Fast Polarization for Processes with Memory

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. Namely, previous works have not addressed fast polarization of the high entropy set under memory. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite-state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both for the high and for the low entropy sets.Comment: 17 pages, 3 figures. Submitted to IEEE Transactions on Information Theor

Fast Pixel Space Convolution for CMB Surveys with Asymmetric Beams and Complex Scan Strategies: FEBeCoP

Precise measurement of the angular power spectrum of the Cosmic Microwave Background (CMB) temperature and polarization anisotropy can tightly constrain many cosmological models and parameters. However, accurate measurements can only be realized in practice provided all major systematic effects have been taken into account. Beam asymmetry, coupled with the scan strategy, is a major source of systematic error in scanning CMB experiments such as Planck, the focus of our current interest. We envision Monte Carlo methods to rigorously study and account for the systematic effect of beams in CMB analysis. Toward that goal, we have developed a fast pixel space convolution method that can simulate sky maps observed by a scanning instrument, taking into account real beam shapes and scan strategy. The essence is to pre-compute the "effective beams" using a computer code, "Fast Effective Beam Convolution in Pixel space" (FEBeCoP), that we have developed for the Planck mission. The code computes effective beams given the focal plane beam characteristics of the Planck instrument and the full history of actual satellite pointing, and performs very fast convolution of sky signals using the effective beams. In this paper, we describe the algorithm and the computational scheme that has been implemented. We also outline a few applications of the effective beams in the precision analysis of Planck data, for characterizing the CMB anisotropy and for detecting and measuring properties of point sources.Comment: 26 pages, 15 figures. New subsection on beam/PSF statistics, new and better figures, more explicit algebra for polarized beams, added explanatory text at many places following referees comments [Accepted for publication in ApJS

Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation

Mesoscopic non-equilibrium thermodynamics is used to formulate a model describing non-homogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of non-interacting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a functions of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.Comment: 33 pages, 6 figure

Out-of-plane focusing grating couplers for silicon photonics integration with optical MRAM technology

We present the design methodology and experimental characterization of compact out-of-plane focusing grating couplers for integration with magnetoresistive random access memory technology. Focusing grating couplers have recently found attention as layer-couplers for photonic-electronic integration. The components we demonstrate are designed for a wavelength of 1550 nm, fabricated in a standard 220 nm SOI photonic platform and optimized given the fabrication restrictions for standard 193-nm UV lithography. For the first time, we extend the design based on the phase matching condition to a two-dimensional (2-D) grating design with two optical input ports. We further present the experimental characterization of the focusing behaviour by spatially probing the emitted beam with a tapered-and-lensed fiber and demonstrate the polarization controlling capabilities of the 2-D FGCs

Thread-Scalable Evaluation of Multi-Jet Observables

A leading-order, leading-color parton-level event generator is developed for use on a multi-threaded GPU. Speed-up factors between 150 and 300 are obtained compared to an unoptimized CPU-based implementation of the event generator. In this first paper we study the feasibility of a GPU-based event generator with an emphasis on the constraints imposed by the hardware. Some studies of Monte Carlo convergence and accuracy are presented for PP -> 2,...,10 jet observables using of the order of 1e11 events.Comment: 16 pages, 5 figures, 3 table

Improved simulation of non-Gaussian temperature and polarization CMB maps

We describe an algorithm to generate temperature and polarization maps of the cosmic microwave background radiation containing non-Gaussianity of arbitrary local type. We apply an optimized quadrature scheme that allows us to predict and control integration accuracy, speed up the calculations, and reduce memory consumption by an order of magnitude. We generate 1000 non-Gaussian CMB temperature and polarization maps up to a multipole moment of l_max = 1024. We validate the method and code using the power spectrum and the fast cubic (bispectrum) estimator and find consistent results. The simulations are provided to the community.Comment: 18 pages, 19 figures. Accepted for publication in ApJS. Simulations can be obtained at http://planck.mpa-garching.mpg.de/cmb/fnl-simulation

High precision simulations of weak lensing effect on Cosmic Microwave Background polarization

We study accuracy, robustness and self-consistency of pixel-domain simulations of the gravitational lensing effect on the primordial CMB anisotropies due to the large-scale structure of the Universe. In particular, we investigate dependence of the results precision on some crucial parameters of such techniques and propose a semi-analytic framework to determine their values so the required precision is a priori assured and the numerical workload simultaneously optimized. Our focus is on the B-mode signal but we discuss also other CMB observables, such as total intensity, T, and E-mode polarization, emphasizing differences and similarities between all these cases. Our semi-analytic considerations are backed up by extensive numerical results. Those are obtained using a code, nicknamed lenS2HAT -- for Lensing using Scalable Spherical Harmonic Transforms (S2HAT) -- which we have developed in the course of this work. The code implements a version of the pixel-domain approach of Lewis (2005) and permits performing the simulations at very high resolutions and data volumes, thanks to its efficient parallelization provided by the S2HAT library -- a parallel library for a calculation of the spherical harmonic transforms. The code is made publicly available.Comment: 20 pages, 14 figures, submitted to A&A, matches version accepted for publication in A&