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

Clinic of Occlusal Balancing

The treatment principles described in this ebook apply to all dental, surgical, orthodontics, implant, prosthetic, postural and behavioral specialties, concerned with the establishment by restoration of the occlusal morphology, to ensure optimal efficiency, during chewing and swallowing. To achieve this, the classic rules of occlusal equilibration, by grinding, must be profoundly modified and replaced by additive techniques restoring lost dental volumes and efficiency of dental functionality. Additive restoration techniques, of lost dental volumes, have been the subject of a thorough reflection on how to implement them with current composite materials. They obey a precise protocol. They will progressively evolve as the computerisation of procedures and the evolution of materials progresses

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Are aerobic fitness and repeated sprint ability linked to fatigue in professional soccer match-play? A pilot study

This investigation examined the association between aerobic fitness and repeated sprint ability and match-related fatigue in 9 professional outfield soccer players. Aerobic fitness using maximal aerobic speed (MAS) was determined via a continuous progressive incremental running test conducted on a motorised treadmill. A repeated sprint ability test (6 successive 6 s sprints separated by 20 s passive recovery) was performed on a non-motorised treadmill to determine mean and best sprint times and a percentage decrement score (%PD). A total of 114 observations of physical performance derived using computerised time motion analyses were collected from 33 matches. Correlations between fitness test and match-play measures were examined for 1) accumulated fatigue: percentage difference between halves for total distance covered per minute, distance run at high-intensities (HIR, actions for 1s duration, >19.1 km/h) per minute, mean recovery time between high-intensity runs, and percentage difference between the distance covered in HIR in the first 5- and 15-minute periods versus the final 5- and 15-minute periods respectively in normal time; and for 2) transient fatigue: percentage difference between the distance covered in HIR in a peak 5-minute period and the subsequent 5-minute period and for the latter compared to the mean for all other 5-minute periods. No significant relationships were observed between MAS and fatigue scores (magnitude of associations: trivial to large). For mean and best sprint times and %PD, the only reported significant correlation (r=0.77, magnitude of association: very large, p<0.05) was between %PD and the % difference across halves for mean recovery time between high-intensity runs (magnitude of other associations: small to large). Criterion measures from tests of aerobic fitness and repeated sprint ability might not accurately depict a player’s capacity to resist fatigue during professional soccer competition

Squad management, injury and match performance in a professional soccer team over a Championship-winning season

Squad management, injury and physical, tactical and technical match performance were investigated in a professional soccer team across five consecutive league seasons (2008–2013, 190 league games) with specific focus on a championship-winning season (2010/11). For each player, match participation and time-loss injuries were recorded, the latter prospectively diagnosed by the team's physician. Defending and attacking tactical and technical performance indicators investigated included ball possession and possession in opponents' half, passes, forward passes, completed passes and forward passes, crosses and completed crosses, goal attempts and goal attempts on target, successful final third entries, free-kicks and 50/50 duels won/lost. Physical performance measures included total distance and distance covered at high-speeds (≥19.1 km/h). Results showed that during the 2010/11 season, squad utilisation was lowest potentially owing to the observed lower match injury occurrence and working days lost to injury thereby increasing player availability. In 2010/11, the team won both its highest number of points and conceded its lowest number of goals especially over the second half of this season. The team also won its highest number of games directly via a goal from a substitute and scored and conceded a goal first on the highest and lowest number of occasions, respectively. While multivariate analysis of variance (MANOVA) detected a significant difference in some attacking and defensive performance indicators across the five seasons, these were generally not distinguishing factors in 2010/11. Similarly, univariate ANOVAs showed a significant difference in running distances covered across seasons, but the trend was for less activity in 2010/11

Quantum network coding for quantum repeaters

This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed the potential of this technique by demonstrating how any classical network coding protocol gives rise to a quantum network coding protocol. They nevertheless primarily focused on an abstract model, in which quantum resource such as quantum registers can be freely introduced at each node. In this work, we present a protocol for quantum network coding under weaker (and more practical) assumptions: our new protocol works even for quantum networks where adjacent nodes initially share one EPR-pair but cannot add any quantum registers or send any quantum information. A typically example of networks satisfying this assumption is {\emph{quantum repeater networks}}, which are promising candidates for the implementation of large scale quantum networks. Our results thus show, for the first time, that quantum network coding techniques can increase the transmission rate in such quantum networks as well.Comment: 9 pages, 11figure

Quantum Algorithms for Matrix Products over Semirings

In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we obtain the following results. We construct a quantum algorithm computing the product of two n x n matrices over the (max,min) semiring with time complexity O(n^{2.473}). In comparison, the best known classical algorithm for the same problem, by Duan and Pettie, has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time quantum algorithm for computing the all-pairs bottleneck paths of a graph with n vertices, while classically the best upper bound for this task is O(n^{2.687}), again by Duan and Pettie. We construct a quantum algorithm computing the L most significant bits of each entry of the distance product of two n x n matrices in time O(2^{0.64L} n^{2.46}). In comparison, prior to the present work, the best known classical algorithm for the same problem, by Vassilevska and Williams and Yuster, had complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for classical algorithms as well, reducing the classical complexity to O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L. The above two algorithms are the first quantum algorithms that perform better than the $\tilde O(n^{5/2})$-time straightforward quantum algorithm based on quantum search for matrix multiplication over these semirings. We also consider the Boolean semiring, and construct a quantum algorithm computing the product of two n x n Boolean matrices that outperforms the best known classical algorithms for sparse matrices. For instance, if the input matrices have O(n^{1.686...}) non-zero entries, then our algorithm has time complexity O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page