Creation and characterization of vortex clusters in atomic Bose-Einstein condensates

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed, or induce clusters of like-signed vortices in 2D Bose-Einstein condensates. We propose new statistical measures of clustering based on Ripley's K-function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

Lumen Border Detection of Intravascular Ultrasound via Denoising of Directional Wavelet Representations

In this paper, intravascular ultrasound (IVUS) grayscale images, acquired with a single-element mechanically rotating transducer, are processed with wavelet denoising and region-based segmentation to extract various layers of lumen contours and plaques. First, IVUS volumetric data is expanded on complex exponential wavelet-like basis functions, also known as Brushlets, which are well localized in time and frequency domains. Brushlets denoising have demonstrated in the past a great aptitude for denoising ultrasound data and removal of blood speckles. A region-based segmentation framework is then applied for detection of lumen border layers, which remains one of the most challenging problems in IVUS image analysis for images acquired with a single element, mechanically rotating 45 MHz transducer. We evaluated hard thresholding for Brushlet denoising, and compared segmentation results to manually traced lumen borders. We observed good agreement and suggest that the proposed algorithm has a great potential to be used as a reliable pre-processing step for accurate lumen border detection

Bayesian Centroid Estimation for Motif Discovery

Biological sequences may contain patterns that are signal important biomolecular functions; a classical example is regulation of gene expression by transcription factors that bind to specific patterns in genomic promoter regions. In motif discovery we are given a set of sequences that share a common motif and aim to identify not only the motif composition, but also the binding sites in each sequence of the set. We present a Bayesian model that is an extended version of the model adopted by the Gibbs motif sampler, and propose a new centroid estimator that arises from a refined and meaningful loss function for binding site inference. We discuss the main advantages of centroid estimation for motif discovery, including computational convenience, and how its principled derivation offers further insights about the posterior distribution of binding site configurations. We also illustrate, using simulated and real datasets, that the centroid estimator can differ from the maximum a posteriori estimator.Comment: 24 pages, 9 figure

An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as appendices

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-

Binary Models for Marginal Independence

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions

“I h 8 u”: Findings from a five-year study of text and e-mail bullying

Copyright @ 2010 British Educational Research Association. The final version of this article is available at the link below.This study charts reports of nasty or threatening text and e-mail messages received by students in academic years 7 and 8 (11-13 years of age) attending 13 secondary schools in the North of England between 2002-2006. Annual surveys were undertaken on behalf of the local education authority (LEA) to monitor bullying. Results indicated that, over five years, the number of pupils receiving one or more nasty or threatening text messages or e-mails increased significantly, particularly among girls. However, receipt of frequent nasty or threatening text and e-mail messages remained relatively stable. For boys, being a victim of direct-physical bullying was associated with receiving nasty or threatening text and e-mail messages; for girls it was being unpopular among peers. Boys received more hate-related messages and girls were primarily the victims of name-calling, Findings are discussed with respect to theoretical and policy developments, and recommendations for future research are offered

Image labeling and grouping by minimizing linear functionals over cones

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization pointof-view. Rather than trying to compute the global minimum - a goal we consider as elusive in these cases - we wish to design optimization approaches which exhibit two relevant properties: First, in each application a solution with guaranteed degree of suboptimality can be computed. Secondly, the computations are based on clearly defined algorithms which do not comprise any (hidden) tuning parameters. In this paper, we focus on the second property and introduce a novel and general optimization technique to the field of computer vision which amounts to compute a sub optimal solution by just solving a convex optimization problem. As representative examples, we consider two binary quadratic energy functionals related to image labeling and perceptual grouping. Both problems can be considered as instances of a general quadratic functional in binary variables, which is embedded into a higher-dimensional space such that sub optimal solutions can be computed as minima of linear functionals over cones in that space (semidefinite programs). Extensive numerical results reveal that, on the average, sub optimal solutions can be computed which yield a gap below 5% with respect to the global optimum in case where this is known