Linear Response of General Observables in Spiking Neuronal Network Models

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.     

隐马尔可夫因子分析模型的半参数贝叶斯分析

因子模型在刻画潜在因素(因子)与观测变量间的影响关系并进而解释多元观测指标(变量)间的相关性方面具有重要作用.在实际应用中,观测数据往往呈现出时序变异多峰,偏态等特性.将经典的因子分析延伸到带有时齐隐马尔可夫模型的动力因子模型,并建立了半参数贝叶斯分析程序.分块GIBBS抽样器用以后验抽样.经验结果展示所建立的统计程序是有效的.     

Molecular simulation of the hydration Gibbs energy of barbiturates

In the present work, molecular dynamics calculations of the Gibbs energy of hydration of 10 different substituted barbiturates in SPC/E water were performed using thermodynamic integration. Given that experimental determination of the Gibbs hydration energy for this class of compounds is currently unfeasible, computer simulations appear as the only alternative for the estimation of this important quantity. Several simulation parameters are discussed and optimized based on calculations for barbituric acid. It is concluded that accounting for electrostatic interactions with the Reaction-Field method can be up to two times faster than with Particle-Mesh-Ewald method, without loss of accuracy. Different number of solvent molecules and simulation lengths were also tested. Lennard-Jones and electrostatic contributions were scaled down to zero in an independent way. It is shown that the electrostatic contribution is dominant (representing approximately 90% of the total Gibbs energy of hydration) and that barbiturate intra-molecular interactions cannot be neglected. The importance of the electrostatic contribution is attributed to the formation of hydrogen bonds between the barbiturates and water, which play an important role in the solvation process. The influence of the different substituents and their contribution to the Gibbs energy of hydration was assessed. Finally, the Lennard-Jones contributions and the total hydration Gibbs energy can both be correlated against molecular weight or partition coefficient data for mono- and di-substituted barbiturates.     

On stable parametric finite element methods for the Stefan problem and the Mullins–Sekerka problem with applications to dendritic growth

We introduce a parametric finite element approximation for the Stefan problem with the Gibbs–Thomson law and kinetic undercooling, which mimics the underlying energy structure of the problem. The proposed method is also applicable to certain quasi-stationary variants, such as the Mullins–Sekerka problem. In addition, fully anisotropic energies are easily handled. The approximation has good mesh properties, leading to a well-conditioned discretization, even in three space dimensions. Several numerical computations, including for dendritic growth and for snow crystal growth, are presented.     

Consistent scheme for computing standard hydrogen electrode and redox potentials

The standard hydrogen electrode (SHE) potential in aqueous solution was evaluated with new computational procedure that provides the Gibbs energy of a proton in aqueous solution from the experimental pK_a value and the Gibbs energy change by deprotonation reactions of several neutral alcohol molecules. With our computational scheme, the CCSD(T)/aug‐cc‐pVDZ method provides the SHE potential of 4.52 V, which is almost the same as the experimental SHE potential. This scheme also reproduces well the redox potentials of several typical reactions within almost 0.1 V. B3LYP also gives excellent redox potentials of the same reactions with almost the same accuracy with our new computational scheme. © 2012 Wiley Periodicals, Inc.     

Invariant measures and disintegrations with applications to Palm and related kernels

Consider a locally compact group G acting measurably on some spaces S and T. We prove a general representation of G-invariant measures on S and the existence of invariant disintegrations of jointly invariant measures on S × T. The results are applied to Palm and related kernels associated with a stationary random pair (ξ,η), where ξ is a random measure on S and η is a random element in T. An erratum to this article can be found at     

Computational Methods for Semiparametric Linear Regression with Censored Data

Abstract

Semiparametric linear regression with censored data assumes a linear relationship between failure time and covariates without specifying the distributional form of the error term. This approach has attracted considerable attention recently. Most notably, rank regression methods have been derived for parameter estimation, hypothesis testing, and goodness-of-fit analysis. The implementation of these methods requires minimizing discrete objective functions with multiple local minima. Conventional optimization algorithms cannot be used to solve such minimization problems. We develop computational methods to implement rank regression procedures using simulated annealing. Two real data sets are used for illustration. Applications of the new algorithms to the modified least squares estimator of Buckley and James and several other related problems are also described.     

On a Relation between Intrinsic and Extrinsic Dirichlet Forms for Interacting Particle Systems

In this paper we extend the result obtained in [AKR98] (see also [AKR96a]) on the representation of the intrinsic pre–Dirichlet form ℰ^Γ of the Poisson measure π_σ in terms of the extrinsic one ℰ^P. More precisely, replacing π_σ by a Gibbs measure μ on the configuration space Γ_X we derive a relation between the intrinsic prend–Dirichlet form ℰ^Γ_μ of the measure μ and the extrinsic one ℰ^P. As a consequence we prove the closability of ℰ^Γ_μ on L²(Γ_X, μ) under very general assumptions on the interaction potential of the Gibbs measures μ.     

Local Stability of McKean–Vlasov Equations Arising from Heterogeneous Gibbs Systems Using Limit of Relative Entropies

A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, the law of large numbers is shown to hold in a multi-class context, resulting in the weak convergence of the empirical vector towards the solution of a McKean–Vlasov system of equations. We then investigate the local stability of the limiting McKean–Vlasov system through the construction of a local Lyapunov function. We first compute the limit of adequately scaled relative entropy functions associated with the explicit stationary distribution of the N-particles system. Using a Laplace principle for empirical vectors, we show that the limit takes an explicit form. Then we demonstrate that this limit satisfies a descent property, which, combined with some mild assumptions shows that it is indeed a local Lyapunov function.     

Stationary distribution for repairable systems

Stationary distribution of repairable systems with limited service and spare devices is considered on an equilibrium set by using the Gibbs potential representation. As an application we consider the reliability of k‐out‐of‐n system. Copyright © 2000 John Wiley & Sons, Ltd.