MLD Relations of Pisot Substitution Tilings

We consider 1-dimensional, unimodular Pisot substitution tilings with three intervals, and discuss conditions under which pairs of such tilings are locally isomorhphic (LI), or mutually locally derivable (MDL). For this purpose, we regard the substitutions as homomorphisms of the underlying free group with three generators. Then, if two substitutions are conjugated by an inner automorphism of the free group, the two tilings are LI, and a conjugating outer automorphism between two substitutions can often be used to prove that the two tilings are MLD. We present several examples illustrating the different phenomena that can occur in this context. In particular, we show how two substitution tilings can be MLD even if their substitution matrices are not equal, but only conjugate in $GL(n,\mathbb{Z})$. We also illustrate how the (in our case fractal) windows of MLD tilings can be reconstructed from each other, and discuss how the conjugating group automorphism affects the substitution generating the window boundaries.Comment: Presented at Aperiodic'09 (Liverpool

Repeatability of innervation zone identification in the external anal sphincter muscle

Knowledge of the distribution of the innervation zones (IZs) of the external anal sphincter (EAS) may be useful for preventing anal sphincter incompetence during vaginal delivery. A method proposed for the automatic estimation of the distribution of IZs of EAS from high-density surface electromyography (EMG) was evaluated for repeatability in continent volunteers. Methods: In 13 healthy female subjects (age: 35 11 years) surface EMG signals were acquired using an anal probe with three circumferential electrode arrays (of 16 contacts each) at different depths within the anal canal (15mm distance between the centers of adjacent arrays), during four independent experimental sessions. Three maximal voluntary contractions (MVCs) of 10 sec were performed for each session for a total of 12 contractions per subject. Repeatability of the estimation of the distribution of IZ was tested by evaluating the coefficient of multiple correlations (CMC) between the IZ distributions estimated from the signals recorded from each subject. Results: A high repeatability (CMC > 0.8) was found comparing IZ distributions estimated from signals recorded by each array within the same session. A slightly lower value was obtained considering signals recorded during different sessions (CMC > 0.7), but a higher value (CMC > 0.8) was obtained after aligning the estimated IZ distributions. The realignment compensates for the operator's error in repositioning the probe in the same position during different sessions. Conclusion: This result justifies clinical studies using high-density surface EMG in routine examinations, providing information about IZs of EAS and assessing the possibilities of preventing neuronal trauma during vaginal delivery

Glassy Mean-Field Dynamics of the Backgammon model

In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of {\it entropy barriers} in configuration space. The model is simple enough to allow for a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow to study the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure

Superfast vocal muscles control song production in songbirds

Journal ArticleBirdsong is a widely used model for vocal learning and human speech, which exhibits high temporal and acoustic diversity. Rapid acoustic modulations are thought to arise from the vocal organ, the syrinx, by passive interactions between the two independent sound generators or intrinsic nonlinear dynamics of sound generating structures. Additionally, direct neuromuscular control could produce such rapid and precisely timed acoustic features if syringeal muscles exhibit rare superfast muscle contractile kinetics. However, no direct evidence exists that avian vocal muscles can produce modulations at such high rates

Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors

Within the phase fluctuation model for the pseudogap state of cuprate superconductors we identify a novel statistical "Berry phase" interaction between the nodal quasiparticles and fluctuating vortices. The effective action describing this model assumes the form of an anisotropic Euclidean quantum electrodynamics in (2+1) dimensions (QED_3) and naturally generates the marginal Fermi liquid behavior for its fermionic excitations. The doping axis in the x-T phase diagram emerges as a quantum critical line which regulates low energy fermiology. We examine the merits of our theory in light of available experiments.Comment: 5 pages REVTeX + 2 PostScript Figures. Final version to appear in PR

Nonequilibrium dynamics of a simple stochastic model

We investigate the low-temperature dynamics of a simple stochastic model, introduced recently in the context of the physics of glasses. The slowest characteristic time at equilibrium diverges exponentially at low temperature. On smaller time scales, the nonequilibrium dynamics of the system exhibits an aging regime. We present an analytical study of the scaling behaviour of the mean energy, of its local correlation and response functions, and of the associated fluctuation-dissipation ratio throughout the regime of low temperature and long times. This analysis includes the aging regime, the convergence to equilibrium, and the crossover behaviour between them.Comment: 36 pages, plain tex, 7 figures, to be published by Journal of Physics

Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of $n$ neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly $\tau = 2$ and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/

Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses

The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition. Using a ``potential function'' we follow the metastable states of the model in temperature, and discuss the possibility of level crossing (which we do not find) and multifurcation (which we find). The dynamics at a given temperature starting from an equilibrium configuration at a different temperature is also discussed. In presence of multifurcation, we find that the equilibrium is never achieved, leading to aging behaviour at slower energy levels than usual aging. The relevance of the observed mechanisms for real structural glasses is discussed, and some numerical simulations of a soft sphere model of glass are presented.Comment: 16 pages, LaTeX, 10 figures (12 postscript files

Synthesis, x-ray structure and anion binding properties of a cryptand-like hybrid calixpyrrole

The novel cryptand in/out-3, containing two tripyrrolemethane units briged by three 1,3- diisopropylidenbenzene arms was readily synthesized by a convergent three-step synthesis. It binds fluoride by inclusion with excellent selectivity with respect to a number of other tested anions. The structure of the free receptor and that of its fluoride complex were investigated in solution by NMR spectroscopy. The solid state X-ray structure of the free cryptand 3 was also determined