Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Proportion of various types of thyroid disorders among newborns with congenital hypothyroidism and normally located gland: A regional cohort study

Objective To determine the proportion of the various types of thyroid disorders among newborns detected by the neonatal TSH screening programme, with a normally located thyroid gland.Patients and methods Of the 882 575 infants screened in our centre between 1981 and 2002, 85 infants with a normally located gland had persistent elevation of serum TSH values (an incidence of 1/10 383). Six of these 85 patients were lost to follow-up and were therefore excluded from the study. During follow-up, patients were classified as having permanent or transient hypothyroidism.Results Among the 79 patients included in the study, transient (n = 30, 38% of cases) and permanent (n = 49, 62% of cases) congenital hypothyroidism (CH) was demonstrated during the follow-up at the age of 0.7 +/- 0.6 years and 2.6 +/- 1.8 years (P < 0.0001), respectively. The proportion of premature births was significantly higher in the group with transient CH (57%) than in the group with permanent CH (2%) (P < 0.0001). A history of iatrogenic iodine overload was identified during the neonatal period in 69% of transient cases. Among permanent CH cases (n = 49), patients were classified as having a goitre (n = 27, 55% of cases), a normal sized and shaped thyroid gland (n = 14, 29% of cases) or a hypoplastic gland (n = 8, 16% of cases). The latter patients demonstrated global thyroid hypoplasia (n = 3), a right hemithyroid (n = 2), hypoplasia of the left lobe (n = 2), or asymmetry in the location of the two lobes (n = 1). Patients with a normal sized and shaped thyroid gland showed a significantly less severe form of hypothyroidism than those with a goitre or a hypoplastic thyroid gland (P < 0.0002). Among permanent CH cases, those with a goitre (n = 27) had an iodine organification defect (n = 10), Pendred syndrome (n = 1), a defect of thyroglobulin synthesis (n = 8), or a defect of sodium iodine symporter (n = 1), and in seven patients no aetiology could be determined. Among permanent cases with a normal sized and shaped thyroid gland (n = 14), a specific aetiology was found in only one patient (pseudohypoparathyroidism) and two patients had Down's syndrome. Among those with a globally hypoplastic gland, a TSH receptor gene mutation was found in two patients.Conclusions A precise description of the phenotype can enhance our understanding of various forms of neonatal hypothyroidism as well as their prevalence and management. It also helps to identify cases of congenital hypothyroidism of unknown aetiology, which will need to be investigated in collaboration with molecular biologists

Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules

We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in finite-size systems without simulating the actual time evolution which can be extremely slow, we propose to focus on first-passage times that satisfy 'backward master equations'. Upon the iterative elimination of configurations, we obtain the exact renormalization rules that can be followed numerically. To test this approach, we study the statistics of some first-passage times for two disordered models : (i) for the random walk in a two-dimensional self-affine random potential of Hurst exponent $H$, we focus on the first exit time from a square of size $L \times L$ if one starts at the square center. (ii) for the dynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, we consider the first passage time $t_f$ to zero-magnetization when starting from a fully magnetized configuration. Besides the expected linear growth of the averaged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaled distribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large $u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simply interpreted in terms of rare events if the sample-to-sample fluctuation exponent for the barrier is $\psi_{width}=1/3$.Comment: 8 pages, 4 figure

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length $N$ and block length $M$ as $\tau_{\perp} \propto M^{1+2\nu}$ (here $\nu\approx 0.6$ is the Flory exponent) and as $\tau_{\parallel} \propto N^2$, although initially the rate of coil flattening is expected to decrease with block size as $\propto M^{-1}$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics.Comment: 4 pages, 4 figures, submited to Europhys. Let

Sequence randomness and polymer collapse transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.Comment: 4 pages, 4 eps figure