Renormalization and Quantum Scaling of Frenkel-Kontorova Models

We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy

Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

The specificity of the familial aggregation of early-onset bipolar disorder: A controlled 10-year follow-up study of offspring of parents with mood disorders.

BACKGROUND: Two major sources of heterogeneity of mood disorders that have been demonstrated in clinical, family and genetic studies are the mood disorder subtype (i.e. bipolar (BPD) and major depressive disorder (MDD)) and age of onset of mood episodes. Using a prospective high-risk study design, our aims were to test the specificity of the parent-child transmission of BPD and MDD and to establish the risk of psychopathology in offspring in function of the age of onset of the parental disorder. METHODS: Clinical information was collected on 208 probands (n=81 with BPD, n=64 with MDD, n=63 medical controls) as well as their 202 spouses and 372 children aged 6-17 years at study entry. Parents and children were directly interviewed every 3 years (mean duration of follow-up=10.6 years). Parental age of onset was dichotomized at age 21. RESULTS: Offspring of parents with early onset BPD entailed a higher risk of BPD HR=7.9(1.8-34.6) and substance use disorders HR=5.0(1.1-21.9) than those with later onset and controls. Depressive disorders were not significantly increased in offspring regardless of parental mood disorder subtype or age of onset. LIMITATIONS: Limited sample size, age of onset in probands was obtained retrospectively, age of onset in co-parents was not adequately documented, and a quarter of the children had no direct interview. CONCLUSIONS: Our results provide support for the independence of familial aggregation of BPD from MDD and the heterogeneity of BPD based on patterns of onset. Future studies should further investigate correlates of early versus later onset BPD

Association of genetic risk scores with body mass index in Swiss psychiatric cohorts.

OBJECTIVE: Weight gain is associated with psychiatric disorders and/or with psychotropic drug treatments. We analyzed in three psychiatric cohorts under psychotropic treatment the association of weighted genetic risk scores (w-GRSs) with BMI by integrating BMI-related polymorphisms from the candidate-gene approach and Genome-Wide Association Studies (GWAS). MATERIALS AND METHODS: w-GRS of 32 polymorphisms associated previously with BMI in general population GWAS and 20 polymorphisms associated with antipsychotics-induced weight gain were investigated in three independent psychiatric samples. RESULTS: w-GRS of 32 polymorphisms were significantly associated with BMI in the psychiatric sample 1 (n=425) and were replicated in another sample (n=177). Those at the percentile 95 (p95) of the score had 2.26 and 2.99 kg/m higher predicted BMI compared with individuals at the percentile 5 (p5) in sample 1 and in sample 3 (P=0.009 and 0.04, respectively). When combining all samples together (n=750), a significant difference of 1.89 kg/m predicted BMI was found between p95 and p5 individuals at 12 months of treatment. Stronger associations were found among men (difference: 2.91 kg/m of predicted BMI between p95 and p5, P=0.0002), whereas no association was found among women. w-GRS of 20 polymorphisms was not associated with BMI. The w-GRS of 52 polymorphisms and the clinical variables (age, sex, treatment) explained 1.99 and 3.15%, respectively, of BMI variability. CONCLUSION: The present study replicated in psychiatric cohorts previously identified BMI risk variants obtained in GWAS analyses from population-based samples. Sex-specific analysis should be considered in further analysis

Ulam method for the Chirikov standard map

We introduce a generalized Ulam method and apply it to symplectic dynamical maps with a divided phase space. Our extensive numerical studies based on the Arnoldi method show that the Ulam approximant of the Perron-Frobenius operator on a chaotic component converges to a continuous limit. Typically, in this regime the spectrum of relaxation modes is characterized by a power law decay for small relaxation rates. Our numerical data show that the exponent of this decay is approximately equal to the exponent of Poincar\'e recurrences in such systems. The eigenmodes show links with trajectories sticking around stability islands.Comment: 13 pages, 13 figures, high resolution figures available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod/ minor corrections in text and fig. 12 and revised discussio

Moving lattice kinks and pulses: an inverse method

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure

Prevalence and correlates of DSM-5 major depressive and related disorders in the community.

Although the DSM-5 has suggested the two new categories of Persistent Depressive Disorders (PDD) and Other Specified Depressive Disorders (OSDD), no study so far has applied the DSM-5 criteria throughout the range of depressive disorders. The aims of the present study were to 1) establish the lifetime prevalence of specific depressive disorders according to the new DSM-5 definitions in a community sample, and 2) determine their clinical relevance in terms of socio-demographic characteristics, comorbidity, course and treatment patterns. The semi-structured Diagnostic Interview for Genetic Studies was administered by masters-level psychologists to a random sample of an urban area (n=3720). The lifetime prevalence was 15.2% for PDD with persistent major depressive episode (MDE), 3.3% for PDD with pure dysthymia, 28.2% for Major Depressive Disorder (MDD) and 9.1% for OSDD. Subjects with PDD with persistent MDE were the most severely affected, followed by those with recurrent MDD, single episode MDD, PDD with pure dysthymia and OSDD and finally those without depressive disorders. Our data provide further evidence for the clinical significance of mild depressive disorders (OSDD), but cast doubt on the pertinence of lumping together PDD with persistent MDE and the former DSM-IV dysthymic disorder within the new PDD category

Localization from quantum interference in one-dimensional disordered potentials

We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of the disordered potential. This is equivalent of assuming a phase randomization of the off-diagonal/interference terms. We demonstrate these results through numerical calculations of the dynamics of ultracold atoms in the one-dimensional speckle and quasiperiodic potentials used in the recent experiments that lead to the observation of Anderson localization for matter waves [Billy et al., Nature 453, 891 (2008); Roati et al., Nature 453, 895 (2008)]. For the quasiperiodic case, we also discuss the implications of using continuos or discrete models.Comment: 5 pages, 3 figures; minor changes, references update

Obesity and atypical depression symptoms: findings from Mendelian randomization in two European cohorts.

Studies considering the causal role of body mass index (BMI) for the predisposition of major depressive disorder (MDD) based on a Mendelian Randomization (MR) approach have shown contradictory results. These inconsistent findings may be attributable to the heterogeneity of MDD; in fact, several studies have documented associations between BMI and mainly the atypical subtype of MDD. Using a MR approach, we investigated the potential causal role of obesity in both the atypical subtype and its five specific symptoms assessed according to the Statistical Manual of Mental Disorders (DSM), in two large European cohorts, CoLaus|PsyCoLaus (n = 3350, 1461 cases and 1889 controls) and NESDA|NTR (n = 4139, 1182 cases and 2957 controls). We first tested general obesity measured by BMI and then the body fat distribution measured by waist-to-hip ratio (WHR). Results suggested that BMI is potentially causally related to the symptom increase in appetite, for which inverse variance weighted, simple median and weighted median MR regression estimated slopes were 0.68 (SE = 0.23, p = 0.004), 0.77 (SE = 0.37, p = 0.036), and 1.11 (SE = 0.39, p = 0.004). No causal effect of BMI or WHR was found on the risk of the atypical subtype or for any of the other atypical symptoms. Our findings show that higher obesity is likely causal for the specific symptom of increase in appetite in depressed participants and reiterate the need to study depression at the granular level of its symptoms to further elucidate potential causal relationships and gain additional insight into its biological underpinnings

Periodic Travelling Waves in Dimer Granular Chains

We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist