Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

In Vitro Release from Reverse Poloxamine/alpha-Cyclodextrin Matrices: Modelling and Comparison of Dissolution Profiles

Gels obtained by complexation of octablock star polyethylene oxide/polypropylene oxide copolymers (Tetronic 90R4) with -cyclodextrin (-CD) were evaluated as matrices for drug release. Both molecules are biocompatible so they can be potentially applied to drug delivery systems. Two different types of matrices of Tetronic 90R4 and -CD were evaluated: gels and tablets. These gels are capable to gelifying in situ and show sustained erosion kinetics in aqueous media. Tablets were prepared by freeze-drying and comprising the gels. Using these two different matrices, the release of two model molecules, L-tryptophan (Trp), and a protein, bovine serum albumin (BSA), was evaluated. The release profiles of these molecules from gels and tablets prove that they are suitable for sustained delivery. Mathematical models were applied to the release curves from tablets to elucidate the drug delivery mechanism. Good correlations were found for the fittings of the release curves to different equations. The results point that the release of Trp from different tablets is always governed by Fickian diffusion, whereas the release of BSA is governed by a combination of diffusion and tablet erosion. 

Pseudomonas aeruginosa exhibits frequent recombination, but only a limited association between genotype and ecological setting

Pseudomonas aeruginosa is an opportunistic pathogen and an important cause of infection, particularly amongst cystic fibrosis (CF) patients. While specific strains capable of patient-to-patient transmission are known, many infections appear to be caused by unique and unrelated strains. There is a need to understand the relationship between strains capable of colonising the CF lung and the broader set of P. aeruginosa isolates found in natural environments. Here we report the results of a multilocus sequence typing (MLST)-based study designed to understand the genetic diversity and population structure of an extensive regional sample of P. aeruginosa isolates from South East Queensland, Australia. The analysis is based on 501 P. aeruginosa isolates obtained from environmental, animal and human (CF and non-CF) sources with particular emphasis on isolates from the Lower Brisbane River and isolates from CF patients obtained from the same geographical region. Overall, MLST identified 274 different sequence types, of which 53 were shared between one or more ecological settings. Our analysis revealed a limited association between genotype and environment and evidence of frequent recombination. We also found that genetic diversity of P. aeruginosa in Queensland, Australia was indistinguishable from that of the global P. aeruginosa population. Several CF strains were encountered frequently in multiple ecological settings; however, the most frequently encountered CF strains were confined to CF patients. Overall, our data confirm a non-clonal epidemic structure and indicate that most CF strains are a random sample of the broader P. aeruginosa population. The increased abundance of some CF strains in different geographical regions is a likely product of chance colonisation events followed by adaptation to the CF lung and horizontal transmission among patients.

Discovering subgroups of patients from DNA copy number data using NMF on compacted matrices

In the study of complex genetic diseases, the identification of subgroups of patients sharing similar genetic characteristics represents a challenging task, for example, to improve treatment decision. One type of genetic lesion, frequently investigated in such disorders, is the change of the DNA copy number (CN) at specific genomic traits. Non-negative Matrix Factorization (NMF) is a standard technique to reduce the dimensionality of a data set and to cluster data samples, while keeping its most relevant information in meaningful components. Thus, it can be used to discover subgroups of patients from CN profiles. It is however computationally impractical for very high dimensional data, such as CN microarray data. Deciding the most suitable number of subgroups is also a challenging problem. The aim of this work is to derive a procedure to compact high dimensional data, in order to improve NMF applicability without compromising the quality of the clustering. This is particularly important for analyzing high-resolution microarray data. Many commonly used quality measures, as well as our own measures, are employed to decide the number of subgroups and to assess the quality of the results. Our measures are based on the idea of identifying robust subgroups, inspired by biologically/clinically relevance instead of simply aiming at well-separated clusters. We evaluate our procedure using four real independent data sets. In these data sets, our method was able to find accurate subgroups with individual molecular and clinical features and outperformed the standard NMF in terms of accuracy in the factorization fitness function. Hence, it can be useful for the discovery of subgroups of patients with similar CN profiles in the study of heterogeneous diseases.

Price Discrimination in Quantity Setting Oligopoly

We analyze a two-stage quantity setting oligopolistic price discrimination game. In the first stage firms choose capacities and in the second stage they simultaneously choose the share that they assign to each segment. At the equilibrium the firms focus more on the high-valuation customers. When the capacities in the first stage are endogenous, the deadweight loss does not vanish with the level of price discrimination, as it does in one-stage games and monopoly. Moreover, the quantity-weighted average price increases with the level of price discrimination as opposed to established results in the literature for one-stage games.

Financial reintegration assistance for veterans of the Irish revolution (1916-23): post-conflict policy in an historical setting

In the aftermath of the Irish revolution and Civil War the governments of independent Ireland introduced various compensation schemes to provide financial reintegration assistance to revolutionary veterans. This would be recognised today as part of a programme for DDR. This paper will examine various service and disability pensions paid to veterans in the context of literature on post-conflict reintegration. It will examine various challenges to reintegration in an effort to analyse the success of revolutionary compensation as a post-conflict reintegration mechanism in independent Ireland after 1922.

Critical evaluation of pulse-echo ultrasonic test method for the determination of setting and mechanical properties of acrylic bone cement: Influence of mixing technique

Currently there is no reliable objective method to quantify the setting properties of acrylic bone cements within an operating theatre environment. Ultrasonic technology can be used to determine the acoustic properties of the polymerising bone cement, which are linked to material properties and provide indications of the physical and chemical changes occurring within the cement. The focus of this study was the critical evaluation of pulse-echo ultrasonic test method in determining the setting and mechanical properties of three different acrylic bone cement when prepared under atmospheric and vacuum mixing conditions. Results indicated that the ultrasonic pulse-echo technique provided a highly reproducible and accurate method of monitoring the polymerisation reaction and indicating the principal setting parameters when compared to ISO 5833 standard, irrespective of the acrylic bone cement or mixing method used. However, applying the same test method to predict the final mechanical properties of acrylic bone cement did not prove a wholly accurate approach. Inhomogeneities within the cement microstructure and specimen geometry were found to have a significant influence on mechanical property predictions. Consideration of all the results suggests that the non-invasive and non-destructive pulse-echo ultrasonic test method is an effective and reliable method for following the full polymerisation reaction of acrylic bone cement in real-time and then determining the setting properties within a surgical theatre environment. However the application of similar technology for predicting the final mechanical properties of acrylic bone cement on a consistent basis may prove difficult.

Droop setting design for multi-terminal HVDC grids considering voltage deviation impacts

In multi-terminal high voltage direct current (HVDC) grids, the widely deployed droop control strategies will cause a non-uniform voltage deviation on the power flow, which is determined by the network topology and droop settings. This voltage deviation results in an inconsistent power flow pattern when the dispatch references are changed, which could be detrimental to the operation and seamless integration of HVDC grids. In this paper, a novel droop setting design method is proposed to address this problem for a more precise power dispatch. The effects of voltage deviations on the power sharing accuracy and transmission loss are analysed. This paper shows that there is a trade-off between minimizing the voltage deviation, ensuring a proper power delivery and reducing the total transmission loss in the droop setting design. The efficacy of the proposed method is confirmed by simulation studies.

An Informant Report Behavior Diary for Measuring Temper Outbursts in an Intervention Setting

Temper outbursts are associated with several psychological disorders and comprise a high priority for intervention. However, the low frequency of outbursts presents a challenge for valid measurement. In the present study an informant report behavior diary for measuring temper outbursts was developed and its validity assessed in a case series. Caregivers of 12 individuals with the neurodevelopmental disorder Prader-Willi syndrome (PWS, in which temper outbursts are common) completed a behavior diary over 4 weeks, and a structured interview. Heart rate and movement data were recorded during a sample of the days subject to diary reporting. Individuals with PWS completed self-report ratings of negative emotion experience. Behavior diaries showed high concordance with the component behaviors and duration of temper outbursts reported in structured interviews; but tended to report a lower frequency. For outbursts reported in diaries during physiological recording, heart rate was consistently elevated above a resting state baseline; and was comparable to that recorded during high physical activity. Available self-report data demonstrated correspondence with the diaries but few self-report data were produced. The present results provide critical proof of principle data supporting the concurrent validity of the ecologically valid, resource efficient diaries, which can be exploited in future research.

Constructing random matrices to represent real ecosystems

Models of complex systems with n components typically have order n² parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.