Density evolution for expectation propagation

Paper presented at 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, Honolulu, HI.Expectation propagation (EP) [1, 2, 3, 4] is a theoretical extension of the belief propagation family of message passing algorithms [5, 6] for statistical inference which allows for efficient handling of models with continuous random variables as well as second or higher order correlation via the use of standard exponential families of probability measures [7, 8, 9]. Here we provide theoretically rigorous justifications for the use of density evolution [10, 11] to analyze the convergence and performance behavior of the family of algorithms in the large system regime by extending and expanding on the corresponding results for belief propagation decoding and turbo decoding

Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We present the probabilistic approach to reconstruction and discuss its optimality and robustness. We detail the derivation of the message passing algorithm for reconstruction and expectation max- imization learning of signal-model parameters. We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm. We also present new efficient seeding matrices, test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe

Photon production from a thermalized quark gluon plasma: quantum kinetics and nonperturbative aspects

We study the production of photons from a quark gluon plasma in local thermal equilibrium by introducing a non-perturbative formulation of the real time evolution of the density matrix. The main ingredient is the real time effective action for the electromagnetic field to $\mathcal{O}(\alpha_{em})$ and to all orders in $\alpha_s$. The real time evolution is completely determined by the solution of a \emph{classical stochastic} non-local Langevin equation which provides a Dyson-like resummation of the perturbative expansion. The Langevin equation is solved in closed form by Laplace transform in terms of the thermal photon polarization. A quantum kinetic description emerges directly from this formulation. We find that photons with $k \lesssim 200 ~{Mev}$ \emph{thermalize} as plasmon quasiparticles in the plasma on time scales $t \sim 10-20 ~{fm}/c$ which is of the order of the lifetime of the QGP expected at RHIC and LHC. We then obtain the direct photon yield to lowest order in $\alpha_{em}$ and to leading logarithmic order in $\alpha_s$ in a \emph{uniform} expansion valid at all time. The yield during a QGP lifetime $t \sim 10 ~{fm}/c$ is systematically larger than that obtained with the equilibrium formulation and the spectrum features a distinct flattening for $k \gtrsim 2.5 ~{Gev}$. We discuss the window of reliability of our results, the theoretical uncertainties in \emph{any} treatment of photon emission from a QGP in LTE and the shortcomings of the customary S-matrix approach.Comment: 31 pages. To appear in Nucl. Phys. A. New section (VII) with response to and criticism of hep-ph/031222

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.Comment: 21 pages, 10 figures, 1 table, to appear in Phys. Rev.

Maximal predictability approach for identifying the right descriptors for electrocatalytic reactions

Density Functional Theory (DFT) calculations are being routinely used to identify new material candidates that approach activity near fundamental limits imposed by thermodynamics or scaling relations. DFT calculations have finite uncertainty and this raises an issue related to the ability to delineate materials that possess high activity. With the development of error estimation capabilities in DFT, there is an urgent need to propagate uncertainty through activity prediction models. In this work, we demonstrate a rigorous approach to propagate uncertainty within thermodynamic activity models. This maps the calculated activity into a probability distribution, and can be used to calculate the expectation value of the distribution, termed as the expected activity. We prove that the ability to distinguish materials increases with reducing uncertainty. We define a quantity, prediction efficiency, which provides a precise measure of the ability to distinguish the activity of materials for a reaction scheme over an activity range. We demonstrate the framework for 4 important electrochemical reactions, hydrogen evolution, chlorine evolution, oxygen reduction and oxygen evolution. We argue that future studies should utilize the expected activity and prediction efficiency to improve the likelihood of identifying material candidates that can possess high activity.Comment: 17 pages, 6 figures; 17 pages of Supporting Informatio

Parallel density matrix propagation in spin dynamics simulations

Several methods for density matrix propagation in distributed computing environments, such as clusters and graphics processing units, are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.Comment: Submitted for publicatio

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure