Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

Edge-weighting of gene expression graphs

In recent years, considerable research efforts have been directed to micro-array technologies and their role in providing simultaneous information on expression profiles for thousands of genes. These data, when subjected to clustering and classification procedures, can assist in identifying patterns and providing insight on biological processes. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges corresponding to gene-sample node couples in the dataset. Biologically meaningful subgraphs can be sought, but performance can be influenced both by the search algorithm, and, by the graph-weighting scheme and both merit rigorous investigation. In this paper, we focus on edge-weighting schemes for bipartite graphical representation of gene expression. Two novel methods are presented: the first is based on empirical evidence; the second on a geometric distribution. The schemes are compared for several real datasets, assessing efficiency of performance based on four essential properties: robustness to noise and missing values, discrimination, parameter influence on scheme efficiency and reusability. Recommendations and limitations are briefly discussed. Keywords: Edge-weighting; weighted graphs; gene expression; bi-clustering

Efficiency of parallelisation of genetic algorithms in the data analysis context

Most real-life data analysis problems are difficult to solve using exact methods, due to the size of the datasets and the nature of the underlying mechanisms of the system under investigation. As datasets grow even larger, finding the balance between the quality of the approximation and the computing time of the heuristic becomes non-trivial. One solution is to consider parallel methods, and to use the increased computational power to perform a deeper exploration of the solution space in a similar time. It is, however, difficult to estimate a priori whether parallelisation will provide the expected improvement. In this paper we consider a well-known method, genetic algorithms, and evaluate on two distinct problem types the behaviour of the classic and parallel implementations.

A framework for identification of similarities between multiple algorithms

This thesis in software engineering presents a novel automated framework to identify similar operations utilized by multiple algorithms for solving related computing problems. It provides a new effective solution to perform multi-application based algorithm analysis, employing fundamentally light-weight static analysis techniques compared to the state-of-art approaches. Significant performance improvements are achieved across the objective algorithms through enhancing the efficiency of the identified similar operations, targeting discrete application domains.

Shortest path and vehicle trajectory aided map-matching for low frequency GPS data

Map-matching algorithms that utilise road segment connectivity along with other data (i.e.position, speed and heading) in the process of map-matching are normally suitable for high frequency (1 Hz or higher) positioning data from GPS. While applying such map-matching algorithms to low frequency data (such as data from a fleet of private cars, buses or light duty vehicles or smartphones), the performance of these algorithms reduces to in the region of 70% in terms of correct link identification, especially in urban and sub-urban road networks. This level of performance may be insufficient for some real-time Intelligent Transport System (ITS) applications and services such as estimating link travel time and speed from low frequency GPS data. Therefore, this paper develops a new weight-based shortest path and vehicle trajectory aided map-matching (stMM) algorithm that enhances the map-matching of low frequency positioning data on a road map. The well-known A* search algorithm is employed to derive the shortest path between two points while taking into account both link connectivity and turn restrictions at junctions. In the developed stMM algorithm, two additional weights related to the shortest path and vehicle trajectory are considered: one shortest path-based weight is related to the distance along the shortest path and the distance along the vehicle trajectory, while the other is associated with the heading difference of the vehicle trajectory. The developed stMM algorithm is tested using a series of real-world datasets of varying frequencies (i.e. 1 s, 5 s, 30 s, 60 s sampling intervals). A high-accuracy integrated navigation system (a high-grade inertial navigation system and a carrier-phase GPS receiver) is used to measure the accuracy of the developed algorithm. The results suggest that the algorithm identifies 98.9% of the links correctly for every 30 s GPS data. Omitting the information from the shortest path and vehicle trajectory, the accuracy of the algorithm reduces to about 73% in terms of correct link identification. The algorithm can process on average 50 positioning fixes per second making it suitable for real-time ITS applications and services.

Approximate nearest-neighbour search with inverted signature slice lists

In this paper we present an original approach for finding approximate nearest neighbours in collections of locality-sensitive hashes. The paper demonstrates that this approach makes high-performance nearest-neighbour searching feasible on Web-scale collections and commodity hardware with minimal degradation in search quality.

Parallel streaming signature EM-tree: A clustering algorithm for web scale applications

The proliferation of the web presents an unsolved problem of automatically analyzing billions of pages of natural language. We introduce a scalable algorithm that clusters hundreds of millions of web pages into hundreds of thousands of clusters. It does this on a single mid-range machine using efficient algorithms and compressed document representations. It is applied to two web-scale crawls covering tens of terabytes. ClueWeb09 and ClueWeb12 contain 500 and 733 million web pages and were clustered into 500,000 to 700,000 clusters. To the best of our knowledge, such fine grained clustering has not been previously demonstrated. Previous approaches clustered a sample that limits the maximum number of discoverable clusters. The proposed EM-tree algorithm uses the entire collection in clustering and produces several orders of magnitude more clusters than the existing algorithms. Fine grained clustering is necessary for meaningful clustering in massive collections where the number of distinct topics grows linearly with collection size. These fine-grained clusters show an improved cluster quality when assessed with two novel evaluations using ad hoc search relevance judgments and spam classifications for external validation. These evaluations solve the problem of assessing the quality of clusters where categorical labeling is unavailable and unfeasible.

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.

Selection criteria in the search for a sperm donor: Behavioural traits versus physical appearance

Despite extensive literature on female mate choice, empirical evidence on women’s mating preferences in the search for a sperm donor is scarce, even though this search, by isolating a male’s genetic impact on offspring from other factors like paternal investment, offers a naturally ”controlled” research setting. In this paper, we work to fill this void by examining the rapidly growing online sperm donor market, which is raising new challenges by offering women novel ways to seek out donor sperm. We not only identify individual factors that influence women’s mating preferences but find strong support for the proposition that behavioural traits (inner values) are more important in these choices than physical appearance (exterior values). We also report evidence that physical factors matter more than resources or other external cues of material success, perhaps because the relevance of good character in donor selection is part of a female psychological adaptation throughout evolutionary history. The lack of evidence on a preference for material resources, on the other hand, may indicate the ability of peer socialization and better access to resources to rapidly shape the female decision process. Overall, the paper makes useful contributions to both the literature on human behaviour and that on decision-making in extreme and highly important situations.

A Monte-Carlo tree search in argumentation

Monte-Carlo Tree Search (MCTS) is a heuristic to search in large trees. We apply it to argumentative puzzles where MCTS pursues the best argumentation with respect to a set of arguments to be argued. To make our ideas as widely applicable as possible, we integrate MCTS to an abstract setting for argumentation where the content of arguments is left unspecified. Experimental results show the pertinence of this integration for learning argumentations by comparing it with a basic reinforcement learning.

Searching for people using semantic soft biometric descriptions

It is not uncommon to hear a person of interest described by their height, build, and clothing (i.e. type and colour). These semantic descriptions are commonly used by people to describe others, as they are quick to communicate and easy to understand. However such queries are not easily utilised within intelligent video surveillance systems, as they are difficult to transform into a representation that can be utilised by computer vision algorithms. In this paper we propose a novel approach that transforms such a semantic query into an avatar in the form of a channel representation that is searchable within a video stream. We show how spatial, colour and prior information (person shape) can be incorporated into the channel representation to locate a target using a particle-filter like approach. We demonstrate state-of-the-art performance for locating a subject in video based on a description, achieving a relative performance improvement of 46.7% over the baseline. We also apply this approach to person re-detection, and show that the approach can be used to re-detect a person in a video steam without the use of person detection.

Exhaustive search of the SNP-sNP interactome identifies epistatic effects on brain volume in two cohorts

The SNP-SNP interactome has rarely been explored in the context of neuroimaging genetics mainly due to the complexity of conducting approximately 10(11) pairwise statistical tests. However, recent advances in machine learning, specifically the iterative sure independence screening (SIS) method, have enabled the analysis of datasets where the number of predictors is much larger than the number of observations. Using an implementation of the SIS algorithm (called EPISIS), we used exhaustive search of the genome-wide, SNP-SNP interactome to identify and prioritize SNPs for interaction analysis. We identified a significant SNP pair, rs1345203 and rs1213205, associated with temporal lobe volume. We further examined the full-brain, voxelwise effects of the interaction in the ADNI dataset and separately in an independent dataset of healthy twins (QTIM). We found that each additional loading in the epistatic effect was associated with approximately 5% greater brain regional brain volume (a protective effect) in both the ADNI and QTIM samples.

Discovery and replication of dopamine-related gene effects on caudate volume in young and elderly populations (N1198) using genome-wide search

The caudate is a subcortical brain structure implicated in many common neurological and psychiatric disorders. To identify specific genes associated with variations in caudate volume, structural magnetic resonance imaging and genome-wide genotypes were acquired from two large cohorts, the Alzheimer's Disease NeuroImaging Initiative (ADNI; N=734) and the Brisbane Adolescent/Young Adult Longitudinal Twin Study (BLTS; N=464). In a preliminary analysis of heritability, around 90% of the variation in caudate volume was due to genetic factors. We then conducted genome-wide association to find common variants that contribute to this relatively high heritability. Replicated genetic association was found for the right caudate volume at single-nucleotide polymorphism rs163030 in the ADNI discovery sample (P=2.36 × 10 -6) and in the BLTS replication sample (P=0.012). This genetic variation accounted for 2.79 and 1.61% of the trait variance, respectively. The peak of association was found in and around two genes, WDR41 and PDE8B, involved in dopamine signaling and development. In addition, a previously identified mutation in PDE8B causes a rare autosomal-dominant type of striatal degeneration. Searching across both samples offers a rigorous way to screen for genes consistently influencing brain structure at different stages of life. Variants identified here may be relevant to common disorders affecting the caudate.

Identifying candidate gene effects by restricting search space in a multivariate genetic analysis of white matter microstructure

Several genetic variants are thought to influence white matter (WM) integrity, measured with diffusion tensor imaging (DTI). Voxel based methods can test genetic associations, but heavy multiple comparisons corrections are required to adjust for searching the whole brain and for all genetic variants analyzed. Thus, genetic associations are hard to detect even in large studies. Using a recently developed multi-SNP analysis, we examined the joint predictive power of a group of 18 cholesterol-related single nucleotide polymorphisms (SNPs) on WM integrity, measured by fractional anisotropy. To boost power, we limited the analysis to brain voxels that showed significant associations with total serum cholesterol levels. From this space, we identified two genes with effects that replicated in individual voxel-wise analyses of the whole brain. Multivariate analyses of genetic variants on a reduced anatomical search space may help to identify SNPs with strongest effects on the brain from a broad panel of genes.

In search of good probability assessors: An experimental comparison of elicitation rules for confidence judgments

In this paper, we use an experimental design to compare the performance of elicitation rules for subjective beliefs. Contrary to previous works in which elicited beliefs are compared to an objective benchmark, we consider a purely subjective belief framework (confidence in one’s own performance in a cognitive task and a perceptual task). The performance of different elicitation rules is assessed according to the accuracy of stated beliefs in predicting success. We measure this accuracy using two main factors: calibration and discrimination. For each of them, we propose two statistical indexes and we compare the rules’ performances for each measurement. The matching probability method provides more accurate beliefs in terms of discrimination, while the quadratic scoring rule reduces overconfidence and the free rule, a simple rule with no incentives, which succeeds in eliciting accurate beliefs. Nevertheless, the matching probability appears to be the best mechanism for eliciting beliefs due to its performances in terms of calibration and discrimination, but also its ability to elicit consistent beliefs across measures and across tasks, as well as its empirical and theoretical properties.