Decomposition of homogeneous polynomials with low rank

Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^{{m+d\choose d}-1}$ but that its minimal decomposition as a sum of $d$-th powers of linear forms $M_1, ..., M_r$ is $F=M_1^d+... + M_r^d$ with $r>s$. We show that if $s+r\leq 2d+1$ then such a decomposition of $F$ can be split in two parts: one of them is made by linear forms that can be written using only two variables, the other part is uniquely determined once one has fixed the first part. We also obtain a uniqueness theorem for the minimal decomposition of $F$ if the rank is at most $d$ and a mild condition is satisfied.Comment: final version. Math. Z. (to appear

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

A microarray analysis of full depth knee cartilage of ovariectomized rats

<p>Abstract</p> <p>Background</p> <p>This short communication focuses the on articular cartilage and the subchondral bone, both of which play important roles in the development of osteoarthritis (OA). There are indications that estrogen-deficiency, as the post-menopausal state, accelerate the development of OA.</p> <p>Findings</p> <p>We investigated, which extracellular matrix (ECM) protein, proteases and different pro-inflammatory factors was up- or down-regulated in the knee joint tissue in response to estrogen-deficiency in rats induced by ovariectomy. These data support previous findings that several metalloproteinases (MMPs) and cysteine proteases are co-regulated with numerous collagens and proteoglycans that are important for cartilage integrity. Furthermore quite a few pro-inflammatory cytokines were regulated by estrogen deprivation.</p> <p>Conclusion</p> <p>We found multiple genes where regulated in the joint by estrogen-deficiency, many of which correspond well with our current knowledge of the pathogenesis of OA. It supports that estrogen-deficiency (e.g. OVX) may accelerate joint deterioration. However, there are also data that draw attention the need for better understanding of the synergy between proteases and tissue turnover.</p

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Determining Signalling Nodes for Apoptosis by a Genetic High-Throughput Screen

With the ever-increasing information emerging from the various sequencing and gene annotation projects, there is an urgent need to elucidate the cellular functions of the newly discovered genes. The genetically regulated cell suicide of apoptosis is especially suitable for such endeavours as it is governed by a vast number of factors.We have set up a high-throughput screen in 96-well microtiter plates for genes that induce apoptosis upon their individual transfection into human cells. Upon screening approximately 100,000 cDNA clones we determined 74 genes that initiate this cellular suicide programme. A thorough bioinformatics analysis of these genes revealed that 91% are novel apoptosis regulators. Careful sequence analysis and functional annotation showed that the apoptosis factors exhibit a distinct functional distribution that distinguishes the cell death process from other signalling pathways. While only a minority of classic signal transducers were determined, a substantial number of the genes fall into the transporter- and enzyme-category. The apoptosis factors are distributed throughout all cellular organelles and many signalling circuits, but one distinct signalling pathway connects at least some of the isolated genes. Comparisons with microarray data suggest that several genes are dysregulated in specific types of cancers and degenerative diseases.Many unknown genes for cell death were revealed through our screen, supporting the enormous complexity of cell death regulation. Our results will serve as a repository for other researchers working with genomics data related to apoptosis or for those seeking to reveal novel signalling pathways for cell suicide

In praise of arrays

Microarray technologies have both fascinated and frustrated the transplant community since their introduction roughly a decade ago. Fascination arose from the possibility offered by the technology to gain a profound insight into the cellular response to immunogenic injury and the potential that this genomic signature would be indicative of the biological mechanism by which that stress was induced. Frustrations have arisen primarily from technical factors such as data variance, the requirement for the application of advanced statistical and mathematical analyses, and difficulties associated with actually recognizing signature gene-expression patterns and discerning mechanisms. To aid the understanding of this powerful tool, its versatility, and how it is dramatically changing the molecular approach to biomedical and clinical research, this teaching review describes the technology and its applications, as well as the limitations and evolution of microarrays, in the field of organ transplantation. Finally, it calls upon the attention of the transplant community to integrate into multidisciplinary teams, to take advantage of this technology and its expanding applications in unraveling the complex injury circuits that currently limit transplant survival

Multiband multi-antenna system for MIMO WLAN box

International audienc

Co-design d'une antenne en mode simple vs différentiel pour un démonstrateur IR-UWB dédié à des applications BAN

National audienc