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

First hitting times for general non-homogeneous 1d diffusion processes: density estimates in small time

Motivated by some applications in neurosciences, we here collect several estimates for the density of the first hitting time of a threshold by a non-homogeneous one-dimensional diffusion process and for the density of the associated process stopped at the threshold. We first remind the reader of the connection between both. We then provide some Gaussian type bounds for the density of the stopped process. We also discuss the stability of the density with respect to the drift. Proofs mainly rely on the parametrix expansion

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

mTORC1 Controls Phase Separation and the Biophysical Properties of the Cytoplasm by Tuning Crowding

International audienceMacromolecular crowding has a profound impact on reaction rates and the physical properties of the cell interior, but the mechanisms that regulate crowding are poorly understood. We developed genetically encoded multimeric nanoparticles (GEMs) to dissect these mechanisms. GEMs are homomultimeric scaffolds fused to a fluorescent protein that self-assemble into bright, stable particles of defined size and shape. By combining tracking of GEMs with genetic and pharmacological approaches, we discovered that the mTORC1 pathway can modulate the effective diffusion coefficient of particles ≥20 nm in diameter more than 2-fold by tuning ribosome concentration, without any discernable effect on the motion of molecules ≤5 nm. This change in ribosome concentration affected phase separation both in vitro and in vivo. Together, these results establish a role for mTORC1 in controlling both the mesoscale biophysical properties of the cytoplasm and biomolecular condensation

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