Student-t processes as alternatives to Gaussian processes

We investigate the Student-t process as an alternative to the Gaussian process as a non-parametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the co-variance kernel of a Gaussian process model. We show surprising equivalences between different hierarchical Gaussian process models leading to Student-t processes, and derive a new sampling scheme for the inverse Wishart process, which helps elucidate these equivalences. Overall, we show that a Student-t process can retain the attractive properties of a Gaussian process - a nonparamet-ric representation, analytic marginal and predictive distributions, and easy model selection through covariance kernels - but has enhanced flexibility, and predictive covariances that, unlike a Gaussian process, explicitly depend on the values of training observations. We verify empirically that a Student-t process is especially useful in situations where there are changes in covariance structure, or in applications such as Bayesian optimization, where accurate predictive covariances are critical for good performance. These advantages come at no additional computational cost over Gaussian processes.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.

Stable dynamic walking over rough terrain: Theory and experiment

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated "dynamic walking" biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems. © 2011 Springer-Verlag.

Molecular systematics and biogeography of Crawfurdia, Metagentiana and Tripterospermum (Gentianaceae) based on nuclear ribosomal and plastid DNA sequences

Background and Aims The systematic position of the genus Metagentiana and its phylogenetic relationships with Crawfurdia, Gentiana and Tripterospermum have not been explicitly addressed. These four genera belong to one of two subtribes (Gentianinae) of Gentianeae. The aim of this paper is to examine the systematic position of Crawfurdia, Metagentiana and Tripterospermum and to clarify their phylogenetic affinities more clearly using ITS and trnL intron sequences.Methods Nucleotide sequences from the internal transcribed spacers (ITS) of nuclear ribosomal DNA and the plastid DNA trnL (UAA) intron were analysed phylogenetically. Ten of fourteen Metagentiana species were sampled, together with 40 species of other genera in the subtribe Gentianinae.Key Results The data support several previously published conclusions relating to the separation of Metagentiana from Gentiana and its closer relationships to Crawfurdia and Tripterospermum based on studies of gross morphology, floral anatomy, chromosomes, palynology, embryology and previous molecular data. The molecular clock hypothesis for the tested sequences in subtribe Gentianinae was not supported by the data (P < 0.05), so the clock-independent non-parametric rate smoothing method was used to estimate divergence time. This indicates that the separation of Crawfurdia, Metagentiana and Tripterospermum from Gentiana occurred about 11.4-21.4 Mya (million years ago), and the current species of these three genera diverged at times ranging from 0.4 to 6.2 Mya.Conclusions The molecular analyses revealed that Crawfurdia, Metagentiana and Tripterospermum do not merit status as three separate genera, because sampled species of Crawfurdia and Tripterospermum are embedded within Metagentiana. The speciation and rapid radiation of these three genera is likely to have occurred in western China as a result of upthrust of the Himalayas during the late Miocene and the Pleistocene.

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds.

Online and Offline Character Recognition Using Alignment to Prototypes

Nearest neighbor classifiers are simple to implement, yet they can model complex non-parametric distributions, and provide state-of-the-art recognition accuracy in OCR databases. At the same time, they may be too slow for practical character recognition, especially when they rely on similarity measures that require computationally expensive pairwise alignments between characters. This paper proposes an efficient method for computing an approximate similarity score between two characters based on their exact alignment to a small number of prototypes. The proposed method is applied to both online and offline character recognition, where similarity is based on widely used and computationally expensive alignment methods, i.e., Dynamic Time Warping and the Hungarian method respectively. In both cases significant recognition speedup is obtained at the expense of only a minor increase in recognition error.

Survival analysis of adult tuberculosis disease

Background: We conducted a survival analysis of all the confirmed cases of Adult Tuberculosis (TB) patients treated in Cork-City, Ireland. The aim of this study was to estimate Survival time (ST), including median time of survival and to assess the association and impact of covariates (TB risk factors) to event status and ST. The outcome of the survival analysis is reported in this paper. Methods: We used a retrospective cohort study research design to review data of 647 bacteriologically confirmed TB patients from the medical record of two teaching hospitals. Mean age 49 years (Range 18–112). We collected information on potential risk factors of all confirmed cases of TB treated between 2008–2012. For the survival analysis, the outcome of interest was ‘treatment failure’ or ‘death’ (whichever came first). A univariate descriptive statistics analysis was conducted using a non- parametric procedure, Kaplan -Meier (KM) method to estimate overall survival (OS), while the Cox proportional hazard model was used for the multivariate analysis to determine possible association of predictor variables and to obtain adjusted hazard ratio. P value was set at <0.05, log likelihood ratio test at >0.10. Data were analysed using SPSS version 15.0. Results: There was no significant difference in the survival curves of male and female patients. (Log rank statistic = 0.194, df = 1, p = 0.66) and among different age group (Log rank statistic = 1.337, df = 3, p = 0.72). The mean overall survival (OS) was 209 days (95%CI: 92–346) while the median was 51 days (95% CI: 35.7–66). The mean ST for women was 385 days (95%CI: 76.6–694) and for men was 69 days (95%CI: 48.8–88.5). Multivariate Cox regression showed that patient who had history of drug misuse had 2.2 times hazard than those who do not have drug misuse. Smokers and alcohol drinkers had hazard of 1.8 while patients born in country of high endemicity (BICHE) had hazard of 6.3 and HIV co-infection hazard was 1.2. Conclusion: There was no significant difference in survival curves of male and female and among age group. Women had a higher ST compared to men. But men had a higher hazard rate compared to women. Anti-TNF, immunosuppressive medication and diabetes were found to be associated with longer ST, while alcohol, smoking, RICHE, BICHE was associated with shorter ST.

Spatial vision in the purple sea urchin Strongylocentrotus purpuratus (Echinoidea).

Recent evidence that echinoids of the genus Echinometra have moderate visual acuity that appears to be mediated by their spines screening off-axis light suggests that the urchin Strongylocentrotus purpuratus, with its higher spine density, may have even more acute spatial vision. We analyzed the movements of 39 specimens of S. purpuratus after they were placed in the center of a featureless tank containing a round, black target that had an angular diameter of 6.5 deg. or 10 deg. (solid angles of 0.01 sr and 0.024 sr, respectively). An average orientation vector for each urchin was determined by testing the animal four times, with the target placed successively at bearings of 0 deg., 90 deg., 180 deg. and 270 deg. (relative to magnetic east). The urchins showed no significant unimodal or axial orientation relative to any non-target feature of the environment or relative to the changing position of the 6.5 deg. target. However, the urchins were strongly axially oriented relative to the changing position of the 10 deg. target (mean axis from -1 to 179 deg.; 95% confidence interval +/- 12 deg.; P<0.001, Moore's non-parametric Hotelling's test), with 10 of the 20 urchins tested against that target choosing an average bearing within 10 deg. of either the target center or its opposite direction (two would be expected by chance). In addition, the average length of the 20 target-normalized bearings for the 10 deg. target (each the vector sum of the bearings for the four trials) were far higher than would be expected by chance (P<10(-10); Monte Carlo simulation), showing that each urchin, whether it moved towards or away from the target, did so with high consistency. These results strongly suggest that S. purpuratus detected the 10 deg. target, responding either by approaching it or fleeing it. Given that the urchins did not appear to respond to the 6.5 deg. target, it is likely that the 10 deg. target was close to the minimum detectable size for this species. Interestingly, measurements of the spine density of the regions of the test that faced horizontally predicted a similar visual resolution (8.3+/-0.5 deg. for the interambulacrum and 11+/-0.54 deg. for the ambulacrum). The function of this relatively low, but functional, acuity - on par with that of the chambered Nautilus and the horseshoe crab - is unclear but, given the bimodal response, is likely to be related to both shelter seeking and predator avoidance.

Investigation and Development of a Fully 3D Tilt Capable Hybrid SPECT - CT System for Dedicated Breast Imaging

X-ray mammography has been the gold standard for breast imaging for decades, despite the significant limitations posed by the two dimensional (2D) image acquisitions. Difficulty in diagnosing lesions close to the chest wall and axilla, high amount of structural overlap and patient discomfort due to compression are only some of these limitations. To overcome these drawbacks, three dimensional (3D) breast imaging modalities have been developed including dual modality single photon emission computed tomography (SPECT) and computed tomography (CT) systems. This thesis focuses on the development and integration of the next generation of such a device for dedicated breast imaging. The goals of this dissertation work are to: [1] understand and characterize any effects of fully 3-D trajectories on reconstructed image scatter correction, absorbed dose and Hounsifeld Unit accuracy, and [2] design, develop and implement the fully flexible, third generation hybrid SPECT-CT system capable of traversing complex 3D orbits about a pendant breast volume, without interference from the other. Such a system would overcome artifacts resulting from incompletely sampled divergent cone beam imaging schemes and allow imaging closer to the chest wall, which other systems currently under research and development elsewhere cannot achieve.

The dependence of x-ray scatter radiation on object shape, size, material composition and the CT acquisition trajectory, was investigated with a well-established beam stop array (BSA) scatter correction method. While the 2D scatter to primary ratio (SPR) was the main metric used to characterize total system scatter, a new metric called ‘normalized scatter contribution’ was developed to compare the results of scatter correction on 3D reconstructed volumes. Scatter estimation studies were undertaken with a sinusoidal saddle (±15° polar tilt) orbit and a traditional circular (AZOR) orbit. Clinical studies to acquire data for scatter correction were used to evaluate the 2D SPR on a small set of patients scanned with the AZOR orbit. Clinical SPR results showed clear dependence of scatter on breast composition and glandular tissue distribution, otherwise consistent with the overall phantom-based size and density measurements. Additionally, SPR dependence was also observed on the acquisition trajectory where 2D scatter increased with an increase in the polar tilt angle of the system.

The dose delivered by any imaging system is of primary importance from the patient’s point of view, and therefore trajectory related differences in the dose distribution in a target volume were evaluated. Monte Carlo simulations as well as physical measurements using radiochromic film were undertaken using saddle and AZOR orbits. Results illustrated that both orbits deliver comparable dose to the target volume, and only slightly differ in distribution within the volume. Simulations and measurements showed similar results, and all measured dose values were within the standard screening mammography-specific, 6 mGy dose limit, which is used as a benchmark for dose comparisons.

Hounsfield Units (HU) are used clinically in differentiating tissue types in a reconstructed CT image, and therefore the HU accuracy of a system is very important, especially when using non-traditional trajectories. Uniform phantoms filled with various uniform density fluids were used to investigate differences in HU accuracy between saddle and AZOR orbits. Results illustrate the considerably better performance of the saddle orbit, especially close to the chest and nipple region of what would clinically be a pedant breast volume. The AZOR orbit causes shading artifacts near the nipple, due to insufficient sampling, rendering a major portion of the scanned phantom unusable, whereas the saddle orbit performs exceptionally well and provides a tighter distribution of HU values in reconstructed volumes.

Finally, the third generation, fully-suspended SPECT-CT system was designed in and developed in our lab. A novel mechanical method using a linear motor was developed for tilting the CT system. A new x-ray source and a custom made 40 x 30 cm2 detector were integrated on to this system. The SPECT system was nested, in the center of the gantry, orthogonal to the CT source-detector pair. The SPECT system tilts on a goniometer, and the newly developed CT tilting mechanism allows ±15° maximum polar tilting of the CT system. The entire gantry is mounted on a rotation stage, allowing complex arbitrary trajectories for each system, without interference from the other, while having a common field of view. This hybrid system shows potential to be used clinically as a diagnostic tool for dedicated breast imaging.

Local models for exploratory analysis of hydrological extremes

Trend analysis is widely used for detecting changes in hydrological data. Parametric methods for this employ pre-specified models and associated tests to assess significance, whereas non-parametric methods generally apply rank tests to the data. Neither approach is suitable for exploratory analysis, because parametric models impose a particular, perhaps unsuitable, form of trend, while testing may confirm that trend is present but does not describe its form. This paper describes semi-parametric approaches to trend analysis using local likelihood fitting of annual maximum and partial duration series and illustrates their application to the exploratory analysis of changes in extremes in sea level and river flow data. Bootstrap methods are used to quantify the variability of estimates.

In vitro release of bovine serum albumin from alginate/HPMC hydrogel beads

In recent years, the use of swelling polymeric matrices for the encapsulation and controlled release of protein drugs has received significant attention. The purpose of the present study was to investigate the release of albumin, a model protein from alginate/hydroxypropyl-methylcellulose (HPMC) gel beads. A hydrogel system comprised of two natural, hydrophilic polymers; sodium alginate and HPMC was studied as a carrier of bovine serum albumin (BSA) which was used as a model protein. The morphology, bead size and the swelling ratio were studied in different physical states; fully swollen, dried and reswollen using scanning electron microscopy and image analysis. Finally the effect of different alginate/HPMC ratios on the BSA release profile in physiological saline solution was investigated. Swelling experiments revealed that the bead diameter increases with the viscosity of the alginate solution while the addition of HPMC resulted in a significant increase of the swelling ratio. The BSA release patterns showed that the addition of HPMC increased the protein-release rate while the release mechanism fitted the Peppas model. Alginate/HPMC beads prepared using the ionic gelation exhibited high BSA loading efficiency for all formulations. The presence of HPMC increased the swelling ability of the alginate beads while the particle size remained unaffected. Incorporation of HPMC in the alginate gels also resulted in improved BSA release in physiological saline solution. All formulations presented a non-Fickian release mechanism described by the Peppas model. In addition, the implementation of non-parametric tests showed significant differences in the release patterns between the alginate/HPMC and the pure alginate beads, respectively.

Simple procedures to assess and compare the ecological niche of species

Hutchinson's (1957; Cold Spring Harbour Symp Quant Biol 22:415-427) niche concept is being used increasingly in the context of global change, and is currently applied to many ecological issues including climate change, exotic species invasion and management of endangered species. For both the marine and terrestrial realms, there is a growing need to assess the breadth of the niches of individual species and to make comparisons among them to forecast the species' capabilities to adapt to global change. In this paper, we describe simple non-parametric multivariate procedures derived from a method originally used in climatology to (1) evaluate the breadth of the ecological niche of a species and (2) examine whether the niches are significantly separated. We first applied the statistical procedures to a simple fictive example of 3 species separated by 2 environmental factors in order to describe the technique. We then used it to quantify and compare the ecological niche of 2 key-structural marine zooplankton copepod species, Calanus finmarchicus and C. helgolandicus, in the northern part of the North Atlantic Ocean using 3 environmental factors. The test demonstrates that the niches of both species are significantly separated and that the coldwater species has a niche larger than that of its warmer-water congeneric species.

Seasonal plankton dynamics along a cross-shelf gradient off northern Spain

The development of population models able to reproduce the dynamics of zooplankton is a central issue when trying to understand how a changing environment would affect zooplankton in the future. Using 10 years of monthly data on phytoplankton and zooplankton abundance in the Bay of Biscay from the IEO's RADIALES time-series programme, we built non-parametric Generalized Additive Models (GAMs) able to reproduce the dynamics of plankton on the basis of environmental factors (nutrients, temperature, upwelling and photoperiod). We found that the interaction between these two plankton components is approximately linear, whereas the effects of environmental factors are non-linear. With the inclusion of the environmental variability, the main seasonal and inter-annual dynamic patterns observed within the studied plankton assemblage indicate the prevalence of bottom-up regulatory control. The statistically deduced models were used to simulate the dynamics of the phytoplankton and zooplankton. A good agreement between observations and simulations was obtained, especially for zooplankton. We are presently developing spatio-temporal GAM models for the North Sea based on the Continuous Plankton Recorder database.

Fracture Mechanics Analysis of the Dentine-Luting Cement Interface.

The objectives of this study were to determine the fracture toughness of adhesive interfaces between dentine and clinically relevant, thin layers of dental luting cements. Cements tested included a conventional glass-ionomer, F (Fuji I), a resin-modified glass-ionomer, FP (Fuji Plus) and a compomer cement, D (DyractCem). Ten miniature short-bar chevron notch specimens were manufactured for each cement, each comprising a 40 µm thick chevron of lute, between two 1.5 mm thick blocks of bovine dentine, encased in resin composite. The interfacial KIC results (MN/m3/2) were median (range): F; 0.152 (0.14-0.16), FP; 0.306 (0.27-0.37), D; 0.351 (0.31-0.37). Non-parametric statistical analysis showed that the fracture toughness of F was significantly lower (p