Q-voter model with independence on signed random graphs: Homogeneous approximations.

The q-voter model with independence is generalized to signed random graphs and studied by means of Monte Carlo simulations and theoretically using the mean-field approximation and different forms of the pair approximation. In the signed network with quenched disorder, positive and negative signs associated randomly with the links correspond to reinforcing and antagonistic interactions, promoting, respectively, the same or opposite orientations of two-state spins representing agents' opinions; otherwise, the opinions are called mismatched. With probability 1-p, the agents change their opinions if the opinions of all members of a randomly selected q neighborhood are mismatched, and with probability p, they choose an opinion randomly.

Q-neighbor Ising model on multiplex networks with partial overlap of nodes.

The q-neighbor Ising model for the opinion formation on multiplex networks with two layers in the form of random graphs (duplex networks), the partial overlap of nodes, and LOCAL&AND spin update rule was investigated by means of the pair approximation and approximate master equations as well as Monte Carlo simulations. Both analytic and numerical results show that for different fixed sizes of the q-neighborhood and finite mean degrees of nodes within the layers the model exhibits qualitatively similar critical behavior as the analogous model on multiplex networks with layers in the form of complete graphs. However, as the mean degree of nodes is decreased the discontinuous ferromagnetic transition, the tricritical point separating it from the continuous transition, and the possible coexistence of the paramagnetic and ferromagnetic phases at zero temperature occur for smaller relative sizes of the overlap.

Pair approximation for the q-voter model with independence on multiplex networks.

The q-voter model with independence is investigated on multiplex networks with full overlap of nodes in the layers. The layers are various complex networks corresponding to different levels of social influence. Detailed studies are performed for the model on multiplex networks with two layers with identical degree distributions, obeying the LOCAL&AND and GLOBAL&AND spin update rules differing by the way in which the q-lobbies of neighbors within different layers exert their joint influence on the opinion of a given agent.

Minimal exactly solved model with the extreme Thouless effect.

We present and analyze a minimal exactly solved model that exhibits a mixed-order phase transition known in the literature as the Thouless effect. Such hybrid transitions do not fit into the modest classification of thermodynamic transitions and, as such, they used to be overlooked or incorrectly identified in the past. The recent series of observations of such transitions in many diverse systems suggest that a new taxonomy of phase transitions is needed.

Cypermethrin blocks a mitochondria-dependent apoptotic signal initiated by deficient N-linked glycosylation within the endoplasmic reticulum.

The endoplasmic reticulum (ER) serves as a critical site of protein synthesis and processing. The temperature-sensitive hamster fibroblast cell line (tsBN7) displays deficient N-linked glycosylation activity at the restrictive temperature and activates cellular apoptosis. Temperature-shifted tsBN7 cells display induction of Grp78 and Gadd153, genes known to be induced by ER stress, and activate apoptosis via the release of cytochrome c from the mitochondria.

Stochastic resonance with spatiotemporal signal controlled by time delays.

Stochastic resonance in two coupled threshold elements with input periodic signals shifted in phase is studied. For fixed phase shift and coupling strength the signal-to-noise ratio at the output of each element can be maximized by introducing proper time delays in the coupling terms which cancel the effect of the phase shift. This shows that in systems of coupled elements driven by spatiotemporal periodic signals stochastic resonance can be controlled by delayed coupling.

Stochastic multiresonance due to interplay between noise and fractals.

Stochastic multiresonance is shown to occur in a general class of threshold-crossing systems, in which a derivative of the threshold-crossing probability with respect to a system parameter is a nonmonotonic function of the noise intensity. As an example, a two-dimensional chaotic map is considered, where the threshold-crossing probability follows the overlap of the fractal structures of chaotic saddles and the basins of escape in noise-induced crisis. The analytic theory is in reasonable agreement with the numerical results for spectral power amplification.

Aperiodic stochastic resonance in chaotic maps.

It is shown by means of numerical simulations that aperiodic stochastic resonance occurs in chaotic one-dimensional maps with various kinds of intermittency. The effect appears in the absence of external noise, as the system control parameter is varied. In the case of input signals slowly varying in time the analytic treatment, using the adiabatic approximation based on the expressions for the mean laminar phase duration, yields the input-output covariance function comparable with numerical results.

Volatility clustering and scaling for financial time series due to attractor bubbling.

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time heat bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit, the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering.

Noisefree stochastic multiresonance near chaotic crises.

We report on the phenomenon of noisefree stochastic multiresonance that appears in a natural way in systems where the threshold crossing probability has a nonmonotonous derivative with respect to the control parameter. In particular, we consider periodically driven chaotic dynamical systems above crisis threshold where the nonmonotonicity is caused by the fractal structure of precritical attractors and, possibly, their basins of attraction. The spectral power amplification as a function of the control parameter can be easily obtained from the postcritical average transient times, and the heights of its multiple maxima can be estimated on the basis of simple geometric models.

Blowout bifurcation and stability of marginal synchronization of chaos.

Blowout bifurcations are investigated in a symmetrized extension of the replacement method of chaotic synchronization which consists of coupling chaotic systems via mutually shared variables. The coupled systems are partly linear with respect to variables that are not shared, and that form orthogonal invariant manifolds in the composite system. If the coupled systems are identical, marginal (projective) synchronization between them occurs.

Stochastic multiresonance in a chaotic map with fractal basins of attraction.

Noise-free stochastic resonance in a chaotic kicked spin model at the edge of the attractor merging crisis is considered. The output signal reflects the occurrence of crisis-induced jumps between the two parts of the attractor. As the control parameter-the amplitude of the magnetic field pulses-is varied, the signal-to-noise ratio shows plateaus and multiple maxima, thus stochastic multiresonance is observed.

Stochastic resonance and noise-enhanced order with spatiotemporal periodic signal.

Stochastic resonance is investigated in a chain of coupled threshold elements driven by independent noises and a plane traveling wave. Both stochastic resonance in an individual element embedded in the chain, characterized by a maximum of the signal-to-noise ratio for nonzero noise intensity, and stochastic resonance with spatiotemporal signal, characterized by a maximum of the spatiotemporal input-output correlation function, are observed. For a wide range of wavelengths of the plane wave an optimum value of coupling exists for which both kinds of stochastic resonance are most pronounced, i.

Stochastic resonance in noisy maps as dynamical threshold-crossing systems.

Interplay of noise and periodic modulation of system parameters for the logistic map in the region after the first bifurcation and for the kicked spin model with Ising anisotropy and damping is considered. For both maps two distinct symmetric states are present that correspond to different phases of the period-2 orbit of the logistic map and to disjoint attractors of the spin map. The periodic force modulates the transition probabilities from any state to the opposite one symmetrically.