Hitting time of a corner for a reflected diffusion in the square

International audienc

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

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

Characterization of Metal Aggregates by Scanning Microscopy: Particle Sizes and Space Distribution in Intermetallic Particles

Various metal aggregates prepared using ionizing radiation were studied by microscopy techniques. A metal deposit onto a carbon felt obtained from solutions containing Pt and Ru was shown to consist of nanometric particles containing both metals. Another study deals with a subnanometric silver aggregate. The nuclearity of the aggregate was studied by scanning tunneling microscopy (STM). Additional information from pulse radiolysis experiments allowed the determination of the Ag73+ stoichiometry. The third material consisted of Ag/Pd submicron powders (70/30 or 75/25% w/w) used in electronics, and made of spherical bimetallic grains; X-ray diffraction showed segregation. The spatial distribution of each metal was obtained by combining space-resolved X-ray microanalysis in the transmission electron microscope, X-ray photoelectron spectroscopy and secondary ion mass spectrometry. Each grain was shown to be core/rind structured (core: pure Ag; rind: 10-15 nm thick 11% Ag/89% Pd w/w alloy)

Xenon isotopes in Archean and Proterozoic insoluble organic matter: a robust indicator of syngenecity?

Insoluble organic materials (kerogens) isolated from ancient sedimentary rocks provide unique insights into the evolution of early life. However, establishing whether these kerogens are indeed syngenetic with the deposition of associated sedimentary host rocks, or contain contribution from episodes of secondary deposition, is not straightforward. Novel geochemical criterions are therefore required to test the syngenetic origin of Archean organic materials. On one hand, the occurrence of mass-independent fractionation of sulphur isotopes (MIF-S) provides a tool to test the Archean origin of ancient sedimentary rocks. Determining the isotope composition of sulphur within kerogens whilst limiting the contribution from associated minerals (e.g., nano-pyrites) is however challenging. On the other end, the Xe isotope composition of the Archean atmosphere has been shown to present enrichments in the light isotopes relative to its modern composition, together with a mono-isotopic deficit in ¹²⁹Xe. Given that the isotopic composition of atmospheric Xe evolved through time by mass dependent fractionation (MDF) until ∼2.5-2.0 Ga, the degree of MDF of Xe isotopes trapped in kerogens could provide a time stamp for the last chemical equilibration between organic matter and the atmosphere. However, the extent to which geological processes could affect the signature of Xe trapped in ancient kerogen remains unclear. In this contribution, we present new Ar, Kr and Xe isotopic data for four kerogens isolated from 3.4 to 1.8 Gy-old cherts and confirm that Xe isotopes from the Archean atmosphere can be retained within kerogens. However, new Xe-derived model ages are lower than expected from the ages of host rocks, indicating that initially trapped Xe components were at least partially lost and/or mixed together with some Xe carried out by younger generations of organic materials, therefore complicating the Xe-based dating method. Whilst non-null Δ³³S values and ¹²⁹Xe deficits relative to modern atmosphere constitute reliable imprints from the Archean atmosphere, using Xe isotopes to provide information on the syngenetic origin of ancient organic matter appears to be a promising - but not unequivocal - tool that calls for further analytical development

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

RNA fusions involving CD28 are rare in peripheral T-cell lymphomas and concentrate mainly in those derived from follicular helper T cells.

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