1,341 research outputs found
Predicting how People Play Games: a Simple Dynamic Model of Choice.
We use the model developed in Sarin and Vahid (1999, GEB) to explain the experiments reported in Erev and Roth (1998, AER). The model supposes that players maximize subject to their "beliefs" which are non-probabilistic and scalar-valued. They are intended to describe the payoffs the players subjectively assess they will obtain from a strategy. In an earlier paper (Sarin and Vahid (1997) we showed that the model predicted behaviour in repeated coordination games remarkably well, and better than equilibrium theory of reinforcement learning models. In this paper we show that the same one-parameter model can also explain behaviour in games with a unique mixed strategy Nash equilibrium better than alternative models. Hence, we obtain further support for the simple dynamic model.Game Theory, Probability
Strategy Similarity and Coordination.
This paper introduces similarity among strategies in the payoff assessment model of choice (Sarin and Vahid (1999, GEB)). The assessments of strategies that are more similar to the chosen strategy are updated more similarly to the chosen strategy. We use this model to explain a recent experiment.Econometric analysis of experimental data; Adaptive learning; Similarity; Coordination games; Payoff assessments without probabilities
Polaritonic states in a dielectric nanoguide: localization and strong coupling
Propagation of light through dielectrics lies at the heart of optics.
However, this ubiquitous process is commonly described using phenomenological
dielectric function and magnetic permeability , i.e. without
addressing the quantum graininess of the dielectric matter. Here, we present a
theoretical study where we consider a one-dimensional ensemble of atoms in a
subwavelength waveguide (nanoguide) as fundamental building blocks of a model
dielectric. By exploring the roles of the atom-waveguide coupling efficiency,
density, disorder, and dephasing, we establish connections among various
features of polaritonic light-matter states such as localization, super and
subradiance, and strong coupling. In particular, we show that coherent multiple
scattering of light among atoms that are coupled via a single propagating mode
can gives rise to Rabi splitting. These results provide important insight into
the underlying physics of strong coupling reported by recent room-temperature
experiments with microcavities and surface plasmons.Comment: 10 pages, 6 figure
An algorithmic proof for the completeness of two-dimensional Ising model
We show that the two dimensional Ising model is complete, in the sense that
the partition function of any lattice model on any graph is equal to the
partition function of the 2D Ising model with complex coupling. The latter
model has all its spin-spin coupling equal to i\pi/4 and all the parameters of
the original model are contained in the local magnetic fields of the Ising
model. This result has already been derived by using techniques from quantum
information theory and by exploiting the universality of cluster states. Here
we do not use the quantum formalism and hence make the completeness result
accessible to a wide audience. Furthermore our method has the advantage of
being algorithmic in nature so that by following a set of simple graphical
transformations, one is able to transform any discrete lattice model to an
Ising model defined on a (polynomially) larger 2D lattice.Comment: 18 pages, 15 figures, Accepted for publication in Physical Review
Fisher information matrix for single molecules with stochastic trajectories
Tracking of objects in cellular environments has become a vital tool in
molecular cell biology. A particularly important example is single molecule
tracking which enables the study of the motion of a molecule in cellular
environments and provides quantitative information on the behavior of
individual molecules in cellular environments, which were not available before
through bulk studies. Here, we consider a dynamical system where the motion of
an object is modeled by stochastic differential equations (SDEs), and
measurements are the detected photons emitted by the moving fluorescently
labeled object, which occur at discrete time points, corresponding to the
arrival times of a Poisson process, in contrast to uniform time points which
have been commonly used in similar dynamical systems. The measurements are
distributed according to optical diffraction theory, and therefore, they would
be modeled by different distributions, e.g., a Born and Wolf profile for an
out-of-focus molecule. For some special circumstances, Gaussian image models
have been proposed. In this paper, we introduce a stochastic framework in which
we calculate the maximum likelihood estimates of the biophysical parameters of
the molecular interactions, e.g., diffusion and drift coefficients. More
importantly, we develop a general framework to calculate the Cram\'er-Rao lower
bound (CRLB), given by the inverse of the Fisher information matrix, for the
estimation of unknown parameters and use it as a benchmark in the evaluation of
the standard deviation of the estimates. There exists no established method,
even for Gaussian measurements, to systematically calculate the CRLB for the
general motion model that we consider in this paper. We apply the developed
methodology to simulated data of a molecule with linear trajectories and show
that the standard deviation of the estimates matches well with the square root
of the CRLB
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