Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations

This paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a compensation to the weaker dissipativity condition, a Sobolev-Nash inequality is assumed for the underlying self-adjoint operator in applications. Some concrete examples are constructed to illustrate the main results.Comment: to appear in Journal of Mathematical Analysis and Application

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti

Random attractors for degenerate stochastic partial differential equations

We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard assumptions of the variational approach to SPDE with compact embeddings in the associated Gelfand triple. This allows spatially much rougher noise than in known results. The approach is based on a construction of strictly stationary solutions to related strongly monotone SPDE. Applications include stochastic generalized porous media equations, stochastic generalized degenerate p-Laplace equations and stochastic reaction diffusion equations. For perturbed, degenerate p-Laplace equations we prove that the deterministic, infinite dimensional attractor collapses to a single random point if enough noise is added.Comment: 34 pages; The final publication is available at http://link.springer.com/article/10.1007%2Fs10884-013-9294-

Random attractors for a class of stochastic partial differential equations driven by general additive noise

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic reaction-diffusion equations, the stochastic $p$-Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time fractional Brownian Motion and space-time L\'evy noise as admissible random perturbations. Moreover, cases where the attractor consists of a single point are considered and bounds for the speed of attraction are obtained.Comment: 30 page

Crystal Field Triplets: A New Route to Non-Fermi Liquid Physics

A model for crystal field triplet ground states on rare earth or actinide ions with dipolar and quadrupolar couplings to conduction electrons is studied for the first time with renormalization group methods. The quadrupolar coupling leads to a new nontrivial, non-Fermi liquid fixed point, which survives in an intermediate valence Anderson model. The calculated magnetic susceptibility displays one parameter scaling, going as $T^{-\alpha}$ ($\alpha \approx 0.4$) at intermediate temperatures, reminiscent of the non-Fermi liquid alloy UCu_{5-x}Pd_x.Comment: 4 pages, 3 figures, REVTe

Climate Change and invasibility of the Antarctic benthos

Benthic communities living in shallow-shelf habitats in Antarctica (<100-m depth) are archaic in their structure and function. Modern predators, including fast-moving, durophagous (skeleton-crushing) bony fish, sharks, and crabs, are rare or absent; slow-moving invertebrates are the top predators; and epifaunal suspension feeders dominate many soft substratum communities. Cooling temperatures beginning in the late Eocene excluded durophagous predators, ultimately resulting in the endemic living fauna and its unique food-web structure. Although the Southern Ocean is oceanographically isolated, the barriers to biological invasion are primarily physiological rather than geographic. Cold temperatures impose limits to performance that exclude modern predators. Global warming is now removing those physiological barriers, and crabs are reinvading Antarctica. As sea temperatures continue to rise, the invasion of durophagous predators will modernize the shelf benthos and erode the indigenous character of marine life in Antarctica

Mapping data elements to terminological resources for integrating biomedical data sources

BACKGROUND: Data integration is a crucial task in the biomedical domain and integrating data sources is one approach to integrating data. Data elements (DEs) in particular play an important role in data integration. We combine schema- and instance-based approaches to mapping DEs to terminological resources in order to facilitate data sources integration. METHODS: We extracted DEs from eleven disparate biomedical sources. We compared these DEs to concepts and/or terms in biomedical controlled vocabularies and to reference DEs. We also exploited DE values to disambiguate underspecified DEs and to identify additional mappings. RESULTS: 82.5% of the 474 DEs studied are mapped to entries of a terminological resource and 74.7% of the whole set can be associated with reference DEs. Only 6.6% of the DEs had values that could be semantically typed. CONCLUSION: Our study suggests that the integration of biomedical sources can be achieved automatically with limited precision and largely facilitated by mapping DEs to terminological resources

Prioritization of fish communities with a view to conservation and restoration on a large scale European basin, the Loire (France)

The hierarchical organization of important sites for the conservation or the restoration of fish communities is a great challenge for managers, especially because of financial or time constraints. In this perspective, we developed a methodology, which is easy to implement in different locations. Based on the fish assemblage characteristics of the Loire basin (France), we created a synthetic conservation value index including the rarity, the conservation status and the species origin. The relationship between this new synthetic index and the Fish-Based Index allowed us to establish a classification protocol of the sites along the Loire including fish assemblages to be restored or conserved. Sites presenting disturbed fish assemblages, a low rarity index, few threatened species, and a high proportion of non-native species were considered as important for the restoration of fish biodiversity. These sites were found mainly in areas where the assemblages are typical of the bream zone, e.g. with a higher number of eurytopic and limnophilic species. On the contrary, important sites for conservation were defined as having an important conservation potential (high RI, a lot of threatened species, and few nonnatives fish species) and an undisturbed fish assemblage similar to the expected community if habitats are undisturbed. Important sites for conservation were found in the Loire basin’s medium reaches which host assemblages typical for the grayling and the barbell zones, e.g. with a higher number of rheophilic species. The synthetic conservation value index could be adapted and completed with other criteria according to management priorities and capacities

Climate warming, marine protected areas and the ocean-scale integrity of coral reef ecosystems

Coral reefs have emerged as one of the ecosystems most vulnerable to climate variation and change. While the contribution of a warming climate to the loss of live coral cover has been well documented across large spatial and temporal scales, the associated effects on fish have not. Here, we respond to recent and repeated calls to assess the importance of local management in conserving coral reefs in the context of global climate change. Such information is important, as coral reef fish assemblages are the most species dense vertebrate communities on earth, contributing critical ecosystem functions and providing crucial ecosystem services to human societies in tropical countries. Our assessment of the impacts of the 1998 mass bleaching event on coral cover, reef structural complexity, and reef associated fishes spans 7 countries, 66 sites and 26 degrees of latitude in the Indian Ocean. Using Bayesian meta-analysis we show that changes in the size structure, diversity and trophic composition of the reef fish community have followed coral declines. Although the ocean scale integrity of these coral reef ecosystems has been lost, it is positive to see the effects are spatially variable at multiple scales, with impacts and vulnerability affected by geography but not management regime. Existing no-take marine protected areas still support high biomass of fish, however they had no positive affect on the ecosystem response to large-scale disturbance. This suggests a need for future conservation and management efforts to identify and protect regional refugia, which should be integrated into existing management frameworks and combined with policies to improve system-wide resilience to climate variation and change

Neurological, Psychiatric, and Biochemical Aspects of Thiamine Deficiency in Children and Adults.

Thiamine (vitamin B1) is an essential nutrient that serves as a cofactor for a number of enzymes, mostly with mitochondrial localization. Some thiamine-dependent enzymes are involved in energy metabolism and biosynthesis of nucleic acids whereas others are part of the antioxidant machinery. The brain is highly vulnerable to thiamine deficiency due to its heavy reliance on mitochondrial ATP production. This is more evident during rapid growth (i.e., perinatal periods and children) in which thiamine deficiency is commonly associated with either malnutrition or genetic defects. Thiamine deficiency contributes to a number of conditions spanning from mild neurological and psychiatric symptoms (confusion, reduced memory, and sleep disturbances) to severe encephalopathy, ataxia, congestive heart failure, muscle atrophy, and even death. This review discusses the current knowledge on thiamine deficiency and associated morbidity of neurological and psychiatric disorders, with special emphasis on the pediatric population, as well as the putative beneficial effect of thiamine supplementation in autism spectrum disorder (ASD) and other neurological conditions