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Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior
We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map
We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place
We present a technique that identifies truly interacting subsystems of a complex system from multichannel data if the recordings are an unknown linear and instantaneous mixture of the true sources. The method is valid for arbitrary noise structure. For this, a blind source separation technique is proposed that diagonalizes antisymmetrized cross- correlation or cross-spectral matrices. The resulting decomposition finds truly interacting subsystems blindly and suppresses any spurious interaction stemming from the mixture. The usefulness of this interacting source analysis is demonstrated in simulations and for real electroencephalography data
In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification
Photo-induced deformations in azobenzene-containing side-chain polymers : molecular dynamics study
(2006)
We perform molecular dynamics simulations of azobenzene containing side-chain liquid crystalline polymer subject to an external model field that mimicks the reorientations of the azobenzenes upon irradiation with polarized light. The smectic phase of the polymer is studied with the field applied parallel to the nematic director, forcing the trans isomers to reorient perpendicularly to the field (the direction of which can be assosiated with the light polarization). The coupling between the reorientation of azobenzenes and mechanical deformation of the sample is found to depend on the field strength. In a weak field the original smectic order is melted gradually with no apparent change in the simulation box shape, whereas in a strong field two regimes are observed. During the first one a rapid melting of the liquid crystalline order is accompanied by the contraction of the polymer along the field direction (the effect similar to the one observed experimentally in azopenzene containing elastomers). During the slower second regime, the smectic layers are rebuilt to accomodate the preferential direction of chromophores perperdicular to the field.
We present UVES observations of the log N(H I) = 21.7 damped Lyman-alpha system at z(abs) = 2.03954 towards the quasar PKS 0458-020. Hi Lyman-alpha emission is detected in the center of the damped Lyman-alpha absorption trough. Metallicities are derived for Mg II, Si II, P II, Cr II, Mn II, Fe II and Zn II and are found to be -1.21 +/- 0.12, - 1.28 +/- 0.20, -1.54 +/- 0.11, -1.66 +/- 0.10, -2.05 +/- 0.11, -1.87 +/- 0.11, -1.22 +/- 0.10, respectively, relative to solar. The depletion factor is therefore of the order of [Zn/Fe] = 0.65. We observe metal absorption lines to be blueshifted compared to the Lyman-alpha emission up to a maximum of similar to 100 and 200 km s(-1) for low and high- ionization species respectively. This can be interpreted either as the consequence of rotation in a large (similar to 7 kpc) disk or as the imprint of a galactic wind. The star formation rate (SFR) derived from the Lyman-alpha emission, 1.6 M-circle dot yr(-1), is compared with that estimated from the observed C II* absorption. No molecular hydrogen is detected in our data, yielding a molecular fraction log f < -6.52. This absence of H-2 can be explained as the consequence of a high ambient UV flux which is one order of magnitude larger than the radiation field in the ISM of our Galaxy and originates in the observed emitting region
Clear-water phase (CWP) is an important event in seasonal plankton succession. We examined the influence of all herbivorous zooplankton on its initiation under different weather and climatic conditions using up to 19 years of observations from the large, deep Lake Constance (Europe) and estimates of relative clearance rates. A CWP occurred regularly, even if daphnid biomass was still very low. CWP was attributed to strong grazing either by a daphnid- dominated zooplankton community or by a diverse assemblage consisting of micro- and meso-zooplankton. Both types of zooplankton communities occurred with approximately the same frequency. The timing of the CWP was unrelated to the North Atlantic Oscillation (NAO) but correlated with the wind-dependent intensity of deep vertical mixing 3 months earlier, during early spring. Less mixing enabled early growth of phytoplankton, ciliates and rotifers despite low temperatures, which prevented daphnid development at this time. This resulted in enhanced grazing of ciliates and rotifers, which increased the importance of phytoplankton less edible for most ciliates, rotifers and daphnids. Ciliates clearly dominated the grazing pressure on phytoplankton throughout spring, maintaining high biomasses together with the phytoplankton for up to 2 months. A CWP was observed when herbivores grazing on larger phytoplankton developed in addition to ciliates
The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a(3). In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a(2). For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a(4), a(5) and a(6) are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0 < epsilon less than or similar to 0.6. We conclude that this behavior of the Sonine coefficients manifests the breakdown of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at most as the boundary area of the region. This area law is rigorously proven to hold true in noncritical harmonic-lattice systems of arbitrary spatial dimension, for general finite-ranged harmonic interactions, regions of arbitrary shape, and states of nonzero temperature. For nearest-neighbor interactions-corresponding to the Klein-Gordon case-upper and lower bounds to the degree of entanglement can be stated explicitly for arbitrarily shaped regions, generalizing the findings of Phys. Rev. Lett. 94, 060503 (2005). These higher-dimensional analogs of the analysis of block entropies in the one-dimensional case show that under general conditions, one can expect an area law for the entanglement in noncritical harmonic many-body systems. The proofs make use of methods from entanglement theory, as well as of results on matrix functions of block- banded matrices. Disordered systems are also considered. We moreover construct a class of examples for which the two- point correlation length diverges, yet still an area law can be proven to hold. We finally consider the scaling of classical correlations in a classical harmonic system and relate it to a quantum lattice system with a modified interaction. We briefly comment on a general relationship between criticality and area laws for the entropy of entanglement