An improvement of the product integration method for a weakly singular Hammerstein equation

We present a new method to solve nonlinear Hammerstein equations with weakly singular kernels. The process to approximate the solution, followed usually, consists in adapting the discretization scheme from the linear case in order to obtain a nonlinear system in a finite dimensional space and solve it by any linearization method. In this paper, we propose to first linearize, via Newton method, the nonlinear operator equation and only then to discretize the obtained linear equations by the product integration method. We prove that the iterates, issued from our method, tends to the exact solution of the nonlinear Hammerstein equation when the number of Newton iterations tends to infinity, whatever the discretization parameter can be. This is not the case when the discretization is done first: in this case, the accuracy of the approximation is limited by the mesh size discretization. A Numerical example is given to confirm the theorical result

Generalization of the Kimeldorf-Wahba correspondence for constrained interpolation

In this paper, we extend the correspondence between Bayes' estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of linear inequality constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpolation is known to be the optimal interpolation function minimizing the norm in the RKHS associated to the GP. In the constrained case, we prove that the Maximum A Posteriori (MAP) or Mode of the posterior distribution is the optimal constrained interpolation function in the RKHS. So, the general correspondence is achieved with the MAP estimator and not the mean of the posterior distribution. A numerical example is given to illustrate this last result

A Product Integration type Method for solving Nonlinear Integral Equations in L

This paper deals with nonlinear Fredholm integral equations of the second kind. We study the case of a weakly singular kernel and we set the problem in the space L 1 ([a, b], C). As numerical method, we extend the product integration scheme from C 0 ([a, b], C) to L 1 ([a, b], C)

Las organizaciones "campesinas" y la transición política en México (fuerzas y debilidades)

Es notorio que desde el fin de las políticas proteccionistas en México, la apertura de sus mercados y el retiro del Estado de la conducción de la economía, las organizaciones campesinas han perdido su capacidad de influir en las políticas públicas. Esta debilidad se debe tanto a la disminución de la participación del campesinado en el PIB agropecuario como a su debilitamiento social frente a la población urbana que representa hoy la enorme mayoría de la población nacional. Es por esta doble situación que el Estado abandonó, en las últimas décadas del siglo pasado, la ideología agrarista que fue el sostén del régimen corporativista del Partido Revolucionario Institucional (PRI) y rompió su tradicional alianza con el campesinado. En este trabajo analizamos la situación actual de las organizaciones campesinas y su relación con la esfera pública en el contexto del nuevo régimen democrático en vigor

A new method for interpolating in a convex subset of a Hilbert space

International audienceIn this paper, interpolating curve or surface with linear inequality constraints is considered as a general convex optimization problem in a Reproducing Kernel Hilbert Space. We propose a new approximation method based on a discretized optimization problem in a finite-dimensional Hilbert space under the same set of constraints. We prove that the approximate solution converges uniformly to the optimal constrained interpolating function. An algorithm is derived and numerical examples with boundedness and mono-tonicity constraints in one and two dimensions are given

Parallel and pseudorandom discrete event system specification vs. networks of spiking neurons: Formalization and preliminary implementation results

International audienceUsual Parallel Discrete Event System Specification (P-DEVS) allows specifying systems from modeling to simulation. However, the framework does not incorporate parallel and stochastic simulations. This work intends to extend P-DEVS to parallel simulations and pseudorandom number generators in the context of a spiking neural network. The discrete event specification presented here makes explicit and centralized the parallel computation of events as well as their routing, making further implementations more easy. It is then expected to dispose of a well defined mathematical and computational framework to deal with networks of spiking neurons

Global Trends in the Status of Bird and Mammal Pollinators

Biodiversity is declining, with direct and indirect effects on ecosystem func-tions and services that are poorly quantified. Here, we develop the first globalassessment of trends in pollinators, focusing on pollinating birds and mam-mals. A Red List Index for these species shows that, overall, pollinating birdand mammal species are deteriorating in status, with more species movingtoward extinction than away from it. On average, 2.5 species per year havemoved one Red List category toward extinction in recent decades, represent-ing a substantial increase in the extinction risk across this set of species. Thismay be impacting the delivery of benefits that these species provide to people.We recommend that the index be expanded to include taxonomic groups thatcontribute more significantly to pollination, such as bees, wasps, and butter-flies, thereby giving a more complete picture of the state of pollinating speciesworldwide

Adherens junction remodeling by the Notch pathway in Drosophila melanogaster oogenesis

Identifying genes involved in the control of adherens junction (AJ) remodeling is essential to understanding epithelial morphogenesis. During follicular epithelium development in Drosophila melanogaster, the main body follicular cells (MBFCs) are displaced toward the oocyte and become columnar. Concomitantly, the stretched cells (StCs) become squamous and flatten around the nurse cells. By monitoring the expression of epithelial cadherin and Armadillo, I have discovered that the rate of AJ disassembly between the StCs is affected in follicles with somatic clones mutant for fringe or Delta and Serrate. This results in abnormal StC flattening and delayed MBFC displacement. Additionally, accumulation of the myosin II heavy chain Zipper is delayed at the AJs that require disassembly. Together, my results demonstrate that the Notch pathway controls AJ remodeling between the StCs and that this role is crucial for the timing of MBFC displacement and StC flattening. This provides new evidence that Notch, besides playing a key role in cell differentiation, also controls cell morphogenesis