Polar Cremona Transformations and Monodromy of Polynomials

Consider the gradient map associated to any non-constant homogeneous polynomial f\in \C[x_0,...,x_n] of degree $d$, defined by \phi_f=grad(f): D(f)\to \CP^n, (x_0:...:x_n)\to (f_0(x):...:f_n(x)) where D(f)=\{x\in \CP^n; f(x)\neq 0\} is the principal open set associated to $f$ and $f_i=\frac{\partial f}{\partial x_i}$. This map corresponds to polar Cremona transformations. In Proposition \ref{p1} we give a new lower bound for the degree $d(f)$ of $\phi_f$ under the assumption that the projective hypersurface $V:f=0$ has only isolated singularities. When $d(f)=1$, Theorem \ref{t4} yields very strong conditions on the singularities of $V$.Comment: 8 page

Synchronous colorectal liver metastasis: A network meta-analysis review comparing classical, combined, and liver-first surgical strategies.

BACKGROUND: In recent years, the management of synchronous colorectal liver metastasis has changed significantly. Alternative surgical strategies to the classical colorectal-first approach have been proposed. These include the liver-first and combined resections approaches. The objectives of this review were to compare the short- and long-term outcomes for all three approaches. METHODS: A systematic review of comparative studies was performed. Evaluated endpoints included surgical outcomes (5-year overall survival, 30-day mortality, and post-operative complications). Pair-wise and network meta-analysis (NMA) were performed to compare survival outcomes. RESULTS: Eighteen studies were included in this review, reporting on 3,605 patients. NMA and pair-wise meta-analysis of the 5-year overall survival did not show significant difference between the three surgical approaches: combined versus colorectal-first, mean odds ratio (OR) 1.02 (95% CI 0.8-1.28, P = 0.93); liver-first versus colorectal-first, mean OR 0.81 (95% CI 0.53-1.26, P = 0.37); liver-first versus combined, mean OR 0.80 (95% CI 0.52-1.24, P = 0.41). In addition NMA of the 30-day mortality among the three approaches also did not observe statistical difference. Analysis of variance showed that mean post-operative complications of all approaches were comparable (P = 0.51). CONCLUSION: There are considerable differences in the peri-operative management of synchronous CLM patients. This meta-analysis demonstrated no clear statistical surgical outcome or survival advantage towards any of the three approaches. J. Surg. Oncol. © 2014 Wiley Periodicals, Inc

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Exposing errors related to weak memory in GPU applications

© 2016 ACM.We present the systematic design of a testing environment that uses stressing and fuzzing to reveal errors in GPU applications that arise due to weak memory effects. We evaluate our approach on seven GPUS spanning three NVIDIA architectures, across ten CUDA applications that use fine-grained concurrency. Our results show that applications that rarely or never exhibit errors related to weak memory when executed natively can readily exhibit these errors when executed in our testing environment. Our testing environment also provides a means to help identify the root causes of such errors, and automatically suggests how to insert fences that harden an application against weak memory bugs. To understand the cost of GPU fences, we benchmark applications with fences provided by the hardening strategy as well as a more conservative, sound fencing strategy

Sparse PLS discriminant analysis: biologically relevant feature selection and graphical displays for multiclass problems

Background: Variable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits.Results: A simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework.Conclusions: sPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets

Pioglitazone improves fat distribution, the adipokine profile and hepatic insulin sensitivity in non-diabetic end-stage renal disease subjects on maintenance dialysis: a randomized cross-over pilot study.

BACKGROUND: Fat redistribution, increased inflammation and insulin resistance are prevalent in non-diabetic subjects treated with maintenance dialysis. The aim of this study was to test whether pioglitazone, a powerful insulin sensitizer, alters body fat distribution and adipokine secretion in these subjects and whether it is associated with improved insulin sensitivity. TRIAL DESIGN: This was a double blind cross-over study with 16 weeks of pioglitazone 45 mg vs placebo involving 12 subjects. METHODS: At the end of each phase, body composition (anthropometric measurements, dual energy X-ray absorptometry (DEXA), abdominal CT), hepatic and muscle insulin sensitivity (2-step hyperinsulinemic euglycemic clamp with 2H2-glucose) were measured and fasting blood adipokines and cardiometabolic risk markers were monitored. RESULTS: Four months treatment with pioglitazone had no effect on total body weight or total fat but decreased the visceral/sub-cutaneous adipose tissue ratio by 16% and decreased the leptin/adiponectin (L/A) ratio from 3.63×10-3 to 0.76×10-3. This was associated with a 20% increase in hepatic insulin sensitivity without changes in muscle insulin sensitivity, a 12% increase in HDL cholesterol and a 50% decrease in CRP. CONCLUSIONS/LIMITATIONS: Pioglitazone significantly changes the visceral-subcutaneous fat distribution and plasma L/A ratio in non diabetic subjects on maintenance dialysis. This was associated with improved hepatic insulin sensitivity and a reduction of cardio-metabolic risk markers. Whether these effects may improve the outcome of non diabetic end-stage renal disease subjects on maintenance dialysis still needs further evaluation. TRIAL REGISTRATION: ClinicalTrial.gov NCT01253928

The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses

This survey may be seen as an introduction to the use of toric and tropical geometry in the analysis of plane curve singularities, which are germs $(C,o)$ of complex analytic curves contained in a smooth complex analytic surface $S$. The embedded topological type of such a pair $(S, C)$ is usually defined to be that of the oriented link obtained by intersecting $C$ with a sufficiently small oriented Euclidean sphere centered at the point $o$, defined once a system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one works more generally over an arbitrary algebraically closed field of characteristic zero, one speaks instead of the combinatorial type of $(S, C)$. One may define it by looking either at the Newton-Puiseux series associated to $C$ relative to a generic local coordinate system $(x,y)$, or at the set of infinitely near points which have to be blown up in order to get the minimal embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this germ by the resolution. Each point of view leads to a different encoding of the combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques diagram, or a weighted dual graph. The three trees contain the same information, which in the complex setting is equivalent to the knowledge of the embedded topological type. There are known algorithms for transforming one tree into another. In this paper we explain how a special type of two-dimensional simplicial complex called a lotus allows to think geometrically about the relations between the three types of trees. Namely, all of them embed in a natural lotus, their numerical decorations appearing as invariants of it. This lotus is constructed from the finite set of Newton polygons created during any process of resolution of $(C,o)$ by successive toric modifications.Comment: 104 pages, 58 figures. Compared to the previous version, section 2 is new. The historical information, contained before in subsection 6.2, is distributed now throughout the paper in the subsections called "Historical comments''. More details are also added at various places of the paper. To appear in the Handbook of Geometry and Topology of Singularities I, Springer, 202

Temporal development of the oral microbiome and prediction of early childhood caries

Human microbiomes are predicted to assemble in a reproducible and ordered manner yet there is limited knowledge on the development of the complex bacterial communities that constitute the oral microbiome. The oral microbiome plays major roles in many oral diseases including early childhood caries (ECC), which afflicts up to 70% of children in some countries. Saliva contains oral bacteria that are indicative of the whole oral microbiome and may have the ability to reflect the dysbiosis in supragingival plaque communities that initiates the clinical manifestations of ECC. The aim of this study was to determine the assembly of the oral microbiome during the first four years of life and compare it with the clinical development of ECC. The oral microbiomes of 134 children enrolled in a birth cohort study were determined at six ages between two months and four years-of-age and their mother’s oral microbiome was determined at a single time point. We identified and quantified 356 operational taxonomic units (OTUs) of bacteria in saliva by sequencing the V4 region of the bacterial 16S RNA genes. Bacterial alpha diversity increased from a mean of 31 OTUs in the saliva of infants at 1.9 months-of-age to 84 OTUs at 39 months-of-age. The oral microbiome showed a distinct shift in composition as the children matured. The microbiome data were compared with the clinical development of ECC in the cohort at 39, 48, and 60 months-of-age as determined by ICDAS-II assessment. Streptococcus mutans was the most discriminatory oral bacterial species between health and current disease, with an increased abundance in disease. Overall our study demonstrates an ordered temporal development of the oral microbiome, describes a limited core oral microbiome and indicates that saliva testing of infants may help predict ECC risk