[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

Sequential anomaly detection in the presence of noise and limited feedback

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: 1) filtering, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2) hedging, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset. © 1963-2012 IEEE.

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Gold mining in the Peruvian Amazon: global prices, deforestation, and mercury imports.

Many factors such as poverty, ineffective institutions and environmental regulations may prevent developing countries from managing how natural resources are extracted to meet a strong market demand. Extraction for some resources has reached such proportions that evidence is measurable from space. We present recent evidence of the global demand for a single commodity and the ecosystem destruction resulting from commodity extraction, recorded by satellites for one of the most biodiverse areas of the world. We find that since 2003, recent mining deforestation in Madre de Dios, Peru is increasing nonlinearly alongside a constant annual rate of increase in international gold price (∼18%/yr). We detect that the new pattern of mining deforestation (1915 ha/year, 2006-2009) is outpacing that of nearby settlement deforestation. We show that gold price is linked with exponential increases in Peruvian national mercury imports over time (R(2) = 0.93, p = 0.04, 2003-2009). Given the past rates of increase we predict that mercury imports may more than double for 2011 (∼500 t/year). Virtually all of Peru's mercury imports are used in artisanal gold mining. Much of the mining increase is unregulated/artisanal in nature, lacking environmental impact analysis or miner education. As a result, large quantities of mercury are being released into the atmosphere, sediments and waterways. Other developing countries endowed with gold deposits are likely experiencing similar environmental destruction in response to recent record high gold prices. The increasing availability of satellite imagery ought to evoke further studies linking economic variables with land use and cover changes on the ground.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

One hundred years of forgetting: A quantitative description of retention

A sample of 210 published data sets were assembled that (a) plotted amount remembered versus time, (b) had 5 or more points, and (c) were smooth enough to fit at least 1 of the functions tested with a correlation coefficient of .90 or greater. Each was fit to 105 different 2-parameter functions. The best fits were to the logarithmic function, the power function, the exponential in the square root of time, and the hyperbola in the square root of time. It is difficult to distinguish among these 4 functions with the available data, but the same set of 4 functions fit most data sets, with autobiographical memory being the exception. Theoretical motivations for the best fitting functions are offered. The methodological problems of evaluating functions and the advantages of searching existing data for regularities before formulating theories are considered.

NlpI-mediated modulation of outer membrane vesicle production through peptidoglycan dynamics in Escherichia coli.

Outer membrane vesicles (OMVs) are ubiquitously secreted from the outer membrane (OM) of Gram-negative bacteria. These heterogeneous structures are composed of OM filled with periplasmic content from the site of budding. By analyzing mutants that have vesicle production phenotypes, we can gain insight into the mechanism of OMV budding in wild-type cells, which has thus far remained elusive. In this study, we present data demonstrating that the hypervesiculation phenotype of the nlpI deletion mutant of Escherichia coli correlates with changes in peptidoglycan (PG) dynamics. Our data indicate that in stationary phase cultures the nlpI mutant exhibits increased PG synthesis that is dependent on spr, consistent with a model in which NlpI controls the activity of the PG endopeptidase Spr. In log phase, the nlpI mutation was suppressed by a dacB mutation, suggesting that NlpI regulates penicillin-binding protein 4 (PBP4) during exponential growth. The data support a model in which NlpI negatively regulates PBP4 activity during log phase, and Spr activity during stationary phase, and that in the absence of NlpI, the cell survives by increasing PG synthesis. Further, the nlpI mutant exhibited a significant decrease in covalent outer membrane (OM-PG) envelope stabilizing cross-links, consistent with its high level of OMV production. Based on these results, we propose that one mechanism wild-type Gram-negative bacteria can use to modulate vesiculation is by altering PG-OM cross-linking via localized modulation of PG degradation and synthesis.

PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Differential developmental trajectories of magnetic susceptibility in human brain gray and white matter over the lifespan

As indicated by several recent studies, magnetic susceptibility of the brain is influenced mainly by myelin in the white matter and by iron deposits in the deep nuclei. Myelination and iron deposition in the brain evolve both spatially and temporally. This evolution reflects an important characteristic of normal brain development and ageing. In this study, we assessed the changes of regional susceptibility in the human brain in vivo by examining the developmental and ageing process from 1 to 83 years of age. The evolution of magnetic susceptibility over this lifespan was found to display differential trajectories between the gray and the white matter. In both cortical and subcortical white matter, an initial decrease followed by a subsequent increase in magnetic susceptibility was observed, which could be fitted by a Poisson curve. In the gray matter, including the cortical gray matter and the iron-rich deep nuclei, magnetic susceptibility displayed a monotonic increase that can be described by an exponential growth. The rate of change varied according to functional and anatomical regions of the brain. For the brain nuclei, the age-related changes of susceptibility were in good agreement with the findings from R2* measurement. Our results suggest that magnetic susceptibility may provide valuable information regarding the spatial and temporal patterns of brain myelination and iron deposition during brain maturation and ageing. © 2013 Wiley Periodicals, Inc.