A mathematical framework for inverse wave problems in heterogeneous media

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical properties of materials. Rocks, manufactured materials, and other wave propagation environments often exhibit spatial heterogeneity in mechanical properties at a wide variety of scales, and coefficient functions representing these properties must mimic this heterogeneity. We show how to choose domains (classes of nonsmooth coefficient functions) and data definitions (traces of weak solutions) so that optimization formulations of inverse wave problems satisfy some of the prerequisites for application of Newton's method and its relatives. These results follow from the properties of a class of abstract first-order evolution systems, of which various physical wave systems appear as concrete instances. Finite speed of propagation for linear waves with bounded, measurable mechanical parameter fields is one of the by-products of this theory

The intervening role of urgency on the association between childhood maltreatment, PTSD, and substance-related problems

A range of risk factors lead to opioid use and substance-related problems (SRP) including childhood maltreatment, elevated impulsivity, and psychopathology. These constructs are highly interrelated such that childhood maltreatment is associated with elevated impulsivity and trauma-related psychopathology such as posttraumatic stress disorder (PTSD), and impulsivity-particularly urgency-and PTSD are related. Prior work has examined the association between these constructs and substance-related problems independently and it is unclear how these multi-faceted constructs (i.e., maltreatment types and positive and negative urgency) are associated with one another and SRP. The current study used structural equation modeling (SEM) to examine the relations among childhood maltreatment, trait urgency, PTSD symptoms, and SRP in a sample of individuals with a history of opioid use. An initial model that included paths from each type of childhood maltreatment, positive and negative urgency, PTSD and SRP did not fit the data well. A pruned model with excellent fit was identified that suggested emotional abuse, positive urgency, and negative urgency were directly related to PTSD symptoms and only PTSD symptoms were directly related to SRP. Furthermore, significant indirect effects suggested that emotional abuse and negative urgency were related to SRP via PTSD symptom severity. These results suggest that PTSD plays an important role in the severity of SRP

Thermally activated reorientation of di-interstitial defects in silicon

We propose a di-interstitial model for the P6 center commonly observed in ion implanted silicon. The di-interstitial structure and transition paths between different defect orientations can explain the thermally activated transition of the P6 center from low-temperature C1h to room-temperature D2d symmetry. The activation energy for the defect reorientation determined by ab initio calculations is 0.5 eV in agreement with the experiment. Our di-interstitial model establishes a link between point defects and extended defects, di-interstitials providing the nuclei for the growth.Comment: 12 pages, REVTeX, Four figures, submitted to Phys. Rev. Let

Seismic tomography is locally ill-posed

We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients

Structural Uncertainty in Onchocerciasis Transmission Models Influences the Estimation of Elimination Thresholds and Selection of Age Groups for Seromonitoring

Background. The World Health Organization recommends monitoring Ov16 serologyin children aged <10 years for stopping mass ivermectin administration. Transmission models can help to identify the most informative age groups for serological monitoring and investigate the discriminatory power of serology-based elimination thresholds.Model predictions will depend on assumed age-exposure patterns and transmission efficiency at low infection levels. Methods. The individual-based transmission model, EPIONCHO-IBM, was used toassess: i) the most informative age groups for serological monitoring using receiveroperator characteristic curves for different elimination thresholds under various age-dependent exposure assumptions, including those of ONCHOSIM (another widely-used model), and ii) the influence of within-human density-dependent parasite establishment (included in EPIONCHO-IBM but not in ONCHOSIM) on positive predictive values for different serological thresholds.Results. When assuming EPIONCHO-IBM exposure patterns, under-10s are themost informative age group for seromonitoring; when assuming ONCHOSIM’s exposure patterns, 5–15-year olds are the most informative (as published elsewhere).Omitting density-dependent parasite establishment results in more lenientseroprevalence thresholds, even for higher baseline infection prevalence and shorter treatment durations.Conclusions. Selecting appropriate seromonitoring age groups depends critically onage-dependent exposure patterns. The role of density dependence on elimination thresholds largely explains differing EPIONCHO-IBM and ONCHOSIM elimination predictions

Balancing equity and efficiency in the Dutch basic benefits package using the principle of proportional shortfall

Economic evaluations are increasingly used to inform decisions regarding the allocation of scarce health care resources. To systematically incorporate societal preferences into these evaluations, quality-adjusted life year gains could be weighted according to some equity principle, the most suitable of which is a matter of frequent debate. While many countries still struggle with equity concerns for priority setting in health care, the Netherlands has reached a broad consensus to use the concept of proportional shortfall. Our study evaluates the concept and its support in the Dutch health care context. We discuss arguments in the Netherlands for using proportional shortfall and difficulties in transitioning from principle to practice. In doing so, we address universal issues leading to a systematic consideration of equity concerns for priority setting in health care. The article thus has relevance to all countries struggling with the formalization of equity concerns for priority setting