14,806 research outputs found
A Continuation Method for Nash Equilibria in Structured Games
Structured game representations have recently attracted interest as models
for multi-agent artificial intelligence scenarios, with rational behavior most
commonly characterized by Nash equilibria. This paper presents efficient, exact
algorithms for computing Nash equilibria in structured game representations,
including both graphical games and multi-agent influence diagrams (MAIDs). The
algorithms are derived from a continuation method for normal-form and
extensive-form games due to Govindan and Wilson; they follow a trajectory
through a space of perturbed games and their equilibria, exploiting game
structure through fast computation of the Jacobian of the payoff function. They
are theoretically guaranteed to find at least one equilibrium of the game, and
may find more. Our approach provides the first efficient algorithm for
computing exact equilibria in graphical games with arbitrary topology, and the
first algorithm to exploit fine-grained structural properties of MAIDs.
Experimental results are presented demonstrating the effectiveness of the
algorithms and comparing them to predecessors. The running time of the
graphical game algorithm is similar to, and often better than, the running time
of previous approximate algorithms. The algorithm for MAIDs can effectively
solve games that are much larger than those solvable by previous methods
Non-stationary patterns of isolation-by-distance: inferring measures of local genetic differentiation with Bayesian kriging
Patterns of isolation-by-distance arise when population differentiation
increases with increasing geographic distances. Patterns of
isolation-by-distance are usually caused by local spatial dispersal, which
explains why differences of allele frequencies between populations accumulate
with distance. However, spatial variations of demographic parameters such as
migration rate or population density can generate non-stationary patterns of
isolation-by-distance where the rate at which genetic differentiation
accumulates varies across space. To characterize non-stationary patterns of
isolation-by-distance, we infer local genetic differentiation based on Bayesian
kriging. Local genetic differentiation for a sampled population is defined as
the average genetic differentiation between the sampled population and fictive
neighboring populations. To avoid defining populations in advance, the method
can also be applied at the scale of individuals making it relevant for
landscape genetics. Inference of local genetic differentiation relies on a
matrix of pairwise similarity or dissimilarity between populations or
individuals such as matrices of FST between pairs of populations. Simulation
studies show that maps of local genetic differentiation can reveal barriers to
gene flow but also other patterns such as continuous variations of gene flow
across habitat. The potential of the method is illustrated with 2 data sets:
genome-wide SNP data for human Swedish populations and AFLP markers for alpine
plant species. The software LocalDiff implementing the method is available at
http://membres-timc.imag.fr/Michael.Blum/LocalDiff.htmlComment: In press, Evolution 201
The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
For two decades, the Colless index has been the most frequently used
statistic for assessing the balance of phylogenetic trees. In this article,
this statistic is studied under the Yule and uniform model of phylogenetic
trees. The main tool of analysis is a coupling argument with another well-known
index called the Sackin statistic. Asymptotics for the mean, variance and
covariance of these two statistics are obtained, as well as their limiting
joint distribution for large phylogenies. Under the Yule model, the limiting
distribution arises as a solution of a functional fixed point equation. Under
the uniform model, the limiting distribution is the Airy distribution. The
cornerstone of this study is the fact that the probabilistic models for
phylogenetic trees are strongly related to the random permutation and the
Catalan models for binary search trees.Comment: Published at http://dx.doi.org/10.1214/105051606000000547 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Real time plasma equilibrium reconstruction in a Tokamak
The problem of equilibrium of a plasma in a Tokamak is a free boundary
problemdescribed by the Grad-Shafranov equation in axisymmetric configurations.
The right hand side of this equation is a non linear source, which represents
the toroidal component of the plasma current density. This paper deals with the
real time identification of this non linear source from experimental
measurements. The proposed method is based on a fixed point algorithm, a finite
element resolution, a reduced basis method and a least-square optimization
formulation
Personal reminiscenses of my father Werner Heisenberg
Talk held at the opening of the exhibition at CERN commemorating Heisenberg's 100th birthday by his daughter Barbara Blum
Tunneling through magnetic molecules with arbitrary angle between easy axis and magnetic field
Inelastic tunneling through magnetically anisotropic molecules is studied
theoretically in the presence of a strong magnetic field. Since the molecular
orientation is not well controlled in tunneling experiments, we consider
arbitrary angles between easy axis and field. This destroys all conservation
laws except that of charge, leading to a rich fine structure in the
differential conductance. Besides single molecules we also study monolayers of
molecules with either aligned or random easy axes. We show that detailed
information on the molecular transitions and orientations can be obtained from
the differential conductance for varying magnetic field. For random easy axes,
averaging over orientations leads to van Hove singularities in the differential
conductance. Rate equations in the sequential-tunneling approximation are
employed. An efficient approximation for their solution for complex molecules
is presented. The results are applied to Mn12-based magnetic molecules.Comment: 10 pages, 10 figures include
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