Limits to the critical current in Bi2Sr2Ca2Cu3Ox tape conductors: The parallel path model

An extensive overview of a model that describes current flow and dissipation in high-quality Bi2Sr2Ca2Cu3Ox superconducting tapes is provided. The parallel path model is based on a superconducting current running in two distinct parallel paths. One of the current paths is formed by grains that are connected at angles below 4°. Dissipation in this strongly linked backbone occurs within the grains and is well described by classical flux-creep theory. The other current path, the weakly linked network, is formed by superconducting grains that are connected at intermediate angles (4°–8°) where dissipation occurs at the grain boundaries. However, grain boundary dissipation in this weakly linked current path does not occur through Josephson weak links, but just as in the strongly linked backbone, is well described by classical flux creep. The results of several experiments on Bi2Sr2Ca2Cu3Ox tapes and single-grained powders that strongly support the parallel path model are presented. The critical current density of Bi2Sr2Ca2Cu3Ox tapes can be scaled as a function of magnetic field angle over the temperature range from 15 K to 77 K. Expressions based on classical flux creep are introduced to describe the dependence of the critical current density of Bi2Sr2Ca2Cu3Ox tapes on the magnetic field and temperature

A Semiparametric Model Selection Criterion with Applications to the Marginal Structural Model

Estimators for the parameter of interest in semiparametric models often depend on a guessed model for the nuisance parameter. The choice of the model for the nuisance parameter can affect both the finite sample bias and efficiency of the resulting estimator of the parameter of interest. In this paper we propose a finite sample criterion based on cross validation that can be used to select a nuisance parameter model from a list of candidate models. We show that expected value of this criterion is minimized by the nuisance parameter model that yields the estimator of the parameter of interest with the smallest mean-squared error relative to the expected value of an initial consistent reference estimator. In a simulation study, we examine the performance of this criterion for selecting a model for a treatment mechanism in a marginal structural model (MSM) of point treatment data. For situations where all possible models cannot be evaluated, we outline a forward/backward model selection algorithm based on the cross validation criterion proposed in this paper and show how it can be used to select models for multiple nuisance parameters. We evaluate the performance of this algorithm in a simulation study of the one-step estimator of the parameter of interest in a MSM where models for both a treatment mechanism and a conditional expectation of the response need to be selected. Finally, we apply the forward model selection algorithm to a MSM analysis of the relationship between boiled water use and gastrointestinal illness in HIV positive men

Optimal Spatial Prediction Using Ensemble Machine Learning

Spatial prediction is an important problem in many scientific disciplines. Super Learner is an ensemble prediction approach related to stacked generalization that uses cross-validation to search for the optimal predictor amongst all convex combinations of a heterogeneous candidate set. It has been applied to non-spatial data, where theoretical results demonstrate it will perform asymptotically at least as well as the best candidate under consideration. We review these optimality properties and discuss the assumptions required in order for them to hold for spatial prediction problems. We present results of a simulation study confirming Super Learner works well in practice under a variety of sample sizes, sampling designs, and data-generating functions. We also apply Super Learner to a real world dataset

Cross-Validating and Bagging Partitioning Algorithms with Variable Importance

We present a cross-validated bagging scheme in the context of partitioning algorithms. To explore the benefits of the various bagging scheme, we compare via simulations the predictive ability of single Classification and Regression (CART) Tree with several previously suggested bagging schemes and with our proposed approach. Additionally, a variable importance measure is explained and illustrated

Determination of the relative concentrations of rare earth ions by x-ray absorption spectroscopy: Application to terbium mixed oxides

A method, based on X-ray absorption spectroscopy (XAS) in the range 0.8–1.5 keV, to determine the relative amounts of rare earth ions in different valencies is explained and tested for the case of terbium mixed oxides. The results are in agreement with those obtained by existing analytical methods. The XAS method is advantageous in that it can be applied where other, conventional, methods break down

Effect of breastfeeding on gastrointestinal infection in infants: A targeted maximum likelihood approach for clustered longitudinal data

The PROmotion of Breastfeeding Intervention Trial (PROBIT) cluster-randomized a program encouraging breastfeeding to new mothers in hospital centers. The original studies indicated that this intervention successfully increased duration of breastfeeding and lowered rates of gastrointestinal tract infections in newborns. Additional scientific and popular interest lies in determining the causal effect of longer breastfeeding on gastrointestinal infection. In this study, we estimate the expected infection count under various lengths of breastfeeding in order to estimate the effect of breastfeeding duration on infection. Due to the presence of baseline and time-dependent confounding, specialized "causal" estimation methods are required. We demonstrate the double-robust method of Targeted Maximum Likelihood Estimation (TMLE) in the context of this application and review some related methods and the adjustments required to account for clustering. We compare TMLE (implemented both parametrically and using a data-adaptive algorithm) to other causal methods for this example. In addition, we conduct a simulation study to determine (1) the effectiveness of controlling for clustering indicators when cluster-specific confounders are unmeasured and (2) the importance of using data-adaptive TMLE.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS727 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimation of the Bivariate Survival Function with Generalized Bivariate Right Censored Data Structures

We propose a bivariate survival function estimator for a general right censored data structure that includes a time dependent covariate process. Firstly, an initial estimator that generalizes Dabrowska\u27s (1988) estimator is introduced. We obtain this estimator by a general methodology of constructing estimating functions in censored data models. The initial estimator is guaranteed to improve on Dabrowska\u27s estimator and remains consistent and asymptotically linear under informative censoring schemes if the censoring mechanism is estimated consistently. We then construct an orthogonalized estimating function which results in a more robust and efficient estimator than our initial estimator. A simulation study demonstrates the performance of the proposed estimators

Locally Efficient Estimation with Bivariate Right Censored Data

Estimation for bivariate right censored data is a problem that has had much study over the past 15 years. In this paper we propose a new class of estimators for the bivariate survivor function based on locally efficient estimation. The locally efficient estimator takes bivariate estimators Fn and Gn of the distributions of the time variables T1,T2 and the censoring variables C1,C2, respectively, and maps them to the resulting estimator. If Fn and Gn are consistent estimators of F and G, respectively, then the resulting estimator will be nonparametrically efficient (thus the term ``locally efficient\u27\u27). However, if either Fn or Gn (but not both) is not a consistent estimator of F or G, respectively, then the estimator will still be consistent and asymptotically normally distributed. We propose a locally efficient estimator which uses a consistent, non-parametric estimator for G and allows the user to supply lower dimensional (semi-parameteric or parametric) model for F. Since the estimator we choose for G will be a consistent estimator of G, the resulting locally efficient estimator will always be consistent and asymptotically normal, and our simulation studies have indicated that using a lower dimensional model for F gives excellent small sample performance. In addition, our algorithm for calculation of the efficient influence curve at true distributions for F and G yields also the efficiency bound which can be used to calculate relative efficiencies for any bivariate estimator. In this paper we will introduce the locally efficient estimator for bivariate right censored data, present an asymptotic theorem, present the results of simulation studies and perform a brief data analysis illustrating the use of the locally efficient estimator