Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Participant, rater, and computer measures of coherence in posttraumatic stress disorder.

We examined the coherence of trauma memories in a trauma-exposed community sample of 30 adults with and 30 without posttraumatic stress disorder. The groups had similar categories of traumas and were matched on multiple factors that could affect the coherence of memories. We compared the transcribed oral trauma memories of participants with their most important and most positive memories. A comprehensive set of 28 measures of coherence including 3 ratings by the participants, 7 ratings by outside raters, and 18 computer-scored measures, provided a variety of approaches to defining and measuring coherence. A multivariate analysis of variance indicated differences in coherence among the trauma, important, and positive memories, but not between the diagnostic groups or their interaction with these memory types. Most differences were small in magnitude; in some cases, the trauma memories were more, rather than less, coherent than the control memories. Where differences existed, the results agreed with the existing literature, suggesting that factors other than the incoherence of trauma memories are most likely to be central to the maintenance of posttraumatic stress disorder and thus its treatment.

Accounting for Posttraumatic Stress Disorder Symptom Severity With Pre- and Posttrauma Measures: A Longitudinal Study of Older Adults.

Using data from a longitudinal study of community-dwelling older adults, we analyzed the most extensive set of known correlates of PTSD symptoms obtained from a single sample to examine the measures' independent and combined utility in accounting for PTSD symptom severity. Fifteen measures identified as PTSD risk factors in published meta-analyses and 12 theoretically and empirically supported individual difference and health-related measures were included. Individual difference measures assessed after the trauma, including insecure attachment and factors related to the current trauma memory, such as self-rated severity, event centrality, frequency of involuntary recall, and physical reactions to the memory, accounted for symptom severity better than measures of pre-trauma factors. In an analysis restricted to prospective measures assessed before the trauma, the total variance explained decreased from 56% to 16%. Results support a model of PTSD in which characteristics of the current trauma memory promote the development and maintenance of PTSD symptoms.

Algorithms for Geometric Matching, Clustering, and Covering

With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from many different sources such as vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which together contain useful high-level information about people's movement patterns.

The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing a matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters.

The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. More specifically, a subset of vertices in the road network are selected to place charging stations so that every shortest path contains enough charging stations and can be traveled by an EV without draining the battery. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this

shortest-path cover problem.

Associations between BMI and home, school and route environmental exposures estimated using GPS and GIS: do we see evidence of selective daily mobility bias in children?

BACKGROUND: This study examined whether objective measures of food, physical activity and built environment exposures, in home and non-home settings, contribute to children's body weight. Further, comparing GPS and GIS measures of environmental exposures along routes to and from school, we tested for evidence of selective daily mobility bias when using GPS data. METHODS: This study is a cross-sectional analysis, using objective assessments of body weight in relation to multiple environmental exposures. Data presented are from a sample of 94 school-aged children, aged 5-11 years. Children's heights and weights were measured by trained researchers, and used to calculate BMI z-scores. Participants wore a GPS device for one full week. Environmental exposures were estimated within home and school neighbourhoods, and along GIS (modelled) and GPS (actual) routes from home to school. We directly compared associations between BMI and GIS-modelled versus GPS-derived environmental exposures. The study was conducted in Mebane and Mount Airy, North Carolina, USA, in 2011. RESULTS: In adjusted regression models, greater school walkability was associated with significantly lower mean BMI. Greater home walkability was associated with increased BMI, as was greater school access to green space. Adjusted associations between BMI and route exposure characteristics were null. The use of GPS-actual route exposures did not appear to confound associations between environmental exposures and BMI in this sample. CONCLUSIONS: This study found few associations between environmental exposures in home, school and commuting domains and body weight in children. However, walkability of the school neighbourhood may be important. Of the other significant associations observed, some were in unexpected directions. Importantly, we found no evidence of selective daily mobility bias in this sample, although our study design is in need of replication in a free-living adult sample.

Safety and efficacy of rivastigmine in adolescents with Down syndrome: long-term follow-up.

Following the completion of a 20-week, open-label study of the safety and efficacy of liquid rivastigmine for adolescents with Down syndrome, 5 of the 10 adolescents in the clinical trial continued long-term rivastigmine therapy and 5 did not. After an average period of 38 months, all 10 subjects returned for a follow-up assessment to determine the safety and efficacy of long-term rivastigmine use. Rivastigmine was well tolerated and overall health appeared to be unaffected by long-term rivastigmine use. Performance change on cognitive and language measures administered at the termination of the open-label clinical trial was compared between the two groups. No between-group difference in median performance change across the long-term period was found, suggesting that the long-term use of rivastigmine does not improve cognitive and language performance. However, two subjects demonstrated remarkable improvement in adaptive function over the long-term period. Both subjects had received long-term rivastigmine therapy. The discussion addresses the challenge of assessing cognitive change in clinical trials using adolescents with Down syndrome as subjects and the use of group versus individual data to evaluate the relevance of medication effects.

Nanotopography-induced changes in focal adhesions, cytoskeletal organization, and mechanical properties of human mesenchymal stem cells.

The growth of stem cells can be modulated by physical factors such as extracellular matrix nanotopography. We hypothesize that nanotopography modulates cell behavior by changing the integrin clustering and focal adhesion (FA) assembly, leading to changes in cytoskeletal organization and cell mechanical properties. Human mesenchymal stem cells (hMSCs) cultured on 350 nm gratings of tissue-culture polystyrene (TCPS) and polydimethylsiloxane (PDMS) showed decreased expression of integrin subunits alpha2, alpha , alpha V, beta2, beta 3 and beta 4 compared to the unpatterned controls. On gratings, the elongated hMSCs exhibited an aligned actin cytoskeleton, while on unpatterned controls, spreading cells showed a random but denser actin cytoskeleton network. Expression of cytoskeleton and FA components was also altered by the nanotopography as reflected in the mechanical properties measured by atomic force microscopy (AFM) indentation. On the rigid TCPS, hMSCs on gratings exhibited lower instantaneous and equilibrium Young's moduli and apparent viscosity. On the softer PDMS, the effects of nanotopography were not significant. However, hMSCs cultured on PDMS showed lower cell mechanical properties than those on TCPS, regardless of topography. These suggest that both nanotopography and substrate stiffness could be important in determining mechanical properties, while nanotopography may be more dominant in determining the organization of the cytoskeleton and FAs.

UNC-6 (netrin) stabilizes oscillatory clustering of the UNC-40 (DCC) receptor to orient polarity.

The receptor deleted in colorectal cancer (DCC) directs dynamic polarizing activities in animals toward its extracellular ligand netrin. How DCC polarizes toward netrin is poorly understood. By performing live-cell imaging of the DCC orthologue UNC-40 during anchor cell invasion in Caenorhabditis elegans, we have found that UNC-40 clusters, recruits F-actin effectors, and generates F-actin in the absence of UNC-6 (netrin). Time-lapse analyses revealed that UNC-40 clusters assemble, disassemble, and reform at periodic intervals in different regions of the cell membrane. This oscillatory behavior indicates that UNC-40 clusters through a mechanism involving interlinked positive (formation) and negative (disassembly) feedback. We show that endogenous UNC-6 and ectopically provided UNC-6 orient and stabilize UNC-40 clustering. Furthermore, the UNC-40-binding protein MADD-2 (a TRIM family protein) promotes ligand-independent clustering and robust UNC-40 polarization toward UNC-6. Together, our data suggest that UNC-6 (netrin) directs polarized responses by stabilizing UNC-40 clustering. We propose that ligand-independent UNC-40 clustering provides a robust and adaptable mechanism to polarize toward netrin.

The normative and the personal life: individual differences in life scripts and life story events among USA and Danish undergraduates.

Life scripts are culturally shared expectations about the order and timing of life events in a prototypical life course. American and Danish undergraduates produced life story events and life scripts by listing the seven most important events in their own lives and in the lives of hypothetical people living ordinary lives. They also rated their events on several scales and completed measures of depression, PTSD symptoms, and centrality of a negative event to their lives. The Danish life script replicated earlier work; the American life script showed minor differences from the Danish life script, apparently reflecting genuine differences in shared events as well as less homogeneity in the American sample. Both consisted of mostly positive events that came disproportionately from ages 15 to 30. Valence of life story events correlated with life script valence, depression, PTSD symptoms, and identity. In the Danish undergraduates, measures of life story deviation from the life script correlated with measures of depression and PTSD symptoms.

The IGNITE network: a model for genomic medicine implementation and research.

BACKGROUND: Patients, clinicians, researchers and payers are seeking to understand the value of using genomic information (as reflected by genotyping, sequencing, family history or other data) to inform clinical decision-making. However, challenges exist to widespread clinical implementation of genomic medicine, a prerequisite for developing evidence of its real-world utility. METHODS: To address these challenges, the National Institutes of Health-funded IGNITE (Implementing GeNomics In pracTicE; www.ignite-genomics.org ) Network, comprised of six projects and a coordinating center, was established in 2013 to support the development, investigation and dissemination of genomic medicine practice models that seamlessly integrate genomic data into the electronic health record and that deploy tools for point of care decision making. IGNITE site projects are aligned in their purpose of testing these models, but individual projects vary in scope and design, including exploring genetic markers for disease risk prediction and prevention, developing tools for using family history data, incorporating pharmacogenomic data into clinical care, refining disease diagnosis using sequence-based mutation discovery, and creating novel educational approaches. RESULTS: This paper describes the IGNITE Network and member projects, including network structure, collaborative initiatives, clinical decision support strategies, methods for return of genomic test results, and educational initiatives for patients and providers. Clinical and outcomes data from individual sites and network-wide projects are anticipated to begin being published over the next few years. CONCLUSIONS: The IGNITE Network is an innovative series of projects and pilot demonstrations aiming to enhance translation of validated actionable genomic information into clinical settings and develop and use measures of outcome in response to genome-based clinical interventions using a pragmatic framework to provide early data and proofs of concept on the utility of these interventions. Through these efforts and collaboration with other stakeholders, IGNITE is poised to have a significant impact on the acceleration of genomic information into medical practice.

Clinical utility of a Web-enabled risk-assessment and clinical decision support program.

PURPOSE: Risk-stratified guidelines can improve quality of care and cost-effectiveness, but their uptake in primary care has been limited. MeTree, a Web-based, patient-facing risk-assessment and clinical decision support tool, is designed to facilitate uptake of risk-stratified guidelines. METHODS: A hybrid implementation-effectiveness trial of three clinics (two intervention, one control). PARTICIPANTS: consentable nonadopted adults with upcoming appointments. PRIMARY OUTCOME: agreement between patient risk level and risk management for those meeting evidence-based criteria for increased-risk risk-management strategies (increased risk) and those who do not (average risk) before MeTree and after. MEASURES: chart abstraction was used to identify risk management related to colon, breast, and ovarian cancer, hereditary cancer, and thrombosis. RESULTS: Participants = 488, female = 284 (58.2%), white = 411 (85.7%), mean age = 58.7 (SD = 12.3). Agreement between risk management and risk level for all conditions for each participant, except for colon cancer, which was limited to those <50 years of age, was (i) 1.1% (N = 2/174) for the increased-risk group before MeTree and 16.1% (N = 28/174) after and (ii) 99.2% (N = 2,125/2,142) for the average-risk group before MeTree and 99.5% (N = 2,131/2,142) after. Of those receiving increased-risk risk-management strategies at baseline, 10.5% (N = 2/19) met criteria for increased risk. After MeTree, 80.7% (N = 46/57) met criteria. CONCLUSION: MeTree integration into primary care can improve uptake of risk-stratified guidelines and potentially reduce "overuse" and "underuse" of increased-risk services.Genet Med 18 10, 1020-1028.