Random real trees

We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable trees, including their branching property, which is analogous to the well-known property of Galton-Watson trees, and the calculation of their fractal dimension. We then consider spatial trees, which combine the genealogical structure of a real tree with spatial displacements, and we explain their connections with superprocesses. In the last section, we deal with a particular conditioning problem for spatial trees, which is closely related to asymptotics for random planar quadrangulations.Comment: 25 page

Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Effects of physical efforts on injury in elite soccer

In this study, the influence of physical efforts on occurrence of match injury in a professional soccer club was investigated. Computerised motion-analysis was used to measure the physical efforts of players during 10 injury situations. Total distance and those covered at different movement intensities were measured across the 5-min period preceding injury. If the final run preceding injury involved a high-intensity action (HIA), the distance, duration and speed of the effort and the recovery time between this and the penultimate HIA were measured. To determine the influence of these physical efforts, the results were compared to a normative profile for players computed from data across 5 games for the same variables; habitual distances covered over a 5-min period and characteristics of and recovery time between HIA. Compared to the normative profile, no differences were reported in physical characteristics during the period leading up to injury or for HIA although the latter were substantially higher in intensity (duration and distance). A lower than normal recovery time between HIA prior to injury was observed (35.6±16.8 s vs. 98.8±17.5 s, p=0.003). Within the limitations of the small sample, these findings may aid in further understanding injury and physical performance in elite soccer

Body size, skeletal maturity and functional characteristics of elite academy soccer players on entry between 1992 and 2003

Secular changes in body size, estimated fatness, skeletal maturation, and functional characteristics of youth soccer players on entry into an elite academy between 1992 and 2003 were compared. Annual selections grouped across time (1992–1995, 1996–1998, 1999–2003), playing position (goalkeeper, defender, midfielder, forward), and by eventual status in the sport (professional, non-professional) were compared. Data for 158 players (age 13.4 ± 0.4 years) at entry into the academy included skeletal age (Greulich-Pyle method), height, weight, relative fatness, four field tests of functional capacities (aerobic, anaerobic, power, speed), and quadriceps concentric strength of the dominant and non-dominant legs. MANCOVA with age as the covariate and chi square were used for comparisons across years. With few exceptions (but notably estimated [Vdot]O2max), results for player size, functional characteristics, and skeletal maturation did not differ among years. Distributions of players by skeletal maturity status and within each playing position also did not differ between years. Although related research has suggested that the anthropometric characteristics of professional players and demands of contemporary professional soccer competition increased over this period, the size, maturity, and functional characteristics of youth players on entry to an elite academy and of graduates who eventually played soccer as professionals generally did not change across annual selections from 1992 to 2003. The results suggest a lack of change in selection philosophies and practices of coaches involved in recruiting players for the academy, which in turn is reflected in consistency of specific evaluation criteria employed over the decade considered

Are physical performance and injury risk in a professional soccer team in match-play affected over a prolonged period of fixture congestion?

In this study, the effects of a prolonged period of fixture congestion (8 successive official matches in 26-days) on physical performance and injury risk and severity in a professional soccer team were investigated. Computerised motion-analysis was used to analyse the overall distance covered and that run at light- (0.0-11.0 km•h-1); low- (11.1-14.0 km•h-1); moderate- (14.1-19.7 km•h-1) and high-intensities (≥19.8 km•h-1) for the team as a whole. Distances were measured in metres per minute. Information on match injuries was recorded prospectively. The overall distance covered varied across successive matches (p<0.001) as more distance was run in games 4 and 7 compared to 2 and 3 respectively (126.6±12.3 m•min-1 and 125.0±13.2 m•min-1 vs. 116.0±8.0 m•min-1 and 115.5±11.0 m•min-1). Distance run in light-intensity exercise also varied (p<0.001) as more distance was covered in game 4 versus 1, 2, 3, 5 and 6 (75.5±3.8 m•min-1 vs. 70.6±2.4 m•min-1, 71.8±3.4 m•min-1, 69.3±2.6 m•min-1, 71.5±3.1 m•min-1, and 70.3±2.8 m•min-1) and in game 8 versus game 3 (73.1±3.8 vs. 69.3±2.6 m•min-1) respectively. When comparing match halves, there were no differences across games in overall or high-intensity distance covered and performance in these measures was similar for matches played before, during and after this period. Globally, no difference over the 8 games combined was observed between the reference team and opponents in any of the performance measures whereas the overall distance covered and that in low- (both p<0.001) and high-intensity running (p=0.040) differed in individual games. The incidence of match injury during the congested fixture period was similar to rates reported outside this period but the mean layoff duration of injuries was substantially shorter during the former (p<0.05). In summary, while the overall distance run and that covered at lower intensities varied across games, high-intensity running performance and injury risk were generally unaffected during a prolonged period of fixture congestion. These results might be linked to squad rotation and post-match recovery strategies in place at the present club

Match injuries in professional soccer: inter-seasonal variation and effects of competition type, match congestion and positional role

In this prospective observational study, injuries sustained in official match-play in players belonging to a professional soccer club were investigated. Incidence and patterns of injury were compared across four-seasons (2005-2006: S1, 2006-2007: S2, 2007-2008: S3 and 2008-2009: S4) and 3 match formats (domestic League/Cup games and European club competition). In addition, the effects of both fixture congestion and the positional role of players were investigated. Injury incidence (per 1 000 match-hours) did not vary between seasons (range 31.2-59.2 observed in S2 and S4, respectively, p=0.12) or fixture formats (range 32.6-40.8 observed in European and League matches, respectively, p=0.49). In contrast, rates varied in players (n=7) who participated in all four seasons as more injuries were sustained in S1 compared to S2 and S3, respectively (88.4 vs. 49.0 vs. 49.2, both p or = 4 days). Finally, the incidence of injury and muscle strains (both p<0.001) varied across positional roles with the highest rates observed in centre-forwards. These findings provide further knowledge on the risk of injury in contemporary professional soccer match-play and may aid in the care and management of playing resources

Feller property and infinitesimal generator of the exploration process

We consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale

Apraxia: a gestural or a cognitive disorder?

François Osiurak1,2 and Didier Le Gall31 Laboratoire d’Etude des Mécanismes Cognitifs (EA 3082), Université de Lyon, France2 Institut Universitaire de France, Paris, France3 Laboratoire de Psychologie des Pays de la Loire (EA 4638), Université d’Angers, FranceCorrespondence to: François Osiurak, Laboratoire d’Etude des Mécanismes Cognitifs (EA 3082), Institut de Psychologie, 5, avenue Pierre Mendès-France, 69676 Bron Cedex, France E-mail: Francois.Osiurak{at}univ-lyon2.frSir,We read with great interest the article by Buxbaum et al. (2014) about the critical brain regions for tool-related and imitative actions. The authors performed voxel-based lesion–symptom mapping with data from 71 left brain-damaged patients. Three types of actions were examined: (i) pantomime to sight of tools (GestTool); (ii) pantomime on imitation (ImTool); and (iii) imitation of meaningless gestures (ImNov). Impairments in all three of the gesture tasks were associated with lesions in left middle and inferior temporal and inferior parietal regions. Moreover, tool-related actions (both GestTool and ImTool) were dependent on left middle and inferior temporal lobe, whereas imitation of meaningless gestures (ImNov) was dependent on left inferior parietal regions. From these findings, the authors drew two conclusions. First, the left inferior parietal lobe might be the basis for the kinematic component of the praxis system, useful for planning movement trajectories in terms of extent, direction and timing. Second, middle and inferior temporal regions might support representational components of the praxis system (e.g. the arm and hand posture associated with the use of a hammer). Note that these conclusions lead to a profound revision of Buxbaum’s initial (2001) model. In this model, the left inferior parietal lobe was viewed