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Based on extensive simulations, we conjecture that critically pinned interfaces in 2-dimensional isotropic random media with short range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in $>2$ dimensions, there is no distinction between fractal (i.e., percolative) and rough but non-fractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed (SWIR) epidemics. It does not include models with long range correlations in the randomness, and models where overhangs are explicitly forbidden (which would imply non-isotropy of the medium)., 5 pages (including 8 figures) of main text + 5 pages (including 7 figures) supplemental material

We present a detailed derivation of some estimators of Shannon entropy for discrete distributions. They hold for finite samples of N points distributed into M "boxes", with N and M -> oo, but N/M < oo. In the high sampling regime (<< 1 points in each box) they have exponentially small biases. In the low sampling regime the errors increase but are still much smaller than for most other estimators. One advantage is that our main estimators are given analytically, with explicitly known analytical formulas for the biases., 5 pages, including 2 figures; revised version with corrected figures

Kopitzki et al (preceeding comment) claim that the relationship between Renormalized and Kullback-Leibler entropies has already been given in their previous papers. Moreover, they argue that the first can give more useful information for e.g. localizing the seizure-generating area in epilepsy patients. In our reply we stress that if the relationship between both entropies would have been known by them, they should have noticed that the condition on the effective temperature is unnecessary. Indeed, this condition led them to choose different reference segments for different channels, even if this was physiologically unplausible. Therefore, we still argue that it is very unlikely that renormalized entropy will give more information than the conventional Kullback-Leibler entropy., 4 pages, 1 figure. Phys. Rev. E, in press

Heat conduction in 1-dimensional anharmonic systems is anomalous in the sense that the conductivity \kappa scales with a positive power of the system size, \kappa ~ L^\alpha. In two dimensions, previous simulations and theoretical arguments gave a logarithmic divergence. For rectangular systems of size L_\| x L_\perp there should be a cross-over from the 2-d to the 1-d behaviour as the aspect ratio r = L_\| / L_\perp increases from r=1 to r >> 1. When taking periodic boundary conditions in the transverse direction, this should be of direct relevance for the heat conduction in single-walled carbon nanotubes. In particular, one expects that k nanotubes of diameter R should conduct heat better than a single nanotube of the same length and of radius kR. We study this cross-over numerically by simulating the Fermi-Pasta-Ulam model. Apart from giving a precise estimate of the exponent \alpha, our most intriguing results are that the divergence does not seem to be logarithmic in d=2 but also power-like, and that the cross-over does not happen at a fixed aspect ratio. Instead, it happens at r=r^* with r^* -> \infty for L -> \infty., Comment: RevTeX, 4 pages, including 7 figures

We study the synchronization between left and right hemisphere rat EEG channels by using various synchronization measures, namely non-linear interdependences, phase-synchronizations, mutual information, cross-correlation and the coherence function. In passing we show a close relation between two recently proposed phase synchronization measures and we extend the definition of one of them. In three typical examples we observe that except mutual information, all these measures give a useful quantification that is hard to be guessed beforehand from the raw data. Despite their differences, results are qualitatively the same. Therefore, we claim that the applied measures are valuable for the study of synchronization in real data. Moreover, in the particular case of EEG signals their use as complementary variables could be of clinical relevance., 32 pages, 1 table, 8 figures

We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted distribution. Instead, it builds weighted instances according to a biased distribution. If the bias is optimal, all weights are equal and importance sampling is perfect. If not, "population control" is applied by cloning/killing configurations with too high/low weight. It uses the fact that nontrivial problems in statistical physics are high dimensional. Therefore, instances are built up in many steps, and the final weight can be guessed at an early stage. In contrast to evolutionary algorithms, the cloning/killing is done such that the wanted distribution is strictly observed without simultaneously keeping a large population in computer memory. We apply this method (which is also closely related to diffusion type quantum Monte Carlo) to several problems of polymer statistics, population dynamics, and percolation., Comment: 21 pages with 16 figures included; talk presented at Heraeus Summer School, Chemnitz, Oct. 2000

Spike-Wave Discharges (SWDs) occur spontaneously in the EEG of WAG/Rij rats. These SWDs are a model for human absence seizures. In order to examine whether non-linear analysis methods can contribute to the analysis of SWDs, we estimated the correlation dimension of the SWDs and compared the value to that of the phase-randomized signals

Evoked Potentials (EPs) are responses that appear in the EEG due to external stimulation. Findings indicate that changes in EPs can be related to changes in frequencies of the pre-stimulus EEG. Auditory EPs of rats (n=8) were measured in reaction to tone-pip stimuli (90 dB, 10.2 kHz, ISI 2s, n=1500). Trials were ranked according to the percentage of delta (1-4 Hz), theta (5-8), alpha (9-12) or beta power (13-30 Hz) in the pre-stimulus EEG. Consecutive AEPs were computed. An increase in beta and a decrease in delta resulted both in an increase in the N60 and P70 component and a decrease in the P150-200 component. These beta and delta changes have been associated with changes in arousal. The increased N60 and P70 components with increases in beta might reflect increased attention due to an increase in arousal. We found that an increase in delta activity, leads to an increase of the late-latency P150-200 component, possibly due to an increased synchronization in the EEG.

We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted distribution. Instead, it builds weighted instances according to a biased distribution. If the bias is optimal, all weights are equal and importance sampling is perfect. If not, "population control" is applied by cloning/killing configurations with too high/low weight. It uses the fact that nontrivial problems in statistical physics are high dimensional. Therefore, instances are built up in many steps, and the final weight can be guessed at an early stage. In contrast to evolutionary algorithms, the cloning/killing is done such that the wanted distribution is strictly observed without simultaneously keeping a large population in computer memory. We apply this method (which is also closely related to diffusion type quantum Monte Carlo) to several problems of polymer statistics, population dynamics, and percolation., 21 pages with 16 figures included; talk presented at Heraeus Summer School, Chemnitz, Oct. 2000

To find a new measure from the EEG that quantifies the effects of anesthetics during surgery, the correlation dimension (CD) of the EEG of eight rats was estimated. To get informed about the anesthetic state, the noxious induced withdrawal reflex (NIWR) was measured, i.e. the force elicited by transcutaneous electrical stimulation of the hind paw. The algorithm of Grassberger and Procaccia (1983) to compute the CD was slightly modified and labeled as "dimensional complexity" (DC). The DC was estimated by applying a fit procedure to find the scaling region in the correlation integral. Experiments were performed under propofol infusion (30 à 40 mg.kg-1.h-1), with repeated bolus injections (3 mg) to induce periods of more profound anesthesia. The DC was compared to the Spectral Edge Frequency (SEF), a linear measure extracted from the power spectrum. The DC and SEF were correlated with the NIWR responses. The DC showed higher and more consistent correlations with the NIWR than the SEF. Correlation coefficients of NIWR and DC mainly varied between 0.6 and 0.8. Conclusion: New parameters from the field of non-linear dynamics can be an aiding tool in detecting effectual changes induced by anesthetics.

Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods., 15 pages, 4 Postscript figures. Submitted to Phys. Rev. E, 1999

We argue that Gaspard and coworkers [Nature 394, 865 (1998)] do not give evidence for microscopic chaos in the sense in which they use the term. The effectively infinite number of molecules in a fluid can generate the same macroscopic disorder without any intrinsic instability. But we argue also that the notion of chaos in infinitely extended systems needs clarification: In a wider sense, even some systems without local instabilities can be considered chaotic., Comment: 2 pages

We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P.~Grassberger, Phys.~Rev.~{\bf E 56} (1997) 3682) leads to very efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences., Comment: 17 pages, 21 figures, needs mprocl.sty (included), appears in Workshop on: Monte Carlo Approach to Biopolymers and Protein Folding, World Scientific 1998

Recently a novel method was developed to determine Dynamical Domains in proteins from molecular dynamics simulations(1) and from X-ray conformers.(2) This method is primarily intended to be used in the analysis of motions in multi-domain proteins. We will show that, using this method, also in a typical single-domain protein of 85 residues characteristic motions can be filtered out, which can be translated into regions of increased and decreased rigidity.

We present Monte Carlo simulations of semidilute solutions of long self-attracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction between non-bonded nearest neighbors. Chain lengths are up to N=2048, system sizes are up to $2^{21}$ lattice sites and $2.8\times 10^5$ monomers. These simulations used the recently introduced pruned-enriched Rosenbluth method which proved extremely efficient, together with a histogram method for estimating finite size corrections. Our most clear result is that chains at the critical point are Gaussian for large $N$, having end-to-end distances $R\sim\sqrt{N}$. Also the distance $T_\Theta-T_c(N)$ (where $T_\Theta = \lim_{N\to\infty} T_c(N)$) scales with the mean field exponent, $T_\Theta -T_c(N)\sim 1/\sqrt{N}$. The critical density seems to scale with a non-trivial exponent similar to that observed in experiments. But we argue that this is due to large logarithmic corrections. These corrections are similar to the very large corrections to scaling seen in recent analyses of $\Theta$-polymers, and qualitatively predicted by the field theoretic renormalization group. The only serious deviation from this simple global picture concerns the N-dependence of the order parameter amplitudes which disagrees with a minimalistic ansatz of de Gennes. But this might be due to problems with finite size scaling. We find that the finite size dependence of the density of states $P(E,n)$ (where $E$ is the total energy and $n$ is the number of chains) is slightly but significantly different from that proposed recently by several authors., Comment: minor changes; Latex, 22 pages, submitted to J. Chem. Phys

The relationship between Regge behaviour of two-body amplitudes and quantum number exchange in multiparticle production is analyzed. An exact bound on the elastic forward peak in terms of inclusive p/sub perpendicular to / correlations is given. Another result is that one cannot obtain alpha /sub rho /'> alpha /sub P/' from overlap calculations, using only the present inclusive data as input. (21 refs).

An unresolved question in epileptology is whether epileptic seizures can be predicted by characterizing measures of the EEG. In a recent comparison of univariate and bivariate measures we have shown the latter to be superior [Mormann et al., Clin Neurophysiol (submitted)]. However, so far only symmetric bivariate measures for synchronization were evaluated. In this study a comparison of 16 different measures for both synchronization and directionality was carried out with respect to their capability to discriminate pre-ictal from inter-ictal intervals with special emphasis placed on statistical validation [Kreuz et al., Phys Rev E, 2004]. Furthermore, we investigated to which extent different measures carry independent and non-redundant information. We analyzed continuous multi-day EEG recorded intracranially from 9 patients (total duration: 860 hours, 66 seizures). Measures included symmetric ones like cross correlation, mutual information and phase synchronization (based on Hilbert and wavelet transform, respectively) as well as asymmetric ones like transfer entropy, non-linear interdependencies and event synchronization. Measure profiles were evaluated using a statistical approach based on Receiver-Operating-Characteristics (ROC). The analysis was performed as in our previous work [Mormann et al., Clin Neurophysiol (submitted)] allowing different lengths of the pre-ictal interval and testing for both a pre-ictal decrease and increase. Two different evaluation schemes were designed focussing either on global or local effects. The significance was estimated using seizure times surrogates [Andrzejak et al., Phys Rev E, 2003]. Finally, redundancies between these measures were quantified using both correlation and cluster analysis. In the first evaluation scheme all measures yielded very poor ROC values and no measure proved to be significant. In the second evaluation scheme performances were considerably higher and, more importantly, for the most part significant. Maximum values were obtained for the indices of phase synchronization, minimum values for the symmetrized versions of the non-linear interdependencies. While the measures of directionality covered the same range as the measures of synchronization, correlation analysis showed that both groups of measures carry independent information. While no significant global effect could be observed, some measures of synchronization as well as some measures of directionality proved capable to detect significant local effects. Due to their non-redundancy a combination of these different approaches appears very promising. However, much more research has to be carried out to evaluate whether these statistical results allow yielding an acceptable performance in a practical implementation.

Item does not contain fulltext Spike-Wave Discharges (SWDs) occur spontaneously in the EEG of WAG/Rij rats. These SWDs are a model for human absence seizures. In order to examine whether non-linear analysis methods can contribute to the analysis of SWDs, we estimated the correlation dimension of the SWDs and compared the value to that of the phase-randomized signals

Item does not contain fulltext Evoked Potentials (EPs) are responses that appear in the EEG due to external stimulation. Findings indicate that changes in EPs can be related to changes in frequencies of the pre-stimulus EEG. Auditory EPs of rats (n=8) were measured in reaction to tone-pip stimuli (90 dB, 10.2 kHz, ISI 2s, n=1500). Trials were ranked according to the percentage of delta (1-4 Hz), theta (5-8), alpha (9-12) or beta power (13-30 Hz) in the pre-stimulus EEG. Consecutive AEPs were computed. An increase in beta and a decrease in delta resulted both in an increase in the N60 and P70 component and a decrease in the P150-200 component. These beta and delta changes have been associated with changes in arousal. The increased N60 and P70 components with increases in beta might reflect increased attention due to an increase in arousal. We found that an increase in delta activity, leads to an increase of the late-latency P150-200 component, possibly due to an increased synchronization in the EEG.

International audience; We used a Contact Dynamics algorithm to investigate some of the statistical properties of the contact network in quasistatically driven assemblies of rigid particles containing from 500 to 4000 particles in two dimensions. We found that the contact network at every stage of deformation is composed of two complementary subnetworks: a "strong" percolating subnetwork of the contacts carrying a force larger than the mean force (containing about 40% of contacts), and a "weak" subnetwork of the contacts carrying a force lower than the mean force. In the strong subnetwork, all contacts are nonsliding and the probability distribution of forces is well fitted by an exponential decay. Almost the whole dissipation takes place inside the weak subnetwork, where the number of forces decays as a power­ law. The weak subnetwork contributes only to the mean pressure (about 25%), whereas the strong subnetwork takes over the whole deviatoric load. The strong subnetwork bears the primary anisotropy induced by shear with the same orientation as the stress tensor, but it gives rise to a secondary anisotropy inside the weak subnetwork with an orientation orthogonal to that of the stress tensor.