672 research outputs found
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.
Research lette
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