627 research outputs found
Two-population replicator dynamics and number of Nash equilibria in random matrix games
We study the connection between the evolutionary replicator dynamics and the
number of Nash equilibria in large random bi-matrix games. Using techniques of
disordered systems theory we compute the statistical properties of both, the
fixed points of the dynamics and the Nash equilibria. Except for the special
case of zero-sum games one finds a transition as a function of the so-called
co-operation pressure between a phase in which there is a unique stable fixed
point of the dynamics coinciding with a unique Nash equilibrium, and an
unstable phase in which there are exponentially many Nash equilibria with
statistical properties different from the stationary state of the replicator
equations. Our analytical results are confirmed by numerical simulations of the
replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure
Random replicators with asymmetric couplings
Systems of interacting random replicators are studied using generating
functional techniques. While replica analyses of such models are limited to
systems with symmetric couplings, dynamical approaches as presented here allow
specifically to address cases with asymmetric interactions where there is no
Lyapunov function governing the dynamics. We here focus on replicator models
with Gaussian couplings of general symmetry between p>=2 species, and discuss
how an effective description of the dynamics can be derived in terms of a
single-species process. Upon making a fixed point ansatz persistent order
parameters in the ergodic stationary states can be extracted from this process,
and different types of phase transitions can be identified and related to each
other. We discuss the effects of asymmetry in the couplings on the order
parameters and the phase behaviour for p=2 and p=3. Numerical simulations
verify our theory. For the case of cubic interactions numerical experiments
indicate regimes in which only a finite number of species survives, even when
the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of
negatively correlated couplings added, figures adde
Statistical mechanics and stability of a model eco-system
We study a model ecosystem by means of dynamical techniques from disordered
systems theory. The model describes a set of species subject to competitive
interactions through a background of resources, which they feed upon.
Additionally direct competitive or co-operative interaction between species may
occur through a random coupling matrix. We compute the order parameters of the
system in a fixed point regime, and identify the onset of instability and
compute the phase diagram. We focus on the effects of variability of resources,
direct interaction between species, co-operation pressure and dilution on the
stability and the diversity of the ecosystem. It is shown that resources can be
exploited optimally only in absence of co-operation pressure or direct
interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended,
references adde
Effects of noise on convergent game learning dynamics
We study stochastic effects on the lagging anchor dynamics, a reinforcement
learning algorithm used to learn successful strategies in iterated games, which
is known to converge to Nash points in the absence of noise. The dynamics is
stochastic when players only have limited information about their opponents'
strategic propensities. The effects of this noise are studied analytically in
the case where it is small but finite, and we show that the statistics and
correlation properties of fluctuations can be computed to a high accuracy. We
find that the system can exhibit quasicycles, driven by intrinsic noise. If
players are asymmetric and use different parameters for their learning, a net
payoff advantage can be achieved due to these stochastic oscillations around
the deterministic equilibrium.Comment: 17 pages, 8 figure
The signal-to-noise analysis of the Little-Hopfield model revisited
Using the generating functional analysis an exact recursion relation is
derived for the time evolution of the effective local field of the fully
connected Little-Hopfield model. It is shown that, by leaving out the feedback
correlations arising from earlier times in this effective dynamics, one
precisely finds the recursion relations usually employed in the signal-to-noise
approach. The consequences of this approximation as well as the physics behind
it are discussed. In particular, it is pointed out why it is hard to notice the
effects, especially for model parameters corresponding to retrieval. Numerical
simulations confirm these findings. The signal-to-noise analysis is then
extended to include all correlations, making it a full theory for dynamics at
the level of the generating functional analysis. The results are applied to the
frequently employed extremely diluted (a)symmetric architectures and to
sequence processing networks.Comment: 26 pages, 3 figure
Parallel dynamics of continuous Hopfield model revisited
We have applied the generating functional analysis (GFA) to the continuous
Hopfield model. We have also confirmed that the GFA predictions in some typical
cases exhibit good consistency with computer simulation results. When a
retarded self-interaction term is omitted, the GFA result becomes identical to
that obtained using the statistical neurodynamics as well as the case of the
sequential binary Hopfield model.Comment: 4 pages, 2 figure
uptake, intracellular distribution and cellular responses
Silver nanoparticles (SNP) are among the most commercialized nanoparticles
worldwide. They can be found in many diverse products, mostly because of their
antibacterial properties. Despite its widespread use only little data on
possible adverse health effects exist. It is difficult to compare biological
data from different studies due to the great variety in sizes, coatings or
shapes of the particles. Here, we applied a novel synthesis approach to obtain
SNP, which are covalently stabilized by a small peptide. This enables a tight
control of both size and shape. We applied these SNP in two different sizes of
20 or 40 nm (Ag20Pep and Ag40Pep) and analyzed responses of THP-1-derived
human macrophages. Similar gold nanoparticles with the same coating (Au20Pep)
were used for comparison and found to be non-toxic. We assessed the
cytotoxicity of particles and confirmed their cellular uptake via transmission
electron microscopy and confocal Raman microscopy. Importantly a majority of
the SNP could be detected as individual particles spread throughout the cells.
Furthermore we studied several types of oxidative stress related responses
such as induction of heme oxygenase I or formation of protein carbonyls. In
summary, our data demonstrate that even low doses of SNP exerted adverse
effects in human macrophages
Limit cycles, complex Floquet multipliers and intrinsic noise
We study the effects of intrinsic noise on chemical reaction systems, which
in the deterministic limit approach a limit cycle in an oscillatory manner.
Previous studies of systems with an oscillatory approach to a fixed point have
shown that the noise can transform the oscillatory decay into sustained
coherent oscillations with a large amplitude. We show that a similar effect
occurs when the stable attractors are limit cycles. We compute the correlation
functions and spectral properties of the fluctuations in suitably co-moving
Frenet frames for several model systems including driven and coupled
Brusselators, and the Willamowski-Roessler system. Analytical results are
confirmed convincingly in numerical simulations. The effect is quite general,
and occurs whenever the Floquet multipliers governing the stability of the
limit cycle are complex, with the amplitude of the oscillations increasing as
the instability boundary is approached.Comment: 15 pages, 8 figure
- …