69 research outputs found
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 is
characterized by the critical exponents of directed percolation: in
dimensions, , , and . Disorder causes a
dramatic change in the critical exponents, to , , and . These exponents govern spreading following
a long crossover period. The usual hyperscaling relation, , 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
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
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
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
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
T-Cell activation: a queuing theory analysis at low agonist density
We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation—for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface
Absorbing-state phase transitions in fixed-energy sandpiles
We study sandpile models as closed systems, with conserved energy density
playing the role of an external parameter. The critical energy density,
, 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
Novel universality class of absorbing transitions with continuously varying critical exponents
The well-established universality classes of absorbing critical phenomena are
directed percolation (DP) and directed Ising (DI) classes. Recently, the pair
contact process with diffusion (PCPD) has been investigated extensively and
claimed to exhibit a new type of critical phenomena distinct from both DP and
DI classes. Noticing that the PCPD possesses a long-term memory effect, we
introduce a generalized version of the PCPD (GPCPD) with a parameter
controlling the memory effect. The GPCPD connects the DP fixed point to the
PCPD point continuously. Monte Carlo simulations show that the GPCPD displays
novel type critical phenomena which are characterized by continuously varying
critical exponents. The same critical behaviors are also observed in models
where two species of particles are coupled cyclically. We suggest that the
long-term memory may serve as a marginal perturbation to the ordinary DP fixed
point.Comment: 13 pages + 10 figures (Full paper version
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