A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Factors influencing robustness and effectiveness of conditional random fields in active learning frameworks

Active learning approaches reduce the annotation cost required by traditional supervised approaches to reach the same effectiveness by actively selecting informative instances during the learning phase. However, effectiveness and robustness of the learnt models are influenced by a number of factors. In this paper we investigate the factors that affect the effectiveness, more specifically in terms of stability and robustness, of active learning models built using conditional random fields (CRFs) for information extraction applications. Stability, defined as a small variation of performance when small variation of the training data or a small variation of the parameters occur, is a major issue for machine learning models, but even more so in the active learning framework which aims to minimise the amount of training data required. The factors we investigate are a) the choice of incremental vs. standard active learning, b) the feature set used as a representation of the text (i.e., morphological features, syntactic features, or semantic features) and c) Gaussian prior variance as one of the important CRFs parameters. Our empirical findings show that incremental learning and the Gaussian prior variance lead to more stable and robust models across iterations. Our study also demonstrates that orthographical, morphological and contextual features as a group of basic features play an important role in learning effective models across all iterations.

Characterization of epitopes for virus-neutralizing monoclonal antibodies to Ross River virus E2 using phage-displayed random peptide libraries

Ross River virus (RRV) is the predominant cause of epidemic polyarthritis in Australia, yet the antigenic determinants are not well defined. We aimed to characterize epitope(s) on RRV-E2 for a panel of monoclonal antibodies (MAbs) that recognize overlapping conformational epitopes on the E2 envelope protein of RRV and that neutralize virus infection of cells in vitro. Phage-displayed random peptide libraries were probed with the MAbs T1E7, NB3C4, and T10C9 using solution-phase and solid-phase biopanning methods. The peptides VSIFPPA and KTAISPT were selected 15 and 6 times, respectively, by all three of the MAbs using solution-phase biopanning. The peptide LRLPPAP was selected 8 times by NB3C4 using solid-phase biopanning; this peptide shares a trio of amino acids with the peptide VSIFPPA. Phage that expressed the peptides VSIFPPA and LRLPPAP were reactive with T1E7 and/or NB3C4, and phage that expressed the peptides VSIFPPA, LRLPPAP, and KTAISPT partially inhibited the reactivity of T1E7 with RRV. The selected peptides resemble regions of RRV-E2 adjacent to sites mutated in neutralization escape variants of RRV derived by culture in the presence of these MAbs (E2 210-219 and 238-245) and an additional region of E2 172-182. Together these sites represent a conformational epitope of E2 that is informative of cellular contact sites on RRV.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.