Formal methods for the development and verification of autonomic IT systems

This chapter explores ways in which rigorous mathematical techniques, termed formal methods, can be employed to improve the predictability and dependability of autonomic computing. Model checking, formal specification, and quantitative verification are presented in the contexts of conflict detection in autonomic computing policies, and of implementation of goal and utility-function policies in autonomic IT systems, respectively. Each of these techniques is illustrated using a detailed case study, and analysed to establish its merits and limitations. The analysis is then used as a basis for discussing the challenges and opportunities of this endeavour to transition the development of autonomic IT systems from the current practice of using ad-hoc methods and heuristic towards a more principled approach. © 2012, IGI Global.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Motion, flash, and flicker:A unified spatiotemporal model of perceived edge sharpening

Blurred edges appear sharper in motion than when they are stationary. We proposed a model of this motion sharpening that invokes a local, nonlinear contrast transducer function (Hammett et al, 1998 Vision Research 38 2099-2108). Response saturation in the transducer compresses or 'clips' the input spatial waveform, rendering the edges as sharper. To explain the increasing distortion of drifting edges at higher speeds, the degree of nonlinearity must increase with speed or temporal frequency. A dynamic contrast gain control before the transducer can account for both the speed dependence and approximate contrast invariance of motion sharpening (Hammett et al, 2003 Vision Research, in press). We show here that this model also predicts perceived sharpening of briefly flashed and flickering edges, and we show that the model can account fairly well for experimental data from all three modes of presentation (motion, flash, and flicker). At moderate durations and lower temporal frequencies the gain control attenuates the input signal, thus protecting it from later compression by the transducer. The gain control is somewhat sluggish, and so it suffers both a slow onset, and loss of power at high temporal frequencies. Consequently, brief presentations and high temporal frequencies of drift and flicker are less protected from distortion, and show greater perceptual sharpening.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Approximate, Average, Dynamic Models of Uncontrolled Rectifiers for Aircraft Applications

To carry out stability and voltage regulation studies on more electric aircraft systems in which there is a preponderance of multi-pulse, rectifier-fed motor-drive equipment, average dynamic models of the rectifier converters are required. Existing methods are difficult to apply to anything other than single converters with a low pulse number. Therefore an efficient, compact method for deriving the approximate, linear, average model of 6- and 12-pulse rectifiers, based on the assumption of a small duration of the overlap angle is presented. The models are validated against detailed simulations and laboratory prototypes.

How checking breeds doubt:reduced performance in a simple working memory task

A paradox of memory research is that repeated checking results in a decrease in memory certainty, memory vividness and confidence [van den Hout, M. A., & Kindt, M. (2003a). Phenomenological validity of an OCD-memory model and the remember/know distinction. Behaviour Research and Therapy, 41, 369–378; van den Hout, M. A., & Kindt, M. (2003b). Repeated checking causes memory distrust. Behaviour Research and Therapy, 41, 301–316]. Although these findings have been mainly attributed to changes in episodic long-term memory, it has been suggested [Shimamura, A. P. (2000). Toward a cognitive neuroscience of metacognition. Consciousness and Cognition, 9, 313–323] that representations in working memory could already suffer from detrimental checking. In two experiments we set out to test this hypothesis by employing a delayed-match-to-sample working memory task. Letters had to be remembered in their correct locations, a task that was designed to engage the episodic short-term buffer of working memory [Baddeley, A. D. (2000). The episodic buffer: a new component in working memory? Trends in Cognitive Sciences, 4, 417–423]. Of most importance, we introduced an intermediate distractor question that was prone to induce frustrating and unnecessary checking on trials where no correct answer was possible. Reaction times and confidence ratings on the actual memory test of these trials confirmed the success of this manipulation. Most importantly, high checkers [cf. VOCI; Thordarson, D. S., Radomsky, A. S., Rachman, S., Shafran, R, Sawchuk, C. N., & Hakstian, A. R. (2004). The Vancouver obsessional compulsive inventory (VOCI). Behaviour Research and Therapy, 42(11), 1289–1314] were less accurate than low checkers when frustrating checking was induced, especially if the experimental context actually emphasized the irrelevance of the misleading question. The clinical relevance of this result was substantiated by means of an extreme groups comparison across the two studies. The findings are discussed in the context of detrimental checking and lack of distractor inhibition as a way of weakening fragile bindings within the episodic short-term buffer of Baddeley's (2000) model. Clinical implications, limitations and future research are considered.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.