An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations

We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th German-Polish Workshop on Stochastic Models, Statistics and Their Application

Socioeconomic position and childhood sedentary time: evidence from the PEACH project.

notes: PMCID: PMC3844440© 2013 Pulsford et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Associations between socioeconomic position (SEP) and sedentary behaviour in children are unclear. Existing studies have used aggregate measures of weekly sedentary time that could mask important differences in the relationship between SEP and sedentary time at different times of the day or between weekdays and weekend days. These studies have also employed a variety of measures of SEP which may be differentially associated with sedentary time. This paper examines associations of multiple indicators of SEP and accelerometer-measured, temporally specific, sedentary time in school children.National Prevention Research InitiativeWorld Cancer Research Fund (WCRF UK

The effect of moving to East Village, the former London 2012 Olympic and Paralympic Games Athletes' Village, on mode of travel (ENABLE London study, a natural experiment)

Background Interventions to encourage active modes of travel (walking, cycling) may improve physical activity levels, but longitudinal evidence is limited and major change in the built environment / travel infrastructure may be needed. East Village (the former London 2012 Olympic Games Athletes Village) has been repurposed on active design principles with improved walkability, open space and public transport and restrictions on residential car parking. We examined the effect of moving to East Village on adult travel patterns. Methods One thousand two hundred seventy-eight adults (16+ years) seeking to move into social, intermediate, and market-rent East Village accommodation were recruited in 2013–2015, and followed up after 2 years. Individual objective measures of physical activity using accelerometry (ActiGraph GT3X+) and geographic location using GPS travel recorders (QStarz) were time-matched and a validated algorithm assigned four travel modes (walking, cycling, motorised vehicle, train). We examined change in time spent in different travel modes, using multilevel linear regresssion models adjusting for sex, age group, ethnicity, housing group (fixed effects) and household (random effect), comparing those who had moved to East Village at follow-up with those who did not. Results Of 877 adults (69%) followed-up, 578 (66%) provided valid accelerometry and GPS data for at least 1 day (≥540 min) at both time points; half had moved to East Village. Despite no overall effects on physical activity levels, sizeable improvements in walkability and access to public transport in East Village resulted in decreased daily vehicle travel (8.3 mins, 95%CI 2.5,14.0), particularly in the intermediate housing group (9.6 mins, 95%CI 2.2,16.9), and increased underground travel (3.9 mins, 95%CI 1.2,6.5), more so in the market-rent group (11.5 mins, 95%CI 4.4,18.6). However, there were no effects on time spent walking or cycling

Accretion, Primordial Black Holes and Standard Cosmology

Primordial Black Holes evaporate due to Hawking radiation. We find that the evaporation time of primordial black holes increase when accretion of radiation is included.Thus depending on accretion efficiency more and more number of primordial black holes are existing today, which strengthens the idea that the primordial black holes are the proper candidate for dark matter.Comment: 11 pages, 3 figure

Virtual patients design and its effect on clinical reasoning and student experience : a protocol for a randomised factorial multi-centre study

Background Virtual Patients (VPs) are web-based representations of realistic clinical cases. They are proposed as being an optimal method for teaching clinical reasoning skills. International standards exist which define precisely what constitutes a VP. There are multiple design possibilities for VPs, however there is little formal evidence to support individual design features. The purpose of this trial is to explore the effect of two different potentially important design features on clinical reasoning skills and the student experience. These are the branching case pathways (present or absent) and structured clinical reasoning feedback (present or absent). Methods/Design This is a multi-centre randomised 2x2 factorial design study evaluating two independent variables of VP design, branching (present or absent), and structured clinical reasoning feedback (present or absent).The study will be carried out in medical student volunteers in one year group from three university medical schools in the United Kingdom, Warwick, Keele and Birmingham. There are four core musculoskeletal topics. Each case can be designed in four different ways, equating to 16 VPs required for the research. Students will be randomised to four groups, completing the four VP topics in the same order, but with each group exposed to a different VP design sequentially. All students will be exposed to the four designs. Primary outcomes are performance for each case design in a standardized fifteen item clinical reasoning assessment, integrated into each VP, which is identical for each topic. Additionally a 15-item self-reported evaluation is completed for each VP, based on a widely used EViP tool. Student patterns of use of the VPs will be recorded. In one centre, formative clinical and examination performance will be recorded, along with a self reported pre and post-intervention reasoning score, the DTI. Our power calculations indicate a sample size of 112 is required for both primary outcomes

Comparison of embedded and added motor imagery training in patients after stroke: Study protocol of a randomised controlled pilot trial using a mixed methods approach

Copyright @ 2009 Schuster et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Two different approaches have been adopted when applying motor imagery (MI) to stroke patients. MI can be conducted either added to conventional physiotherapy or integrated within therapy sessions. The proposed study aims to compare the efficacy of embedded MI to an added MI intervention. Evidence from pilot studies reported in the literature suggests that both approaches can improve performance of a complex motor skill involving whole body movements, however, it remains to be demonstrated, which is the more effective one.Methods/Design: A single blinded, randomised controlled trial (RCT) with a pre-post intervention design will be carried out. The study design includes two experimental groups and a control group (CG). Both experimental groups (EG1, EG2) will receive physical practice of a clinical relevant motor task ('Going down, laying on the floor, and getting up again') over a two week intervention period: EG1 with embedded MI training, EG2 with MI training added after physiotherapy. The CG will receive standard physiotherapy intervention and an additional control intervention not related to MI.The primary study outcome is the time difference to perform the task from pre to post-intervention. Secondary outcomes include level of help needed, stages of motor task completion, degree of motor impairment, balance ability, fear of falling measure, motivation score, and motor imagery ability score. Four data collection points are proposed: twice during baseline phase, once following the intervention period, and once after a two week follow up. A nested qualitative part should add an important insight into patients' experience and attitudes towards MI. Semi-structured interviews of six to ten patients, who participate in the RCT, will be conducted to investigate patients' previous experience with MI and their expectations towards the MI intervention in the study. Patients will be interviewed prior and after the intervention period.Discussion: Results will determine whether embedded MI is superior to added MI. Findings of the semi-structured interviews will help to integrate patient's expectations of MI interventions in the design of research studies to improve practical applicability using MI as an adjunct therapy technique

An open-source tool to identify active travel from hip-worn accelerometer, GPS and GIS data.

BACKGROUND: Increases in physical activity through active travel have the potential to have large beneficial effects on populations, through both better health outcomes and reduced motorized traffic. However accurately identifying travel mode in large datasets is problematic. Here we provide an open source tool to quantify time spent stationary and in four travel modes(walking, cycling, train, motorised vehicle) from accelerometer measured physical activity data, combined with GPS and GIS data. METHODS: The Examining Neighbourhood Activities in Built Living Environments in London study evaluates the effect of the built environment on health behaviours, including physical activity. Participants wore accelerometers and GPS receivers on the hip for 7 days. We time-matched accelerometer and GPS, and then extracted data from the commutes of 326 adult participants, using stated commute times and modes, which were manually checked to confirm stated travel mode. This yielded examples of five travel modes: walking, cycling, motorised vehicle, train and stationary. We used this example data to train a gradient boosted tree, a form of supervised machine learning algorithm, on each data point (131,537 points), rather than on journeys. Accuracy during training was assessed using five-fold cross-validation. We also manually identified the travel behaviour of both 21 participants from ENABLE London (402,749 points), and 10 participants from a separate study (STAMP-2, 210,936 points), who were not included in the training data. We compared our predictions against this manual identification to further test accuracy and test generalisability. RESULTS: Applying the algorithm, we correctly identified travel mode 97.3% of the time in cross-validation (mean sensitivity 96.3%, mean active travel sensitivity 94.6%). We showed 96.0% agreement between manual identification and prediction of 21 individuals' travel modes (mean sensitivity 92.3%, mean active travel sensitivity 84.9%) and 96.5% agreement between the STAMP-2 study and predictions (mean sensitivity 85.5%, mean active travel sensitivity 78.9%). CONCLUSION: We present a generalizable tool that identifies time spent stationary and time spent walking with very high precision, time spent in trains or vehicles with good precision, and time spent cycling with moderate precisionIn studies where both accelerometer and GPS data are available this tool complements analyses of physical activity, showing whether differences in PA may be explained by differences in travel mode. All code necessary to replicate, fit and predict to other datasets is provided to facilitate use by other researchers

Dirac Equation with Spin Symmetry for the Modified P\"oschl-Teller Potential in DD-dimensions

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$.Comment: 9 pages and 1tabl

Primordial Black Holes: sirens of the early Universe

Primordial Black Holes (PBHs) are, typically light, black holes which can form in the early Universe. There are a number of formation mechanisms, including the collapse of large density perturbations, cosmic string loops and bubble collisions. The number of PBHs formed is tightly constrained by the consequences of their evaporation and their lensing and dynamical effects. Therefore PBHs are a powerful probe of the physics of the early Universe, in particular models of inflation. They are also a potential cold dark matter candidate.Comment: 21 pages. To be published in "Quantum Aspects of Black Holes", ed. X. Calmet (Springer, 2014

Prospective association between objective measures of childhood motor coordination and sedentary behaviour in adolescence and adulthood

BACKGROUND: Higher levels of gross motor coordination are positively associated with physical activity in childhood, but little is known about how they relate to sedentary behaviour. The aim of this study was to investigate the longitudinal association between gross motor coordination at childhood and sedentary behaviour in adolescence and adulthood. METHODS: Data were from the 1970 British Cohort Study (the age 10, 16, and 42-year surveys). At age 10 the participant's mother provided information on how often participants watched TV and played sports and a health visitor administered several tests to assess gross motor coordination. At aged 16 and 42-years participants reported their daily screen and TV time, respectively, and physical activity status. We examined associations between gross motor coordination at age 10 with sedentary behaviour and physical activity at age 16 and 42, using logistic regression. RESULTS: In multivariable models, higher levels of gross motor coordination were associated with lower odds of high screen time (n = 3073; OR 0.79, 95% CI 0.64, 0.98) at 16-years although no associations with physical activity were observed (OR 1.16, 95% CI 0.93, 1.44). Similar associations were observed with TV time in adulthood when participants were aged 42, and in addition high gross motor coordination was also associated with physical activity participation (n = 4879; OR 1.18, 95 % CI 1.02, 1.36). CONCLUSIONS: Intervention efforts to increase physical activity participation and reduce sedentary behaviour over the life course may be best targeted towards children with low gross motor coordination