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 $\varepsilon$ and magnetic permeability $\mu$, 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