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

Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

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

Differential selection pressures exerted by host resistance quantitative trait loci on a pathogen population: a case study in an apple × Venturia inaequalis pathosystem

Understanding how pathogens evolve according to pressures exerted by their plant hosts is essential for the derivation of strategies aimed at the durable management of resistant cultivars. The spectrum of action of the resistance factors in the partially resistant cultivars is thought to be an important determinant of resistance durability. However, it has not yet been demonstrated whether the pressures exerted by quantitative resistance are different according to their spectrum of action.To investigate selection pressures exerted by apple genotypes harbouring various resistance quantitative trait loci (QTLs) on a mixed inoculum of the scab disease agent, Venturia inaequalis, we monitored V. inaequalis isolate proportions on diseased apple leaves of an F1 progeny using quantitative pyrosequencing technology and QTL mapping. Broad-spectrum resistances did not exert any differential selection pressures on the mixed inoculum, whereas narrow-spectrum resistances decreased the frequencies of some isolates in the mixture relative to the susceptible host genotypes. Our results suggest that the management of resistant cultivars should be different according to the spectrum of action of their resistance factors. The pyramiding of broad-spectrum factors or the use of a mixture of apple genotypes that carry narrow-spectrum resistance factors are two possible strategies for the minimization of resistance erosion

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

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

Neural parameters estimation for brain tumor growth modeling

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personalize the model, i.e. find a relevant set of parameters, with respect to the tumor dynamics of a particular patient, the model is informed from empirical data, e.g., medical images obtained from diagnostic modalities, such as magnetic-resonance imaging. Existing model-observation coupling schemes require a large number of forward integrations of the biophysical model and rely on simplifying assumption on the functional form, linking the output of the model with the image information. In this work, we propose a learning-based technique for the estimation of tumor growth model parameters from medical scans. The technique allows for explicit evaluation of the posterior distribution of the parameters by sequentially training a mixture-density network, relaxing the constraint on the functional form and reducing the number of samples necessary to propagate through the forward model for the estimation. We test the method on synthetic and real scans of rats injected with brain tumors to calibrate the model and to predict tumor progression

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