STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

An investigation of localised soil heterogeneities on solute transport using a multisegment percolation system

A multisegment percolation system (MSPS) consisting of 25 individual collection wells was constructed to study the effects of localised soil heterogeneities on the transport of solutes in the vadose zone. In particular, this paper discusses the transport of water and nutrients (NO3-, Cl-, PO43-) through structurally stable, free-draining agricultural soil from Victoria, Australia. A solution of nutrients was irrigated onto the surface of a large undisturbed soil core over a 12-h period. This was followed by a continuous irrigation of distilled water at a fate which did not cause pending for a further 18 days. During this time, the volume of leachate and the concentration of nutrients in the leachate of each well were measured. Very significant variation in drainage patterns across a small spatial scale was observed. Leaching of nitrate-nitrogen and chloride from the core occurred two days after initial application. However, less than 1% of the total applied phosphate-phosphorus leached from the soil during the 18-day experiment, indicating strong adsorption. Our experiments indicate considerable heterogeneity in water flow patterns and solute leaching on a small spatial scale. These results have significant ramifications for modelling solute transport and predicting nutrient loadings on a larger scale.

Bishadowing and hyperbolicity

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

In vitro digestion and stability assessment of b-lactoglobulin/riboflavin nanostructures

B-Lactoglobulin (b-Lg) is the major protein fraction of bovine whey serum and a primary gelling agent. b-Lg has a high nutritional value, is stable at low pH being highly resistant to proteolytic degradation in the stomach, besides, it has the ability of acting as an encapsulating agent. This study aims at assessing the ability of b-Lg nanostructures to associate a nutraceutical - i.e. riboflavin - and release it in a controlled manner throughout an in vitro gastrointestinal (GI) system. For this reason b-Lg nanostructures loaded with riboflavin were critically characterized in terms of their morphology (i.e. size, polydispersity, -potential and shape) by dynamic light scattering (DLS) and transmission electron microscopy (TEM), and efficiency to associate to riboflavin through spectrofluorimetry. Furthermore, these nanocomplexes were evaluated in an in vitro GI model, simulating the physiological conditions. Stable b-Lg nanostructures were obtained at pH 6, of spherical shape, characterized by particle size of 172±1 nm, low polydispersity (i.e. PDI of 0.06±0.02), -potential of -32±3 mV and association efficiency (AE) of 26±1 %. b-Lg nanostructures showed to be stable upon their passage throughout stomach (i.e. particle size, PDI and potential of 248±10 nm, 0.18±0.03 and 18±3 mV, respectively). Concerning their passage throughout the intestine, such nanostructures were mostly degraded in the duodenum. Regarding riboflavin, a release of about 11 % was observed after their passage through stomach, while 35 %, 38 % and 5 % were the released percentages of the total riboflavin associated observed after passage through duodenum, jejunum and ileum, respectively. Hence,b-Lg nanostructures showed to be suitable carriers for riboflavin until the intestine, where their degradation occurs. b-Lg also showed to be structurally stable, under food simulant conditions (yoghurt simulant, composed of 3 % acetic acid), over 14 days, with a protective effect upon riboflavin activity, releasing it in a 7 day period.

Immunological and protective properties of novel malaria blood stage peptide antigens

ABSTRACT Malaria is a major worldwide public health problem, with transmission occurring throughout Africa, Asia, Oceania and Latin America. Over two billion people live in malarious areas of the world and it is estimated that 300-500 million cases and 1.5-2.7 million deaths occur annually. The increase in multi-drug resistant parasites and insecticide-resistant vectors has made the development of malaria vaccine a public health priority. The published genome offers tremendous opportunity for the identification of new antigens that can befast-tracked for vaccine development. We identified potential protein antigens present on the surface of asexual malaria blood stages through bioinformatics and published transcriptome and proteorné analysis. Amongst the proteins identified, we selected those that contain predicted a-helical coiled-coil regions, which are generally short and structurally stable as isolated fragments. Peptides were synthesized and used to immunize mice. Most peptides tested were immunogenic as demonstrated in ELISA assays, and induced antibodies of varying titres. In immunofluorescence assays, anti-sera from immunized mice reacted with native proteins expressed at different intraerythrocytic developmental stages of the parasite's cycle. In parallel in vitro ADCI functional studies, human antibodies affinity purified on some of these peptides inhibited parasite growth in association with monocytes in magnitudes similar to that seen in semiimmune African adults. Siudies using human immune sera taken from different malaria endemic regions, demonstrated that majority of peptides were recognized at high prevalence. 73 peptides were next tested in longitudinal studies in two cohorts separated in space and time in coastal Kenya. In these longitudinal analyses, antibody responses to peptides were sequentially examined in two cohorts of children at risk of clinical malaria in order to characterize the level of peptide recognition by age, and the role of anti-peptide antibodies in protection from clinical malaria. Ten peptides were associated ?with a significantly reduced odds ratio for an episode of clinical malaria in the first cohort of children and two of these peptides (LR146 and ÁS202.11) were associated with a significantly reduced odds ratio in both cohorts. This study has identified proteins PFB0145c and MAL6P1.37 among others as likely targets of protective antibodies. Our findings support further studies to systematically assess immunogenicity of peptides of interest in order to establish clear criteria for optimal design of potential vaccine constructs to be tested in clinical trials. RESUME La malaria est un problème de santé publique mondial principalement en Afrique, en Asie, en Océanie et en Amérique latine. Plus de 2 milliards de personnes vivent dans des régions endémiques et le nombre de cas par année est estimé entre 300 et 500 millions. 1.5 à 2.7 millions de décès surviennent annuellement dans ces zones. L'augmentation de la résistance aux médicaments et aux insecticides fait du développement d'un vaccin une priorité. Le séquençage complet du génome du parasite offre l'opportunité d'identifier de nouveaux antigènes qui peuvent rapidement mener au développement d'un vaccin. Des protéines antigéniques potentielles présentes à la surface des globules rouges infectés ont été identifiées par bioinformatique et par l'analyse du protéome et du transcriptome. Nous avons sélectionné, parmi ces protéines, celles contenant des motifs dits "a helical coiled-coil" qui sont généralement courts et structurellement stables. Ces régions ont été obtenues par synthèse peptidique et utilisées pour immuniser des souris. La plupart des peptides testés sont immunogéniques et induisent un titre variable d'anticorps déterminé par ELISA. Les résultats de tests d'immunofluorescence indiquent que les sera produits chez la souris reconnaissent les protéines natives exprimées aux différents stades de développement du parasite. En parallèle, des études d'ADCI in vitro montrent qué des anticorps humains purifiés à partir de ces peptides associés à des monocytes inhibent la croissance du parasite aussi bien que celle observée chez des adultes africains protégés. Des études d'antigénicité utilisant des sera de personnes protégées de différents âges vivant dans des régions endémiques montrent que la majorité des peptides sont reconnus avec une haute prévalence. 73 peptides ont été testés dans une étude longitudinale avec 2 cohortes de la côte du Kenya. Ces 2 groupes viennent de zones bien distinctes et les prélèvements n'ont pas été effectués pendant la même période. Dans cette étude, la réponse anticorps contre les peptides synthétiques a été testée dans les 2 cohortes d'enfants à risque de développer un épisode de malaria afin de caractériser le niveau de reconnaissance des peptides en fonction de l'âge et de déterminer le rôle des anticorps anti-peptides dans la protection contre la malaria. Parmi ces peptides, 10 sont associés à une réduction significative des risques de développer un épisode de malaria dans la première cohorte alors qu'un seul (LR146 et AS202.11) l'est dans les 2 cohortes. Cette étude a identifié, parmi d'autres, les protéines PFB0145c et MAL6P1.37 comme pouvant être la cible d'anticorps. Ces résultats sont en faveur de futures études qui évalueraient systématiquement l'immunogénicité des peptides d'intérêt dans le but d'établir des critères de sélection clairs pour le développement d'un vaccin. Résumé pour un large public La malaria est un problème de santé publique mondial principalement en Afrique, en Asie, en Océanie et en Amérique latine. Plus de 2 milliards de personnes vivent dans des régions endémiques et le nombre de cas par année est estimé entre 300 et 500 millions. 1.5 à 2.7 millions de décès surviennent annuellement dans ces zones. La résistance aux médicaments et aux insecticides augmente de plus en plus d'où la nécessité de développer un vaccin. Le séquençage complet du génome (ensemble des gènes) de P. falciparum a conduit au développement de nouvelles .études à large échelle dans le domaine des protéines du parasite (protéome) ; dans l'utilisation d'algorithmes, de techniques informatiques et statistiques pour l'analyse de données biologiques (bioinformatique) et dans les technologies de transcription et de profiles d'expression (transcriptome). Nous avons identifié, en utilisant les outils ci-dessus, des nouvelles protéines antigéniques qui sont présentes au stade sanguin de la malaria. Nous avons sélectionné, parmi ces protéines, celles contenant un motif dit "a-helical coiled-coil" qui sont des domaines impliqués dans un large éventail de fonctions biologiques. Des peptides représentant ces régions structurellement stables ont été synthétisés et utilisés pour immuniser des souris. La plupart des peptides testés sont immunogéniques et induisent un titre variable d'anticorps déterminé par ELISA. Les résultats de tests d'immunofluorescence indiquent que plusieurs sera de souris immunisées avec ces peptides reconnaissent les protéines natives exprimées à la surface des globules rouges infectés. En parallèle, des études d'ADCI in vitro montrent que des anticorps humains purifiés à partir de ces peptides en présence de monocytes inhibent la croissance du parasite de manière similaire à celle observée chez des adultes africains protégés. Des études d'antigénicité utilisant des sera de personnes immunes de différents âges (adultes et enfants) vivant dans des régions endémiques montrent que la majorité des peptides sont reconnus avec une haute prévalence. 73 peptides ont été testés dans des études épidémiologiques dans 2 villages côtiers du Kenya Ces 2 groupes vivent dans des zones bien distinctes et les prélèvements n'ont pas été effectués pendant la même période. Dans ces études, la réponse anticorps dirigée contre les peptides synthétiques a été testée en utilisant 467 échantillons sanguins d'enfants à risque de développer un épisode de malaria afin de caractériser le niveau de reconnaissance des peptides en fonction de l'âge et de déterminer le rôle des anticorps anti-peptides dans la protection contre la malaria cérébrale. Parmi ces peptides, 10 sont associés à une protection contre un épisode de malaria dans le premier village alors qu'un seul l'est dans les 2 villages. Ces résultats sont en faveur de futures études qui évalueraient systématiquement l'immunogénicité des peptides intéressants dans le but d'établir des critères de sélection clairs pour le développement d'un vaccin.

Functional characterization on invertebrate and vertebrate tissues of tachykinin peptides from octopus venoms

It has been previously shown that octopus venoms contain novel tachykinin peptides that despite being isolated from an invertebrate, contain the motifs characteristic of vertebrate tachykinin peptides rather than being more like conventional invertebrate tachykinin peptides. Therefore, in this study we examined the effect of three variants of octopus venom tachykinin peptides on invertebrate and vertebrate tissues. While there were differential potencies between the three peptides, their relative effects were uniquely consistent between invertebrate and vertebrae tissue assays. The most potent form (OCT-TK-III) was not only the most anionically charged but also was the most structurally stable. These results not only reveal that the interaction of tachykinin peptides is more complex than previous structure–function theories envisioned, but also reinforce the fundamental premise that animal venoms are rich resources of novel bioactive molecules, which are useful investigational ligands and some of which may be useful as lead compounds for drug design and development.

Parameter Estimation in Chaotic Systems

This report examines how to estimate the parameters of a chaotic system given noisy observations of the state behavior of the system. Investigating parameter estimation for chaotic systems is interesting because of possible applications for high-precision measurement and for use in other signal processing, communication, and control applications involving chaotic systems. In this report, we examine theoretical issues regarding parameter estimation in chaotic systems and develop an efficient algorithm to perform parameter estimation. We discover two properties that are helpful for performing parameter estimation on non-structurally stable systems. First, it turns out that most data in a time series of state observations contribute very little information about the underlying parameters of a system, while a few sections of data may be extraordinarily sensitive to parameter changes. Second, for one-parameter families of systems, we demonstrate that there is often a preferred direction in parameter space governing how easily trajectories of one system can "shadow'" trajectories of nearby systems. This asymmetry of shadowing behavior in parameter space is proved for certain families of maps of the interval. Numerical evidence indicates that similar results may be true for a wide variety of other systems. Using the two properties cited above, we devise an algorithm for performing parameter estimation. Standard parameter estimation techniques such as the extended Kalman filter perform poorly on chaotic systems because of divergence problems. The proposed algorithm achieves accuracies several orders of magnitude better than the Kalman filter and has good convergence properties for large data sets.

Mapping the immune response to the outer domain of a human immunodeficiency virus-1 clade C gp120

The outer domain (OD) of human immunodeficiency virus (HIV)-1 gp120 represents an attractive, if difficult, target for a beneficial immune response to HIV infection. Unlike the entire gp120, the OD is structurally stable and contains the surfaces that interact with both the primary and secondary cellular receptors. The primary strain-specific neutralizing target, the V3 loop, lies within the OD, as do epitopes for two cross-reactive neutralizing monoclonal antibodies (mAbs), b12 and 2G12, and the contact sites for a number of inhibitory lectins. The OD is poorly immunogenic, at least in the context of complete gp120, but purposeful OD immunization can lead to a substantial antibody response. Here, we map the antibody generated following immunization with a clade C OD. In contrast to published data for the clade B OD, the majority of the polyclonal response to the complete clade C OD is to the V3 loop; deletion of the loop substantially reduces immunogenicity. When the loop sequence was substituted for the epitope for 2F5, a well-characterized human cross-neutralizing mAb, a polyclonal response to the epitope was generated. A panel of mAbs against the clade C OD identified two mAbs that reacted with the loop and were neutralizing for clade C but not B isolates. Other mAbs recognized both linear and conformational epitopes in the OD. We conclude that, as for complete gp120, V3 immunodominance is a property of OD immunogens, that the responses can be neutralizing and that it could be exploited for the presentation of other epitopes.

Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Bio-fabrication and physiological self-release of tissue equivalents using smart peptide amphiphile templates

In this study we applied a smart biomaterial formed from a self-assembling, multi-functional synthetic peptide amphiphile (PA) to coat substrates with various surface chemistries. The combination of PA coating and alignment-inducing functionalised substrates provided a template to instruct human corneal stromal fibroblasts to adhere, become aligned and then bio-fabricate a highlyordered, multi-layered, three-dimensional tissue by depositing an aligned, native-like extracellular matrix. The newly-formed corneal tissue equivalent was subsequently able to eliminate the adhesive properties of the template and govern its own complete release via the action of endogenous proteases. Tissues recovered through this method were structurally stable, easily handled, and carrier-free. Furthermore, topographical and mechanical analysis by atomic force microscopy showed that tissue equivalents formed on the alignment-inducing PA template had highly-ordered, compact collagen deposition, with a two-fold higher elastic modulus compared to the less compact tissues produced on the non-alignment template, the PA-coated glass. We suggest that this technology represents a new paradigm in tissue engineering and regenerative medicine, whereby all processes for the biofabrication and subsequent self-release of natural, bioprosthetic human tissues depend solely on simple templatetissue feedback interactions.

In the mood: the dynamics of collective sentiments on Twitter

We study the relationship between the sentiment levels of Twitter users and the evolving network structure that the users created by @-mentioning each other. We use a large dataset of tweets to which we apply three sentiment scoring algorithms, including the open source SentiStrength program. Specifically we make three contributions. Firstly we find that people who have potentially the largest communication reach (according to a dynamic centrality measure) use sentiment differently than the average user: for example they use positive sentiment more often and negative sentiment less often. Secondly we find that when we follow structurally stable Twitter communities over a period of months, their sentiment levels are also stable, and sudden changes in community sentiment from one day to the next can in most cases be traced to external events affecting the community. Thirdly, based on our findings, we create and calibrate a simple agent-based model that is capable of reproducing measures of emotive response comparable to those obtained from our empirical dataset.

Test of the adiabatic nucleation model in SeTe and GeSnSe glasses

Se1-yTey and Ge1-ySnySe2.5 glasses, with compositions Y less than or equal to 0.5 and Y less than or equal to 0.6 respectively, are investigated. These glasses show a glass transition temperature (T-g) above the stability limit, indicated by the Adiabatic Nucleation Model (ANM). This effect has to be so because, other-wise, when cooled, these undercooled liquids would crystallize by generalized nucleation near the stability limit and no T-g could be observed. This shows that Se1-yTey glasses for Y < 0.5 are structurally stable. Limiting cases are pure Te and Se50Te50, which have T'(g)'s on the stability limit. Pure amorphous Te has to be obtained by fast quenching techniques, where the effective (fast quenching) T-g(*) is higher and Se50Te50 tends to crystallize easily. (C) 2004 Elsevier B.V. All rights reserved.

Suppressing Fermi Acceleration in a Driven Elliptical Billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)