A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech. Ana

Características fenotípicas de 44 progênies de Maytenus ilicifolia Mart. ex Reiss. cultivadas no município de Ponta Grossa, PR.

Resumo

De novo SCN1A mutations in Dravet syndrome and related epileptic encephalopathies are largely of paternal origin

Background: Dravet syndrome is a severe infantile epileptic encephalopathy caused in approximately 80% of cases by mutations in the voltage gated sodium channel subunit gene SCN1A. The majority of these mutations are de novo. The parental origin of de novo mutations varies widely among genetic disorders and the aim of this study was to determine this for Dravet syndrome. Methods: 91 patients with de novo SCN1A mutations and their parents were genotyped for single nucleotide polymorphisms (SNPs) in the region surrounding their mutation. Allele specific polymerase chain reaction (PCR) based on informative SNPs was used to separately amplify and sequence the paternal and maternal alleles to determine in which parental chromosome the mutation arose. Results: The parental origin of SCN1A mutations was established in 44 patients for whom both parents were available and SNPs were informative. The mutations were of paternal origin in 33 cases and of maternal origin in the remaining 11 cases. De novo mutation of SCN1A most commonly, but not exclusively, originates from the paternal chromosome. The average age of parents originating mutations did not differ from that of the general population. Conclusions: The greater frequency of paternally derived mutations in SCN1A is likely to be due to the greater chance of mutational events during the increased number of mitoses which occur during spermatogenesis compared to oogenesis, and the greater susceptibility to mutagenesis of the methylated DNA characteristic of sperm cells.Sarah E. Heron, Ingrid E. Scheffer, Xenia Iona, Sameer M. Zuberi, Rachael Birch, Jacinta M. McMahon, Carla M. Bruce, Samuel F. Berkovic, John C. Mulle

Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory

Hubbell's 2001 neutral theory unifies biodiversity and biogeography by modelling steady-state distributions of species richness and abundances across spatio-temporal scales. Accurate predictions have issued from its core premise that all species have identical vital rates. Yet no ecologist believes that species are identical in reality. Here I explain this paradox in terms of the ecological equivalence that species must achieve at their coexistence equilibrium, defined by zero net fitness for all regardless of intrinsic differences between them. I show that the distinction of realised from intrinsic vital rates is crucial to evaluating community resilience. An analysis of competitive interactions reveals how zero-sum patterns of abundance emerge for species with contrasting life-history traits as for identical species. I develop a stochastic model to simulate community assembly from a random drift of invasions sustaining the dynamics of recruitment following deaths and extinctions. Species are allocated identical intrinsic vital rates for neutral dynamics, or random intrinsic vital rates and competitive abilities for niche dynamics either on a continuous scale or between dominant-fugitive extremes. Resulting communities have steady-state distributions of the same type for more or less extremely differentiated species as for identical species. All produce negatively skewed log-normal distributions of species abundance, zero-sum relationships of total abundance to area, and Arrhenius relationships of species to area. Intrinsically identical species nevertheless support fewer total individuals, because their densities impact as strongly on each other as on themselves. Truly neutral communities have measurably lower abundance/area and higher species/abundance ratios. Neutral scenarios can be parameterized as null hypotheses for testing competitive release, which is a sure signal of niche dynamics. Ignoring the true strength of interactions between and within species risks a substantial misrepresentation of community resilience to habitat los

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Acquired resistance of human T cells to sulfasalazine: stability of the resistant phenotype and sensitivity to non-related DMARDs.

2.5 weeks) resumption of SSZ resistance and ABCG2 expression as in the original CEM/SSZ cells. CEM/SSZ cells displayed diminished sensitivity to the DMARDs leflunomide (5.1-fold) and methotrexate (1.8-fold), were moderately more sensitive (1.6-2.0 fold) to cyclosporin A and chloroquine, and markedly more sensitive (13-fold) to the glucocorticoid dexamethasone as compared with parental CEM cells. CONCLUSION: The drug efflux pump ABCG2 has a major role in conferring resistance to SSZ. The collateral sensitivity of SSZ resistant cells for some other (non-related) DMARDs may provide a further rationale for sequential mono- or combination therapies with distinct DMARDs upon decreased efficacy of SSZ

From Social Data Mining to Forecasting Socio-Economic Crisis

Socio-economic data mining has a great potential in terms of gaining a better understanding of problems that our economy and society are facing, such as financial instability, shortages of resources, or conflicts. Without large-scale data mining, progress in these areas seems hard or impossible. Therefore, a suitable, distributed data mining infrastructure and research centers should be built in Europe. It also appears appropriate to build a network of Crisis Observatories. They can be imagined as laboratories devoted to the gathering and processing of enormous volumes of data on both natural systems such as the Earth and its ecosystem, as well as on human techno-socio-economic systems, so as to gain early warnings of impending events. Reality mining provides the chance to adapt more quickly and more accurately to changing situations. Further opportunities arise by individually customized services, which however should be provided in a privacy-respecting way. This requires the development of novel ICT (such as a self- organizing Web), but most likely new legal regulations and suitable institutions as well. As long as such regulations are lacking on a world-wide scale, it is in the public interest that scientists explore what can be done with the huge data available. Big data do have the potential to change or even threaten democratic societies. The same applies to sudden and large-scale failures of ICT systems. Therefore, dealing with data must be done with a large degree of responsibility and care. Self-interests of individuals, companies or institutions have limits, where the public interest is affected, and public interest is not a sufficient justification to violate human rights of individuals. Privacy is a high good, as confidentiality is, and damaging it would have serious side effects for society.Comment: 65 pages, 1 figure, Visioneer White Paper, see http://www.visioneer.ethz.c

Serum antimüllerian hormone levels best reflect the reproductive decline with age in normal women with proven fertility: A longitudinal study

Objective: The aim of this study was to assess which of the basal ovarian reserve markers provides the best reflection of the changes occurring in ovarian function over time (i.e., reproductive aging). Design: Prospective longitudinal study. Setting: Healthy volunteers in an academic research center. Patient(s): Eighty-one women with normal reproductive performance during the course of their lives were longitudinally assessed. In this select group of women, becoming chronologically older was considered as a proxy variable for becoming older from a reproductive point of view. Intervention(s): The women were assessed twice, with on average a 4-year interval (T 1 and T 2). The number of antral follicles on ultrasound (AFC) and blood levels of antimüllerian hormone (AMH), FSH, inhibin B, and E 2 were assessed. Main Outcome Measure(s): Longitudinal changes of the markers mentioned and the consistency of these parameters over time. Result(s): The mean ages at T 1 and T 2 were 39.6 and 43.6 years, respectively. Although AFC was strongly associated with age in a cross-sectional fashion, it did not change over time. The AMH, FSH, and inhibin B levels showed a significant change over time, in contrast to E 2 levels. The AMH and AFC were highly correlated with age both at T 1 and T 2, whereas FSH and inhibin B predominantly changed in women more than 40 years of age. To assess the consistency of these parameters over time, we investigated whether a woman's individual level above or below the mean of her age group at T 1 remained above or below the mean of her age group at T 2. Serum AMH concentrations showed the best consistency, with AFC as second best. The FSH and inhibin B showed only modest consistency, whereas E 2 showed no consistency at all. Conclusion(s): These results indicate that serum AMH represents the best endocrine marker to assess the age-related decline of reproductive capacity