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

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

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

"Minimal clinically important difference" estimates of 6 commonly-used performance tests in patients with chronic musculoskeletal pain completing a work-related multidisciplinary rehabilitation program.

Functional tests are widely used to measure performance in patients with chronic musculoskeletal pain. Our objective was to determine the Minimal Clinically Important Differences (MCID) for the 6-min walk test (6MWT), the Steep Ramp Test (SRT), the 1-min stair climbing test (1MSCT), the sit-to-stand test (STS), the Jamar dynamometer test (JAM) and the lumbar Progressive Isoinertial Lifting Evaluation (PILE) in chronic musculoskeletal pain patients. A single-center prospective observational study was conducted in a rehabilitation center. Patients with upper-limb, lower-limb or neck/back lesions were included over a period of 21 months. We used the anchor-based method as a reference method, supplemented by the distribution-based and opinion-based approaches, to determine the MCIDs. 838 chronic musculoskeletal pain patients were included. The estimation method and thelesion location had a significant influence on the results. MCIDs were estimated at +75m and +60m for the 6MWT (lower-limb and neck/back lesions, respectively), +18 steps for the 1MSCT (lower-limb and neck/back lesions) and +6kg for the JAM (upper limb lesions). The anchor-based method could not provide valid estimations for the three other scales, but distribution and opinion-based methods provided rough values of MCIDs for the SRT (+39w to +61w), the STS (-5 sec to -7 sec) and the PILE (+4kg to +7kg). The above MCID estimations for the 6MWT, 1MSCT and JAM can be used in chronic musculoskeletal pain patients participating in vocational multidisciplinary rehabilitation programs or in therapeutic trials. The use of specific anchors might give better estimations of MCIDs for the three other scales in future research

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

Activity of the antiarrhythmic drug amiodarone against Leishmania (L.) infantum: an in vitro and in vivo approach

<div><p>Abstract Background: Considering the high toxicity and limited therapies available for treating visceral leishmaniasis (VL), the drug repositioning approach represents a faster way to deliver new therapies to the market. Methods: In this study, we described for the first time the activity of a potent antiarrhythmic, amiodarone (AMD), against L. (L.)infantum and its in vitro and in vivo activity. Results: The evaluation against promastigotes has shown that amiodarone presents leishmanicidal effect against the extracellular form, with an IC50 value of 10 μM. The activity was even greater against amastigotes in comparison with promastigotes with an IC50 value of 0.5 μM. The selectivity index in relation to the intracellular form demonstrated that the antiparasitic activity was approximately 56 times higher than its toxicity to mammalian cells. Investigation of the in vivo AMD activity in the L. infantum-infected hamster model showed that 51 days after the initial infection, amiodarone was unable to reduce the parasite burden in the spleen and liver when treated for 10 consecutive days, intraperitoneally, at 50 mg/kg/day, as determined by qPCR. Although not statistically significant, AMD was able to reduce the parasite burden by 20% in the liver when treated for 10 consecutive days, orally, at 100 mg/kg/day; no reduction in the spleen was found by qPCR. Conclusions: Our findings may help further drug design studies seeking new AMD derivatives that may provide new candidates with an in vitro selectivity close to or even greater than that observed in the prototype delivering effectiveness in the experimental model of VL.</p></div