the baths and other relevant parameters. The motor shows a current reversal when another parameter (a phase shift) is varied. Analytical predictions and results from numerical simulations are performed and agree very well. Generic properties of this type of motor are discussed.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the C(k)-topology, k=2, ..., infinity, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Detecting periodicity with horizontal visibility graphs

The horizontal visibility algorithm was recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are in its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.

Cell-Adhesive Responses to Tenascin-C Splice Variants Involve Formation of Fascin Microspikes

Tenascin-C is an adhesion-modulating matrix glycoprotein that has multiple effects on cell behavior. Tenascin-C transcripts are expressed in motile cells and at sites of tissue modeling during development, and alternative splicing generates variants that encode different numbers of fibronectin type III repeats. We have examined the in vivo expression and cell adhesive properties of two full-length recombinant tenascin-C proteins: TN-190, which contains the eight constant fibronectin type III repeats, and TN-ADC, which contains the additional AD2, AD1, and C repeats. In situ hybridization with probes specific for the AD2, AD1, and C repeats shows that these splice variants are expressed at sites of active tissue modeling and fibronectin expression in the developing avian feather bud and sternum. Transcripts incorporating the AD2, AD1, and C repeats are present in embryonic day 10 wing bud but not in embryonic day 10 lung. By using a panel of nine cell lines in attachment assays, we have found that C2C12, G8, and S27 myoblastic cells undergo concentration-dependent adhesion to both variants, organize actin microspikes that contain the actin-bundling protein fascin, and do not assemble focal contacts. On a molar basis, TN-ADC is more active than TN-190 in promoting cell attachment and irregular cell spreading. The addition of either TN-190 or TN-ADC in solution to C2C12, COS-7, or MG-63 cells adherent on fibronectin decreases cell attachment and results in decreased organization of actin microfilament bundles, with formation of cortical membrane ruffles and retention of residual points of substratum contact that contain filamentous actin and fascin. These data establish a biochemical similarity in the processes of cell adhesion to tenascin-C and thrombospondin-1, also an “antiadhesive” matrix component, and also demonstrate that both the adhesive and adhesion-modulating properties of tenascin-C involve similar biochemical events in the cortical cytoskeleton. In addition to these generic properties, TN-ADC is less active in adhesion modulation than TN-190. The coordinated expression of different tenascin-C transcripts during development may, therefore, provide appropriate microenvironments for regulated changes in cell shape, adhesion, and movement.

On constructing folding heteropolymers.

Simplified models of the protein-folding process have led to valuable insights into the generic properties of the folding of heteropolymers. On the basis of theoretical arguments, Shakhnovich and Gutin [(1993) Proc. Natl. Acad. Sci. USA 90, 7195-7199] have proposed a specific method to generate folding sequences for one of these. Here we present a model of folding in heteropolymers that is comparable in simplicity but different in spirit to the one studied by Shakhnovich and Gutin. In our model, the proposed recipe for constructing folding sequence fails. We find that, as a rule, the construction of folding sequences is impossible to achieve by looking at the native conformation only. Rather, competing conformations have to be taken into account too. An evolutionary algorithm that generates folding sequences by optimizing both stability of the native state and folding time is described. Remarkably, this algorithm produces, among others, sequences that fold reproducibly to metastable states.

A framework and tool support for the systematic testing of model-based specifications

Formal specifications can precisely and unambiguously define the required behavior of a software system or component. However, formal specifications are complex artifacts that need to be verified to ensure that they are consistent, complete, and validated against the requirements. Specification testing or animation tools exist to assist with this by allowing the specifier to interpret or execute the specification. However, currently little is known about how to do this effectively. This article presents a framework and tool support for the systematic testing of formal, model-based specifications. Several important generic properties that should be satisfied by model-based specifications are first identified. Following the idea of mutation analysis, we then use variants or mutants of the specification to check that these properties are satisfied. The framework also allows the specifier to test application-specific properties. All properties are tested for a range of states that are defined by the tester in the form of a testgraph, which is a directed graph that partially models the states and transitions of the specification being tested. Tool support is provided for the generation of the mutants, for automatically traversing the testgraph and executing the test cases, and for reporting any errors. The framework is demonstrated on a small specification and its application to three larger specifications is discussed. Experience indicates that the framework can be used effectively to test small to medium-sized specifications and that it can reveal a significant number of problems in these specifications.

TCR{alpha} Genes Direct MHC Restriction in the Potent Human T Cell Response to a Class I-Bound Viral Epitope

The underlying generic properties of {alpha}β TCRs that control MHC restriction remain largely unresolved. To investigate MHC restriction, we have examined the CTL response to a viral epitope that binds promiscuously to two human leukocyte Ags (HLAs) that differ by a single amino acid at position 156. Individuals expressing either HLA-B*3501 (156Leucine) or HLA-B*3508 (156Arginine) showed a potent CTL response to the 407HPVGEADYFEY417 epitope from EBV. Interestingly, the response was characterized by highly restricted TCR β-chain usage in both HLA-B*3501+ and HLA-B*3508+ individuals; however, this conserved TRBV9+ β-chain was associated with distinct TCR {alpha}-chains depending upon the HLA-B*35 allele expressed by the virus-exposed host. Functional assays confirmed that TCR {alpha}-chain usage determined the HLA restriction of the CTLs. Structural studies revealed significant differences in the mobility of the peptide when bound to HLA-B*3501 or HLA-B*3508. In HLA-B*3501, the bulged section of the peptide was disordered, whereas in HLA-B*3508 the bulged epitope adopted an ordered conformation. Collectively, these data demonstrate not only that mobile MHC-bound peptides can be highly immunogenic but can also stimulate an extremely biased TCR repertoire. In addition, TCR {alpha}-chain usage is shown to play a critical role in controlling MHC restriction between closely related allomorphs.

Bosonisation as The Hubbard-Stratonovich transformation

The problem of strongly correlated electrons in one dimension attracted attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [1] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [2] (1963) and Mattis and Lieb [3] (1963). A considerable contribution to the understanding of generic properties of the 1D electron liquid has been made by Dzyaloshinskii and Larkin [4] (1973) and Efetov and Larkin [5] (1976). Despite the fact that the main features of the 1D electron liquid were captured and described by the end of 70’s, the investigators felt dissatisfied with the rigour of the theoretical description. The most famous example is the paper by Haldane [6] (1981) where the author developed the fundamentals of a modern bosonisation technique, known as the operator approach. This paper became famous because the author has rigourously shown how to construct the Fermi creation/anihilation operators out of the Bose ones. The most recent example of such a dissatisfaction is the review by von Delft and Schoeller [7] (1998) who revised the approach to the bosonisation and came up with what they called constructive bosonisation.

A manual of botany, for the northern and middle states of America : containing generic and specific descriptions of the indigenous plants and common cultivated exotics, growing north of Virginia, to which is prefixed a grammar and vocabulary : also the natural orders of Linneus and of Jussieu, with the medicinal properties of each order /

Includes index.

Potential beneficial properties of bacteriocin-producing lactic acid bacteria isolated from smoked salmon

Aims: To evaluate the probiotic properties of strains isolated from smoked salmon and previously identified as bacteriocin producers. Methods and Results: Strains Lactobacillus curvatus ET06, ET30 and ET31, Lactobacillus fermentum ET35, Lactobacillus delbrueckii ET32, Pediococcus acidilactici ET34 and Enterococcus faecium ET05, ET12 and ET88 survived conditions simulating the gastrointestinal tract (GIT) and produced bacteriocins active against several strains of Listeria monocytogenes, but presented very low activity against other lactic acid bacteria (LAB). Cell-free supernatants containing bacteriocins, added to 3-h-old cultures of L. monocytogenes 603, suppressed growth over 12 h. Auto-aggregation was strain-specific, and values ranged from 7 center dot 2% for ET35 to 12 center dot 1% for ET05. Various degrees of co-aggregation with L. monocytogenes 603, Lactobacillus sakei ATCC 15521 and Enterococcus faecalis ATCC 19443 were observed. Adherence of the bacteriocinogenic strains to Caco-2 cells was within the range reported for Lactobacillus rhamnosus GG, a well-known probiotic. The highest levels of hydrophobicity were recorded for Lact. curvatus (61 center dot 9-64 center dot 6%), Lact. fermentum (78 center dot 9%), Lact. delbrueckii (43 center dot 7%) and Ped. acidilactici (51 center dot 3%), which are higher than the one recorded for Lact. rhamnosus GG (53 center dot 3%). These strains were highly sensitive to several antibiotics and affected by several drugs from different generic groups in a strain-dependent manner. Conclusions: Smoked salmon is a rich source of probiotic LAB. All strains survived conditions simulating the GIT and produced bacteriocins active against various pathogens. Adherence to Caco-2 cells was within the range reported for Lact. rhamnosus GG, a well-known probiotic. In addition, the high hydrophobicity readings recorded define the strains as good probiotics. Significance and Impact of the Study: Smoked salmon contains a number of different probiotic LAB and could be marketed as having a potential beneficial effect.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.