An asymptotic bound for secant varieties of Segre varieties

This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape (P^n)^4, with 1 < n < 11, except at most \sigma_199((P^8)^4) and \sigma_357((P^10)^4).Comment: 14 page

SYNAPS: A library for dedicated applications in symbolic numeric computing,

International audienceWe present an overview of the open source library synaps. We describe some of the representative algorithms of the library and illustrate them on some explicit computations, such as solving polynomials and computing geometric information on implicit curves and surfaces. Moreover, we describe the design and the techniques we have developed in order to handle a hierarchy of generic and specialized data-structures and routines, based on a view mechanism. This allows us to construct dedicated plugins, which can be loaded easily in an external tool. Finally, we show how this design allows us to embed the algebraic operations, as a dedicated plugin, into the external geometric modeler axel

Investigating Bacterial Sources of Toxicity as an Environmental Contributor to Dopaminergic Neurodegeneration

Parkinson disease (PD) involves progressive neurodegeneration, including loss of dopamine (DA) neurons from the substantia nigra. Select genes associated with rare familial forms of PD function in cellular pathways, such as the ubiquitin-proteasome system (UPS), involved in protein degradation. The misfolding and accumulation of proteins, such as α-synuclein, into inclusions termed Lewy Bodies represents a clinical hallmark of PD. Given the predominance of sporadic PD among patient populations, environmental toxins may induce the disease, although their nature is largely unknown. Thus, an unmet challenge surrounds the discovery of causal or contributory neurotoxic factors that could account for the prevalence of sporadic PD. Bacteria within the order Actinomycetales are renowned for their robust production of secondary metabolites and might represent unidentified sources of environmental exposures. Among these, the aerobic genera, Streptomyces, produce natural proteasome inhibitors that block protein degradation and may potentially damage DA neurons. Here we demonstrate that a metabolite produced by a common soil bacterium, S. venezuelae, caused DA neurodegeneration in the nematode, Caenorhabditis elegans, which increased as animals aged. This metabolite, which disrupts UPS function, caused gradual degeneration of all neuronal classes examined, however DA neurons were particularly vulnerable to exposure. The presence of DA exacerbated toxicity because neurodegeneration was attenuated in mutant nematodes depleted for tyrosine hydroxylase (TH), the rate-limiting enzyme in DA production. Strikingly, this factor caused dose-dependent death of human SH-SY5Y neuroblastoma cells, a dopaminergic line. Efforts to purify the toxic activity revealed that it is a highly stable, lipophilic, and chemically unique small molecule. Evidence of a robust neurotoxic factor that selectively impacts neuronal survival in a progressive yet moderate manner is consistent with the etiology of age-associated neurodegenerative diseases. Collectively, these data suggest the potential for exposures to the metabolites of specific common soil bacteria to possibly represent a contributory environmental component to PD

Cell-specific microarray profiling experiments reveal a comprehensive picture of gene expression in the C. elegans nervous system

A novel strategy for profiling Caenorhabditis elegans cells identifies transcripts highly enriched in either the embryonic or larval C. elegans nervous system, including 19 conserved transcripts of unknown function that are also expressed in the mammalian brain

A gene expression fingerprint of C. elegans embryonic motor neurons

BACKGROUND: Differential gene expression specifies the highly diverse cell types that constitute the nervous system. With its sequenced genome and simple, well-defined neuroanatomy, the nematode C. elegans is a useful model system in which to correlate gene expression with neuron identity. The UNC-4 transcription factor is expressed in thirteen embryonic motor neurons where it specifies axonal morphology and synaptic function. These cells can be marked with an unc-4::GFP reporter transgene. Here we describe a powerful strategy, Micro-Array Profiling of C. elegans cells (MAPCeL), and confirm that this approach provides a comprehensive gene expression profile of unc-4::GFP motor neurons in vivo. RESULTS: Fluorescence Activated Cell Sorting (FACS) was used to isolate unc-4::GFP neurons from primary cultures of C. elegans embryonic cells. Microarray experiments detected 6,217 unique transcripts of which ~1,000 are enriched in unc-4::GFP neurons relative to the average nematode embryonic cell. The reliability of these data was validated by the detection of known cell-specific transcripts and by expression in UNC-4 motor neurons of GFP reporters derived from the enriched data set. In addition to genes involved in neurotransmitter packaging and release, the microarray data include transcripts for receptors to a remarkably wide variety of signaling molecules. The added presence of a robust array of G-protein pathway components is indicative of complex and highly integrated mechanisms for modulating motor neuron activity. Over half of the enriched genes (537) have human homologs, a finding that could reflect substantial overlap with the gene expression repertoire of mammalian motor neurons. CONCLUSION: We have described a microarray-based method, MAPCeL, for profiling gene expression in specific C. elegans motor neurons and provide evidence that this approach can reveal candidate genes for key roles in the differentiation and function of these cells. These methods can now be applied to generate a gene expression map of the C. elegans nervous system