GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

A survey: Particle Swarm Optimization based algorithms to solve premature convergence problem

Particle Swarm Optimization (PSO) is a biologically inspired computational search and optimization method based on the social behaviors of birds flocking or fish schooling. Although, PSO is represented in solving many well-known numerical test problems, but it suffers from the premature convergence. A number of basic variations have been developed due to solve the premature convergence problem and improve quality of solution founded by the PSO. This study presents a comprehensive survey of the various PSO-based algorithms. As part of this survey, the authors have included a classification of the approaches and they have identify the main features of each proposal. In the last part of the study, some of the topics within this field that are considered as promising areas of future research are listed.

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

This paper describes algorithms that can identify patterns of brain structure and function associated with Alzheimer's disease, schizophrenia, normal aging, and abnormal brain development based on imaging data collected in large human populations. Extraordinary information can be discovered with these techniques: dynamic brain maps reveal how the brain grows in childhood, how it changes in disease, and how it responds to medication. Genetic brain maps can reveal genetic influences on brain structure, shedding light on the nature-nurture debate, and the mechanisms underlying inherited neurobehavioral disorders. Recently, we created time-lapse movies of brain structure for a variety of diseases. These identify complex, shifting patterns of brain structural deficits, revealing where, and at what rate, the path of brain deterioration in illness deviates from normal. Statistical criteria can then identify situations in which these changes are abnormally accelerated, or when medication or other interventions slow them. In this paper, we focus on describing our approaches to map structural changes in the cortex. These methods have already been used to reveal the profile of brain anomalies in studies of dementia, epilepsy, depression, childhood- and adult-onset schizophrenia, bipolar disorder, attention-deficit/hyperactivity disorder, fetal alcohol syndrome, Tourette syndrome, Williams syndrome, and in methamphetamine abusers. Specifically, we describe an image analysis pipeline known as cortical pattern matching that helps compare and pool cortical data over time and across subjects. Statistics are then defined to identify brain structural differences between groups, including localized alterations in cortical thickness, gray matter density (GMD), and asymmetries in cortical organization. Subtle features, not seen in individual brain scans, often emerge when population-based brain data are averaged in this way. Illustrative examples are presented to show the profound effects of development and various diseases on the human cortex. Dynamically spreading waves of gray matter loss are tracked in dementia and schizophrenia, and these sequences are related to normally occurring changes in healthy subjects of various ages.

Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

New graph-based algorithms to efficiently solve large scale open pit mining optimisation problems

In the mining optimisation literature, most researchers focused on two strategic-level and tactical-level open-pit mine optimisation problems, which are respectively termed ultimate pit limit (UPIT) or constrained pit limit (CPIT). However, many researchers indicate that the substantial numbers of variables and constraints in real-world instances (e.g., with 50-1000 thousand blocks) make the CPIT’s mixed integer programming (MIP) model intractable for use. Thus, it becomes a considerable challenge to solve the large scale CPIT instances without relying on exact MIP optimiser as well as the complicated MIP relaxation/decomposition methods. To take this challenge, two new graph-based algorithms based on network flow graph and conjunctive graph theory are developed by taking advantage of problem properties. The performance of our proposed algorithms is validated by testing recent large scale benchmark UPIT and CPIT instances’ datasets of MineLib in 2013. In comparison to best known results from MineLib, it is shown that the proposed algorithms outperform other CPIT solution approaches existing in the literature. The proposed graph-based algorithms leads to a more competent mine scheduling optimisation expert system because the third-party MIP optimiser is no longer indispensable and random neighbourhood search is not necessary.

Prognostic value of BRAF mutations in localized cutaneous melanoma

BACKGROUND: BRAF mutations are frequent in melanoma but their prognostic significance remains unclear. OBJECTIVE: We sought to further evaluate the prognostic value of BRAF mutations in localized cutaneous melanoma. METHODS: We undertook an observational retrospective study of 147 patients with localized invasive (stages I and II) cutaneous melanomas to determine the prognostic value of BRAF mutation status. RESULTS: After a median follow-up of 48 months, patients with localized melanomas with BRAF-mutant melanomas exhibited poorer disease-free survival than those with BRAF-wt genotype (hazard ratio 2.2, 95% confidence interval 1.1-4.3) even after adjustment for Breslow thickness, tumor ulceration, location, age, sex, and tumor mitotic rate. LIMITATIONS: The retrospective design and the small number of events are limitations. CONCLUSIONS: Our findings suggest that reappraisal of clinical treatment approaches for patients with localized melanoma harboring tumors with BRAF mutation might be warranted

A Bayesian Framework for the Assessment of Vision-based Weed and Fruit Detection and Classification Algorithms

This paper proposes new metrics and a performance-assessment framework for vision-based weed and fruit detection and classification algorithms. In order to compare algorithms, and make a decision on which one to use fora particular application, it is necessary to take into account that the performance obtained in a series of tests is subject to uncertainty. Such characterisation of uncertainty seems not to be captured by the performance metrics currently reported in the literature. Therefore, we pose the problem as a general problem of scientific inference, which arises out of incomplete information, and propose as a metric of performance the(posterior) predictive probabilities that the algorithms will provide a correct outcome for target and background detection. We detail the framework through which these predicted probabilities can be obtained, which is Bayesian in nature. As an illustration example, we apply the framework to the assessment of performance of four algorithms that could potentially be used in the detection of capsicums (peppers).

Development of innovative robust stability enhancement algorithms for distribution systems containing distributed generators

This project was a step forward in improving the voltage profile of traditional low voltage distribution networks with high photovoltaic generation or high peak demand. As a practical and economical solution, the developed methods use a Dynamic Voltage Restorer or DVR, which is a series voltage compensator, for continuous and communication-less power quality enhancement. The placement of DVR in the network is optimised in order to minimise its power rating and cost. In addition, new approaches were developed for grid synchronisation and control of DVR which are integrated with the voltage quality improvement algorithm for stable operation.

Robust nanostructured silver and copper fabrics with localized surface plasmon resonance property for effective visible light induced reductive catalysis

Inspired by high porosity, absorbency, wettability and hierarchical ordering on the micrometer and nanometer scale of cotton fabrics, a facile strategy is developed to coat visible light active metal nanostructures of copper and silver on cotton fabric substrates. The fabrication of nanostructured Ag and Cu onto interwoven threads of a cotton fabric by electroless deposition creates metal nanostructures that show a localized surface plasmon resonance (LSPR) effect. The micro/nanoscale hierarchical ordering of the cotton fabrics allows access to catalytically active sites to participate in heterogeneous catalysis with high efficiency. The ability of metals to absorb visible light through LSPR further enhances the catalytic reaction rates under photoexcitation conditions. Understanding the mode of electron transfer during visible light illumination in Ag@Cotton and Cu@Cotton through electrochemical measurements provides mechanistic evidence on the influence of light in promoting electron transfer during heterogeneous catalysis for the first time. The outcomes presented in this work will be helpful in designing new multifunctional fabrics with the ability to absorb visible light and thereby enhance light-activated catalytic processes.