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

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

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/

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

Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses

We present an analysis of the data on aging in the three-dimensional Edwards Anderson spin glass model with nearest neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean field theory. We measure the parameter $x(q)$ describing the violation of the relation among correlation and response function implied by the fluctuation dissipation theorem.Comment: LaTeX 10 pages + 4 figures (appended as uuencoded compressed tar-file), THP81-9

Fragile-glass behavior of a short range pp-spin model

In this paper we propose a short range generalization of the $p$-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom-line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We however encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin glass susceptibility investigating the behavior of the correlation length in the system. We find that the the increase of the relaxation time is not accompanied by any growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.Comment: 8 pages, LaTeX, 8 postscript figure

Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers

We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.Comment: 21 pages; part of the "Special Topic Issue on the Glass Transition