Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

A toolbox for animal call recognition

Monitoring the natural environment is increasingly important as habit degradation and climate change reduce theworld’s biodiversity.We have developed software tools and applications to assist ecologists with the collection and analysis of acoustic data at large spatial and temporal scales.One of our key objectives is automated animal call recognition, and our approach has three novel attributes. First, we work with raw environmental audio, contaminated by noise and artefacts and containing calls that vary greatly in volume depending on the animal’s proximity to the microphone. Second, initial experimentation suggested that no single recognizer could dealwith the enormous variety of calls. Therefore, we developed a toolbox of generic recognizers to extract invariant features for each call type. Third, many species are cryptic and offer little data with which to train a recognizer. Many popular machine learning methods require large volumes of training and validation data and considerable time and expertise to prepare. Consequently we adopt bootstrap techniques that can be initiated with little data and refined subsequently. In this paper, we describe our recognition tools and present results for real ecological problems.

Robust facial feature extraction and matching

Automated feature extraction and correspondence determination is an extremely important problem in the face recognition community as it often forms the foundation of the normalisation and database construction phases of many recognition and verification systems. This paper presents a completely automatic feature extraction system based upon a modified volume descriptor. These features form a stable descriptor for faces and are utilised in a reversible jump Markov chain Monte Carlo correspondence algorithm to automatically determine correspondences which exist between faces. The developed system is invariant to changes in pose and occlusion and results indicate that it is also robust to minor face deformations which may be present with variations in expression.

State cycles, initialization and the Trivium stream cipher

Trivium is a keystream generator for a binary additive synchronous stream cipher. It was selected in the final portfolio for the Profile 2 category of the eSTREAM project. The keystream generator is constructed using bit- based shift registers. In this paper we present an alternate representation of Trivium using word-based shift registers, with a word size of three bits. This representation is useful for determining cycles of internal state values. Under this representation it is clear that the state space can be partitioned into subspaces and that over some of these subspaces the state update function is effectively linear. The role of the initialization process is critical in ensuring the states used for generating keystream are updated nonlinearly at some point, as the state update function alone does not provide this.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

The phylogeny of Ureaplasma urealyticum based on the mba gene fragment

Sequencing of mba gene fragments of reference strains of Ureaplasma urealyticum serovars 1, 3, 6, 14, in addition to 33 clinical U. urealyticum isolates is reported. A phylogenetic tree deduced from an alignment of these sequences clearly demonstrates two major clusters (confidence limit 100%), which equate to the parvo and T960 biovars, and five types which we have designated mba 1, 3, 6, 8 and X. These relationships are supported by bootstrap analysis. Polymorphisms within the mba fragment of types mba 1, 3, and 6 were used to define nine subtypes (mba 1a, 1b, 3a, 3b, 3c, 3d, 3e, 6a, and 6b) thus facilitating high resolution typing of U. urealyticum. Inclusion of the reference strains for serovars 1, 3, 6, and 8 in the mba typing scheme showed that the results of this analysis are broadly consistent with currently accepted serotyping. In addition a ure gene fragment from nine of the clinical isolates was amplified and sequenced. Comparisons of the sequences clearly distinguished the two biovars of U. urealyticum; however this fragment was invariant within the parvo biovar. This study has shown that the sequence of the mba can reveal the fine details of the relationships between U. urealyticum isolates and also supports the significant evolutionary gap between the two biovars.

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.

Fourier Lucas-Kanade Algorithm

In this paper we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one pre-processes the source image and template/model with a bank of filters (e.g. oriented edges, Gabor, etc.) as: (i) it can handle substantial illumination variations, (ii) the inefficient pre-processing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, (iii) unlike traditional LK the computational cost is invariant to the number of filters and as a result far more efficient, and (iv) this approach can be extended to the inverse compositional form of the LK algorithm where nearly all steps (including Fourier transform and filter bank pre-processing) can be pre-computed leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to non-rigid object alignment tasks that are considered extensions of the LK algorithm such as those found in Active Appearance Models (AAMs).

Comparing genotyping algorithms for Illumina's Infinium whole-genome SNP BeadChips

Background Illumina's Infinium SNP BeadChips are extensively used in both small and large-scale genetic studies. A fundamental step in any analysis is the processing of raw allele A and allele B intensities from each SNP into genotype calls (AA, AB, BB). Various algorithms which make use of different statistical models are available for this task. We compare four methods (GenCall, Illuminus, GenoSNP and CRLMM) on data where the true genotypes are known in advance and data from a recently published genome-wide association study. Results In general, differences in accuracy are relatively small between the methods evaluated, although CRLMM and GenoSNP were found to consistently outperform GenCall. The performance of Illuminus is heavily dependent on sample size, with lower no call rates and improved accuracy as the number of samples available increases. For X chromosome SNPs, methods with sex-dependent models (Illuminus, CRLMM) perform better than methods which ignore gender information (GenCall, GenoSNP). We observe that CRLMM and GenoSNP are more accurate at calling SNPs with low minor allele frequency than GenCall or Illuminus. The sample quality metrics from each of the four methods were found to have a high level of agreement at flagging samples with unusual signal characteristics. Conclusions CRLMM, GenoSNP and GenCall can be applied with confidence in studies of any size, as their performance was shown to be invariant to the number of samples available. Illuminus on the other hand requires a larger number of samples to achieve comparable levels of accuracy and its use in smaller studies (50 or fewer individuals) is not recommended.

Recognising facial expressions with noisy data

Techniques to improve the automated analysis of natural and spontaneous facial expressions have been developed. The outcome of the research has applications in several fields including national security (eg: expression invariant face recognition); education (eg: affect aware interfaces); mental and physical health (eg: depression and pain recognition).

Robust vision-based underwater homing using self-similar landmarks

Next-generation autonomous underwater vehicles (AUVs) will be required to robustly identify underwater targets for tasks such as inspection, localization, and docking. Given their often unstructured operating environments, vision offers enormous potential in underwater navigation over more traditional methods; however, reliable target segmentation often plagues these systems. This paper addresses robust vision-based target recognition by presenting a novel scale and rotationally invariant target design and recognition routine based on self-similar landmarks that enables robust target pose estimation with respect to a single camera. These algorithms are applied to an AUV with controllers developed for vision-based docking with the target. Experimental results show that the system performs exceptionally on limited processing power and demonstrates how the combined vision and controller system enables robust target identification and docking in a variety of operating conditions.

Interpersonal, intrapersonal, extrapersonal? Qualitatively investigating coordinative couplings between rowers in Olympic sculling

Coordinative couplings are commonly classified as interpersonal and intrapersonal. Interpersonal coordination is normally thought of as between organisms but a subset can also be considered where the co-actors movements are coupled to an environmental rhythm. This can be termed extrapersonal coordination. This study explores how coordination is achieved in a situation that demands that at least one actor makes use of extrapersonal sources. In this case multi-seat rowing, where one actor cannot see the other one behind them. A qualitative approach using experiential knowledge from expert rowers (N=9) and coaches (N=4) was used to examine how interpersonal coordination was achieved and maintained in 2 person rowing boats. It was reported that where possible, both rowers coordinated their movements by coupling with an invariant provided by the boat. This invariant is underpinned by perception of water flow past the boat; which is in turn used to determine changes in acceleration - 'rowing with the boat.' Bow seat also identified the rower in front and stroke seat identified the looming of the stern as viable alternative sources for coupling.

Crowd monitoring using computer vision

Novel computer vision techniques have been developed for automatic monitoring of crowed environments such as airports, railway stations and shopping malls. Using video feeds from multiple cameras, the techniques enable crowd counting, crowd flow monitoring, queue monitoring and abnormal event detection. The outcome of the research is useful for surveillance applications and for obtaining operational metrics to improve business efficiency.

Dealing with shadows : capturing intrinsic scene appearance for image-based outdoor localisation

In outdoor environments shadows are common. These typically strong visual features cause considerable change in the appearance of a place, and therefore confound vision-based localisation approaches. In this paper we describe how to convert a colour image of the scene to a greyscale invariant image where pixel values are a function of underlying material property not lighting. We summarise the theory of shadow invariant images and discuss the modelling and calibration issues which are important for non-ideal off-the-shelf colour cameras. We evaluate the technique with a commonly used robotic camera and an autonomous car operating in an outdoor environment, and show that it can outperform the use of ordinary greyscale images for the task of visual localisation.

Training-free probability models for whole-image based place recognition

Whole-image descriptors such as GIST have been used successfully for persistent place recognition when combined with temporal filtering or sequential filtering techniques. However, whole-image descriptor localization systems often apply a heuristic rather than a probabilistic approach to place recognition, requiring substantial environmental-specific tuning prior to deployment. In this paper we present a novel online solution that uses statistical approaches to calculate place recognition likelihoods for whole-image descriptors, without requiring either environmental tuning or pre-training. Using a real world benchmark dataset, we show that this method creates distributions appropriate to a specific environment in an online manner. Our method performs comparably to FAB-MAP in raw place recognition performance, and integrates into a state of the art probabilistic mapping system to provide superior performance to whole-image methods that are not based on true probability distributions. The method provides a principled means for combining the powerful change-invariant properties of whole-image descriptors with probabilistic back-end mapping systems without the need for prior training or system tuning.