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

Secoviridae: a proposed family of plant viruses within the order Picornavirales that combines the families Sequiviridae and Comoviridae, the unassigned genera Cheravirus and Sadwavirus, and the proposed genus Torradovirus

The order Picornavirales includes several plant viruses that are currently classified into the families Comoviridae (genera Comovirus, Fabavirus and Nepovirus) and Sequiviridae (genera Sequivirus and Waikavirus) and into the unassigned genera Cheravirus and Sadwavirus. These viruses share properties in common with other picornavirales (particle structure, positive-strand RNA genome with a polyprotein expression strategy, a common replication block including type III helicase, a 3C-like cysteine proteinase and type I RNA-dependent RNA polymerase). However, they also share unique properties that distinguish them from other picornavirales. They infect plants and use specialized proteins or protein domains to move through their host. In phylogenetic analysis based on their replication proteins, these viruses form a separate distinct lineage within the picornavirales branch. To recognize these common properties at the taxonomic level, we propose to create a new family termed “Secoviridae” to include the genera Comovirus, Fabavirus, Nepovirus, Cheravirus, Sadwavirus, Sequivirus and Waikavirus. Two newly discovered plant viruses share common properties with members of the proposed family Secoviridae but have distinct specific genomic organizations. In phylogenetic reconstructions, they form a separate sub-branch within the Secoviridae lineage. We propose to create a new genus termed Torradovirus (type species, Tomato torrado virus) and to assign this genus to the proposed family Secoviridae

NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio

A simple proof of Duquesne's theorem on contour processes of conditioned Galton-Watson trees

We give a simple new proof of a theorem of Duquesne, stating that the properly rescaled contour function of a critical aperiodic Galton-Watson tree, whose offspring distribution is in the domain of attraction of a stable law of index $\theta \in (1,2]$, conditioned on having total progeny $n$, converges in the functional sense to the normalized excursion of the continuous-time height function of a strictly stable spectrally positive L\'evy process of index $\theta$. To this end, we generalize an idea of Le Gall which consists in using an absolute continuity relation between the conditional probability of having total progeny exactly $n$ and the conditional probability of having total progeny at least $n$. This new method is robust and can be adapted to establish invariance theorems for Galton-Watson trees having $n$ vertices whose degrees are prescribed to belong to a fixed subset of the positive integers.Comment: 16 pages, 2 figures. Published versio

Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module

Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We compare their asymptotic complexity to that of previous algorithms given by Gekeler, Narayanan and Garai-Papikian and discuss their practical behavior. In particular, we find that all three approaches represent either an improvement in complexity or an expansion of the parameter space over which the algorithm may be applied. Some experimental results are also presented

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

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

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term