A Symbolic Transformation Language and its Application to a Multiscale Method

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.Comment: 36 page

Homology and Cohomology of E-infinity Ring Spectra

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for categories of algebras over many other operads

COMMENTS ABOUT HIGGS FIELDS, NONCOMMUTATIVE GEOMETRY AND THE STANDARD MODEL

We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their interest, the relations with noncommutative geometry, the existence (or lack of existence) of phenomenological predictions, the relation with Lie super-algebras etc.Comment: pp 20, LaTeX file, no figures, also available via anonymous ftp at ftp://cpt.univ-mrs.fr/ or via gopher gopher://cpt.univ-mrs.fr

Higher categories, colimits, and the blob complex

We summarize our axioms for higher categories, and describe the blob complex. Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$ to any n-manifold W. The 0-th homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W=S^1 they coincide). The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold W. We outline the important properties of the blob complex, and sketch the proof of a generalization of Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.Comment: 7 page

The antioxidative protecting role of the Mediterranean diet [Antioksidativno protektivno djelovanje mediteranske dijete]

Recent meta-analysis shows that adherence to a Mediterranean diet (MD) can significantly decrease the risk of overall mortality, mortality from cardiovascular diseases, as well as incidence of mortality from cancer, and incidence of Parkinson's and Alzheimer's disease. All of these diseases could be linked to oxidative stress (OS) as antioxidative effect of MD is getting more attention nowadays. Although a lot of research has been done in this area and it suggests antioxidative protective role of MD, the presented evidence is still inconclusive. The aim of this paper is to review studies investigating the effect of MD on OS, as well as to identify the areas for further research

The gut-brain axis, BDNF, NMDA and CNS disorders

Gastro-intestinal (GI) microbiota and the ‘gut-brain axis’ are proving to be increasingly relevant to early brain development and the emergence of psychiatric disorders. This review focuses on the influence of the GI tract on Brain-Derived Neurotrophic Factor (BDNF) and its relationship with receptors for N-methyl-d-aspartate (NMDAR), as these are believed to be involved in synaptic plasticity and cognitive function. NMDAR may be associated with the development of schizophrenia and a range of other psychopathologies including neurodegenerative disorders, depression and dementias. An analysis of the routes and mechanisms by which the GI microbiota contribute to the pathophysiology of BDNF-induced NMDAR dysfunction could yield new insights relevant to developing novel therapeutics for schizophrenia and related disorders. In the absence of GI microbes, central BDNF levels are reduced and this inhibits the maintenance of NMDAR production. A reduction of NMDAR input onto GABA inhibitory interneurons causes disinhibition of glutamatergic output which disrupts the central signal-to-noise ratio and leads to aberrant synaptic behaviour and cognitive deficits. Gut microbiota can modulate BDNF function in the CNS, via changes in neurotransmitter function by affecting modulatory mechanisms such as the kynurenine pathway, or by changes in the availability and actions of short chain fatty acids (SCFAs) in the brain. Interrupting these cycles by inducing changes in the gut microbiota using probiotics, prebiotics or antimicrobial drugs has been found promising as a preventative or therapeutic measure to counteract behavioural deficits and these may be useful to supplement the actions of drugs in the treatment of CNS disorders