Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems

We present a general formalism for computing the largest Lyapunov exponent and its fluctuations in spatially extended systems described by diffusive fluctuating hydrodynamics, thus extending the concepts of dynamical system theory to a broad range of non-equilibrium systems. Our analytical results compare favourably with simulations of a lattice model of heat conduction. We further show how the computation of the Lyapunov exponent for the Symmetric Simple Exclusion Process relates to damage spreading and to a two-species pair annihilation process, for which our formalism yields new finite size results

Grandes déviations d'exposants de Lyapunov dans les systèmes étendus

Lyapunov exponents are natural observables to quantify the chaoticity of a trajectory. They thus appear as good candidates to discriminate between different dynamical regimes, allowing to study phenomena such as the onset of turbulence—which goes hand in hand with the emergence of chaotic trajectories in an otherwise regular flow—or the glass transition—which can be seen as a transition from diffusive dynamics to an arrested, frozen-in, and ergodicity-breaking regime.The present thesis strives to apply the thermodynamic formalism of Sinai, Ruelle and Bowen—which transposes in trajectory space the language of equilibrium statistical physics—to fluctuations of Lyapunov exponents in spatially extended systems, for which only few results are available.We begin by presenting a numerical method to sample trajectories of atypical chaoticity in spatially extended systems, hence revealing their various dynamical structures. We also exhibit how this algorithm can be used to measure the dynamical free energy, opening the way for the study of dynamical phase transitions resulting from the possible coexistence of these structures. This method is in particular applied to the Fermi-Pasta-Ulam-Tsingou (FPU) chain of anharmonic oscillators.Next, we show how fluctuations of the largest Lyapunov exponent in systems of interacting particles with underlying diffusive dynamics can be analytically characterized. Carrying out this program allows us to establish interesting connections with damage spreading and reaction-diffusion processes.Les exposants de Lyapunov sont une observable naturelle pour quantifier la chaoticité d'une trajectoire. Ils peuvent donc être utilisés pour distinguer des régimes dynamiques différents, ce qui peut permettre l'étude de phénomènes tels que l'apparition de la turbulence, qui correspond à l'émergence de trajectoires chaotiques dans un écoulement auparavant régulier, ou la transition vitreuse, qui peut être vue comme le passage d'une dynamique diffusive à un régime gelé. L'objet de cette thèse est d'appliquer le formalisme thermodynamique de Sinai, Ruelle et Bowen, qui transpose dans l'espace des trajectoires le langage de la physique statistique d'équilibre, aux fluctuations d'exposants de Lyapunov dans les systèmes étendus pour lesquelles peu de résultats sont disponibles.Dans un premier temps, on présente une méthode numérique pour échantillonner des trajectoires de chaoticité atypique dans un système étendu, révélant ainsi ses différentes structures dynamiques. Cet algorithme permet également de mesurer l'énergie libre dynamique, ouvrant la voie à l'étude des transitions de phase dynamique dues à l'éventuelle coexistence de ces différentes structures. Il est ensuite appliqué notamment à la chaîne d'oscillateurs anharmoniques de Fermi-Pasta-Ulam-Tsingou (FPU). On montre dans un second temps comment déterminer analytiquement les fluctuations du plus grand exposant de Lyapunov dans des systèmes de particules en interaction dont la dynamique sous-jacente est diffusive. Ce faisant, on établit des liens avec la propagation de défauts et les processus de réaction-diffusion

Hearing loss in inherited peripheral neuropathies: Molecular diagnosis by NGS in a French series

International audienceBackground: The most common inherited peripheral neuropathy is Charcot-Marie-Tooth disease (CMT), with a prevalence of 1/2500. Other symptoms can be associated to the condition, such as hearing loss. Currently, no global hearing impairment assessment has been determined, and the physiopathology is not well known.Methods: The aim of the study was to analyze among a French series of 3,412 patients with inherited peripheral neuropathy (IPN), the ones who also suffer from hearing loss, to establish phenotype-genotype correlations. An NGS strategy for IPN one side and nonsyndromic hearing loss (NSHL) on the other side, were performed.Results: Hearing loss (HL) was present in only 44 patients (1.30%). The clinical data of 27 patients were usable. Demyelinating neuropathy was diagnosed in 15 cases and axonal neuropathy in 12 cases. HL varied from mild to profound. Five cases of auditory neuropathy were noticed. Diagnosis was made for 60% of these patients. Seven novel pathogenic variants were discovered in five different genes: PRPS1; MPZ; SH3TC2; NEFL; and ABHD12. Two patients with PMP22 variant, had also an additional variant in COCH and MYH14 respectively. No pathogenic variant was found at the DFNB1 locus. Genotype-phenotype correlations do exist, especially with SH3TC2, PRPS1, ABHD12, NEFL, and TRPV4.Conclusion: Involvement of PMP22 is not enough to explain hearing loss in patients suffering from IPN. HL can be due to cochlear impairment and/or auditory nerve dysfunction. HL is certainly underdiagnosed, and should be evaluated in every patient suffering from IPN

Large national series of patients with Xq28 duplication involving MECP2: Delineation of brain MRI abnormalities in 30 affected patients.

Xq28 duplications encompassing MECP2 have been described in male patients with a severe neurodevelopmental disorder associated with hypotonia and spasticity, severe learning disability, stereotyped movements, and recurrent pulmonary infections. We report on standardized brain magnetic resonance imaging (MRI) data of 30 affected patients carrying an Xq28 duplication involving MECP2 of various sizes (228 kb to 11.7 Mb). The aim of this study was to seek recurrent malformations and attempt to determine whether variations in imaging features could be explained by differences in the size of the duplications. We showed that 93% of patients had brain MRI abnormalities such as corpus callosum abnormalities (n = 20), reduced volume of the white matter (WM) (n = 12), ventricular dilatation (n = 9), abnormal increased hyperintensities on T2-weighted images involving posterior periventricular WM (n = 6), and vermis hypoplasia (n = 5). The occipitofrontal circumference varied considerably between >+2SD in five patients and <-2SD in four patients. Among the nine patients with dilatation of the lateral ventricles, six had a duplication involving L1CAM. The only patient harboring bilateral posterior subependymal nodular heterotopia also carried an FLNA gene duplication. We could not demonstrate a correlation between periventricular WM hyperintensities/delayed myelination and duplication of the IKBKG gene. We thus conclude that patients with an Xq28 duplication involving MECP2 share some similar but non-specific brain abnormalities. These imaging features, therefore, could not constitute a diagnostic clue. The genotype-phenotype correlation failed to demonstrate a relationship between the presence of nodular heterotopia, ventricular dilatation, WM abnormalities, and the presence of FLNA, L1CAM, or IKBKG, respectively, in the duplicated segment

Large national series of patients with Xq28 duplication involving MECP2: Delineation of brain MRI abnormalities in 30 affected patients

International audienceXq28 duplications encompassing MECP2 have been described in male patients with a severe neurodevelopmental disorder associated with hypotonia and spasticity, severe learning disability, stereotyped movements, and recurrent pulmonary infections. We report on standardized brain magnetic resonance imaging (MRI) data of 30 affected patients carrying an Xq28 duplication involving MECP2 of various sizes (228 kb to 11.7 Mb). The aim of this study was to seek recurrent malformations and attempt to determine whether variations in imaging features could be explained by differences in the size of the duplications. We showed that 93% of patients had brain MRI abnormalities such as corpus callosum abnormalities (n = 20), reduced volume of the white matter (WM) (n = 12), ventricular dilatation (n = 9), abnormal increased hyperintensities on T2-weighted images involving posterior periventricular WM (n = 6), and vermis hypoplasia (n = 5). The occipitofrontal circumference varied considerably between \textgreater+2SD in five patients and \textless-2SD in four patients. Among the nine patients with dilatation of the lateral ventricles, six had a duplication involving L1CAM. The only patient harboring bilateral posterior subependymal nodular heterotopia also carried an FLNA gene duplication. We could not demonstrate a correlation between periventricular WM hyperintensities/delayed myelination and duplication of the IKBKG gene. We thus conclude that patients with an Xq28 duplication involving MECP2 share some similar but non-specific brain abnormalities. These imaging features, therefore, could not constitute a diagnostic clue. The genotype-phenotype correlation failed to demonstrate a relationship between the presence of nodular heterotopia, ventricular dilatation, WM abnormalities, and the presence of FLNA, L1CAM, or IKBKG, respectively, in the duplicated segment. © 2015 Wiley Periodicals, In

Further delineation of the MECP2 duplication syndrome phenotype in 59 French male patients, with a particular focus on morphological and neurological features

IF 5.751International audienceThe Xq28 duplication involving the MECP2 gene (MECP2 duplication) has been mainly described in male patients with severe developmental delay (DD) associated with spasticity, stereotypic movements and recurrent infections. Nevertheless, only a few series have been published. We aimed to better describe the phenotype of this condition, with a focus on morphological and neurological features. Through a national collaborative study, we report a large French series of 59 affected males with interstitial MECP2 duplication. Most of the patients (93%) shared similar facial features, which evolved with age (midface hypoplasia, narrow and prominent nasal bridge, thick lower lip, large prominent ears), thick hair, livedo of the limbs, tapered fingers, small feet and vasomotor troubles. Early hypotonia and global DD were constant, with 21% of patients unable to walk. In patients able to stand, lower limbs weakness and spasticity led to a singular standing habitus: flexion of the knees, broad-based stance with pseudo-ataxic gait. Scoliosis was frequent (53%), such as divergent strabismus (76%) and hypermetropia (54%), stereotypic movements (89%), without obvious social withdrawal and decreased pain sensitivity (78%). Most of the patients did not develop expressive language, 35% saying few words. Epilepsy was frequent (59%), with a mean onset around 7.4 years of age, and often (62%) drug-resistant. Other medical issues were frequent: constipation (78%), and recurrent infections (89%), mainly lung. We delineate the clinical phenotype of MECP2 duplication syndrome in a large series of 59 males. Pulmonary hypertension appeared as a cause of early death in these patients, advocating its screening early in life