Towards the Modeling of Neuronal Firing by Gaussian Processes

This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the firing densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's firing probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes characterized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal firing densities are not available.Comment: 10 pages, 3 figures, to be published in Scientiae Mathematicae Japonica

Seismic Vulnerability Assessment of a Historical Church: Limit Analysis and Nonlinear Finite Element Analysis

The seismic vulnerability of a historical Basilica church located in Italy is studied by means of limit analysis and nonlinear finite element (FE) analysis. Attention is posed to the failure mechanisms involving the façade of the church and its interaction with the lateral walls. In particular, the limit analysis and the nonlinear FE analysis provide an estimate of the load collapse multiplier of the failure mechanisms. Results obtained from both approaches are in agreement and can support the selection of possible retrofitting measures to decrease the vulnerability of the church under seismic loads

The Cochlear Tuning Curve

The tuning curve of the cochlea measures how large an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to infer what a sound was on the basis of the cochlear output. A simple model is presented showing that only two elements are sufficient for establishing the cochlear tuning curve: a broadly tuned traveling wave, moving unidirectionally from high to low frequencies, and a set of mechanosensors poised at the threshold of an oscillatory (Hopf) instability. These two components suffice to generate the various frequency-response regimes which are needed for a cochlear tuning curve with a high slope

Simulation of sample paths for Gauss-Markov processes in the presence of a reflecting boundary

Algorithms for the simulation of sample paths of Gauss–Markov processes, restricted from below by particular time-dependent reflecting boundaries, are proposed. These algorithms are used to build the histograms of first passage time density through specified boundaries and for the estimation of related moments. Particular attention is dedicated to restricted Wiener and Ornstein–Uhlenbeck processes due to their central role in the class of Gauss–Markov processes

A lattice study of the strangeness content of the nucleon

We determine the quark contributions to the nucleon spin Delta s, Delta u and Delta d as well as their contributions to the nucleon mass, the sigma-terms. This is done by computing both, the quark line connected and disconnected contributions to the respective matrix elements, using the non-perturbatively improved Sheikholeslami-Wohlert Wilson Fermionic action. We simulate n_F=2 mass degenerate sea quarks with a pion mass of about 285 MeV and a lattice spacing a = 0.073 fm. The renormalization of the matrix elements involves mixing between contributions from different quark flavours. The pion-nucleon sigma-term is extrapolated to physical quark masses exploiting the sea quark mass dependence of the nucleon mass. We obtain the renormalized value sigma_{piN}=38(12) MeV at the physical point and the strangeness fraction f_{Ts}=sigma_s/m_N=0.012(14)(+10-3) at our larger than physical sea quark mass. For the strangeness contribution to the nucleon spin we obtain in the MSbar scheme at the renormalization scale of 2.71 GeV Delta s = -0.020(10)(2).Comment: 7 pages, 3 figures, Invited Talk at the 33rd Erice School on Nuclear Physics, Erice, 16-24 September 2011, Ital

Large Loops of Magnetic Current and Confinement in Four Dimensional U(1)U(1) Lattice Gauge Theory

We calculate the heavy quark potential from the magnetic current due to monopoles in four dimensional $U(1)$ lattice gauge theory. The magnetic current is found from link angle configurations using the DeGrand-Toussaint identification method. The link angle configurations are generated in a cosine action simulation on a $24^4$ lattice. The magnetic current is resolved into large loops which wrap around the lattice and simple loops which do not. Wrapping loops are found only in the confined phase. It is shown that the long range part of the heavy quark potential, in particular the string tension, can be calculated solely from the large, wrapping loops of magnetic current.Comment: 15 pages (Latex file plus 3 postscript files appended), Univeristy of Illinois Preprint ILL-(TH)-93-\#1