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J. Chevallier A. Duarte E. Löcherbach G. Ost 《Stochastic Processes and their Applications》2019,129(1):1-27
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis. 相似文献
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Scheibler Nihoul L. Grünhut Herzfeld C. Killing Märcker Ost P. Dobriner Prager Farnsteiner und R. Hefelmann 《Fresenius' Journal of Analytical Chemistry》1897,36(1):48-51
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H. Ost und Kusserow 《Fresenius' Journal of Analytical Chemistry》1897,36(1):395-402
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H. Ost 《Fresenius' Journal of Analytical Chemistry》1891,30(1):631-633
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A series of inequalities are developed relating the spectral radius ?(A ° B) of the Schur product A ° B of two nonnegative matrices A and B with those of ?(A ° A) and ?(B ° B) yielding . As a corollary it is proved that the spectral radius of the Schur powers ?r = ?(A[r]), A[r] = A ° A °?°A (r factors) satisfies is decreasing while is increasing, the latter provided A is a stochastic matrix. The entropy of a finite stationary Markov chain is identified with . A number of majorization comparisons for the spectral radius of Schur powers is given. 相似文献
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R. Ost K. Bethge H. Gemmeke L. Lassen D. Scholz 《Zeitschrift für Physik A Hadrons and Nuclei》1974,266(5):369-371
Three-particle correlations in the reaction208Pb+6Li were studied near the Coulomb threshold between \(E_{6_{Li} } = 24\) and 30 MeV. Three reaction mechanisms contribute predominantly to the observed coincidences of the charged particles: 1. Coulomb excitation of the 2.184 MeV,J=3+ state of6Li, followed by the decay intoα+d, 2. Deuteron pick-up of the6Li to the ground state of8Be and sequential decay into twoα-particles and 3. Neutron-transfer to the ground state and the first excited states of209Pb:208Pb(6Li,αp). The last two reaction mechanisms explain the previously measured large contributions to theα-channel relative to thed-channel. 相似文献