We have investigated information transmission in an array of threshold units that have signal-dependent noise and a common input signal. We demonstrate a phenomenon similar to stochastic resonance and suprathreshold stochastic resonance with additive noise and show that information transmission can be enhanced by a nonzero level of noise. By comparing system performance to one with additive noise we also demonstrate that the information transmission of weak signals is significantly better with signal-dependent noise. Indeed, information rates are not compromised even for arbitrary small input signals. Furthermore, by an appropriate selection of parameters, we observe that the information can be made to be (almost) independent of the level of the noise, thus providing a robust method of transmitting information in the presence of noise. These result could imply that the ability of hair cells to code and transmit sensory information in biological sensory systems is not limited by the level of signal-dependent noise.

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles $(F\propto {\delta }^n)$ with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient $p_c$, defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent $n$. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction $(n=3∕2)$. The expression for $p_c$ in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

The $n$-alkanes ${\mathrm{C}}_{16}{\mathrm{H}}_{34}$, ${\mathrm{C}}_{17}{\mathrm{H}}_{36}$, ${\mathrm{C}}_{19}{\mathrm{H}}_{40}$, and ${\mathrm{C}}_{25}{\mathrm{H}}_{52}$ have been imbibed and solidified in mesoporous, crystalline silicon with a mean pore diameter of $10\mathrm{nm}$. The structures and phase sequences have been determined by x-ray diffractometry. Apart from a reduction and the hysteresis of the melting-freezing transition, we find a set of six discrete orientation states (“domains”) of the confined alkane crystals with respect to the lattice of the silicon host. The growth process responsible for the domain selection is interpreted as a nanoscale version of the Bridgman technique known from single-crystal growth. Oxidation of the pore walls leads to extrusion of the hydrocarbons upon crystallization, whereas the solidified $n$-alkanes investigated in nonoxidized, porous silicon are thermodynamically stable.

Based on the Fröhlich-Kirkwood theory of dielectrics and homogenization theory, a cubic equation is proposed for the outer-region dielectric constant of a globular protein in aqueous solution. The results for simple test cases confirm that a soluble globular protein may be considered to consist of a hydrophobic core surrounded by a hydrophilic external surface. Considering the widespread debate and ambiguity about the dielectric constant of proteins, the equation is expected to provide a straightforward way to determine the critical parameter for characterizing the relaxation of a protein in response to a charged perturbation.

We study the kinetics of the reaction front in the $A+B\to C$ reaction-diffusion system with reactants initially separated by a semipermeable membrane. The semipermeable membrane allows only one reactant species to go through (“penetrating species”) while the other reactant species is sterically prohibited from penetration. Theoretically, the ratio of the diffusive fluxes of the two species has been defined before as a control parameter and it was predicted [Chopard et al., Phys. Rev. E 56, 5343 (1997)] to give rise to a localization-delocalization transition of the reaction front. In this paper we show the experimental realization of a dynamical localization-delocalization transition, in a system consisting of the reactants ${\mathrm{Ca}}^{2+}$ and calcium green-1 dextran, separated by a finite-sized cellulose membrane. The dynamical transition results from the continuous change in time of the flux of the penetrating species at the reaction boundary. Here this time-dependent flux is attributed to the free diffusion of the penetrating species through a membrane with a finite thickness. The dynamical transition is exemplified by the kinetic behavior of the front characteristics which exhibits several time regimes — an early time, an intermediate time, and an asymptotic time regime. The crossover times between these regimes are found to depend on the membrane thickness, a parameter not considered before to our knowledge. Monte Carlo simulations show good agreement with the finite-time experiments.

The complex behavior that occurs when traffic lights are synchronized is studied. Two strategies are considered: all lights in phase, and a “green wave” with a propagating green signal. It is found that traffic variables such as traveling time, velocity, and fuel consumption, near resonance, follow critical scaling laws. For the green wave, it is shown that time and velocity scaling laws hold even for random separation between traffic lights. These results suggest the concept of transient resonances, which can be induced by adaptively changing the phase of traffic lights. This may be important to consider when designing strategies for traffic control in cities, where short trajectories, and thus transient solutions, are likely to be relevant.

We study the simplest possible order one single-layer perceptron with two inputs, using the delta rule with online learning, in order to derive closed form expressions for the mean convergence rates. We investigate the rate of convergence in weight space of the weight vectors corresponding to each of the 14 out of 16 linearly separable rules. These vectors follow zigzagging lines through the piecewise constant vector field to their respective attractors. Based on our studies, we conclude that a single-layer perceptron with $N$ inputs will converge in an average number of steps given by an $N\text{th}$ order polynomial in $\frac{t}{l}$, where $t$ is the threshold, and $l$ is the size of the initial weight distribution. Exact values for these averages are provided for the five linearly separable classes with $N=2$. We also demonstrate that the learning rate is determined by the attractor size, and that the attractors of a single-layer perceptron with $N$ inputs partition ${\mathbb{R}}^N\oplus {\mathbb{R}}^N$.

The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be applied to solve the inverse problem, namely, to find the equivalent local potential starting from a particular bound-state wave function and the corresponding energy. In order to check the method, we apply it to several cases which are analytically solvable: the nonrelativistic harmonic oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the semirelativistic harmonic oscillator. The potential is accurately computed in each case. In particular, our procedure deals efficiently with both nonrelativistic and semirelativistic kinematics.

We study front propagation in the reaction-diffusion process $A\leftrightarrow 2A$ on a one-dimensional lattice with hard core interaction between the particles. We propose a two-site self-consistent method to make analytic estimates for the front velocity that are in good agreement with the simulation results for all parameter regimes. We expect that the simplicity of the method will allow one to use this technique for estimating the front velocity in other reaction diffusion processes as well.

We consider triad dynamics as it was recently considered by Antal et al. [Phys. Rev. E 72, 036121 (2005)] as an approach to social balance. Here we generalize the topology from all-to-all to the regular one of a two-dimensional triangular lattice. The driving force in this dynamics is the reduction of frustrated triads in order to reach a balanced state. The dynamics is parametrized by a so-called propensity parameter $p$ that determines the tendency of negative links to become positive. As a function of $p$ we find a phase transition between different kinds of absorbing states. The phases differ by the existence of an infinitely connected (percolated) cluster of negative links that forms whenever $p⩽p_c$. Moreover, for $p⩽p_c$, the time to reach the absorbing state grows powerlike with the system size $L$, while it increases logarithmically with $L$ for $p>p_c$. From a finite-size scaling analysis we numerically determine the static critical exponents $\beta$ and ${\nu }_{\perp }$ together with $\gamma$, $\tau$, $\sigma$, and the dynamical critical exponents ${\nu }_{\Vert }$ and $\delta$. The exponents satisfy the hyperscaling relations. We also determine the fractal dimension $d_f$ that satisfies a hyperscaling relation as well. The transition of triad dynamics between different absorbing states belongs to a universality class with different critical exponents. We generalize the triad dynamics to four-cycle dynamics on a square lattice. In this case, again there is a transition between different absorbing states, going along with the formation of an infinite cluster of negative links, but the usual scaling and hyperscaling relations are violated.

A model for information spreading in a population of $N$ mobile agents is extended to $d$-dimensional regular lattices. This model, already studied on two-dimensional lattices, also takes into account the degeneration of information as it passes from one agent to the other. Here, we find that the structure of the underlying lattice strongly affects the time $\tau$ at which the whole population has been reached by information. By comparing numerical simulations with mean-field calculations, we show that dimension $d=2$ is marginal for this problem and mean-field calculations become exact for $d>2$. Nevertheless, the striking nonmonotonic behavior exhibited by the final degree of information with respect to $N$ and the lattice size $L$ appears to be geometry independent.

The compaction dynamics of a granular media subject to a sequence of vertical taps made of fluid pulses is investigated via molecular dynamics simulations. Our study focuses on three different levels: macroscopic (volume fraction), mesoscopic (Voronoï volumes, force distributions), and microscopic (grain displacements). We show that the compaction process has many characteristics which are reminiscent of the slow dynamics of glass forming systems, as previously suggested. For instance, the mean volume fraction slowly increases in time and approaches a stationary value following a stretched exponential law, and the associated compaction time diverges as the tapping intensity decreases. The study of microscopic quantities also put in evidence the existence of analogies with the dynamics of glass formers, as the existence of dynamical heterogeneities and spatially correlated motion of grains; however, it also shows that there are important qualitative differences, as, for instance, in the role of the cage effect. Correlations between geometry and dynamics of the system at the grain level are put in evidence by comparing a particle Voronoï volume and its displacement in a single tap.

The relaxation and breakup of Newtonian droplets is considered using the advected field approach. This method allows one to follow the deformation of interfaces using an order parameter field [Biben et al., Europhys. Lett. 63, 623 (2003)] based on a Ginzburg-Landau equation. Using this method, it is possible to follow the breakup of droplets and stability curves can be obtained in both two- and three-dimensional shear and elongational flows. Finally, relaxation of a droplet is considered, following the application of an elongational flow. The results are compared with previous experimental data [Ha and Leal, Phys. Fluids 13, 1568 (2001)], and are found to be in satisfactory agreement. The method is general enough to be applied to other non-Newtonian fluids, such as Oldroyd-B fluids or viscoplastic materials.

This paper presents the model for pattern formation in the course of stable (unfaceted) and unstable (faceted) crystal growth from the vapor phase, which is influenced by the rapid spatiotemporal variations of the substrate and film temperature. In the model, such variations result from the interference heating of a substrate by weak pulsed laser beams. The ensuing form of the temperature field perturbation from the ground state is fairly generic and simple, and thus it may as well serve to model other situations. In the stable case the surface relaxational dynamics is influenced by surface diffusion transport of adatoms from the hot to the cold regions of a substrate; this leads to the accumulation of mass in the cold regions and depletion in the hot regions. In the unstable case the underlying faceting instability coupled to the directed diffusion transport leads to the formation of the stationary hill-and-valley structure, where the hills may terminate sharply or have the rough tops. The characteristic lateral scale of this structure increases as the wavelength of the temperature nonuniformity decreases, but the coarsening rate of the transients decreases. By effectively redistributing adatoms through the enhanced, spatially inhomogeneous diffusion the mechanism also delays the onset of the spatiotemporal chaos as the growth rate increases. These scenarios are modeled using the framework of the classical continuum theory of the morphological evolution, enriched with the recently developed regularization method for the ill-posed, unstable evolution partial differential equation (PDE), and coupled to the concept of the spatiotemporal oscillatory surface temperature as the “tailoring force” for the evolution dynamics. A mass-conserving finite volume method is developed that is capable of the accurate computation of the large-slope solutions of the unstable, strongly nonlinear, sixth order evolution PDE for the surface height.

We study competitive dynamics among sidebranches in the crystal growth of dendrites. Numerical simulations are performed with a coupled map lattice to investigate the competitive dynamics among dendritic branches. A simple form of interaction via a diffusion field is estimated from the numerical simulations of the coupled map lattice. We propose a needle model on the basis of the competitive interaction, and perform numerical simulations of it. The size distribution of the dendritic branches exhibits a power law in the needle model.

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and “hopping” effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

We apply an information-theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher-point multi-information between any two spike trains, conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their ex vivo development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient, network diameter, and assortative mixing. Specifically we show that these networks are weakly disassortative small-world graphs, which differ significantly in their structure from randomized graphs with the same degree. We expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks, derived from time series data.

Circadian rhythms are daily oscillations in behaviors that persist in constant light/dark conditions with periods close to $24\mathrm{h}$. A striking feature of these rhythms is that their periods remain fairly constant over a wide range of physiological temperatures, a feature called temperature compensation. Although circadian rhythms have been associated with periodic oscillations in mRNA and protein levels, the question of how to construct a network of chemical reactions that is temperature compensated remains unanswered. We discuss a general framework for building such a network.

Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal et al. [T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E 72, 036121 (2005)]. We generalize their triad dynamics to $k$-cycle dynamics for arbitrary integer $k$. We derive the phase structure, determine the stationary solutions, and calculate the time it takes to reach a frozen state. The main difference in the phase structure as a function of $k$ is related to $k$ being even or odd. As a second generalization we dilute the all-to-all coupling as considered by Antal et al. to a random network with connection probability $w<1$. Interestingly, this model can be mapped to a satisfiability problem of computer science. The phase of social balance in our original interpretation then becomes the phase of satisfaction of all logical clauses in the satisfiability problem. In common to the cases we study, the ideal solution without any frustration always exists, but the question actually is as to whether this solution can be found by means of a local stochastic algorithm within a finite time. The answer depends on the choice of parameters. After establishing the mapping between the two classes of models, we generalize the social-balance problem to a diluted network topology for which the satisfiability problem is usually studied. On the other hand, in connection with the satisfiability problem we generalize the random local algorithm to a $p$-random local algorithm, including a parameter $p$ that corresponds to the propensity parameter in the social balance problem. The qualitative effect of the inclusion of this parameter is a bias towards the optimal solution and a reduction of the needed simulation time.