Laws of large numbers and Langevin approximations for stochastic neural field equations

In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. Though the latter divergence is not necessary. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably rescaled, converges to a centered Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the Chemical Langevin Equation in the present setting. On a technical level we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces and by this are able to incorporate spatial structures of the underlying model.Comment: 38 page

Large Deviations for Nonlocal Stochastic Neural Fields

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a $Q$-Wiener process and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substanial difficulties but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multi-scale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Comment: 29 page

Genetic parameters of the gestation length in Tyrolean Fleckvieh

International audienc

Detection of antihydrogen annihilations with a Si-micro-strip and pure CsI detector

In 2002, the ATHENA collaboration reported the creation and detection of cold (~15 K) antihydrogen atoms [1]. The observation was based on the complete reconstruction of antihydrogen annihilations, simultaneous and spatially correlated annihilations of an antiproton and a positron. Annihilation byproducts are measured with a cylindrically symmetric detector system consisting of two layers of double sided Si-micro-strip modules that are surrounded by 16 rows of 12 pure CsI crystals (13 x 17.5 x 17 mm^3). This paper gives a brief overview of the experiment, the detector system, and event reconstruction. Reference 1. M. Amoretti et al., Nature 419, 456 (2002).Comment: 7 pages, 5 figures; Proceedings for the 8th ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applications (Como, Italy October 2003) to be published by World Scientific (style file included

The ALICE silicon pixel detector read-out electronics

The ALICE silicon pixel detector (SPD) constitutes the two innermost layers of the ALICE inner tracker system. The SPD contains 10 million pixels segmented in 120 detector modules (half staves), which are connected to the offdetector electronics with bidirectional optical links. Raw data from the on-detector electronics are sent to 20 FPGA-based processor cards (Routers) each carrying three 2-channel linkreceiver daughter-cards. The routers process the data and send them to the ALICE DAQ system via the ALICE detector data link (DDL). The SPD control, configuration and data monitoring is performed via the VME interface of the routers. This paper describes the detector readout and control via the off-detector electronics

Performance of ALICE pixel prototypes in high energy beams

The two innermost layers of the ALICE inner tracking system are instrumented with silicon pixel detectors. Single chip assembly prototypes of the ALICE pixels have been tested in high energy particle beams at the CERN SPS. Detection efficiency and spatial precision have been studied as a function of the threshold and the track incidence angle. The experimental method, data analysis and main results are presented.Comment: 10 pages, 9 figures, contribution to PIX2005 Workshop, Bonn (Germany), 5-8 September 200