Critical Dynamics of the Contact Process with Quenched Disorder

We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized by the critical exponents of directed percolation: in $2+1$ dimensions, $\delta = 0.46$, $\eta = 0.214$, and $z = 1.13$. Disorder causes a dramatic change in the critical exponents, to $\delta \simeq 0.60$, $\eta \simeq -0.42$, and $z \simeq 0.24$. These exponents govern spreading following a long crossover period. The usual hyperscaling relation, $4 \delta + 2 \eta = d z$, is violated. Our results support the conjecture by Bramson, Durrett, and Schonmann [Ann. Prob. {\bf 19}, 960 (1991)], that in two or more dimensions the disordered CP has only a single phase transition.Comment: 11 pages, REVTeX, four figures available on reques

Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.Comment: 11 pages, 3 figure

Multi-Timescale Perceptual History Resolves Visual Ambiguity

When visual input is inconclusive, does previous experience aid the visual system in attaining an accurate perceptual interpretation? Prolonged viewing of a visually ambiguous stimulus causes perception to alternate between conflicting interpretations. When viewed intermittently, however, ambiguous stimuli tend to evoke the same percept on many consecutive presentations. This perceptual stabilization has been suggested to reflect persistence of the most recent percept throughout the blank that separates two presentations. Here we show that the memory trace that causes stabilization reflects not just the latest percept, but perception during a much longer period. That is, the choice between competing percepts at stimulus reappearance is determined by an elaborate history of prior perception. Specifically, we demonstrate a seconds-long influence of the latest percept, as well as a more persistent influence based on the relative proportion of dominance during a preceding period of at least one minute. In case short-term perceptual history and long-term perceptual history are opposed (because perception has recently switched after prolonged stabilization), the long-term influence recovers after the effect of the latest percept has worn off, indicating independence between time scales. We accommodate these results by adding two positive adaptation terms, one with a short time constant and one with a long time constant, to a standard model of perceptual switching

Sympatric speciation and extinction driven by environment dependent sexual selection

A theoretical model is studied to investigate the possibility of sympatric speciation driven by sexual selection and ecological diversi¢cation. In particular, we focus on the rock-dwelling haplochromine cichlid species in Lake Victoria. The high speciation rate in these cichlids has been explained by their apparent ability to specialize rapidly to a large diversity of feeding niches. Seehausen and colleagues, however, demonstrated the importance of sexual selection in maintaining reproductive barriers between species. Our individual-orientated model integrates both niche di¡erentiation and a Fisherian runaway process, which is limited by visibility constraints. The model shows rapid sympatric speciation or extinction of species, depending on the strength of sexual selection

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure

Dynamics of temporally interleaved percept-choice sequences: interaction via adaptation in shared neural populations

At the onset of visually ambiguous or conflicting stimuli, our visual system quickly ‘chooses’ one of the possible percepts. Interrupted presentation of the same stimuli has revealed that each percept-choice depends strongly on the history of previous choices and the duration of the interruptions. Recent psychophysics and modeling has discovered increasingly rich dynamical structure in such percept-choice sequences, and explained or predicted these patterns in terms of simple neural mechanisms: fast cross-inhibition and slow shunting adaptation that also causes a near-threshold facilitatory effect. However, we still lack a clear understanding of the dynamical interactions between two distinct, temporally interleaved, percept-choice sequences—a type of experiment that probes which feature-level neural network connectivity and dynamics allow the visual system to resolve the vast ambiguity of everyday vision. Here, we fill this gap. We first show that a simple column-structured neural network captures the known phenomenology, and then identify and analyze the crucial underlying mechanism via two stages of model-reduction: A 6-population reduction shows how temporally well-separated sequences become coupled via adaptation in neurons that are shared between the populations driven by either of the two sequences. The essential dynamics can then be reduced further, to a set of iterated adaptation-maps. This enables detailed analysis, resulting in the prediction of phase-diagrams of possible sequence-pair patterns and their response to perturbations. These predictions invite a variety of future experiments

Analysis of Oscillator Neural Networks for Sparsely Coded Phase Patterns

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical neurodynamics to our model, we theoretically investigate the model's associative memory capability by evaluating its maximum storage capacities and deriving its basins of attraction. It is shown that, as in the Hopfield model, the storage capacity diverges as the activity level decreases. We consider various practically and theoretically important cases. For example, it is revealed that a dynamically adjusted threshold mechanism enhances the retrieval ability of the associative memory. It is also found that, under suitable conditions, the network can recall patterns even in the case that patterns with different activity levels are stored at the same time. In addition, we examine the robustness with respect to damage of the synaptic connections. The validity of these theoretical results is confirmed by reasonable agreement with numerical simulations.Comment: 23 pages, 11 figure

Absorbing-state phase transitions in fixed-energy sandpiles

We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure

Are Damage Spreading Transitions Generically in the Universality Class of Directed Percolation?

We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in the same universality class as directed percolation. We conjecture that also other damage spreading transitions should be in this universality class, unless they coincide with other transitions (as in the Ising model with Glauber dynamics) and provided the probability for a locally damaged state to become healed is not zero.Comment: 10 pages, LATE