Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.Comment: 6 pages, 3 figure

State Space Partitions of Stochastic Chaotic Maps

The finest resolution that can be achieved in any real chaotic system is limited by the presence of noise. This noise can be used to define neighborhoods of the deterministic periodic orbits using the local eigenfunctions of the Fokker-Planck operator and its adjoint. We extend the work of D. Lippolis to include hyperbolic periodic orbits. The dynamics along the stable and unstable directions are separated. The neighborhoods on the stable and unstable manifolds can be defined in the same way as the neighborhoods for entirely stable or entirely unstable orbits. The neighborhoods are then returned to the original coordinates. The Fokker-Planck evolution can be described as a finite Markov transition graph between these neighborhoods. Its spectral determinant is used to calculate the time averages of observables. We apply this technique to calculate long time observables of the Lozi map.Undergraduat

Mise au point de techniques analytiques pour la spéciation du sélénium dans les boues de stations d'épuration d'eaux résiduaires urbaines

Les stations d'épuration d'eaux résiduaires sont une des étapes du cycle du sélénium dans l'environnement et contribuent à sa redistribution dans le milieu naturel. Très peu étudié jusqu'à présent dans ces milieux, le sélénium n'en est pas moins un élément très important du point de vue écotoxicologique, sa teneur dans les boues de stations d'épuration destinées à l'épandage agricole faisant par ailleurs l'objet d'une norme.Nous avons mis au point des techniques permettant la détermination spécifique de l'élément total dans ce type d'échantillon, par minéralisation classique ou assistée par micro-ondes et dosage par Voltamétrie de Redissolution Cathodique Différentielle Pulsée (DPCSV) et Spectrométrie d'Absorption Atomique ElectroThermique (ETAAS). Le contrôle qualité a été effectué sur deux échantillons certifiés fournis par le Bureau Communautaire de Référence (BCR) : la boue CRM 145 R et la boue CRM 007.Cependant, lorsqu'on parle de risque toxicologique, il est important de s'intéresser à la détermination des différentes formes sous lesquelles cet élément peut être présent. Nous avons pour cela réalisé des extractions parallèles (spéciation de phases) du sélénium contenu dans les boues afin de déterminer quel pourcentage du sélénium total est réellement et potentiellement disponible pour les végétaux lors d'un épandage sur sol agricole. La spéciation d'espèces a été brièvement abordée dans le but de déterminer les teneurs en Se(IV) et Se(VI), espèces les plus toxiques.The great effort undertaken for about twenty years to improve the quality of surface waters has led to the construction of numerous waste water treatment plants, generating an increasing amount of sludge. Waste water and sludge treatment processes represent an important point in the hydrological cycle at which the disposal of substantial quantities of trace elements to the environment may be regulated. From the law on waste recovery and disposal in 1975 to the European guideline about wastes in 1991, the priority has been given to waste recovery and recycling. With increasing pressure to ban all sludge dumping at sea, and considering the prohibitive costs of land-filling and incineration, there is a great tendency to dispose of sludge on land (40% in 1988 to 60% in 1992).Although numerous studies have demonstrated the intrinsic value of sludge for soil amendment, given its nitrogen, phosphorus and homogeneous organic matter content, evidence has accumulated in recent years that numerous environmental problems can arise because of the presence in sludges of high amounts of certain trace elements (potentially toxic to plants and to human beings and liable to be concentrated along the food chain), among which selenium is particularly interesting.Selenium presents a complex case, as it is also an essential element for living organisms (including humans). The amendment with sewage sludge is sometimes used to increase the selenium content in crops, and afterwards in cattle, when there is a proven lack of this element in a given place. Nevertheless the boundary between essentiality and toxicity is relatively narrow and is expressed at trace levels. It is thus particularly important to survey the selenium concentrations encountered in sewage sludge, especially as guidelines and regulations concerning these data will probably be strengthened. Presently, in France, sludge must not contain more than 200 mg Se·kg-1 dry weight and must not be used on soils containing more than 10 mg Se·kg-1 dry weight (AFNOR U 44-041 norm). This norm concerns only the total amount of selenium contained in sludge and does not take into account the different species (organic and inorganic Se(-II), Se(0), Se(IV) and Se(VI)) that could be present.First of all we had to develop methods for the classical and microwave-assisted wet digestion of sewage sludge, and the determination of their total selenium concentration by Differential Pulse Cathodic Stripping Voltammetry (DPCSV) and ElectroThermal Atomic Absorption Spectrometry (ETAAS). Quality assurance involved the analysis of two BCR (Community Bureau of Reference) certified sewage sludge reference materials (CRM 145 R and CRM 007) and the different techniques were then applied to natural samples from a representative French sewage treatment plant located in the city of Tarbes (South-West of France). The mixture HNO3-H2O2-H2O led to the best results for the digestion and analysis of certified samples, caused few problems for the analysis by DPCSV and ETAAS, and was therefore retained. The decrease of the digestion duration obtained by the use of microwaves was particularly interesting (from one to three days on a hot plate to less than one hour by the Microdigest 301 (PROLABO, France)), and reproducibility was also acceptable (between 3 and 10%). Concentrations obtained for the sewage sludge from the Tarbes treatment plant were very much lower than those for NF U 44-041: 1.08±0.11 mg Se·kg-1 dry weight.However knowledge of speciation, that is to say the determination of the different physicochemical forms of selenium present in a given medium, is necessary when speaking of the toxicological risk represented by an element. The mobility of selenium and its toxicity to the biosphere are related to its association with various sludge or soil constituents as well as to its total concentration. "Soft" or partial extraction techniques are necessary when the aim of the study to determine trace element speciation. The extractants used must separate selenium from the matrix without inducing any loss or change in the partitioning of individual chemical species. In parallel extractions the mechanisms involved for each extractant must correspond to processes occurring in nature and are then associated with special fractions of selenium: soluble, exchangeable, "oxidizable", and "mineral" fractions .Parallel extractions with three types of extractants were chosen for this study and applied first to CRM 007: warm water (soluble fraction), ammonium phosphate-citric acid (soluble + exchangeable fraction) and sodium hydroxide (soluble + exchangeable + "oxidizable" fraction). The soluble, exchangeable, "oxidizable" and "mineral" fractions represent respectively : 11%, 14%, 39% and 36%. The same procedure was then applied to natural samples from Tarbes giving the following results: 36% soluble, 22% exchangeable, 42% "oxidizable". The sodium hydroxide extraction procedure allowed us to extract the entire Se content of this sludge (1.07±0.03 mg Se·kg-1 dry weight), showing that all the selenium present is potentially available after agricultural land application. It was then possible in this fraction to deal with the species speciation of selenium by the mean of a separation of inorganic and organic species on an Amberlite CG-400 resin and a specific analysis by DPCSV. Se(IV) and Se(VI) represent respectively between 30 and 40% and between 2 and 20% of total selenium in the sludges from Tarbes

Reassessing the cardiac box: A comprehensive evaluation of the relationship between thoracic gunshot wounds and cardiac injury

Background: High energy missiles can cause cardiac injury regardless of entrance site. This study assesses the adequacy of the anatomic borders of the current “cardiac box” to predict cardiac injury. Methods: Retrospective autopsy review was performed to identify patients with penetrating torso gunshot wounds 2011-2013. Using a circumferential grid system around the thorax, logistic regression analysis was performed to detect differences in rates of cardiac injury from entrance/exit wounds in the “cardiac box” vs. the same for entrance/exit wounds outside the box. Analysis was repeated to identify regions to compare risk of cardiac injury between the current cardiac box and other regions of the thorax. Results: Over the study period, 263 patients (89% male, mean age = 34 years, median injuries/person = 2) sustained 735 wounds [80% gunshot wounds (GSWs], and 239 patients with 620 GSWs were identified for study. Of these, 95 (34%) injured the heart. Of the 257 GSWs entering the cardiac box, 31% caused cardiac injury while 21% GSWs outside the cardiac box (n = 67) penetrated the heart, suggesting that the current “cardiac box” is a poor predictor of cardiac injury relative to the thoracic non-"cardiac box" regions [Relative Risk (RR) 0.96; p=0.82]. The regions from the anterior to posterior midline of the left thorax provided the highest positive predictive value (41%) with high sensitivity (90%) while minimizing false positives making this region the most statistically significant discriminator of cardiac injury (RR 2.9; p=0.01). Conclusion: For GSWs, the current cardiac box is inadequate to discriminate whether a gunshot wound will cause a cardiac injury. As expected, entrance wounds nearest to the heart are the most likely to result in cardiac injury, but, from a clinical standpoint, it is best to think outside the “box” for GSWs to the thorax

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Comparative profiling identifies C13orf3 as a component of the Ska complex required for mammalian cell division

Proliferation of mammalian cells requires the coordinated function of many proteins to accurately divide a cell into two daughter cells. Several RNAi screens have identified previously uncharacterised genes that are implicated in mammalian cell division. The molecular function for these genes needs to be investigated to place them into pathways. Phenotypic profiling is a useful method to assign putative functions to uncharacterised genes. Here, we show that the analysis of protein localisation is useful to refine a phenotypic profile. We show the utility of this approach by defining a function of the previously uncharacterised gene C13orf3 during cell division. C13orf3 localises to centrosomes, the mitotic spindle, kinetochores, spindle midzone, and the cleavage furrow during cell division and is specifically phosphorylated during mitosis. Furthermore, C13orf3 is required for centrosome integrity and anaphase onset. Depletion by RNAi leads to mitotic arrest in metaphase with an activation of the spindle assembly checkpoint and loss of sister chromatid cohesion. Proteomic analyses identify C13orf3 (Ska3) as a new component of the Ska complex and show a direct interaction with a regulatory subunit of the protein phosphatase PP2A. All together, these data identify C13orf3 as an important factor for metaphase to anaphase progression and highlight the potential of combined RNAi screening and protein localisation analyses

Anthrax Toxins Inhibit Neutrophil Signaling Pathways in Brain Endothelium and Contribute to the Pathogenesis of Meningitis

Anthrax meningitis is the main neurological complication of systemic infection with Bacillus anthracis approaching 100% mortality. The presence of bacilli in brain autopsies indicates that vegetative bacteria are able to breach the blood-brain barrier (BBB). The BBB represents not only a physical barrier but has been shown to play an active role in initiating a specific innate immune response that recruits neutrophils to the site of infection. Currently, the basic pathogenic mechanisms by which B. anthracis penetrates the BBB and causes anthrax meningitis are poorly understood.Using an in vitro BBB model, we show for the first time that B. anthracis efficiently invades human brain microvascular endothelial cells (hBMEC), the single cell layer that comprises the BBB. Furthermore, transcriptional profiling of hBMEC during infection with B. anthracis revealed downregulation of 270 (87%) genes, specifically key neutrophil chemoattractants IL-8, CXCL1 (Gro alpha) and CXCL2 (Gro beta), thereby strongly contrasting hBMEC responses observed with other meningeal pathogens. Further studies using specific anthrax toxin-mutants, quantitative RT-PCR, ELISA and in vivo assays indicated that anthrax toxins actively suppress chemokine production and neutrophil recruitment during infection, allowing unrestricted proliferation and dissemination of the bacteria. Finally, mice challenged with B. anthracis Sterne, but not the toxin-deficient strain, developed meningitis.These results suggest a significant role for anthrax toxins in thwarting the BBB innate defense response promoting penetration of bacteria into the central nervous system. Furthermore, establishment of a mouse model for anthrax meningitis will aid in our understanding of disease pathogenesis and development of more effective treatment strategies