A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations

Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster--Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behavior of the perturbed chain is studied. Applications are given to numerical approximations of a randomly impulsed ODE, an Itô stochastic differential equation (SDE), and a parabolic stochastic partial differential equation (SPDE) subject to space-time Brownian noise. Existing perturbation theories for geometrically ergodic Markov chains are not readily applicable to these situations since they require very stringent hypotheses on the perturbations

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE

An event based topic learning pipeline for neuroimaging literature mining

Neuroimaging text mining extracts knowledge from neuroimaging texts and has received widespread attention. Topic learning is an important research focus of neuroimaging text mining. However, current neuroimaging topic learning researches mainly used traditional probability topic models to extract topics from literature and cannot obtain high-quality neuroimaging topics. The existing topic learning methods also cannot meet the requirements of topic learning oriented to full-text neuroimaging literature. In this paper, three types of neuroimaging research topic events are defined to describe the process and result of neuroimaging researches. An event based topic learning pipeline, called neuroimaging Event-BTM, is proposed to realize topic learning from full-text neuroimaging literature. The experimental results on the PLoS One data set show that the accuracy and completeness of the proposed method are significantly better than the existing main topic learning methods

Neural field models with threshold noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches

Deep context of citations using machine‑learning models in scholarly full‑text articles

Information retrieval systems for scholarly literature rely heavily not only on text matching but on semantic- and context-based features. Readers nowadays are deeply interested in how important an article is, its purpose and how influential it is in follow-up research work. Numerous techniques to tap the power of machine learning and artificial intelligence have been developed to enhance retrieval of the most influential scientific literature. In this paper, we compare and improve on four existing state-of-the-art techniques designed to identify influential citations. We consider 450 citations from the Association for Computational Linguistics corpus, classified by experts as either important or unimportant, and further extract 64 features based on the methodology of four state-of-the-art techniques. We apply the Extra-Trees classifier to select 29 best features and apply the Random Forest and Support Vector Machine classifiers to all selected techniques. Using the Random Forest classifier, our supervised model improves on the state-of-the-art method by 11.25%, with 89% Precision-Recall area under the curve. Finally, we present our deep-learning model, the Long Short-Term Memory network, that uses all 64 features to distinguish important and unimportant citations with 92.57% accuracy