Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies

We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and computed from the linear syzygies of its parametrization if the base points are isolated and form locally a complete intersection

The implicit equation of a canal surface

A canal surface is an envelope of a one parameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie geometries, we relate the equation of the canal surface to the equation of a dual variety of a certain curve in 5-dimensional projective space. We define the \mu-basis for arbitrary dimension and give a simple algorithm for its computation. This is then applied to the dual variety, which allows us to deduce the implicit equations of the the dual variety, the canal surface and any offset to the canal surface.Comment: 26 pages, to be published in Journal of Symbolic Computatio

Matrix representations for toric parametrizations

In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over P^2 established in [BJ03] and [BC05]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case T = P^1 x P^1 in detail and give numerous examples.Comment: 20 page

Dissecting the effect of genetic variation on the hepatic expression of drug disposition genes across the collaborative cross mouse strains

A central challenge in pharmaceutical research is to investigate genetic variation in response to drugs. The Collaborative Cross (CC) mouse reference population is a promising model for pharmacogenomic studies because of its large amount of genetic variation, genetic reproducibility, and dense recombination sites. While the CC lines are phenotypically diverse, their genetic diversity in drug disposition processes, such as detoxification reactions, is still largely uncharacterized. Here we systematically measured RNA-sequencing expression profiles from livers of 29 CC lines under baseline conditions. We then leveraged a reference collection of metabolic biotransformation pathways to map potential relations between drugs and their underlying expression quantitative trait loci (eQTLs). By applying this approach on proximal eQTLs, including eQTLs acting on the overall expression of genes and on the expression of particular transcript isoforms, we were able to construct the organization of hepatic eQTL-drug connectivity across the CC population. The analysis revealed a substantial impact of genetic variation acting on drug biotransformation, allowed mapping of potential joint genetic effects in the context of individual drugs, and demonstrated crosstalk between drug metabolism and lipid metabolism. Our findings provide a resource for investigating drug disposition in the CC strains, and offer a new paradigm for integrating biotransformation reactions to corresponding variations in DNA sequences

Microarray and deep sequencing cross-platform analysis of the mirRNome and isomiR variation in response to epidermal growth factor

BACKGROUND: Epidermal Growth Factor (EGF) plays an important function in the regulation of cell growth, proliferation, and differentiation by binding to its receptor (EGFR) and providing cancer cells with increased survival responsiveness. Signal transduction carried out by EGF has been extensively studied at both transcriptional and post-transcriptional levels. Little is known about the involvement of microRNAs (miRNAs) in the EGF signaling pathway. miRNAs have emerged as major players in the complex networks of gene regulation, and cancer miRNA expression studies have evidenced a direct involvement of miRNAs in cancer progression. RESULTS: In this study, we have used an integrative high content analysis approach to identify the specific miRNAs implicated in EGF signaling in HeLa cells as potential mediators of cancer mediated functions. We have used microarray and deep-sequencing technologies in order to obtain a global view of the EGF miRNA transcriptome with a robust experimental cross-validation. By applying a procedure based on Rankprod tests, we have delimited a solid set of EGF-regulated miRNAs. After validating regulated miRNAs by reverse transcription quantitative PCR, we have derived protein networks and biological functions from the predicted targets of the regulated miRNAs to gain insight into the potential role of miRNAs in EGF-treated cells. In addition, we have analyzed sequence heterogeneity due to editing relative to the reference sequence (isomiRs) among regulated miRNAs. CONCLUSIONS: We propose that the use of global genomic miRNA cross-validation derived from high throughput technologies can be used to generate more reliable datasets inferring more robust networks of co-regulated predicted miRNA target genes

Multiple platform assessment of the EGF dependent transcriptome by microarray and deep tag sequencing analysis

<p>Abstract</p> <p>Background</p> <p>Epidermal Growth Factor (EGF) is a key regulatory growth factor activating many processes relevant to normal development and disease, affecting cell proliferation and survival. Here we use a combined approach to study the EGF dependent transcriptome of HeLa cells by using multiple long oligonucleotide based microarray platforms (from Agilent, Operon, and Illumina) in combination with digital gene expression profiling (DGE) with the Illumina Genome Analyzer.</p> <p>Results</p> <p>By applying a procedure for cross-platform data meta-analysis based on RankProd and GlobalAncova tests, we establish a well validated gene set with transcript levels altered after EGF treatment. We use this robust gene list to build higher order networks of gene interaction by interconnecting associated networks, supporting and extending the important role of the EGF signaling pathway in cancer. In addition, we find an entirely new set of genes previously unrelated to the currently accepted EGF associated cellular functions.</p> <p>Conclusions</p> <p>We propose that the use of global genomic cross-validation derived from high content technologies (microarrays or deep sequencing) can be used to generate more reliable datasets. This approach should help to improve the confidence of downstream <it>in silico </it>functional inference analyses based on high content data.</p

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Implicitisation de surfaces algébriques rationnelles avec la méthode des syzygies

The implicitization of a rational algebraic surface, i.e. the passage from a parametrization to an implicit representation, is a classical geometric problem. In this thesis we use the theory of syzygies to represent a surface implicitly by a matrix whose maximal-sized minors have the implicit equation of the surface as their greatest common divisor. In the first two chapters, we treat two special classes of surfaces for which it is always possible to construct a square representation matrix corresponding to the resultant of a μ-basis: ruled surfaces and canal surfaces. In the following chapters, the general case of rational surfaces parametrized over a two-dimensional toric variety is studied. We show that a representation matrix can be constructed only using linear syzygies and we give a simple and efficient algorithm for its computation.L'implicitisation d'une surface algébrique rationnelle, c'est-à-dire le passage de la paramétrisation à une représentation implicite, est unproblème géométrique classique. Dans ce travail de thèse, nous utilisons la théorie des syzygies pour représenter implicitement une surface par une matrice dont les mineurs de taille maximale ont l'équation implicite comme plus grand diviseur commun. Dans les deux premiers chapitres, nous traitons deux classes de surfaces spéciales pour lesquelles il est toujours possible de construire une matrice carrée qui correspond au résultant d'une μ-base : les surfaces réglées et les surfaces canales. Dans les chapitres suivants, le cas général de surfaces rationnelles paramétrées sur une variété torique de dimension 2 est étudié. Nous montrons qu'une telle matrice peut être construite en n'utilisant que des syzygies linéaires et nous décrivons un algorithme simple et efficace pour son calcul