Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Instability of the expression of morphological and phenological descriptors to environmental variation in white oat.

Made available in DSpace on 2018-01-11T23:31:30Z (GMT). No. of bitstreams: 1 445750711013.pdf: 442070 bytes, checksum: 9b519c484cf8867bc90e3d467624c188 (MD5) Previous issue date: 2018-01-10bitstream/item/170731/1/445750711013.pd

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

The aetiologies of epilepsy

The identification of the aetiology of a patient's epilepsy is instrumental in the diagnosis, prognostic counselling and management of the epilepsies. Indeed, the aetiology can be important for determining the recurrence risk of single seizures and so for making a diagnosis of epilepsy. Here, we divide the aetiologies into six categories: structural, genetic, infectious, metabolic, immune (all of which are part of the International League Against Epilepsy [ILAE] classification system) and neurodegenerative (which we have considered separately because of its growing importance in epilepsy). These are not mutually exclusive categories and many aetiologies fall into more than one category. Indeed, genetic factors probably play a role, to varying degrees, in the risk of seizures in all people with epilepsy. In each of the categories, we discuss what we regard as the most important aetiologies; importance being determined not only by prevalence but also by clinical significance. The introduction contains information suitable for level 1 competency (entry level), whilst the subsequent sections contain information aimed at level 2 competency (proficiency level) as part of the new ILAE competency-based curriculum. As we move towards precision medicine and targeted therapies, so aetiologies will play an even greater role in the management of epilepsy

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure