Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation

We revisit the problem of exact CMB likelihood and power spectrum estimation with the goal of minimizing computational cost through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and here we develop it into a fully working computational framework for large-scale polarization analysis, adopting \WMAP\ as a worked example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8\% at $\ell\le32$, and a maximum shift in the mean values of a joint distribution of an amplitude--tilt model of 0.006$\sigma$. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation that requires less than 3 GB of memory and 2 CPU minutes per iteration for $\ell \le 32$, rendering low-$\ell$ QML CMB power spectrum analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ

Bayesian Power Spectrum Analysis of the First-Year WMAP data

We present the first results from a Bayesian analysis of the WMAP first year data using a Gibbs sampling technique. Using two independent, parallel supercomputer codes we analyze the WMAP Q, V and W bands. The analysis results in a full probabilistic description of the information the WMAP data set contains about the power spectrum and the all-sky map of the cosmic microwave background anisotropies. We present the complete probability distributions for each C_l including any non-Gaussianities of the power spectrum likelihood. While we find good overall agreement with the previously published WMAP spectrum, our analysis uncovers discrepancies in the power spectrum estimates at low l multipoles. For example we claim the best-fit Lambda-CDM model is consistent with the C_2 inferred from our combined Q+V+W analysis with a 10% probability of an even larger theoretical C_2. Based on our exact analysis we can therefore attribute the "low quadrupole issue" to a statistical fluctuation.Comment: 5 pages. 4 figures. For additional information and data see http://www.astro.uiuc.edu/~iodwyer/research#wma

Optical waveguide characterization of a tristable antiferroelectric liquid crystal cell

Copyright © 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics 95 (2004) and may be found at http://link.aip.org/link/?JAPIAU/95/2246/1The optical convergent-beam waveguide technique has been used to characterize a homogeneously aligned 3 µm cell containing a liquid crystal in the antiferroelectric phase. The director structure has been quantified with the cell at 0 V and at ±50 V dc, and three distinct states have been observed. From the optical data collected, it is found that the material forms a tilted-bookshelf ferroelectric structure in the presence of a suitable voltage, and the characteristic alternating (anticlinic) structure of the antiferroelectric phase when the cell is short-circuited. The biaxiality of the antiferroelectric state has been measured, and (approximately) uniaxial refractive indices, the cone angle, and layer tilt have been determined for the ferroelectric state

Coupled surface plasmons and optical guided wave exploration of near-surface director profile

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 49. DOI: 10.1088/1367-2630/9/3/049For a liquid crystal (LC) cell with thin silver claddings it is possible, using a high index coupling prism, to excite both surface plasmon modes and ordinary optical guided modes. In a situation where the tilt of the director varies from homogeneous to homeotropic through the cell, then for p-polarized incident radiation the p-polarized surface plasmon mode and the ordinary guided waves may couple to each other. When the plane containing the director is normal to the incident plane, there is also polarization conversion leading to strong coupling between the p-polarized surface plasmon and s-like guided modes. From theoretical analyses together with numerical modelling it is shown how this coupling between the surface plasmon mode and guided waves gives a high sensitivity to the surface director tilt profile near the walls, higher than that of the surface plasmon mode alone. Experimental confirmation of this has been realized using a hybrid aligned nematic (HAN) LC cell with the director in a plane normal to the incident plane. The results fully confirm the model predictions showing that this coupling of surface plasmons to guided waves provides a powerful tool for near-surface director studies

Influence of Bioactive Components of the Mediterranean Diet on Inflammation and Healthy Aging

The Mediterranean diet is characterized by an increased consumption of fruits, vegetables, grains, and fish. Olive oil and herbs and spices are also essential components of this food regimen. Such a diet is associated with a reduced risk of cardiovascular disease, overall mortality, reduced incidence of Parkinson’s and Alzheimer’s diseases, and reduced cognitive impairment. Some of the bioactive components that exert beneficial effects are ω-3 fatty acids, polyphenols, and alkaloids that have neuroprotective, anti-inflammatory, antioxidant, antimicrobial, and gluco-regulating properties. These beneficial effects contribute to improved health including organ health and cognitive function. While the number of such bioactive plant constituents is numerous, this review will examine the role of specific bioactives and vitamins and assess the molecular mechanisms including the antioxidant and anti-inflammatory beneficial effects of the bioactive components in the Mediterranean diet

Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 99. DOI: 10.1088/1367-2630/9/4/099A detailed optical study of the iridescent outer-shell of the beetle Plusiotis boucardi has revealed a novel microstructure which controls both the polarization and wavelength of reflected light. A previously unreported hexagonal array across the integument of the beetle exhibits highly localized regions of reflection of only red and green left-handed circularly-polarized light. Optical and transmission electron microscopy (TEM) imaging reveals the origin of this effect as an array of 'bowl-shaped' recesses on the elytra that are formed from a dual-pitch helicoidal layer. Reflectivity spectra collected from the beetle are compared to theoretical data produced using a multi-layer optics model for modelling chiral, optically anisotropic media such as cholesteric liquid crystals. Excellent agreement is obtained between data and theory produced using a model that incorporates an upper isotropic layer (of cuticular wax), followed by a short pitch (310 (± 1) nm) overlying a longer pitch (370 (±1) nm) helicoidal layer of optically anisotropic material. These layers are backed by an absorbing underlayer. Synthetic replication of this form of structure may provide a route to the fabrication of tuneable micro-mirrors for optical applications

Tuneable Fabry–Perot etalon for terahertz radiation

Copyright © 2008 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 10, article 033012. DOI:10.1088/1367-2630/10/3/033012An indium tin oxide-clad liquid crystal filled Fabry–Perot etalon structure has been shown to act as an effective narrow-band filter at terahertz frequencies. An applied voltage, which controls the alignment of the nematic liquid crystal allows the refractive index of the core to be tuned. Transmission spectra show well-defined resonant peaks which shift in position when the alignment is changed from planar to homeotropic. The measured transmission spectra agree well with the results of a multilayer optics model and the birefringence of the liquid crystals over this frequency range are determined as Δn = 0.15(± 0.01) and Δn = 0.08(± 0.01) for E7 and ZLI 2293, respectively