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The acquisition of a scene-specific normal behaviour model underlies many existing approaches to the problem of automated video surveillance. Since it is unrealistic to acquire a comprehensive set of labelled behaviours for every surveyed scenario, modelling normal behaviour typically corresponds to modelling the distribution of a large collection of unlabelled examples. In general, however, it would be desirable to be able to filter an unlabelled dataset to remove potentially anomalous examples. This thesis proposes a simple semi-supervised learning framework that could allow a human operator to efficiently filter the examples used to construct a normal behaviour model by providing occasional feedback: Specifically, the classification output of the model under construction is used to filter the incoming sequence of unlabelled examples so that human approval is requested before incorporating any example classified as anomalous, while all other examples are automatically used for training. A key component of the proposed framework is an incremental one-class learning algorithm which can be trained on a sequence of normal examples while allowing new examples to be classified at any stage during training. The proposed algorithm represents an initial set of training examples with a kernel density estimate, before using merging operations to incrementally construct a Gaussian mixture model while minimising an information-theoretic cost function. This algorithm is shown to outperform an existing state-of-the-art approach without requiring off-line model selection. Throughout this thesis behaviours are considered in terms of whole motion trajectories: in order to apply the proposed algorithm, trajectories must be encoded with fixed length vectors. To determine an appropriate encoding strategy, an empirical comparison is conducted to determine the relative class-separability afforded by several different trajectory representations for a range of datasets. The results obtained suggest that the choice of representation makes a small but consistent difference to class separability, indicating that cubic B-Spline control points (fitted using least-squares regression) provide a good choice for use in subsequent experiments. The proposed semi-supervised learning framework is tested on three different real trajectory datasets. In all cases the rate of human intervention requests drops steadily, reaching a usefully low level of 1% in one case. A further experiment indicates that once a sufficient number of interventions has been provided, a high level of classification performance can be achieved even if subsequent requests are ignored. The automatic incorporation of unlabelled data is shown to improve classification performance in all cases, while a high level of classification performance is maintained even when unlabelled data containing a high proportion of anomalous examples is presented.

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We address the problem of the DNA sequences developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic, with long-range correlations, and the other random and delta correlated. The generator of the deterministic evolution is a nonlinear map, belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules which determine the DNA path, whereas the noise mimics the influence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an a-stable Levy process with 1 < a < 2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are cancelled on the short-range scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the Copying Mistake Map (CMM). We carry out our analysis of several DNA sequences, and of their CMM realizations, with a variety of techniques, and we especially focus on a method of regression to equilibrium, which we call the Onsager Analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are difficult to detect, since the exon "dynamics" is shown to be determined by theentaglement of three distinct and independent CMM's. Finally we study the validity of the stationary assumption in DNA sequences and we discuss a biological model for the short-range random process based on a folding mechanism of the nucleic acid in the cell nucleus.

We introduce and examine the analytic properties of the three electromagnetic transition form factors of the Sigma*-Lambda hyperon transition. In the first part of the thesis, we discuss the interaction Lagrangian for the hyperons at hand. We calculate the decay rate of the Dalitz decay  Sigma* Lambda -&gt; e+e- in the one-photon approximation in terms of the form factors, as well as the differential cross section of the scattering e+e- -&gt; Sigma*bar Lambda in the one-photon approximation. In the second part of the thesis, we build up the machinery for calculation of the form factors using dispersion relations, performing an analytic continuation from the timelike, q2 &gt; 0, to the spacelike, q2 &lt; 0, region of the virtual photon invariant mass q2. Due to an anomalous cut in the triangle diagram arising from a two-pion saturation of the photon-hyperon vertex, there is an additional term in the dispersive integral. We use the scalar three-point function as a model for the examination of the dispersive approach with the anomalous cut. The one-loop diagram is calculated both directly and using dispersion relations. After comparison of the two methods, they are found to coincide when the anomalous contribution is added to the dispersive integral in the case of the octet Sigma exchange. By examination of the branch points of the logarithm in the discontinuity, we deduce the structure of the Riemann surface of the unitarity cut and present trajectories of the branch points. The result of our analysis of the analytic structure yields a correct dispersive relation for the electromagnetic transition form factors. This opens the way for the calculation of these form factors in the low-energy region for both space- and timelike q2. As an outlook, we present preliminary calculations for the hyperon-pion scattering amplitude using the unitarity and the anomalous contribution in a once-subtracted dispersion relation. Finally we present the corresponding preliminary unsubtracted dispersive calculations for the form factors.

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the motion is Fickian with a diffusion coefficient D that depends on the concentration and type of obstacles present in the system. For intermediate times, the mean-square displacement of the particle often increases approximately as t α , with α < 1, typical of what is generally called anomalous diffusion. However, it is not clear how one can identify or choose a time or displacement interval that would give a reliable estimate of α. In this paper, we use two exact numerical approaches to obtain diffusion data for a simple Lattice Monte Carlo model in both time limits. This allows us to propose an objective definition of the transient regime and a unique value for α. Furthermore, our methodology directly gives us the length scale over which the transient regime switches to the steady-state regime. We test our proposed approach using several types of obstacle systems, and we introduce the novel concept of excess diffusion lengths. Finally, we show that the values of the parameters describing the anomalous transient regime depend on the Monte Carlo moves used to describe the dynamics of the particle, and we propose a new algorithm that correctly models the short time diffusion of a particle on a lattice.

The genus Phytophthora comprises numerous plant pathogens in both natural and managed ecosystems. For Phytophthora spp. that infect roots, dispersal occurs in soil water through a combination of advection and swimming of specialized motile propagules (zoospores). Specific biological and physico-chemical processes, however, remain poorly understood, due to difficulties in studying phenomena in opaque media and lack of a theoretical framework for analyzing transport of motile microorganisms. The goal of this research was to elucidate the impacts of advection and swimming on zoospore movement in a saturated, ideal soil. The work was accomplished in two stages, (i) conceptualization of 3-dimensional topography and flow field heterogeneity at the subpore-scale, and (ii) observation of behavior of zoospore suspensions infiltrated into saturated media. Chapter 2 introduces a 3-dimensional particle tracking method and presents two studies investigating particle transport in simplified 'ideal pores'. The first study describes 'avoidance' by latex microspheres of a volume surrounding orthogonal grain contacts and the second describes 'capture', translation, and retention of microspheres under conditions unfavorable to deposition. Chapter 3 expands on the first study and demonstrates, with the aid of computational fluid dynamics, that low flow zones associated with orthogonal grain contacts are minimally connected to the main flow. Thus, probability of entry into these regions for large, non-Brownian particles by advection alone is low. In zoospore infiltration experiments, zoospore plumes 'converged' rather than dispersing as expected. To assess the possibility of zoospore auto-aggregation driving this 'convergence', Chapter 4 delves into the 'pattern swimming' observed in free-swimming zoospore suspensions, concluding that the concentrating is an example of bioconvection. Chapter 5 introduces a conceptual model to explain the anomalous zoospore plume behavior. Random walk simulations replicated plume convergence but were less successful at modeling anisotropic dispersion. At low infiltration rates (<100 μm s⁻¹), simulations predict that zoospores will remain at or near the soil surface, resulting in greater opportunity to find host tissues or to be transported with surface water. Further investigation is necessary to develop a robust theoretical framework with appropriate conceptualization of the subpore hydrodynamic environment for predicting transport of zoospores and other motile microorganisms in porous media. / Graduation date: 2011

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This dissertation focuses on the study of spin-dependent transport in systems with strong spin-orbit coupling within their band structure. In particular we focus on the anomalous Hall effect, the spin Hall effect, and the Aharonov-Casher effect whose origins, are linked to the presence of spin-orbit coupling. Given the theoretical controversy surrounding these effects we further simplify our studies to semiconductor systems where the band structure is much simpler than in metallic systems with heavy elements. To obtain finite analytical results we focus on reduced dimensions (two and one dimensions) which can be explored experimentally. To set the stage, we discuss the origins of the strong spin-orbit coupling in semiconductors deriving the effective interaction from the Dirac equation. We discuss in detail the skew scattering contribution to the anomalous Hall effect in two-dimensional systems, which is dominant for systems with low impurity concentrations, and find that it is reduced when the two chiral subbands are partially occupied in an electron gas and vanishes for a hole gas, regardless of the band filling. We also present calculations for all contributing mechanisms. We propose a device to test this prediction and study the crossover from the intrinsic to the extrinsic anomalous Hall effect. We calculate all contributions to the anomalous Hall effect in electron systems using the Kubo-Streda formalism. We find that all contributions vanish when both subbands are occupied and that the skew scattering contribution dominates when only the majority subband is occupied. We calculate the interference effects due to spin-orbit interaction in mesoscopic ring structures patterned from HgTe quantum wells related to the Aharonov-Casher effect and the spin Hall effect. We find that the transport properties are affected by the carrier density as well as the spin orbit interaction. We find that the conductivity is larger in hole gas systems. We also show that devices with inhomogenous spin orbit interaction exhibit an electrically controlled spin-flipping mechanism.