Particle systems with a singular mean-field self-excitation. Application to neuronal networks

We discuss the construction and approximation of solutions to a nonlinear McKean-Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of neurons which interact with one another. Each time a proportion of neurons 'spike', the whole network instantaneously receives an excitatory kick. The instantaneous nature of the excitation makes the system singular and prevents the application of standard results from the literature. Making use of the Skorohod M1 topology, we prove that, for the right notion of a 'physical' solution, the nonlinear equation can be approximated either by a finite particle system or by a delayed equation. As a by-product, we obtain the existence of 'synchronized' solutions, for which a macroscopic proportion of neurons may spike at the same time

Renewables Intermittency: Operational Limits and Implications for Long-Term Energy System Models

In several regions of the world, the share of intermittent renewables (such as wind and solar PV) in electricity generation is rapidly increasing. The current share of these renewable energy sources (RES) can still more or less be handled by existing systems and flexibility, benefiting from remaining excess capacity of dispatchable (backup) generation and links to other grids that can balance the intermittency. However, often higher levels of intermittent RES are envisaged for the future, posing significant challenges on system operation and planning. In assessing possible energy futures, long-term energy system models are typically used. The representation of RES in such models needs careful attention, as intermittent RES come with a number of specific characteristics, making them different from conventional dispatchable generation. This paper focuses on technical implications related to systems trying to achieve high shares of renewable electricity. The relevance of demand and RES generation profiles are demonstrated. After some threshold, a sharp decreasing relationship between installed RES capacity and marginal contribution in terms of generation is identified; therefore, even with perfect backup, a technical limit exists on achievable RES shares. The impact of RES on net demand peak reduction is also addressed. In the absence of system flexibility, substantial backup is required to ensure reliable electricity provision. The role of different flexibility instruments is explored and is found to be significant. Reflections are provided on options to include these aspects in long-term energy system models

Taille de la population d’Avahi laniger dans la réserve d’Ambodiriana-Manompana, Nord-est de Madagascar

Avahi laniger est le seul lémurien nocturne appartenant à la famille des Indriidae qui habite les forêts humides de l’est de Madagascar (Mittermeier et. al., 2010) dont une partie disparaît chaque année (exploitation du bois, pratique du «tavy» ou culture sur brûlis) (Beaucent and Fayolle, 2011; Lehman and Wright, 2000). La fragmentation et la destruction de leur habitat ainsi que la chasse menacent la survie de nombreuses espèces de lémuriens incluant celle de A. laniger (Jenkins et. al., 2011; Rakotondravony and Rabenandrasana, 2011; Anderson, Rowcliffe and Cowlishaw, 2007). Nous avons réalisé, entre fin Avril et Mai 2012, une étude de densité de la population de A. laniger au sein de l’aire protégée de Manompana-Ambodiriana afin d’estimer la taille de la population totale et de déterminer l’impact du projet de conservation menée par l’Association de Défense de la Forêt d’Ambodiriana (ADEFA) qui recherche l’évolution démographique à moyen terme de cette espèce."LABEX" TULIP: (ANR-10-LABX-41), fct fellowship: (SFRH/BD/64875/2009)

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

Verticalization of bacterial biofilms

Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional structure with a vertically-aligned core. Here, we elucidate the physical mechanism underpinning this transition using a combination of agent-based and continuum modeling. We find that verticalization proceeds through a series of localized mechanical instabilities on the cellular scale. For short cells, these instabilities are primarily triggered by cell division, whereas long cells are more likely to be peeled off the surface by nearby vertical cells, creating an "inverse domino effect". The interplay between cell growth and cell verticalization gives rise to an exotic mechanical state in which the effective surface pressure becomes constant throughout the growing core of the biofilm surface layer. This dynamical isobaricity determines the expansion speed of a biofilm cluster and thereby governs how cells access the third dimension. In particular, theory predicts that a longer average cell length yields more rapidly expanding, flatter biofilms. We experimentally show that such changes in biofilm development occur by exploiting chemicals that modulate cell length.Comment: Main text 10 pages, 4 figures; Supplementary Information 35 pages, 15 figure

A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation, modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (e.g. the mean pressure) and to track particles. All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean model is adopted. An adaptive algorithm that computes the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200

Phase III study of ACVBP versus ACVBP plus rituximab for patients with localized low-risk diffuse large B-cell lymphoma (LNH03-1B)

Background The superiority of a chemotherapy with doxorubicin, cyclophosphamide, vindesine, bleomycin and prednisone (ACVBP) in comparison with cyclophosphamide, doxorubicin, vincristin and prednisone plus radiotherapy for young patients with localized diffuse large B-cell lymphoma (DLBCL) was previously demonstrated. We report the results of a trial which evaluates the role of rituximab combined with ACVBP (R-ACVBP) in these patients. Patients and methods Untreated patients younger than 66 years with stage I or II DLBCL and no adverse prognostic factors of the age-adjusted International Prognostic Index were randomly assigned to receive three cycles of ACVBP plus sequential consolidation with or without the addition of four infusions of rituximab. Results A total of 223 patients were randomly allocated to the study, 110 in the R-ACVBP group and 113 in the ACVBP group. After a median follow-up of 43 months, our 3-year estimate of event-free survival was 93% in the R-ACVBP group and 82% in the ACVBP group (P = 0.0487). Three-year estimate of progression-free survival was increased in the R-ACVBP group (95% versus 83%, P = 0.0205). Overall survival did not differ between the two groups with a 3-year estimates of 98% and 97%, respectively (P = 0.686). Conclusion In young patients with low-risk localized DLBCL, rituximab combined with three cycles of ACVBP plus consolidation is significantly superior to ACVBP plus consolidation alon

Quasi-continuous Interpolation Scheme for Pathways between Distant Configurations

A quasi-continuous interpolation (QCI) scheme is introduced for characterizing physically realistic initial pathways from which to initiate transition state searches and construct kinetic transition networks. Applications are presented for peptides, proteins, and a morphological transformation in an atomic cluster. The first step in each case involves end point alignment, and we describe the use of a shortest augmenting path algorithm for optimizing permutational isomers. The QCI procedure then employs an interpolating potential, which preserves the covalent bonding framework for the biomolecules and includes repulsive terms between unconstrained atoms. This potential is used to identify an interpolating path by minimizing contributions from a connected set of images, including terms corresponding to minima in the interatomic distances between them. This procedure detects unphysical geometries in the line segments between images. The most difficult cases, where linear interpolation would involve chain crossings, are treated by growing the structure an atom at a time using the interpolating potential. To test the QCI procedure, we carry through a series of benchmark calculations where the initial interpolation is coupled to explicit transition state searches to produce complete pathways between specified local minima.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/H042660/1]This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in the Journal of Chemical Theory and Computation, copyright © American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/ct300483