12,405 research outputs found
Stochastic fictitious play with continuous action sets
Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games
On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
Periodic spin textures in a degenerate F=1 Rb spinor Bose gas
We report on the spin textures produced by cooling unmagnetized Rb F=1
spinor gases into the regime of quantum degeneracy. At low temperatures,
magnetized textures form that break translational symmetry and display
short-range periodic magnetic order characterized by one- or two-dimensional
spatial modulations with wavelengths much smaller than the extent of the
quasi-two-dimensional degenerate gas. Spin textures produced upon cooling spin
mixtures with a non-zero initial magnetic quadrupole moment also show
ferromagnetic order that, at low temperature, coexists with the spatially
modulated structure.Comment: 6 pages, revised substantially following reviewer comments and
further analysi
Spontaneously modulated spin textures in a dipolar spinor Bose-Einstein condensate
Helical spin textures in a Rb F=1 spinor Bose-Einstein condensate are
found to decay spontaneously toward a spatially modulated structure of spin
domains. This evolution is ascribed to magnetic dipolar interactions that
energetically favor the short-wavelength domains over the long-wavelength spin
helix. This is confirmed by eliminating the dipolar interactions by a sequence
of rf pulses and observing a suppression of the formation of the short-range
domains. This study confirms the significance of magnetic dipole interactions
in degenerate Rb F=1 spinor gases
Amplification of Fluctuations in a Spinor Bose Einstein Condensate
Dynamical instabilities due to spin-mixing collisions in a Rb F=1
spinor Bose-Einstein condensate are used as an amplifier of quantum spin
fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in
quantitative agreement with mean-field calculations. We quantify the
microscopic spin fluctuations of the initially paramagnetic condensate by
applying this amplifier and measuring the resulting macroscopic magnetization.
The magnitude of these fluctuations is consistent with predictions of a
beyond-mean-field theory. The spinor-condensate-based spin amplifier is thus
shown to be nearly quantum-limited at a gain as high as 30 dB
The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics
For the phenomenological description of magnetohydrodynamic turbulence
competing models exist, e.g. Boldyrev [Phys.Rev.Lett. \textbf{96}, 115002,
2006] and Gogoberidze [Phys.Plas. \textbf{14}, 022304, 2007], which predict the
same Eulerian inertial-range scaling of the turbulent energy spectrum although
they employ fundamentally different basic interaction mechanisms. {A relation
is found that links} the Lagrangian frequency spectrum {with} the
autocorrelation timescale of the turbulent fluctuations, ,
and the associated cascade timescale, . Thus, the
Lagrangian energy spectrum can serve to identify weak
() and strong
() interaction mechanisms providing
insight into the turbulent energy cascade. The new approach is illustrated by
results from direct numerical simulations of two- and three-dimensional
incompressible MHD turbulence.Comment: accepted for publication in PR
DRASTIC—INSIGHTS:querying information in a plant gene expression database
DRASTIC––Database Resource for the Analysis of Signal Transduction In Cells (http://www.drastic.org.uk/) has been created as a first step towards a data-based approach for constructing signal transduction pathways. DRASTIC is a relational database of plant expressed sequence tags and genes up- or down-regulated in response to various pathogens, chemical exposure or other treatments such as drought, salt and low temperature. More than 17700 records have been obtained from 306 treatments affecting 73 plant species from 512 peer-reviewed publications with most emphasis being placed on data from Arabidopsis thaliana. DRASTIC has been developed by the Scottish Crop Research Institute and the Abertay University and allows rapid identification of plant genes that are up- or down-regulated by multiple treatments and those that are regulated by a very limited (or perhaps a single) treatment. The INSIGHTS (INference of cell SIGnaling HypoTheseS) suite of web-based tools allows intelligent data mining and extraction of information from the DRASTIC database. Potential response pathways can be visualized and comparisons made between gene expression patterns in response to various treatments. The knowledge gained informs plant signalling pathways and systems biology investigations
Coherence-enhanced imaging of a degenerate Bose gas
We present coherence-enhanced imaging, an in situ technique that uses Raman
superradiance to probe the spatial coherence properties of an ultracold gas.
Applying this method, we obtain a spatially resolved measurement of the
condensate number and more generally, of the first-order spatial correlation
function in a gas of Rb atoms. We observe the enhanced decay of
propagating spin gratings in high density regions of a Bose condensate, a decay
we ascribe to collective, non-linear atom-atom scattering. Further, we directly
observe spatial inhomogeneities that arise generally in the course of extended
sample superradiance.Comment: 4 pages, 4 figure
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