We correct claims about lower bounds on mutual information (MI) between real-valued random variables made by Kraskov et al., Phys. Rev. E 69, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions. This is so in spite of the invariance of MI under reparametrizations, because linear correlations are not invariant under them. The simplest bounds are obtained for Gaussians, but the most interesting ones for practical purposes are obtained for uniform marginal distributions. The latter can be enforced in general by using the ranks of the individual variables instead of their actual values, in which case one obtains bounds on MI in terms of Spearman correlation coefficients. We show with gene expression data that these bounds are in general nontrivial, and the degree of their (non)saturation yields valuable insight.

The kagome lattice has coordination number $4$, and it is mechanically isostatic when nearest-neighbor sites are connected by central-force springs. A lattice of $N$ sites has $O(\sqrt{N})$ zero-frequency floppy modes that convert to finite-frequency anomalous modes when next-nearest-neighbor (NNN) springs are added. We use the coherent potential approximation to study the mode structure and mechanical properties of the kagome lattice in which NNN springs with spring constant $\kappa$ are added with probability $\mathcal{P}=\Delta z/4$, where $\Delta z=z-4$ and $z$ is the average coordination number. The effective medium static NNN spring constant ${\kappa }_m$ scales as ${\mathcal{P}}^2$ for $\mathcal{P}\ll \kappa$ and as $\mathcal{P}$ for $\mathcal{P}\gg \kappa$, yielding a frequency scale ${\omega }^{*}~\Delta z$ and a length scale $l^{*}~(\Delta z){}^{-1}$. To a very good approximation at small nonzero frequency, ${\kappa }_m(\mathcal{P},\omega )/{\kappa }_m(\mathcal{P},0)$ is a scaling function of $\omega /{\omega }^{*}$. The Ioffe-Regel limit beyond which plane-wave states become ill-defined is reached at a frequency of order ${\omega }^{*}$.

The transformation properties of entropy production under phase-space partitioning, lumping, or the elimination of intermediate steps and variables in the presence of widely separated time scales are studied. Conditions are derived under which dissipation remains invariant. In systems subjected to external periodic driving the adiabatic, asymptotic, and transient entropy productions are evaluated and the extent to which they can be separately non-negative is determined.

Many physical and chemical processes, such as folding of biopolymers, are best described as dynamics on large combinatorial energy landscapes. A concise approximate description of the dynamics is obtained by partitioning the microstates of the landscape into macrostates. Since most landscapes of interest are not tractable analytically, the probabilities of transitions between macrostates need to be extracted numerically from the microscopic ones, typically by full enumeration of the state space or approximations using the Arrhenius law. Here, we propose to approximate transition probabilities by a Markov chain Monte Carlo method. For landscapes of the number partitioning problem and an RNA switch molecule, we show that the method allows for accurate probability estimates with significantly reduced computational cost.

We explore the two-dimensional generalized contact process with two absorbing states by means of large-scale Monte-Carlo simulations. In part of the phase diagram, an infinitesimal creation rate of active sites between inactive domains is sufficient to take the system from the inactive phase to the active phase. The system, therefore, displays two different nonequilibrium phase transitions. The critical behavior of the generic transition is compatible with the generalized voter universality class, implying that the symmetry-breaking and absorbing transitions coincide. In contrast, the transition at zero domain-boundary activation rate is not critical.

The effects of particle shape on the vibrational properties of colloidal glasses are studied experimentally. “Ellipsoidal glasses” are created by stretching polystyrene spheres to different aspect ratios and then suspending the resulting ellipsoidal particles in water at a high packing fraction. By measuring displacement correlations between particles, we extract vibrational properties of the corresponding “shadow” ellipsoidal glass with the same geometric configuration and interactions as the “source” suspension but without damping. Low-frequency modes in glasses composed of ellipsoidal particles with major-to-minor axis aspect ratios of $~$1.1 are observed to have predominantly rotational character. In contrast, low-frequency modes in glasses of ellipsoidal particles with larger aspect ratios ($~$3.0) exhibit a mixed rotational and translational character. All glass samples were characterized by a distribution of particles with different aspect ratios. Interestingly, even within the same sample it was found that small-aspect-ratio particles participate relatively more in rotational modes, while large-aspect-ratio particles tend to participate relatively more in translational modes.

We study the shape relaxation of spherical giant unilamellar vesicles which have been deformed far from equilibrium into ellipsoids using optical tweezers. The relaxation back to a sphere is determined by elastic constants of the vesicles, and their excess area, parameters that are obtained for each stretched vesicle from shape fluctuations in thermal equilibrium, as well as low Reynolds number fluid flow. The relaxation time could be compared favorably to a simple formula which encompasses the joint effect of membrane rigidity and fluid flow. The time constant of the stretched vesicle is slower than that of its thermal fluctuations, which agrees with a recent theory; however, it is one order of magnitude faster than predicted.

Several recent studies of energy transfer in photosynthetic light harvesting complexes have revealed a subtle interplay between coherent and decoherent dynamic contributions to the overall transfer efficiency in these open quantum systems. In this work we systematically investigate the impact of temporal and spatial correlations in environmental fluctuations on excitation transport in the Fenna-Matthews-Olson photosynthetic complex. We demonstrate that the exact nature of the correlations can have a large impact on the efficiency of light harvesting. In particular, we find that (i) spatial correlations can enhance coherences in the site basis while slowing transport, and (ii) the overall efficiency of transport is optimized at a finite temporal correlation that produces maximum overlap between the environmental power spectrum and the excitonic energy differences, which in turn results in enhanced driving of transitions between excitonic states.

We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of analytical expressions for rheological quantities such as shear viscosity and normal stress differences. In agreement to full-blown numerical calculations and experiments we find a shear-thickening or -thinning behavior depending on whether the particles are contractile or extensile. Moreover, our analytical approach predicts that the normal stress differences can change their sign in contrast to passive suspensions.

The cuticle of the longhorn beetle Pseudomyagrus waterhousei shows a diffuse pattern of mixed blue and violet colors. These colorations arise from a dense layer of droplet-shaped scales covering the dorsal parts of the cuticle. In spite of their lack of iridescence, these colors are shown to be structural and produced by an aggregate of internally ordered photonic-crystal grains. Computer simulations confirm that the blue and violet colors are caused by face-centered-cubic crystallites which dominantly expose their (111) surface to illumination and viewing.

In a cell, organelles and vesicles are usually transported by cooperation of several motor proteins, including plus-end-directed motor kinesin and minus-end-directed motor dynein. In recent years, many biophysical models have been constructed to understand the mechanism of this transport; however, so far, its basic principle has not been completely understood. In this paper, we will present a model that is based on recent experimental results and existing theoretical models. In this model, each motor is regarded as a head-spring system. The head can bind to or detach from the track stochastically, and step forward or backward with a fixed step size $L$ and force-dependent transition rates. The spring connects the head to the cargo tightly. The position of the cargo is determined by the force-balance condition. An obvious characteristic of our model is that the motors interact with each other and do not share the external load equally. Results indicate that the basic properties of the cargo, including its mean velocity and stall force (definitions are given in the text), are greatly affected by the intermotor interaction. Stated simplistically, the mean velocity and (average) stall force decrease with the intermotor interaction. Therefore, in a sense, the intermotor interaction is negative to the cooperate motion of motors. However, if the cargo is pulled by motors from the same species, its (average) stall force is usually larger than that of the single motor; this means that under external load, the velocity of cargo transported by several motors might be higher than the single-motor cases. We can infer from this that the cooperation of motors is beneficial to draw big cargoes, while it is not as beneficial as one might expect to improve motion velocity when the external load is low.

Several nonparametric estimators of the probability distribution of interspike intervals are introduced. The methods are suitable for simultaneous spike trains observed in a time window of length comparable with the mean interspike interval. This reflects the situation in which a high number of input spike trains converge to a single cortical neuron that has to react in a relatively short time. The simulation study is performed to compare the estimators. For that purpose, several types of stationary point processes are considered as the models of neuronal activity. The methods permit one to estimate the distribution of interspike intervals even if practically none of them are observed. The Kaplan-Meier estimator seems to be the most flexible and reliable among all studied methods, but no direct conclusions as to how real neurons work can be deduced from it.

Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([K${}_o^{+}$]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an “injury current” ($I_S$) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels ($I_{\mathrm{Katp}}$). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 291, H1088 (2006)] as a function of three ischemia-relevant parameters [K${}_o^{+}$], $I_S$, and $I_{\mathrm{Katp}}$. In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [K${}_o^{+}$] and $I_{\mathrm{Katp}}$ significantly altered the bifurcation structure of $I_S$, including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.

We study theoretically and experimentally the effect of long-range correlations in the material microstructure on the stress concentration in the vicinity of the notch tip. We find that while in a fractal continuum the notch-tip displacements obey the classic asymptotic for a linear elastic continuum, the power-law decay of notch-tip stresses is controlled by the long-range density correlations. The corresponding notch-size effect on fracture strength is in good agreement with the experimental tests performed on notched sheets of different kinds of paper. In particular, we find that there is no stress concentration if the fractal dimension of the fiber network is $D⩽d-0.5$, where $d$ is the topological dimension of the paper sheet.

We introduce a simple model to study movie competition in recommender systems. Movies of heterogeneous quality compete against each other through viewers’ reviews and generate interesting dynamics at the box office. By assuming mean-field interactions between the competing movies, we show that the runaway effect of popularity spreading is triggered by defeating the average review score, leading to box-office hits: Popularity rises and peaks before fade-out. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical box-office forms, revealing the significant role of competition in understanding box-office dynamics.

Percolation theory provides a tool for linking microstructure and macroscopic material properties. In this paper, percolation theory is applied to the analysis of microtomographic images for the purpose of deriving scaling laws for upscaling of properties. We have tested the acquisition of quantities such as percolation threshold, crossover length, fractal dimension, and critical exponent of correlation length from microtomography. By inflating or deflating the target phase and percolation analysis, we can get a critical model and an estimation of the percolation threshold. The crossover length is determined from the critical model by numerical simulation. The fractal dimension can be obtained either from the critical model or from the relative size distribution of clusters. Local probabilities of percolation are used to extract the critical exponent of the correlation length. For near-isotropic samples such as sandstone and bread, the approach works very well. For strongly anisotropic samples, such as highly deformed rock (mylonite) and a tree branch, the percolation threshold and fractal dimension can be assessed with accuracy. However, the uncertainty of the correlation length makes it difficult to accurately extract its critical exponents. Therefore, this aspect of percolation theory cannot be reliably used for upscaling properties of strongly anisotropic media. Other methods of upscaling have to be used for such media.

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first break up into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.

Density waves in a dusty plasma emerge spontaneously at low gas pressures and high dust densities. These acousticlike wave modes were studied in a radio-frequency discharge under microgravity conditions. The complex three-dimensional wave pattern shows a spatially varying wavelength that leads to bifurcations, i.e., topological defects, where wave fronts split or merge. The calculation of instantaneous wave attributes from the spatiotemporal evolution of the dust density allows a precise analysis of those structures. Investigations of the spatial frequency distribution inside the wave field revealed that the wave frequency decreases from the bulk to the edge of the cloud in terms of frequency jumps. Between those jumps, regions of almost constant frequency appear. The formation of frequency clusters is strongly correlated with defects that occur exclusively at the cluster boundaries. It is shown that the nonlinearity of the waves has a significant influence on the topology of the wave pattern.

We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton’s eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.