Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Geometry vs appearance for discriminating between posed and spontaneous emotions

Spontaneous facial expressions differ from posed ones in appearance, timing and accompanying head movements. Still images cannot provide timing or head movement information directly. However, indirectly the distances between key points on a face extracted from a still image using active shape models can capture some movement and pose changes. This information is superposed on information about non-rigid facial movement that is also part of the expression. Does geometric information improve the discrimination between spontaneous and posed facial expressions arising from discrete emotions? We investigate the performance of a machine vision system for discrimination between posed and spontaneous versions of six basic emotions that uses SIFT appearance based features and FAP geometric features. Experimental results on the NVIE database demonstrate that fusion of geometric information leads only to marginal improvement over appearance features. Using fusion features, surprise is the easiest emotion (83.4% accuracy) to be distinguished, while disgust is the most difficult (76.1%). Our results find different important facial regions between discriminating posed versus spontaneous version of one emotion and classifying the same emotion versus other emotions. The distribution of the selected SIFT features shows that mouth is more important for sadness, while nose is more important for surprise, however, both the nose and mouth are important for disgust, fear, and happiness. Eyebrows, eyes, nose and mouth are important for anger.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Does emotion modulate the blink reflex in human conditioning? Startle potentiation during pleasant and unpleasant cues in the picture-picture paradigm

Emotional processes modulate the size of the eyeblink startle reflex in a picture-viewing paradigm, but it is unclear whether emotional processes are responsible for blink modulation in human conditioning. Experiment 1 involved an aversive differential conditioning phase followed by an extinction phase in which acoustic startle probes were presented during CS+, CS-, and intertrial intervals. Valence ratings and affective priming showed the CS+ was unpleasant postacquisition. Blink startle magnitude was larger during CS+ than during CS-. Experiment 2 used the same design in two groups trained with pleasant or unpleasant pictorial USs. Ratings and affective priming indicated that the CS+ had become pleasant or unpleasant in the respective group. Regardless of CS valence, blink startle was larger during CS+ than CS- in both groups. Thus, startle was not modulated by CS valence.

Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data

In this paper we present a sequential Monte Carlo algorithm for Bayesian sequential experimental design applied to generalised non-linear models for discrete data. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple re-weighting step. We also consider a flexible parametric model for the stimulus-response relationship together with a newly developed hybrid design utility that can produce more robust estimates of the target stimulus in the presence of substantial model and parameter uncertainty. The algorithm is applied to hypothetical clinical trial or bioassay scenarios. In the discussion, potential generalisations of the algorithm are suggested to possibly extend its applicability to a wide variety of scenarios

Associations between young children's emotion attributions and prediction of outcome in differing social situations

Associations between young children's attributions of emotion at different points in a story, and with regard to their own prediction about the story's outcome, were investigated using two hypothetical scenarios of social and emotional challenge (social entry and negative event). First grade children (N = 250) showed an understanding that emotions are tied to situational cues by varying the emotions they attributed both between and within scenarios. Furthermore, emotions attributed to the main protagonist at the beginning of the scenarios were differentially associated with children's prediction of a positive or negative outcome and with the valence of the emotion attributed at the end of the scenario. Gender differences in responses to some items were also found. © 2010 The British Psychological Society.

Solder joint defects classification using the Log-Gabor Filter, the Discrete Wavelet Transform and the Discrete Cosine Transform

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure project quality and reliability. This paper proposes the use of the Log-Gabor filter bank, Discrete Wavelet Transform and Discrete Cosine Transform for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Towards spontaneous facial expression recognition in real-world video

Facial expression is an important channel of human social communication. Facial expression recognition (FER) aims to perceive and understand emotional states of humans based on information in the face. Building robust and high performance FER systems that can work in real-world video is still a challenging task, due to the various unpredictable facial variations and complicated exterior environmental conditions, as well as the difficulty of choosing a suitable type of feature descriptor for extracting discriminative facial information. Facial variations caused by factors such as pose, age, gender, race and occlusion, can exert profound influence on the robustness, while a suitable feature descriptor largely determines the performance. Most present attention on FER has been paid to addressing variations in pose and illumination. No approach has been reported on handling face localization errors and relatively few on overcoming facial occlusions, although the significant impact of these two variations on the performance has been proved and highlighted in many previous studies. Many texture and geometric features have been previously proposed for FER. However, few comparison studies have been conducted to explore the performance differences between different features and examine the performance improvement arisen from fusion of texture and geometry, especially on data with spontaneous emotions. The majority of existing approaches are evaluated on databases with posed or induced facial expressions collected in laboratory environments, whereas little attention has been paid on recognizing naturalistic facial expressions on real-world data. This thesis investigates techniques for building robust and high performance FER systems based on a number of established feature sets. It comprises of contributions towards three main objectives: (1) Robustness to face localization errors and facial occlusions. An approach is proposed to handle face localization errors and facial occlusions using Gabor based templates. Template extraction algorithms are designed to collect a pool of local template features and template matching is then performed to covert these templates into distances, which are robust to localization errors and occlusions. (2) Improvement of performance through feature comparison, selection and fusion. A comparative framework is presented to compare the performance between different features and different feature selection algorithms, and examine the performance improvement arising from fusion of texture and geometry. The framework is evaluated for both discrete and dimensional expression recognition on spontaneous data. (3) Evaluation of performance in the context of real-world applications. A system is selected and applied into discriminating posed versus spontaneous expressions and recognizing naturalistic facial expressions. A database is collected from real-world recordings and is used to explore feature differences between standard database images and real-world images, as well as between real-world images and real-world video frames. The performance evaluations are based on the JAFFE, CK, Feedtum, NVIE, Semaine and self-collected QUT databases. The results demonstrate high robustness of the proposed approach to the simulated localization errors and occlusions. Texture and geometry have different contributions to the performance of discrete and dimensional expression recognition, as well as posed versus spontaneous emotion discrimination. These investigations provide useful insights into enhancing robustness and achieving high performance of FER systems, and putting them into real-world applications.