A consistent treatment of link and writhe for open rods, and their relation to end rotation

We combine and extend the work of Alexander & Antman \cite{alexander.82} and Fuller \cite{fuller.71,fuller.78} to give a framework within which precise definitions can be given of topological and geometrical quantities characterising the contortion of open rods undergoing large deformations under end loading. We use these definitions to examine the extension of known results for closed rods to open rods. In particular, we formulate the analogue of the celebrated formula $Lk=Tw+Wr$ (link equals twist plus writhe) for open rods and propose an end rotation, through which the applied end moment does work, in the form of an integral over the length of the rod. The results serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations.Comment: 17 pages, 4 figure

Recursion Aware Modeling and Discovery For Hierarchical Software Event Log Analysis (Extended)

This extended paper presents 1) a novel hierarchy and recursion extension to the process tree model; and 2) the first, recursion aware process model discovery technique that leverages hierarchical information in event logs, typically available for software systems. This technique allows us to analyze the operational processes of software systems under real-life conditions at multiple levels of granularity. The work can be positioned in-between reverse engineering and process mining. An implementation of the proposed approach is available as a ProM plugin. Experimental results based on real-life (software) event logs demonstrate the feasibility and usefulness of the approach and show the huge potential to speed up discovery by exploiting the available hierarchy.Comment: Extended version (14 pages total) of the paper Recursion Aware Modeling and Discovery For Hierarchical Software Event Log Analysis. This Technical Report version includes the guarantee proofs for the proposed discovery algorithm

Tuplix Calculus

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplication, clearing and encapsulation. We provide two examples of applications; one on incremental financial budgeting, and one on modular financial budget design.Comment: 22 page

Giant bubble pinch-off

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a downward jet. Only in the limiting case of large Froude number the neck radius $h$ scales as $h(-\log h)^{1/4} \propto \tau^{1/2}$, the purely inertial scaling. For any finite Froude number the collapse is slower, and a second length-scale, the curvature of the void, comes into play. Both length-scales are found to exhibit power-law scaling in time, but with different exponents depending on the Froude number, signaling the non-universality of the bubble pinch-off.Comment: 5 pages, 2 figures. Figure quality was reduced considerably and converted to greyscale to decrease file siz

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

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