Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Evaluation and comparison of mammalian subcellular localization prediction methods

Background: Determination of the subcellular location of a protein is essential to understanding its biochemical function. This information can provide insight into the function of hypothetical or novel proteins. These data are difficult to obtain experimentally but have become especially important since many whole genome sequencing projects have been finished and many resulting protein sequences are still lacking detailed functional information. In order to address this paucity of data, many computational prediction methods have been developed. However, these methods have varying levels of accuracy and perform differently based on the sequences that are presented to the underlying algorithm. It is therefore useful to compare these methods and monitor their performance. Results: In order to perform a comprehensive survey of prediction methods, we selected only methods that accepted large batches of protein sequences, were publicly available, and were able to predict localization to at least nine of the major subcellular locations (nucleus, cytosol, mitochondrion, extracellular region, plasma membrane, Golgi apparatus, endoplasmic reticulum (ER), peroxisome, and lysosome). The selected methods were CELLO, MultiLoc, Proteome Analyst, pTarget and WoLF PSORT. These methods were evaluated using 3763 mouse proteins from SwissProt that represent the source of the training sets used in development of the individual methods. In addition, an independent evaluation set of 2145 mouse proteins from LOCATE with a bias towards the subcellular localization underrepresented in SwissProt was used. The sensitivity and specificity were calculated for each method and compared to a theoretical value based on what might be observed by random chance. Conclusion: No individual method had a sufficient level of sensitivity across both evaluation sets that would enable reliable application to hypothetical proteins. All methods showed lower performance on the LOCATE dataset and variable performance on individual subcellular localizations was observed. Proteins localized to the secretory pathway were the most difficult to predict, while nuclear and extracellular proteins were predicted with the highest sensitivity.

Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Novel visualization methods for protein data

Visualization of high-dimensional data has always been a challenging task. Here we discuss and propose variants of non-linear data projection methods (Generative Topographic Mapping (GTM) and GTM with simultaneous feature saliency (GTM-FS)) that are adapted to be effective on very high-dimensional data. The adaptations use log space values at certain steps of the Expectation Maximization (EM) algorithm and during the visualization process. We have tested the proposed algorithms by visualizing electrostatic potential data for Major Histocompatibility Complex (MHC) class-I proteins. The experiments show that the variation in the original version of GTM and GTM-FS worked successfully with data of more than 2000 dimensions and we compare the results with other linear/nonlinear projection methods: Principal Component Analysis (PCA), Neuroscale (NSC) and Gaussian Process Latent Variable Model (GPLVM).

When do conservation planning methods deliver? Quantifying the consequences of uncertainty

The rapid global loss of biodiversity has led to a proliferation of systematic conservation planning methods. In spite of their utility and mathematical sophistication, these methods only provide approximate solutions to real-world problems where there is uncertainty and temporal change. The consequences of errors in these solutions are seldom characterized or addressed. We propose a conceptual structure for exploring the consequences of input uncertainty and oversimpli?ed approximations to real-world processes for any conservation planning tool or strategy. We then present a computational framework based on this structure to quantitatively model species representation and persistence outcomes across a range of uncertainties. These include factors such as land costs, landscape structure, species composition and distribution, and temporal changes in habitat. We demonstrate the utility of the framework using several reserve selection methods including simple rules of thumb and more sophisticated tools such as Marxan and Zonation. We present new results showing how outcomes can be strongly affected by variation in problem characteristics that are seldom compared across multiple studies. These characteristics include number of species prioritized, distribution of species richness and rarity, and uncertainties in the amount and quality of habitat patches. We also demonstrate how the framework allows comparisons between conservation planning strategies and their response to error under a range of conditions. Using the approach presented here will improve conservation outcomes and resource allocation by making it easier to predict and quantify the consequences of many different uncertainties and assumptions simultaneously. Our results show that without more rigorously generalizable results, it is very dif?cult to predict the amount of error in any conservation plan. These results imply the need for standard practice to include evaluating the effects of multiple real-world complications on the behavior of any conservation planning method.

Computational mechanics reveals nanosecond time correlations in molecular dynamics of liquid systems

Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated. © 2008 Elsevier B.V. All rights reserved.

The application of parallel processing methods to vibrational analysis

The trend in modal extraction algorithms is to use all the available frequency response functions data to obtain a global estimate of the natural frequencies, damping ratio and mode shapes. Improvements in transducer and signal processing technology allow the simultaneous measurement of many hundreds of channels of response data. The quantity of data available and the complexity of the extraction algorithms make considerable demands on the available computer power and require a powerful computer or dedicated workstation to perform satisfactorily. An alternative to waiting for faster sequential processors is to implement the algorithm in parallel, for example on a network of Transputers. Parallel architectures are a cost effective means of increasing computational power, and a larger number of response channels would simply require more processors. This thesis considers how two typical modal extraction algorithms, the Rational Fraction Polynomial method and the Ibrahim Time Domain method, may be implemented on a network of transputers. The Rational Fraction Polynomial Method is a well known and robust frequency domain 'curve fitting' algorithm. The Ibrahim Time Domain method is an efficient algorithm that 'curve fits' in the time domain. This thesis reviews the algorithms, considers the problems involved in a parallel implementation, and shows how they were implemented on a real Transputer network.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

Methods in mind

The evolution of cognitive neuroscience has been spurred by the development of increasingly sophisticated investigative techniques to study human cognition. In Methods in Mind, experts examine the wide variety of tools available to cognitive neuroscientists, paying particular attention to the ways in which different methods can be integrated to strengthen empirical findings and how innovative uses for established techniques can be developed. The book will be a uniquely valuable resource for the researcher seeking to expand his or her repertoire of investigative techniques. Each chapter explores a different approach. These include transcranial magnetic stimulation, cognitive neuropsychiatry, lesion studies in nonhuman primates, computational modeling, psychophysiology, single neurons and primate behavior, grid computing, eye movements, fMRI, electroencephalography, imaging genetics, magnetoencephalography, neuropharmacology, and neuroendocrinology. As mandated, authors focus on convergence and innovation in their fields; chapters highlight such cross-method innovations as the use of the fMRI signal to constrain magnetoencephalography, the use of electroencephalography (EEG) to guide rapid transcranial magnetic stimulation at a specific frequency, and the successful integration of neuroimaging and genetic analysis. Computational approaches depend on increased computing power, and one chapter describes the use of distributed or grid computing to analyze massive datasets in cyberspace. Each chapter author is a leading authority in the technique discussed.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Application of Artificial Intelligence Methods to Computer Design of Inorganic Compounds

In this paper the main problems for computer design of materials, which would have predefined properties, with the use of artificial intelligence methods are presented. The DB on inorganic compound properties and the system of DBs on materials for electronics with completely assessed information: phase diagram DB of material systems with semiconducting phases and DB on acousto-optical, electro-optical, and nonlinear optical properties are considered. These DBs are a source of information for data analysis. Using the DBs and artificial intelligence methods we have predicted thousands of new compounds in ternary, quaternary and more complicated chemical systems and estimated some of their properties (crystal structure type, melting point, homogeneity region etc.). The comparison of our predictions with experimental data, obtained later, showed that the average reliability of predicted inorganic compounds exceeds 80%. The perspectives of computational material design with the use of artificial intelligence methods are considered.

The Computational Analysis of Bulgarian Dialect Pronunciation

The paper presents a computational analysis of Bulgarian dialect variation, concentrating on pronunciation differences. It describes the phonetic data set compiled during the project* ‘Measuring Linguistic Unity and Diversity in Europe’ that consists of the pronunciations of 157 words collected at 197 sites from all over Bulgaria. We also present the results of analyzing this data set using various quantitative methods and compare them to the traditional scholarship on Bulgarian dialects. The results have shown that various dialectometrical techniques clearly identify east-west division of the country along the ‘jat’ border, as well as the third group of varieties in the Rodopi area. The rest of the groups specified in the traditional atlases either were not confirmed or were confirmed with a low confidence.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.