Computer-intensive Methods Research Articles

PARALLEL 3D FINITE-DIFFERENCE TIME-DOMAIN METHOD ON MULTI-GPU SYSTEMS

Finite-difference time-domain (FDTD) is a popular but computational intensive method to solve Maxwell's equations for electrical and optical devices simulation. This paper presents implementations of three-dimensional FDTD with convolutional perfect match layer (CPML) absorbing boundary conditions on graphics processing unit (GPU). Electromagnetic fields in Yee cells are calculated in parallel millions of threads arranged as a grid of blocks with compute unified device architecture (CUDA) programming model and considerable speedup factors are obtained versus sequential CPU code. We extend the parallel algorithm to multiple GPUs in order to solve electrically large structures. Asynchronous memory copy scheme is used in data exchange procedure to improve the computation efficiency. We successfully use this technique to simulate pointwise source radiation and validate the result by comparison to high precision computation, which shows favorable agreements. With four commodity GTX295 graphics cards on a single personal computer, more than 4000 million Yee cells can be updated in one second, which is hundreds of times faster than traditional CPU computation.

Computational intensive methods for prediction and imputation in time series analysis

One of the main goals in times series analysis is to forecast future values. Many forecasting methods have been developed and the most successful are based on the concept of exponential smoothing, based on the principle of obtaining forecasts as weighted combinations of past observations. Classical procedures to obtain forecast intervals assume a known distribution for the error process, what is not true in many situations. A bootstrap methodology can be used to compute distribution free forecast intervals. First an adequately chosen model is fitted to the data series. Afterwards, and inspired on sieve bootstrap, an AR(p) is used to filter the series of the random component, under the stationarity hypothesis. The centered residuals are then resampled and the initial series is reconstructed. This methodology will be used to obtain forecasting intervals and for treating missing data, which often appear in a real time series. An automatic procedure was developed in language and will be applied in simulation studies as well as in real examples. 122 M.M. Neves and C. Cordeiro

A brief introduction to computer-intensive methods, with a view towards applications in spatial statistics and stereology

Computer-intensive methods may be defined as data analytical procedures involving a huge number of highly repetitive computations. We mention resampling methods with replacement (bootstrap methods), resampling methods without replacement (randomization tests) and simulation methods. The resampling methods are based on simple and robust principles and are largely free from distributional assumptions. Bootstrap methods may be used to compute confidence intervals for a scalar model parameter and for summary statistics from replicated planar point patterns, and for significance tests. For some simple models of planar point processes, point patterns can be simulated by elementary Monte Carlo methods. The simulation of models with more complex interaction properties usually requires more advanced computing methods. In this context, we mention simulation of Gibbs processes with Markov chain Monte Carlo methods using the Metropolis-Hastings algorithm. An alternative to simulations on the basis of a parametric model consists of stochastic reconstruction methods. The basic ideas behind the methods are briefly reviewed and illustrated by simple worked examples in order to encourage novices in the field to use computer-intensive methods.

Efron's Bootstrap

Abstract The bootstrap was introduced by Brad Efron in the Late 1970s. It is a computer-intensive method for approximating the sampling distribution of any statistic derived from a random sample. Here Dennis Boos and Leonard Stefanski give simple examples to show how the bootstrap is used and help to explain its enormous success as a tool of statistical inference.

Measuring and comparing the accuracy of species distribution models with presence-absence data

Species distribution models have been widely used to predict species distributions for various purposes, including conservation planning, and climate change impact assessment. The success of these applications relies heavily on the accuracy of the models. Various measures have been proposed to assess the accuracy of the models. Rigorous statistical analysis should be incorporated in model accuracy assessment. However, since relevant information about the statistical properties of accuracy measures is scattered across various disciplines, ecologists find it difficult to select the most appropriate ones for their research. In this paper, we review accuracy measures that are currently used in species distribution modelling (SDM), and introduce additional metrics that have potential applications in SDM. For the commonly used measures (which are also intensively studied by statisticians), including overall accuracy, sensitivity, specificity, kappa, and area and partial area under the ROC curves, promising methods to construct confidence intervals and statistically compare the accuracy between two models are given. For other accuracy measures, methods to estimate standard errors are given, which can be used to construct approximate confidence intervals. We also suggest that as general tools, computer-intensive methods, especially bootstrap and randomization methods can be used in constructing confidence intervals and statistical tests if suitable analytic methods cannot be found. Usually, these computer-intensive methods provide robust results.

Optimal k-circulant supersaturated designs

Optimal k-circulant supersaturated designs have been constructed in literature using computer intensive methods. A systematic method of construction for multi-level experiments based on balanced incomplete block designs is presented in this paper. The method is also applicable to two-level experiments. Illustrative examples are also given.

An Experimental Evaluation of Boosting Methods for Classification

In clinical medicine, the accuracy achieved by classification rules is often not sufficient to justify their use in daily practice. In order to improve classifiers it has become popular to combine single classification rules into a classification ensemble. Two popular boosting methods will be compared with classical statistical approaches. Using data from a clinical study on the diagnosis of breast tumors and by simulation we will compare AdaBoost with gradient boosting ensembles of regression trees. We will also consider a tree approach and logistic regression as traditional competitors. In logistic regression we allow to select non- linear effects by the fractional polynomial approach. Performance of the classifiers will be assessed by estimated misclassification rates and the Brier score. We will show that boosting of simple base classifiers gives classification rules with improved predictive ability. However, the performance of boosting classifiers was not generally superior to the performance of logistic regression. In contrast to the computer-intensive methods the latter are based on classifiers which are much easier to interpret and to use. In medical applications, the logistic regression model remains a method of choice or, at least, a serious competitor of more sophisticated techniques. Refinement of boosting methods by using optimized number of boosting steps may lead to further improvement.

A Multistep, Cluster-Based Multivariate Chart for Retrospective Monitoring of Individuals

The presence of several outliers in an individuals retrospective multivariate control chart distorts both the sample mean vector and covariance matrix, making the classical Hotelling's T2 approach unreliable for outlier detection. To overcome the distortion or masking, we propose a computer-intensive multistep cluster-based method. Compared with classical and robust estimation procedures, simulation studies show that our method is usually better and sometimes much better at detecting randomly occurring outliers as well as outliers arising from shifts in the process location. Additional comparisons based on real data are given.

Linear Regression Model Selection Based on Robust Bootstrapping Technique

Problem statement: Bootstrap approach had introduced new advancement in modeling and model evaluation. It was a computer intensive method that can replace theoretical formulation with extensive use of computer. The Ordinary Least Squares (OLS) method often used to estimate the parameters of the regression models in the bootstrap procedure. Unfortunately, many statistics practitioners are not aware of the fact that the OLS method can be adversely affected by the existence of outliers. As an alternative, a robust method was put forward to overcome this problem. The existence of outliers in the original sample may create problem to the classical bootstrapping estimates. There was possibility that the bootstrap samples may contain more outliers than the original dataset, since the bootstrap re-sampling is with replacement. Consequently, the outliers will have an unduly effect on the classical bootstrap mean and standard deviation. Approach: In this study, we proposed to use a robust bootstrapping method which was less sensitive to outliers. In the robust bootstrapping procedure, we proposed to replace the classical bootstrap mean and standard deviation with robust location and robust scale estimates. A number of numerical examples were carried out to assess the performance of the proposed method. Results: The results suggested that the robust bootstrap method was more efficient than the classical bootstrap. Conclusion/Recommendations: In the presence of outliers in the dataset, we recommend using the robust bootstrap procedure as its estimates are more reliable.

Robust testing in the logistic regression model

We are interested in testing hypotheses that concern the parameter of a logistic regression model. A robust Wald-type test based on a weighted Bianco and Yohai [ Bianco, A.M., Yohai, V.J., 1996. Robust estimation in the logistic regression model. In: H. Rieder (Ed) Robust Statistics, Data Analysis, and Computer Intensive Methods In: Lecture Notes in Statistics, vol. 109, Springer Verlag, New York, pp. 17–34] estimator, as implemented by Croux and Haesbroeck [Croux, C., Haesbroeck, G., 2003. Implementing the Bianco and Yohai estimator for logistic regression. Computational Statististics and Data Analysis 44, 273–295], is proposed. The asymptotic distribution of the test statistic is derived. We carry out an empirical study to get a further insight into the stability of the p -value. Finally, a Monte Carlo study is performed to investigate the stability of both the level and the power of the test, for different choices of the weight function.

Assessing Symmetry Using Quantiles and L-Moments

Measures of distributional symmetry based on quantiles, L-moments, and trimmed L-moments are briefly reviewed, and (asymptotic) sampling properties of commonly used estimators considered. Standard errors are estimated using both analytical and computer-intensive methods. Simulation is used to assess results when sampling from some known distributions; bootstrapping is used on sample data to estimate standard errors, construct confidence intervals, and test a hypothesis of distributional symmetry. Symmetry measures based on 2- or 3-trimmed L-moments have some advantages over other measures in terms of their existence. Their estimators are generally well behaved, even in relatively small samples.

ModuleDigger: an itemset mining framework for the detection of cis-regulatory modules

BackgroundThe detection of cis-regulatory modules (CRMs) that mediate transcriptional responses in eukaryotes remains a key challenge in the postgenomic era. A CRM is characterized by a set of co-occurring transcription factor binding sites (TFBS). In silico methods have been developed to search for CRMs by determining the combination of TFBS that are statistically overrepresented in a certain geneset. Most of these methods solve this combinatorial problem by relying on computational intensive optimization methods. As a result their usage is limited to finding CRMs in small datasets (containing a few genes only) and using binding sites for a restricted number of transcription factors (TFs) out of which the optimal module will be selected.ResultsWe present an itemset mining based strategy for computationally detecting cis-regulatory modules (CRMs) in a set of genes. We tested our method by applying it on a large benchmark data set, derived from a ChIP-Chip analysis and compared its performance with other well known cis-regulatory module detection tools.ConclusionWe show that by exploiting the computational efficiency of an itemset mining approach and combining it with a well-designed statistical scoring scheme, we were able to prioritize the biologically valid CRMs in a large set of coregulated genes using binding sites for a large number of potential TFs as input.

Computer-intensive methods for sensory data analysis, exemplified by Durbin’s rank test

Durbin’s rank test, a Friedman-type test in balanced incomplete block designs (BIBDs), has wide applications in sensory analysis. The chi-square approximation, which is commonly used for Durbin’s rank test, is not adequate for small BIBDs. This paper discusses some computer-intensive methods including Monte Carlo test and permutation (randomization) test for Durbin’s rank test. S-Plus programs for the procedures are developed and are available upon request.

Numerical design of Alberich anechoic coatings with superellipsoidal cavities of mixed sizes

Thin rubber coatings with cavities in a doubly periodic lattice are able to reduce reflections of underwater sound by redistributing normally incident energy such that absorption in the surrounding rubber is enhanced. For spherical scatterers, the anechoic effect can be studied numerically by the layer-multiple-scattering (LMS) method. In comparison to more flexible but also more computer intensive methods, such as finite-element method modeling, there are two important advantages. An improved physical understanding of the anechoic effect can be achieved by simplified semianalytical analysis, and the high computational speed allows modern global optimization techniques to be applied for coating design. In this paper, the flexibility of the LMS method is improved by combination with an efficient algorithm for numerical computation of transition matrices for superellipsoidal scatterers. (A superellipsoid is a generalization of an ellipsoid, allowing more box-filling shapes, for example.) Extensions to mixtures of nonspherical scatterers of different types are also considered, in order to enhance the broadband performance. Symmetry properties are used to reduce the size of the pertinent equation systems. Examples of numerical coating design for underwater acoustic applications are presented, using differential evolution algorithms for the optimization.

Docking and Biomolecular Simulations on Computer Grids: Status and Trends

This article outlines the recent developments in the field of large-scale parallel computing applied to molecular simulations, also including some original, preliminary contributions of the authors. It is not meant to be an exhaustive review paper, but rather an introductive material aimed at narrowing the “cultural gap” between the developers and users of molecular simulations (chemists, medicinal chemists and biologists – typical workstation users) and the informatics experts in massively parallel computing. The article starts with a brief overview of the existing molecular simulation techniques, in emphasizing the weaknesses of present approaches and the need for more computer-intensive methods. Docking procedures are the most discussed, given the high importance of this application in computer-aided drug design. An introduction to computer grids is logically pursued with the presentation of some of the most promising large-scale parallel molecular simulations already performed. Eventually, the authors own research program, Docking@Grid, is briefly discussed.

Inductive effect of methyl group in the light of HMO and DFT methods

Inductive effect parameter h Me of methyl group and the Coulomb integral α of sp 2 hybridized carbon have been estimated from the HOMO energies of a series of methylbenzenes calculated by DFT/B3LYP method using the basis sets 6-31++G ∗∗ and 6-311+G(2d,p). By correlating the DFT results with those from Coulson–Longuet-Higgins perturbation method in HMO formalism and with charge transfer transition energies of three series of CT complexes of methylbenzenes, it is established that the fundamental concepts used by organic chemists and the simple Hückel method still serve as a useful and easy alternative to the present-day computer-intensive methods in explaining experimental trends at least for π-conjugated systems. The parameter ( h Me) value has been shown to be transferable from one series of compounds to another. Further it has been shown that h Et is about 15% higher than h Me, which is supported by the experimental observation that ethyl group exerts greater +I effect than methyl.

Quantitative analysis of Streptococcus pneumoniae TIGR4 response to in vitro iron restriction by 2‐D LC ESI MS/MS

Understanding the growth of bacterial pathogens in a micronutrient restricted host environment can identify potential virulence proteins that help overcome this nutritional barrier to productive infection. In this study, we investigated the pneumococcal protein expression response to iron limitation using an in vitro model. We identified S. pneumoniae TIGR4 proteins by 2-D LC ESI MS/MS and determined significant changes in protein expression in response to iron restriction using computer-intensive random resampling methods. Differential protein expression was studied in the context of a S. pneumoniae TIGR4 protein interaction network using Pathway Studio. Our analysis showed that pneumococcal iron restriction response was marked by increased expression of known virulence factors like PsaA. It involved changes in the expression of stress response, and phase variation and biofilm formation proteins. The net effect of changes in all these biological processes could increase the virulence of S. pneumoniae TIGR4 during in vivo infection.

Statistical identification of seismicity phases

We propose a statistical methodology to detect and quantify different seismicity phases on the basis of variations in certain characteristic features of seismic phenomenon, taking as examples two of the most studied aspects of seismicity: the occurrence rate and interevent time. Our objective is to provide an overall, compact picture of the activity, given a sufficiently long sequence of events, by identifying the flow of patterns that are singly described by well-known physical models in limited time intervals. We assume that the sequence of events recorded in a seismically active region represents the set of an unknown number of consecutive phases, and that in each phase, the observations are the realization of a different version of the same stochastic process, in our case the Poisson or the Dirichlet process. The quantities to be estimated are the number of phases, the instants in which the system passes from one phase to another and the model parameters. We have formulated this problem in the framework of a multiple change-point problem. The inference is made possible by exploiting recently developed computer-intensive methods based on the stochastic simulation of Markov chains. The data analysed are from the region of Kresna in southwestern Bulgaria. This area was hit by two strong earthquakes in the last century, one of MS = 7.8 magnitude in 1904, and another of MS = 6.7 magnitude in 1931.

A Collection of Computer-Intensive Methods

A Collection of Computer-Intensive Methods

Thinking the Unthinkable: Modern Non-Parametric Re-sampling Methods

Classical parametric tests compare observed statistics to theoretical sampling distributions. Re-sampling is a revolutionary methodology because it departs from theoretical distributions; the inference is based upon repeated sampling within the same empirical sample. This definition encompasses Monte Carlo simulation, cross validation tests, jackknife and bootstrap procedures. The need for such methods is heightened by the vast amounts of data being collected in the modern information age, and by the increasingly complex scientific questions being asked. These factors have together led to the rapid development of modern non-parametric methods. An appealing feature of re-sampling methods is the way they combine an intuitive and layman-friendly applied aspect with challenging and elegant mathematics. Purpose of this review is to divulge the theoretical foundations of re-sampling and to facilitate a coherent use of this computational intensive research method.