495 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
Optimizing evacuation flow in a two-channel exclusion process
We use a basic setup of two coupled exclusion processes to model a stylised
situation in evacuation dynamics, in which evacuees have to choose between two
escape routes. The coupling between the two processes occurs through one common
point at which particles are injected, the process can be controlled by
directing incoming individuals into either of the two escape routes. Based on a
mean-field approach we determine the phase behaviour of the model, and
analytically compute optimal control strategies, maximising the total current
through the system. Results are confirmed by numerical simulations. We also
show that dynamic intervention, exploiting fluctuations about the mean-field
stationary state, can lead to a further increase in total current.Comment: 16 pages, 6 figure
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Active Device Fabrication Using Fiber Encapsulation Additive Manufacturing
Fiber Encapsulation Additive Manufacturing (FEAM) is a novel solid freeform
fabrication process in which a fiber and a matrix are co-deposited simultaneously within a single
printer along straight and curved 2-D and 3-D paths. Using a FEAM approach in which the fiber
is a metal wire and the matrix is a thermoplastic polymer, simple electromechanical devices such
as voice coils, inductive sensors, and membrane switches have been successfully produced. This
paper will present an overview of the FEAM process, describe several fabricated devices, and
discuss recent developments in controllably stopping and starting the wire, and in creating
electrical junctions between individual wires, which together enable much more complex devices
to be made.Mechanical Engineerin
Algebraic coarsening in voter models with intermediate states
The introduction of intermediate states in the dynamics of the voter model
modifies the ordering process and restores an effective surface tension. The
logarithmic coarsening of the conventional voter model in two dimensions is
eliminated in favour of an algebraic decay of the density of interfaces with
time, compatible with Model A dynamics at low temperatures. This phenomenon is
addressed by deriving Langevin equations for the dynamics of appropriately
defined continuous fields. These equations are analyzed using field theoretical
arguments and by means of a recently proposed numerical technique for the
integration of stochastic equations with multiplicative noise. We find good
agreement with lattice simulations of the microscopic model.Comment: 11 pages, 5 figures; minor typos correcte
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
Analysing multiparticle quantum states
The analysis of multiparticle quantum states is a central problem in quantum
information processing. This task poses several challenges for experimenters
and theoreticians. We give an overview over current problems and possible
solutions concerning systematic errors of quantum devices, the reconstruction
of quantum states, and the analysis of correlations and complexity in
multiparticle density matrices.Comment: 20 pages, 4 figures, prepared for proceedings of the "Quantum
[Un]speakables II" conference (Vienna, 2014
Statistical Mechanics of Dilute Batch Minority Games with Random External Information
We study the dynamics and statics of a dilute batch minority game with random
external information. We focus on the case in which the number of connections
per agent is infinite in the thermodynamic limit. The dynamical scenario of
ergodicity breaking in this model is different from the phase transition in the
standard minority game and is characterised by the onset of long-term memory at
finite integrated response. We demonstrate that finite memory appears at the
AT-line obtained from the corresponding replica calculation, and compare the
behaviour of the dilute model with the minority game with market impact
correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added,
figure added, typos correcte
Vertrauen in virtuellen Communities: Konzeption und Umsetzung vertrauensunterstützender Komponenten in der Domäne Healthcare
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
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