Quantitative exponential bounds for the renewal theorem with spread-out distributions

We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace transform of some related random variable. Our proof is based on a coupling construction relying on discrete-time Markovian structures that underly the renewal processes and on Lyapunov-Doeblin type arguments.Comment: Accepted for publication in Markov Processes and Related Field

Bayesian analysis of 210Pb dating

In many studies of environmental change of the past few centuries, 210Pb dating is used to obtain chronologies for sedimentary sequences. One of the most commonly used approaches to estimate the ages of depths in a sequence is to assume a constant rate of supply (CRS) or influx of `unsupported' 210Pb from the atmosphere, together with a constant or varying amount of `supported' 210Pb. Current 210Pb dating models do not use a proper statistical framework and thus provide poor estimates of errors. Here we develop a new model for 210Pb dating, where both ages and values of supported and unsupported 210Pb form part of the parameters. We apply our model to a case study from Canada as well as to some simulated examples. Our model can extend beyond the current CRS approach, deal with asymmetric errors and mix 210Pb with other types of dating, thus obtaining more robust, realistic and statistically better defined estimates.Comment: 22 Pages, 4 Figure

Dynamic survival analysis: modelling the hazard function via ordinary differential equations

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for modelling the dynamics of the hazard function using systems of autonomous ordinary differential equations (ODEs). This modelling approach can be used to provide qualitative and quantitative analyses of the evolution of the hazard function over time. Our proposal capitalises on the extensive literature of ODEs which, in particular, allow for establishing basic rules or laws on the dynamics of the hazard function via the use of autonomous ODEs. We show how to implement the proposed modelling framework in cases where there is an analytic solution to the system of ODEs or where an ODE solver is required to obtain a numerical solution. We focus on the use of a Bayesian modelling approach, but the proposed methodology can also be coupled with maximum likelihood estimation. A simulation study is presented to illustrate the performance of these models and the interplay of sample size and censoring. Two case studies using real data are presented to illustrate the use of the proposed approach and to highlight the interpretability of the corresponding models. We conclude with a discussion on potential extensions of our work and strategies to include covariates into our framework.Comment: R and Python code available at: https://github.com/FJRubio67/ODESur

On narrowing coated conductor film: emergence of granularity-induced field hysteresis of transport critical current

Critical current density Jc in polycrystalline or granular superconducting material is known to be hysteretic with applied field H due to the focusing of field within the boundary between adjacent grains. This is of concern in the so-called coated conductors wherein superconducting film is grown on a granular, but textured surface of a metal substrate. While previous work has mainly been on Jc determined using induced or magnetization currents, the present work utilizes transport current via an applied potential in strip geometry. It is observed that the effect is not as pronounced using transport current, probably due to a large difference in criterion voltage between the two types of measurements. However, when the films are narrowed by patterning into 200-, 100-, or 80-micron, the hysteresis is clearly seen, because of the forcing of percolation across higher-angle grain boundaries. This effect is compared for films grown on ion-beam-assisted-deposited (IBAD) YSZ substrate and those grown on rolling-assisted-biaxially-textures substrates (RABiTS) which have grains that are about ten times larger. The hysteresis is more pronounced for the latter, which is more likely to have a weak grain boundary spanning the width of the microbridge. This is also of concern to applications in which coated conductors will be striated in order to reduce of AC losses.Comment: text-only: 10 pages, plus 5 figures on 5 page

Charge injection instability in perfect insulators

We show that in a macroscopic perfect insulator, charge injection at a field-enhancing defect is associated with an instability of the insulating state or with bistability of the insulating and the charged state. The effect of a nonlinear carrier mobility is emphasized. The formation of the charged state is governed by two different processes with clearly separated time scales. First, due to a fast growth of a charge-injection mode, a localized charge cloud forms near the injecting defect (or contact). Charge injection stops when the field enhancement is screened below criticality. Secondly, the charge slowly redistributes in the bulk. The linear instability mechanism and the final charged steady state are discussed for a simple model and for cylindrical and spherical geometries. The theory explains an experimentally observed increase of the critical electric field with decreasing size of the injecting contact. Numerical results are presented for dc and ac biased insulators.Comment: Revtex, 7pages, 4 ps figure

ERBlox: Combining Matching Dependencies with Machine Learning for Entity Resolution

Entity resolution (ER), an important and common data cleaning problem, is about detecting data duplicate representations for the same external entities, and merging them into single representations. Relatively recently, declarative rules called matching dependencies (MDs) have been proposed for specifying similarity conditions under which attribute values in database records are merged. In this work we show the process and the benefits of integrating three components of ER: (a) Classifiers for duplicate/non-duplicate record pairs built using machine learning (ML) techniques, (b) MDs for supporting both the blocking phase of ML and the merge itself; and (c) The use of the declarative language LogiQL -an extended form of Datalog supported by the LogicBlox platform- for data processing, and the specification and enforcement of MDs.Comment: To appear in Proc. SUM, 201