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

The impact of in-season national team soccer play on injury and player availability in a professional club

This study investigated the impact of in-season national team duty on injury rates and player availability in a professional soccer club. Time-loss injuries and exposure time during club and national team duties were recorded prospectively over 5 seasons (2009–2014). A time-loss injury was sustained by 37.7% of squad members participating in national duty, all injuries occurring in match-play. The incidence (per 1000 h exposure) for national team player match-play injuries did not differ (P = 0.608) to that for all players in club competitions: 48.0 (95% CI 20.9–75.5) vs. 41.9 (95% CI 36.5–47.4), incidence rate ratio = 1.2 (CI: 0.8–2.4). The majority (58%) of national team injuries resulted in a layoff ≤1 week. Of all working days lost to injury generally, 5.2% were lost through injury on national duty. Injury incidence in the week following national duty was comparable (P = 0.818) in players participating or not: 7.8 (95% CI 3.6–12.0) vs. 7.1 (95% CI: 4.6–9.6), incidence rate ratio = 1.1 (CI: 0.7–2.7). While approximately 40% of participating players incurred a time-loss injury on national duty, no training injuries were sustained and injuries made up a negligible part of overall club working days lost to injury. Following duty, players had a similar injury risk to peers without national obligations

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

Transport property study of MgO-GaAs(001) contacts for spin injection devices

International audienceThe electrical properties of Au/MgO/n-GaAs(001) tunnel structures have been investigated with capacitance-voltage and current-voltage measurements at room temperature with various MgO thicknesses between 0.5 and 6.0nm. For an oxide thickness higher than 2nm and for low bias voltages, the voltage essentially drops across the oxide and the structure progressively enters the high-current mode of operation with increasing reverse bias voltage, the property sought in spin injection devices. In this mode, we demonstrate that a large amount of charge accumulates at the MgO/GaAsinterface in interface traps located in the semiconductor band gap

Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.Comment: 20 pages. typos corrected, added a remark after Proposition 2.3, simplified the last part of Example 2.

Crise suicidaire et maladie d’Alzheimer débutante : intérêt d’une analyse neuropsychologique détaillée

RésuméIntroduction Le risque de développer une maladie d’Alzheimer augmente avec l’âge. Le rôle de celle-ci comme un facteur de risque indépendant de suicide n’est pas bien compris et demeure complexe et mal élucidé. L’objectif de cet article est d’envisager une compréhension neuropsychologique de la crise suicidaire dans le cas d’une maladie d’Alzheimer débutante. Méthode Une évaluation cognitive globale (Mini-Mental State Examination, Batterie Rapide d’Évaluation Frontale) complétée de l’exploration de l’inhibition cognitive selon ses fonctions d’accès (tâche de lecture en présence de distracteurs), de suppression (Trail Making Test), et de freinage (Stroop, Hayling, Go/No-Go) a été réalisée chez une femme souffrant d’une maladie d’Alzheimer (MMSE à 21/30) avant et après réalisation d’une tentative de suicide dans un contexte de dépression. Résultats L’échelle d’Hamilton était cotée à 24/52, l’échelle de dépression de Cornell à 21/38. L’intentionnalité suicidaire était modérée avec un score à 15/25 à l’échelle d’intentionnalité suicidaire de Beck. Initialement préservées, le déclin des fonctions exécutives a coïncidé avec l’émergence d’une crise suicidaire dans un contexte de dépression chez une patiente souffrant de maladie d’Alzheimer. Les fonctions de l’inhibition cognitive étaient altérées dans ses trois composantes, après ajustement des facteurs de confusion. Conclusion Une évaluation détaillée des fonctions exécutives et singulièrement de l’inhibition cognitive dans la population des patients atteints d’une maladie d’Alzheimer permettrait de détecter les personnes les plus à risque de passage à l’acte et de proposer une surveillance plus étroite dans le cadre des soins généraux de leur maladie. AbstractIntroduction The role of Alzheimer\u27s disease as a risk factor for suicide is unclear. The aim of this study was to understand neuropsychological component of the suicidal crisis in Alzheimer\u27s disease. Method Using an extensive neuropsychological battery, different aspects of cognitive inhibition were particularly examined: Access to relevant information (using the Reading with distraction task), suppression of no longer relevant information (Trail Making Test, Rule Shift Cards), and restraint of cognitive resources to relevant information (Stroop test, Hayling Sentence Completion test, Go/No-Go). One female Alzheimer depressed case was assessed before and after a suicide attempt. Results Ten days after the patient\u27s suicide attempt, dementia was still moderate with a MMSE score at 21/30 but with a worsening of executive functions (FAB at 8/18) in the context of depression and suicide. The Hamilton-Depression Rating Scale was at 24 (maximal score at 52), and the Cornell Scale for Depression was at 21 (maximal score at 38). Suicidal intent was moderate with a score of 9 on the Beck Suicide Intent Scale (maximal score at 25). The patient did not present a delirium, psychotic symptoms, or anosognosia. Her episodic memory was altered as shown by her semantic performance on verbal fluency (naming 12 animals in 120 seconds) and on lexical fluency (naming 8 words beginning with the letter P). Initially preserved, executive function declined during a suicidal crisis in a context of depression in Alzheimer\u27s disease case. Neuropsychological testing confirmed a dysexecutive syndrome (FAS at 8/18), with an impairment in her conceptualization capacity (MCST) and a deficit in cognitive inhibition and its access (reading task in the presence of distractors), deletion (TMT) and restraint (Stroop, Go/No-Go, Hayling) functions. Computed tomography has shown no signs of intracranial expansive process. Conclusion Assessing predictors of suicide and means of completion in patients with dementia may help the development of interventions to reduce risk of suicide among the growing population of individuals with dementia. Because of Alzheimer\u27s-related cognitive inhibition impairment, identification and intervention addressing the complex issues of depression, executive dysfunction and dementia may help clinicians to mitigate the risk of suicide in patients with Alzheimer\u27s disease

Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page