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The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals that reach our detectors, while most lie below the confusion limit and are undetected. Similarly to voices in a crowded room, the collection of unresolved signals gives rise to a background that is well-described via stochastic variables and, hence, referred to as the stochastic GW background (SGWB). In this review, we provide an overview of stochastic GW signals and characterise them based on features of interest such as generation processes and observational properties. We then review the current detection strategies for stochastic backgrounds, offering a ready-to-use manual for stochastic GW searches in real data. In the process, we distinguish between interferometric measurements of GWs, either by ground-based or space-based laser interferometers, and timing-residuals analyses with pulsar timing arrays (PTAs). These detection methods have been applied to real data both by large GW collaborations and smaller research groups, and the most recent and instructive results are reported here. We close this review with an outlook on future observations with third generation detectors, space-based interferometers, and potential noninterferometric detection methods proposed in the literature.

In this work, we introduce TorsiFlex, a user-friendly software written in Python 3 and designed to find all the torsional conformers of flexible acyclic molecules in an automatic fashion. For the mapping of the torsional potential energy surface, the algorithm implemented in TorsiFlex combines two searching strategies: preconditioned and stochastic. The former is a type of systematic search based on chemical knowledge and should be carried out before the stochastic (random) search. The algorithm applies several validation tests to accelerate the exploration of the torsional space. For instance, the optimized structures are stored and this information is used to prevent revisiting these points and their surroundings in future iterations. TorsiFlex operates with a dual-level strategy by which the initial search is carried out at an inexpensive electronic structure level of theory and the located conformers are reoptimized at a higher level. Additionally, the program takes advantage of conformational enantiomerism, when possible. As a case study, and in order to exemplify the effectiveness and capabilities of this program, we have employed TorsiFlex to locate the conformers of the twenty proteinogenic amino acids in their neutral canonical form. TorsiFlex has produced a number of conformers that roughly doubles the amount of the most complete work to date. Graphical Abstract

Constraint satisfaction problems (CSP) are at the core of numerous scientific and technological applications. However, CSPs belong to the NP-complete complexity class, for which the existence (or not) of efficient algorithms remains a major unsolved question in computational complexity theory. In the face of this fundamental difficulty heuristics and approximation methods are used to approach instances of NP (e.g., decision and hard optimization problems). The human brain efficiently handles CSPs both in perception and behavior using spiking neural networks (SNNs), and recent studies have demonstrated that the noise embedded within an SNN can be used as a computational resource to solve CSPs. Here, we provide a software framework for the implementation of such noisy neural solvers on the SpiNNaker massively parallel neuromorphic hardware, further demonstrating their potential to implement a stochastic search that solves instances of P and NP problems expressed as CSPs. This facilitates the exploration of new optimization strategies and the understanding of the computational abilities of SNNs. We demonstrate the basic principles of the framework by solving difficult instances of the Sudoku puzzle and of the map color problem, and explore its application to spin glasses. The solver works as a stochastic dynamical system, which is attracted by the configuration that solves the CSP. The noise allows an optimal exploration of the space of configurations, looking for the satisfiability of all the constraints; if applied discontinuously, it can also force the system to leap to a new random configuration effectively causing a restart.

Finding reasonably good solutions using a fewer number of objective function evaluations has long been recognized as a good attribute of an optimization algorithm. This becomes more important, especially when dealing with very high-dimensional optimization problems, since contemporary algorithms often need a high number of iterations to converge. Furthermore, the excessive computational effort required to handle the large number of design variables involved in the optimization of large-scale steel double-layer grids with complex configurations is perceived as the main challenge for contemporary structural optimization techniques. This paper aims to enhance the convergence properties of the standard guided stochastic search (GSS) algorithm to handle computationally expensive and very high-dimensional optimization problems of steel double-layer grids. To this end, a repair deceleration mechanism (RDM) is proposed, and its efficiency is evaluated through challenging test examples of steel double-layer grids. First, parameter tuning based on rigorous analyses of two preliminary test instances is performed. Next, the usefulness of the proposed RDM is further investigated through two very high-dimensional instances of steel double-layer grids, namely a 21,212-member free-form double-layer grid, and a 25,514-member double-layer multi-dome, with 21,212 and 25,514 design variables, respectively. The obtained numerical results indicate that the proposed RDM can significantly enhance the convergence rate of the GSS algorithm, rendering it an efficient tool to handle very high-dimensional sizing optimization problems.

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical biomarkers. Based on the metaphor of statistically derived \"factors\" as representing biological \"subpathway\" structure, we explore the decomposition of fitted sparse factor models into pathway subcomponents and investigate how these components overlay multiple aspects of known biological activity. Our methodology is based on sparsity modeling of multivariate regression, ANOVA, and latent factor models, as well as a class of models that combines all components. Hierarchical sparsity priors address questions of dimension reduction and multiple comparisons, as well as scalability of the methodology. The models include practically relevant non-Gaussian/nonparametric components for latent structure, underlying often quite complex non-Gaussianity in multivariate expression patterns. Model search and fitting are addressed through stochastic simulation and evolutionary stochastic search methods that are exemplified in the oncogenic pathway studies. Supplementary supporting material provides more details of the applications, as well as examples of the use of freely available software tools for implementing the methodology.

Multi-subject functional magnetic resonance imaging (fMRI) data has been increasingly used to study the population-wide relationship between human brain activity and individual biological or behavioral traits. A common method is to regress the scalar individual response on imaging predictors, known as a scalar-on-image (SI) regression. Analysis and computation of such massive and noisy data with complex spatio-temporal correlation structure is challenging. In this article, motivated by a psychological study on human affective feelings using fMRI, we propose a joint Ising and Dirichlet Process (Ising-DP) prior within the framework of Bayesian stochastic search variable selection for selecting brain voxels in high-dimensional SI regressions. The Ising component of the prior makes use of the spatial information between voxels, and the DP component groups the coefficients of the large number of voxels to a small set of values and thus greatly reduces the posterior computational burden. To address the phase transition phenomenon of the Ising prior, we propose a new analytic approach to derive bounds for the hyperparameters, illustrated on 2- and 3-dimensional lattices. The proposed method is compared with several alternative methods via simulations, and is applied to the fMRI data collected from the KLIFF hand-holding experiment.

Meta-heuristic methods are global optimization algorithms which are widely used in the engineering issues, nowadays. In this paper, a new stochastic search for optimization is presented using variable variance Gaussian distribution sampling. The main idea in searching for algorithm is to regenerate new samples around each solution with a Guassian distribution. Numerical simulations have revealed that the new presented algorithm outperformed some evolutionary algorithms.

Summary In this paper a new model of radial basis function (RBF) neural network based on a novel stochastic search algorithm is presented for short‐term load forecast (STLF). STLF is an important operation function in both regulated and deregulated power systems. Accurate STLF is effective for area generation control and resource dispatch as well as electricity market clearing. The proposed STLF method optimizes the structure of the RBF‐based forecasting engine. Random selection of the number of hidden neurons may cause overfitting or underfitting problem of the network. For this purpose, a new stochastic search algorithm is presented to find the optimum number of neurons for the hidden layer. To demonstrate the effectiveness of the proposed STLF approach, it is tested on three real‐world engineering case studies, and the obtained results are compared with the results of several other recently published STLF methods. These comparisons confirm the validity of the developed approach. Copyright © 2015 John Wiley & Sons, Ltd.

Humans are concurrently exposed to chemically, structurally and toxicologically diverse chemicals. A critical challenge for environmental epidemiology is to quantify the risk of adverse health outcomes resulting from exposures to such chemical mixtures and to identify which mixture constituents may be driving etiologic associations. A variety of statistical methods have been proposed to address these critical research questions. However, they generally rely solely on measured exposure and health data available within a specific study. Advancements in understanding of the role of mixtures on human health impacts may be better achieved through the utilization of external data and knowledge from multiple disciplines with innovative statistical tools. In this paper we develop new methods for health analyses that incorporate auxiliary information about the chemicals in a mixture, such as physicochemical, structural and/or toxicological data. We expect that the constituents identified using auxiliary information will be more biologically meaningful than those identified by methods that solely utilize observed correlations between measured exposure. We develop flexible Bayesian models by specifying prior distributions for the exposures and their effects that include auxiliary information and examine this idea over a spectrum of analyses from regression to factor analysis. The methods are applied to study the effects of volatile organic compounds on emergency room visits in Atlanta. We find that including cheminformatic information about the exposure variables improves prediction and provides a more interpretable model for emergency room visits for respiratory diseases.

This article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors. Goals are (1) to estimate the conditional response distribution addressing the distributional changes across the predictor space, and (2) to identify important predictors for the response distribution change both within local regions and globally. We first introduce the probit stick-breaking process (PSBP) as a prior for an uncountable collection of predictor-dependent random distributions and propose a PSBP mixture (PSBPM) of normal regressions for modeling the conditional distributions. A global variable selection structure is incorporated to discard unimportant predictors, while allowing estimation of posterior inclusion probabilities. Local variable selection is conducted relying on the conditional distribution estimates at different predictor points. An efficient stochastic search sampling algorithm is proposed for posterior computation. The methods are illustrated through simulation and applied to an epidemiologic study.