Constrained and Unconstrained Optimal Discounted Control of Piecewise Deterministic Markov Processes

International audienceThe main goal of this paper is to study the infinite-horizon expected discounted continuous-time optimal control problem of piecewise deterministic Markov processes with the control acting continuously on the jump intensity $\lambda$ and on the transition measure $Q$ of the process but not on the deterministic flow $\phi$. The contributions of the paper are for the unconstrained as well as the constrained cases. The set of admissible control strategies is assumed to be formed by policies, possibly randomized and depending on the history of the process, taking values in a set valued action space. For the unconstrained case we provide sufficient conditions based on the three local characteristics of the process $\phi$, $\lambda$, $Q$ and the semicontinuity properties of the set valued action space, to guarantee the existence and uniqueness of the integro-differential optimality equation (the so-called Bellman--Hamilton--Jacobi equation) as well as the existence of an optimal (and $\delta$-optimal, as well) deterministic stationary control strategy for the problem. For the constrained case we show that the values of the constrained control problem and an associated infinite dimensional linear programming (LP) problem are the same, and moreover we provide sufficient conditions for the solvability of the LP problem as well as for the existence of an optimal feasible randomized stationary control strategy for the constrained problem

'Choosing shoes': a preliminary study into the challenges facing clinicians in assessing footwear for rheumatoid patients

Background: Footwear has been accepted as a therapeutic intervention for the foot affected by rheumatoid arthritis (RA). Evidence relating to the objective assessment of footwear in patients with RA is limited. The aims of this study were to identify current footwear styles, footwear characteristics, and factors that influence footwear choice experienced by patients with RA. Methods: Eighty patients with RA were recruited from rheumatology clinics during the summer months. Clinical characteristics, global function, and foot impairment and disability measures were recorded. Current footwear, footwear characteristics and the factors associated with choice of footwear were identified. Suitability of footwear was recorded using pre-determined criteria for assessing footwear type, based on a previous study of foot pain. Results: The patients had longstanding RA with moderate-to severe disability and impairment. The foot and ankle assessment demonstrated a low-arch profile with both forefoot and rearfoot structural deformities. Over 50% of shoes worn by patients were opentype footwear. More than 70% of patients’ footwear was defined as being poor. Poor footwear characteristics such as heel rigidity and sole hardness were observed. Patients reported comfort (17%) and fit (14%) as important factors in choosing their own footwear. Only five percent (5%) of patients wore therapeutic footwear. Conclusions: The majority of patients with RA wear footwear that has been previously described as poor. Future work needs to aim to define and justify the specific features of footwear that may be of benefit to foot health for people with RA

An evaluation of seasonal variations in footwear worn by adults with inflammatory arthritis: a cross-sectional observational study using a web-based survey

Background: Foot problems are common in adults with inflammatory arthritis and therapeutic footwear can be effective in managing arthritic foot problems. Accessing appropriate footwear has been identified as a major barrier, resulting in poor adherence to treatment plans involving footwear. Indeed, previous New Zealand based studies found that many people with rheumatoid arthritis and gout wore inappropriate footwear. However, these studies were conducted in a single teaching hospital during the New Zealand summer therefore the findings may not be representative of footwear styles worn elsewhere in New Zealand, or reflect the potential influence of seasonal climate changes. The aim of the study was to evaluate seasonal variations in footwear habits of people with inflammatory arthritic conditions in New Zealand. Methods: A cross-sectional study design using a web-based survey. The survey questions were designed to elicit demographic and clinical information, features of importance when choosing footwear and seasonal footwear habits, including questions related to the provision of therapeutic footwear/orthoses and footwear experiences. Results: One-hundred and ninety-seven participants responded who were predominantly women of European descent, aged between 46–65 years old, from the North Island of New Zealand. The majority of participants identified with having either rheumatoid arthritis (35%) and/or osteoarthritis (57%) and 68% reported established disease (>5 years duration). 18% of participants had been issued with therapeutic footwear. Walking and athletic shoes were the most frequently reported footwear type worn regardless of the time of year. In the summer, 42% reported wearing sandals most often. Comfort, fit and support were reported most frequently as the footwear features of greatest importance. Many participants reported difficulties with footwear (63%), getting hot feet in the summer (63%) and the need for a sandal which could accommodate a supportive insole (73%). Conclusions: Athletic and walking shoes were the most popular style of footwear reported regardless of seasonal variation. During the summer season people with inflammatory arthritis may wear sandals more frequently in order to accommodate disease-related foot deformity. Healthcare professionals and researchers should consider seasonal variation when recommending appropriate footwear, or conducting footwear studies in people with inflammatory arthritis, to reduce non-adherence to prescribed footwear

Foot pain and foot health in an educated population of adults: results from the Glasgow Caledonian University Alumni Foot Health Survey

Abstract Background Foot pain is common amongst the general population and impacts negatively on physical function and quality of life. Associations between personal health characteristics, lifestyle/behaviour factors and foot pain have been studied; however, the role of wider determinants of health on foot pain have received relatively little attention. Objectives of this study are i) to describe foot pain and foot health characteristics in an educated population of adults; ii) to explore associations between moderate-to-severe foot pain and a variety of factors including gender, age, medical conditions/co-morbidity/multi-morbidity, key indicators of general health, foot pathologies, and social determinants of health; and iii) to evaluate associations between moderate-to-severe foot pain and foot function, foot health and health-related quality-of-life. Methods Between February and March 2018, Glasgow Caledonian University Alumni with a working email address were invited to participate in the cross-sectional electronic survey (anonymously) by email via the Glasgow Caledonian University Alumni Office. The survey was constructed using the REDCap secure web online survey application and sought information on presence/absence of moderate-to-severe foot pain, patient characteristics (age, body mass index, socioeconomic status, occupation class, comorbidities, and foot pathologies). Prevalence data were expressed as absolute frequencies and percentages. Multivariate logistic and linear regressions were undertaken to identify associations 1) between independent variables and moderate-to-severe foot pain, and 2) between moderate-to-severe foot pain and foot function, foot health and health-related quality of life. Results Of 50,228 invitations distributed, there were 7707 unique views and 593 valid completions (median age [inter-quartile range] 42 [31–52], 67.3% female) of the survey (7.7% response rate). The sample was comprised predominantly of white Scottish/British (89.4%) working age adults (95%), the majority of whom were overweight or obese (57.9%), and in either full-time or part-time employment (82.5%) as professionals (72.5%). Over two-thirds (68.5%) of the sample were classified in the highest 6 deciles (most affluent) of social deprivation. Moderate-to-severe foot pain affected 236/593 respondents (39.8%). High body mass index, presence of bunions, back pain, rheumatoid arthritis, hip pain and lower occupation class were included in the final multivariate model and all were significantly and independently associated with moderate-to-severe foot pain (p < 0.05), except for rheumatoid arthritis (p = 0.057). Moderate-to-severe foot pain was significantly and independently associated lower foot function, foot health and health-related quality of life scores following adjustment for age, gender and body mass index (p < 0.05). Conclusions Moderate-to-severe foot pain was highly prevalent in a university-educated population and was independently associated with female gender, high body mass index, bunions, back pain, hip pain and lower occupational class. Presence of moderate-to-severe foot pain was associated with worse scores for foot function, foot health and health-related quality-of-life. Education attainment does not appear to be protective against moderate-to-severe foot pain

Asteroseismology

Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly evolving field are followed by introductions to the most important concepts and methods on the basis of example. Previous and potential applications of asteroseismology are reviewed and future trends are attempted to be foreseen.Comment: 38 pages, 13 figures, to appear in: "Planets, Stars and Stellar Systems", eds. T. D. Oswalt et al., Springer Verla

Study of Bc+B_c^+ decays to the K+K−π+K^+K^-\pi^+ final state and evidence for the decay Bc+→χc0π+B_c^+\to\chi_{c0}\pi^+

A study of $B_c^+\to K^+K^-\pi^+$ decays is performed for the first time using data corresponding to an integrated luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. Evidence for the decay $B_c^+\to\chi_{c0}(\to K^+K^-)\pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $\frac{\sigma(B_c^+)}{\sigma(B^+)}\times\mathcal{B}(B_c^+\to\chi_{c0}\pi^+)$ to be $(9.8^{+3.4}_{-3.0}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times 10^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma(B_c^+)$ and $\sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $\bar b c$ weak annihilation is found for the region $m(K^-\pi^+)<1.834\mathrm{\,Ge\kern -0.1em V\!/}c^2$, with a significance of 2.4 standard deviations.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-022.html, link to supplemental material inserted in the reference

Rapidly measured indicators of recreational water quality and swimming-associated illness at marine beaches: a prospective cohort study

<p>Abstract</p> <p>Introduction</p> <p>In the United States and elsewhere, recreational water quality is monitored for fecal indicator bacteria to help prevent swimming-associated illnesses. Standard methods to measure these bacteria take at least 24 hours to obtain results. Molecular approaches such as quantitative polymerase chain reaction (qPCR) can estimate these bacteria faster, in under 3 hours. Previously, we demonstrated that measurements of the fecal indicator bacteria <it>Enterococcus </it>using qPCR were associated with gastrointestinal (GI) illness among swimmers at freshwater beaches. In this paper, we report on results from three marine beach sites.</p> <p>Methods</p> <p>We interviewed beach-goers and collected water samples at marine beaches affected by treated sewage discharges in Mississippi in 2005, and Rhode Island and Alabama in 2007. Ten to twelve days later, we obtained information about gastrointestinal, respiratory, eye, ear and skin symptoms by telephone. We tested water samples for fecal indicator organisms using qPCR and other methods.</p> <p>Results</p> <p>We enrolled 6,350 beach-goers. The occurrence of GI illness among swimmers was associated with a log₁₀-increase in exposure to qPCR-determined estimates of fecal indicator organisms in the genus <it>Enterococcus </it>(AOR = 2.6, 95% CI 1.3-5.1) and order <it>Bacteroidales </it>(AOR = 1.9, 95% CI 1.3-2.9). Estimates of organisms related to <it>Clostridium perfringens </it>and a subgroup of organisms in the genus <it>Bacteroides </it>were also determined by qPCR in 2007, as was F+ coliphage, but relationships between these indicators and illness were not statistically significant.</p> <p>Conclusions</p> <p>This study provides the first evidence of a relationship between gastrointestinal illness and estimates of fecal indicator organisms determined by qPCR at marine beaches.</p