Stochastic approximations and differential inclusions II: applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Feasibility of a prehabilitation program before major abdominal surgery: a pilot prospective study.

To assess the feasibility of a prehabilitation program and its effects on physical performance and outcomes after major abdominal surgery. In this prospective pilot study, patients underwent prehabilitation involving three training sessions per week for 3 weeks preoperatively. The feasibility of delivering the intervention was assessed based on recruitment and adherence to the program. Its impacts on fitness (oxygen uptake (VO <sub>2</sub> )) and physical performance (Timed Up and Go Test, 6-Minute Walk Test) were evaluated. From May 2017 to January 2020, 980 patients were identified and 44 (4.5%) were invited to participate. The main obstacles to patient recruitment were insufficient time (<3 weeks) prior to scheduled surgery (n = 276, 28%) and screening failure (n = 312, 32%). Of the 44 patients, 24 (55%) declined to participate, and 20 (23%) were included. Of these, six (30%) were not adherent to the program. Among the remaining 14 patients, VO <sub>2</sub> at ventilatory threshold significantly increased from 9.7 to 10.9 mL/min/kg. No significant difference in physical performance was observed before and after prehabilitation. Although prehabilitation seemed to have positive effects on exercise capacity, logistic and patient-related difficulties were encountered. The program is not feasible in its current form for all-comers

Diagnostic yield and cost analysis of electrocardiographic screening in Swiss paediatric athletes

OBJECTIVES Athletes performing sports on high level are at increased risk for sudden cardiac death. This includes paediatric athletes, even though data on screening strategies in this age group remain scarce. This study aimed to assess electrocardiogram interpretation criteria in paediatric athletes and to evaluate the cost of screening. METHODS National, multicentre, retrospective, observational study on 891 athletes of paediatric age (<18 years) evaluated by history, physical examination and 12-lead electrocardiogram. The primary outcome measure was abnormal electrocardiogram findings according to the International Recommendations for Electrographic Interpretation in Athletes. The secondary outcome measure was cost of screening. RESULTS 19 athletes (2.1%) presented abnormal electrocardiogram findings requiring further investigations, mainly abnormal T-wave inversion. These 19 athletes were predominantly males, performing endurance sports with a mean volume of 10 weekly hours for a mean duration of 6 years of training. Further investigations did not identify any relevant pathology. All athletes were cleared for competition with regular follow-up. Total costs of the screening were 108,860 USD (122 USD per athlete). CONCLUSIONS Our study using the International Recommendations for Electrographic Interpretation in Athletes identified a low count of abnormal findings in paediatric athletes, yet raising substantially the cost of screening. Hence, the utility of electrocardiogram-inclusive screening of paediatric athletes remains to be elucidated by longitudinal data

Recruitment of low-income pregnant women into a dietary and dental care intervention: lessons from a feasibility trial

Background: There are difficulties in carrying out research in low-income urban communities, but the methodological challenges and suggestions on how to deal with them are often undocumented. The aims of this study are to describe the challenges of recruiting and enrolling low-income pregnant women with periodontitis to a clinical trial on vitamin D/calcium milk fortification and periodontal therapy and also to describe the patient-, study protocol- and setting-related factors related to women’s ineligibility and refusal to participate in the study. Methods: A mixed-method sequential exploratory design was applied. Qualitative and quantitative data on recruitment to a 2 × 2 factorial feasibility clinical trial were used. Eighteen women attending the health centre in a low-income area in Duque de Caxias (Rio de Janeiro, Brazil) took part in focus group discussions, and the data were thematically analysed. Quantitative data were analysed using appropriate descriptive statistics, including absolute and relative frequencies. Results: Of all referrals (767), 548 (78.5%) did not meet the initial eligibility criteria. The main reason for exclusion (58%) was advanced gestational age (> 20 weeks) at first prenatal appointment. In the periodontal examination (dental screen), the main reason for exclusion was the presence of extensive caries (64 out of 127 exclusions). Non-participation of those eligible after the periodontal examination was approximately 24% (22 out 92 eligible women) and predominantly associated with patient-related barriers (e.g. transportation barriers, family obligations, patients being unresponsive to phone calls and disconnected telephones). The study recruited 70 women with periodontitis in 53 weeks and did not reach the benchmark of 120 women in 36 weeks (58.3% of the original target). Recruitment was severely hindered by health centre closures due to general strikes. The recruitment yields were 9.1% (70/767) of all women contacted at first prenatal visit and 76.1% (70/92) of those screened eligible and enrolled in the trial. Women did not report concerns regarding random allocation and considered fortified milk as a healthful and safe food for pregnant women. Some women reported that financial constraints (e.g. transportation costs) could hinder participation in the study. Conclusion: Engagement between the research team and health centre staff (e.g. nurses) facilitated referral and recruitment, yet some pregnant women failed to participate in the study largely due to significant patient-related sociodemographic barriers and setting-related factors. Our data illustrate the complexity of overcoming recruitment and enrolment challenges for clinical trials in resource-limited settings. Trial registration: ClinicalTrials.gov, NCT03148483. Registered on 11 May 2017

Transcultural adaptation and validation of a French version of the Prosthetic Limb Users Survey of Mobility 12-item Short-Form (PLUS-M/FC-12) in active amputees.

The PLUS-M 12-item Short-Form is a self-questionnaire that assesses the perceived capacity of lower limb amputees (LLAs) to perform a number of daily-life activities. Its psychometric properties are excellent (intraclass correlation coefficient [ICC]&gt;0.9, fast administration and scoring, normative data available), and it can be used in clinical practice or for research purposes. We aimed to develop a French version of this questionnaire and to assess its psychometric properties. We followed international recommendations for translation and cross-cultural validation of questionnaires. In total, 52 LLAs (age 53±16, 40 males, 28/12/12 transtibial/Gritti-Stokes/transfemoral, 20/28/4 ischemic/traumatic/other) participated. Criterion and construct validities were assessed with the Pearson correlation coefficient (PCC) between the PLUS-M 12-item Short-Form and other constructs (Prosthetic-Profile-of-the-Amputee-Locomotor Capabilities Index, Activities-specific Balance Confidence scale, 2-min walking test and Timed Up and Go test), internal consistency with the Cronbach α and reliability with the ICC in 46 individuals who completed the questionnaire twice in a 7-day interval. The mean (SD) PLUS-M 12-item Short-Form T-score was 56.1 (7.8; range 40.3 to 71.4). Construct and criterion validity, internal consistency and reliability ranged from low to excellent (r=0.43 to 0.84, P&lt;10 &lt;sup&gt;-2&lt;/sup&gt; to 0.002; Cronbach α=0.90, ICC=0.89 [0.81-0.94]). We found no floor or ceiling effect. The French version of the PLUS-M 12-item Short-Form has good to excellent psychometric properties, comparable to those of the original version. Its use could definitely be proposed for both clinical and research purposes, once its validation is completed by assessing other psychometric qualities, especially sensitivity to change