Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.

Competitive adsorption between bovine serum albumin and collagen observed by atomic force microscope

Atomic force microscopy (AFM) was used to study the competitive adsorption between bovine serum albumin (BSA) and type I collagen on hydrophilic and hydrophobic silicon wafers. BSA showed a grain shape and the type I collagen displayed fibril-like molecules with relatively homogeneous height and width, characterized with clear twisting (helical formation). These AFM images illustrated that quite a lot of type I collagen appeared in the adsorption layer on hydrophilic surface in a competitive adsorption state, but the adsorption of BSA was more preponderant than that of type I collagen on hydrophobic silicon wafer surface. The experiments showed that the influence of BSA on type I collagen adsorption on hydrophilic surface was less than that on hydrophobic surface.

Adsorption of human serum albumin onto gold: a combined electrochemical and ellipsometric study

Human serum albumin adsorption onto gold surfaces was investigated by electrochemical and ellipsometric methods. Albumin adsorption onto gold was confirmed by the change of the open circuit potential of gold and by the ellipsometric parameter variation during albumin immobilization. In both experiments the parameters reached stable values within 10-15 min. The albumin adsorption layer thickness measured with the ellipsometer was about 1.5 nm. The adsorption of albumin Under applied potential was also investigated and it was found that both positive and negative applied potential promote albumin adsorption. Changes in the optical parameters of bare gold and albumin adsorbed onto gold surface under applied potential were investigated with in Situ ellipsometry. The similarity and reversibility of the optical changes showed that adsorbed albumin was stable on the gold surface Under the applied potential range (-200-600 mV). The cyclic voltammograms of K3Fe(CN)(6) on the modified gold surface showed that albumin Could partly block the oxidation and reduction reaction. (C) 2004 Elsevier Inc. All rights reserved.

Competitive adsorption of collagen and bovine serum albumin - effect of the surface wettability

The competitive adsorption of collagen and bovine serum albumin (BSA) on surfaces with varied wettability was investigated with imaging ellipsometry, and ellipsometry. Silane modified silicon surfaces were used as substrates. The results showed that surface wettability had an important effect on protein competitive adsorption. With the decrease of surface wettability, the adsorption of collagen from the mixture solution of collagen and BSA decreased, while the adsorption of BSA increased. (C) 2003 Elsevier B.V. All rights reserved.

An overview of sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, are numerical techniques based on Importance Sampling for solving the optimal state estimation problem. The task of calibrating the state-space model is an important problem frequently faced by practitioners and the observed data may be used to estimate the parameters of the model. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed for this task accompanied with a discussion of their advantages and limitations.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Adsorption of His-tagged peptide to Ni, Cu and Au (100) surfaces: Molecular dynamics simulation

Molecular dynamics (MD) simulations are performed to study the interaction of His-tagged peptide with three different metal surfaces in explicit water. The equilibrium properties are analyzed by using pair correlation functions (PCF) to give an insight into the behavior of the peptide adsorption to metal surfaces in water solvent. The intermolecular interactions between peptide residues and the metal surfaces are evaluated. By pulling the peptide away from the peptide in the presence of solvent water, peeling forces are obtained and reveal the binding strength of peptide adsorption on nickel, copper and gold. From the analysis of the dynamics properties of the peptide interaction with the metal surfaces, it is shown that the affinity of peptide to Ni surface is the strongest, while on Cu and An the affinity is a little weaker. In MD simulations including metals, the His-tagged region interacts with the substrate to an extent greater than the other regions. The work presented here reveals various interactions between His-tagged peptide and Ni/Cu/Au surfaces. The interesting affinities and dynamical properties of the peptide are also derived. The results give predictions for the structure of His-tagged peptide adsorbing on three different metal surfaces and show the different affinities between them, which assist the understanding of how peptides behave on metal surfaces and of how designers select amino sequences in molecule devices design. (c) 2007 Elsevier Ltd. All rights reserved.

表面等离子体激元共振与生物分子相互作用分析

对表面等离子体激元共振(surface plasmon resonance, SPR)的原理和在生物学研究方面的应用进行了综述。这种技术可以直接原位、实时地跟踪生物学实验研究系统, 而不需要附加参数如进行标记等手段, 具有高敏感性, 也可以连续监测吸附或解吸附过程。目前有关的应用涉及到生物学结合分析、动力学及亲和力测定、免疫识别研究、结构与活性研究和核酸研究等多个领域。