On coupled systems of Kolmogorov equations with applications to stochastic differential games

We prove that a family of linear bounded evolution operators $({\bf G}(t,s))_{t\ge s\in I}$ can be associated, in the space of vector-valued bounded and continuous functions, to a class of systems of elliptic operators $\bm{\mathcal A}$ with unbounded coefficients defined in I\times \Rd (where $I$ is a right-halfline or $I=\R$) all having the same principal part. We establish some continuity and representation properties of $({\bf G}(t,s))_{t \ge s\in I}$ and a sufficient condition for the evolution operator to be compact in C_b(\Rd;\R^m). We prove also a uniform weighted gradient estimate and some of its more relevant consequence

Ergodic BSDEs with Multiplicative and Degenerate Noise

In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type we can give a stochastic representation of a large class of Ergodic HJB equations; morever our general results can be applied to get the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs

Welfare assessment: correlations and integration between a Qualitative Behavioural Assessment and a clinical/health protocol applied in veal calves farms

This study is aimed at finding correlations and possible integration among Qualitative Behavioural Assessment (QBA) and a specific protocol of clinical/health evaluation. Both welfare assessment methods were based on direct animal observation and were applied in 24 Italian veal calves farms at 3 weeks (wks) of rearing. Principal component analysis (PCA) summarized 20 QBA descriptors on two main components (PC1 and PC2) with eigenvalues above 4 and explaining 29.6 and 20.3% of the variation respectively. PCA on residuals obtained after correcting for housing condition yielded highly similar results, indicating that the rearing environment of the calves was not an important determinant of the observer reliability of QBA. A relationship was found between QBA PC2 and the presence of signs of cross-sucking recorded during the clinical visit (presence PC2=1.11 vs. absence PC2=-1.55,

Analysis of Relationship between Training Load and Recovery Status in Adult Soccer Players: a Machine Learning Approach

Abstract Periods of intensified training may increase athletes' fatigue and impair their recovery status. Therefore, understanding internal and external load markers-related to fatigue is crucial to optimize their weekly training loads. The current investigation aimed to adopt machine learning (ML) techniques to understand the impact of training load parameters on the recovery status of athletes. Twenty-six adult soccer players were monitored for six months, during which internal and external load parameters were daily collected. Players' recovery status was assessed through the 10-point total quality recovery (TQR) scale. Then, different ML algorithms were employed to predict players' recovery status in the subsequent training session (S-TQR). The goodness of the models was evaluated through the root mean squared error (RMSE), mean absolute error (MAE), and Pearson's Correlation Coefficient (r). Random forest regression model produced the best performance (RMSE=1.32, MAE=1.04, r = 0.52). TQR, age of players, total decelerations, average speed, and S-RPE recorded in the previous training were recognized by the model as the most relevant features. Thus, ML techniques may help coaches and physical trainers to identify those factors connected to players' recovery status and, consequently, driving them toward a correct management of the weekly training loads

Singular Limit of BSDEs and Optimal Control of two Scale Stochastic Systems in Infinite Dimensional Spaces

In this paper we study by probabilistic techniques the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is represented as the solution of a backward stochastic differential equation (BSDE) that it is shown to converge towards a reduced BSDE. The noise is assumed to be additive both in the slow and the fast equations for the state. Some non degeneracy condition on the slow equation is required. The limit BSDE involves the solution of an ergodic BSDE and is itself interpreted as the value function of an auxiliary stochastic control problem on a reduced state space

Effect of Number of Players and Maturity on Ball-Drills Training Load in Youth Basketball

This study aimed to assess the basketball ball-drills workload analyzing: (1) the effect of varying the number of players involved on physiological and technical demands; (2) the temporal changes in players’ responses across bouts; and (3) the relationship of players’ workload with their maturation status and training age. Twelve young male basketball players (mean ± SD; age 13.9 ± 0.7 years; height 1.76 ± 0.06 m; body mass 65.7 ± 12.5 kg; HRmax 202 ± 8 beat·min−1) completed three bouts of 4 min interspersed by 2 min of passive recovery of two vs. two and four vs. four ball-drills. The mean percentage of HRmax (%HRmax) and ratings of perceived exertion (RPE) were collected. Technical actions (TAs) (dribbles, passes, shots, interceptions, steals, rebounds, and turnovers) were calculated through notational analysis. Players’ genitalia development (GD) and pubic hair (PH) growth were assessed using Tanner scale. Results showed a higher %HRmax (p = 0.018), RPE (p = 0.042), dribbles (p = 0.007), shots (p = 0.003), and rebounds (p = 0.006) in two vs. two compared to four vs. four condition. Furthermore, a statistical difference was found for %HRmax (p = 0.005) and number of passes (p = 0.020) between bouts. In addition, no correlation between GD, PH, and training age with %HRmax, RPE, and TAs was found. These findings suggest that variations of the number of players involved affect ball-drills workload and that ball-drills training intensity varies across bouts. Finally, ball-drills elicit an adequate training stimulus, regardless of players’ maturation status and training age