Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms

We extend the analysis of Gabor transforms on a Cosmic Microwave Background (CMB) temperature map (Hansen, Gorski and Hivon 2002) to polarisation. We study the temperature and polarisation power spectra on the cut sky, the so-called pseudo power spectra. The transformation kernels relating the full-sky polarisation power spectra and the polarisation pseudo power spectra are found to be similar to the kernel for the temperature power spectrum. This fact is used to construct a fast power spectrum estimation algorithm using the pseudo power spectrum of temperature and polarisation as data vectors in a maximum likelihood approach. Using the pseudo power spectra as input to the likelihood analysis solves the problem of having to invert huge matrices which makes the standard likelihood approach infeasible.Comment: 32 pages, 25 figures, submitted to MNRA

The galaxy halo formation in the absence of violent relaxation and a universal density profile of the halo center

While N-body simulations testify for a cuspy profile of the central region of the dark matter haloes, observations favor a shallow, cored density profile of the central region of, at least, some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter haloes if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse to be not too intensive, the profile is universal: it depends almost not at all on the properties of the initial perturbation and is very akin, but not identical, to the Einasto profile with small Einasto index $n\sim 0.5$. We estimate the size of the 'central core' of the distribution, i.e., the extent of the very central region with a respectively gentle profile, and show that the cusp formation is unlikely, even if the dark matter is cold. The obtained profile is in a good agreement with observational data for, at least, some types of galaxies, but clearly disagrees with N-body simulations.Comment: 8 pages, 4 figure

Gauge invariant grid discretization of Schr\"odinger equation

Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that obtained by a straightforward discretization of the continuous Hamiltonian by means of balanced difference methods, and with a tight-binding Hamiltonian. The proposed Hamiltonian and the balanced difference one are used to compute the energy spectrum of a charged particle in a two-dimensional parabolic potential in the presence of a perpendicular, constant magnetic field. With this example we point out how a "naive" discretization gives rise to an explicit breaking of the gauge invariance and to large errors in the computed eigenvalues and corresponding probability densities; in particular, the error on the eigenfunctions may lead to very poor estimates of the mean values of some relevant physical quantities on the corresponding states. On the contrary, the proposed discretized Hamiltonian allows a reliable computation of both the energy spectrum and the probability densities.Comment: 7 pages, 4 figures, discussion about tight-binding Hamiltonians adde

Myths and Truths Concerning Estimation of Power Spectra

It is widely believed that maximum likelihood estimators must be used to provide optimal estimates of power spectra. Since such estimators require require of order N_d^3 operations they are computationally prohibitive for N_d greater than a few tens of thousands. Because of this, a large and inhomogeneous literature exists on approximate methods of power spectrum estimation. These range from manifestly sub-optimal, but computationally fast methods, to near optimal but computationally expensive methods. Furthermore, much of this literature concentrates on the power spectrum estimates rather than the equally important problem of deriving an accurate covariance matrix. In this paper, I consider the problem of estimating the power spectrum of cosmic microwave background (CMB) anisotropies from large data sets. Various analytic results on power spectrum estimators are derived, or collated from the literature, and tested against numerical simulations. An unbiased hybrid estimator is proposed that combines a maximum likelihood estimator at low multipoles and pseudo-C_\ell estimates at high multipoles. The hybrid estimator is computationally fast, nearly optimal over the full range of multipoles, and returns an accurate and nearly diagonal covariance matrix for realistic experimental configurations (provided certain conditions on the noise properties of the experiment are satisfied). It is argued that, in practice, computationally expensive methods that approximate the N_d^3 maximum likelihood solution are unlikely to improve on the hybrid estimator, and may actually perform worse. The results presented here can be generalised to CMB polarization and to power spectrum estimation using other types of data, such as galaxy clustering and weak gravitational lensing.Comment: 27 pages, 15 figures, MNRAS in press. Resubmission matches accepted versio

Fast, exact CMB power spectrum estimation for a certain class of observational strategies

We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {\em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_\ell$ with unprecedented efficiency.Comment: RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RT

Suppression of HD-cooling in protogalactic gas clouds by Lyman-Werner radiation

It has been shown that HD molecules can form efficiently in metal-free gas collapsing into massive protogalactic halos at high redshift. The resulting radiative cooling by HD can lower the gas temperature to that of the cosmic microwave background, T_CMB=2.7(1+z)K, significantly below the temperature of a few 100 K achievable via H_2-cooling alone, and thus reduce the masses of the first generation of stars. Here we consider the suppression of HD-cooling by UV irradiation in the Lyman-Werner (LW) bands. We include photo-dissociation of both H_2 and HD, and explicitly compute the self-shielding and shielding of both molecules by neutral hydrogen as well as the shielding of HD by H_2. We use a simplified dynamical collapse model, and follow the chemical and thermal evolution of the gas, in the presence of a UV background. We find that a LW flux of J_crit = 1e-22 erg/cm^2/sr/s/Hz is able to suppress HD cooling and thus prevent collapsing primordial gas from reaching temperatures below 100 K. The main reason for the lack of HD cooling for J>J_crit is the partial photo-dissociation of H_2, which prevents the gas from reaching sufficiently low temperatures (T<150K) for HD to become the dominant coolant; direct HD photo-dissociation is unimportant except for a narrow range of fluxes and column densities. Since the prevention of HD-cooling requires only partial H_2 photo-dissociation, the critical flux J_crit is modest, and is below the UV background required to reionize the universe at redshift z=10-20. We conclude that HD-cooling can reduce the masses of typical stars only in rare halos forming well before the epoch of reionization.Comment: 14 pages with 9 figures, submitted to MNRA

Fossil HII Regions: Self-Limiting Star Formation at High Redshift

Recent results by the WMAP satellite suggest that the intergalactic medium was significantly reionized at redshifts as high as z~17. At this early epoch, the first ionizing sources likely appeared in the shallow potential wells of mini-halos with virial temperatures T < 10^4 K. Once such an ionizing source turns off, its surrounding HII region Compton cools and recombines. Nonetheless, we show that the ``fossil'' HII regions left behind remain at high adiabats, prohibiting gas accretion and cooling in subsequent generations of mini-halos. Thus, early star formation is self-limiting. We quantify this effect to show that star formation in mini-halos cannot account for the bulk of the electron scattering opacity measured by WMAP, which must be due to more massive objects. We argue that gas entropy, rather than IGM metallicity, regulates the evolution of the global ionizing emissivity, and impedes full reionization until lower redshifts. We discuss several important consequences of this early entropy floor for reionization. It reduces gas clumping, curtailing the required photon budget for reionization. An entropy floor also prevents H2 formation and cooling, due to reduced gas densities: it greatly enhances feedback from UV photodissociation of H2. An early X-ray background would also furnish an entropy floor to the entire IGM; thus, X-rays impede rather than enhance H2 formation. Future 21cm observations may probe the topology of fossil HII regions.Comment: Submitted to MNRA

Regulation of caspase-3 processing by cIAP2 controls the switch between pro-inflammatory activation and cell death in microglia.

Cell Death and Disease is an open-access journal published by Nature Publishing Group. This work is licensed under a Creative Commons Attribution 4.0 International Licence. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons licence, users will need to obtain permission from the licence holder to reproduce the material.The activation of microglia, resident immune cells of the central nervous system, and inflammation-mediated neurotoxicity are typical features of neurodegenerative diseases, for example, Alzheimer's and Parkinson's diseases. An unexpected role of caspase-3, commonly known to have executioner role for apoptosis, was uncovered in the microglia activation process. A central question emerging from this finding is what prevents caspase-3 during the microglia activation from killing those cells? Caspase-3 activation occurs as a two-step process, where the zymogen is first cleaved by upstream caspases, such as caspase-8, to form intermediate, yet still active, p19/p12 complex; thereafter, autocatalytic processing generates the fully mature p17/p12 form of the enzyme. Here, we show that the induction of cellular inhibitor of apoptosis protein 2 (cIAP2) expression upon microglia activation prevents the conversion of caspase-3 p19 subunit to p17 subunit and is responsible for restraining caspase-3 in terms of activity and subcellular localization. We demonstrate that counteracting the repressive effect of cIAP2 on caspase-3 activation, using small interfering RNA targeting cIAP2 or a SMAC mimetic such as the BV6 compound, reduced the pro-inflammatory activation of microglia cells and promoted their death. We propose that the different caspase-3 functions in microglia, and potentially other cell types, reside in the active caspase-3 complexes formed. These results also could indicate cIAP2 as a possible therapeutic target to modulate microglia pro-inflammatory activation and associated neurotoxicity observed in neurodegenerative disorders

Using XDAQ in Application Scenarios of the CMS Experiment

XDAQ is a generic data acquisition software environment that emerged from a rich set of of use-cases encountered in the CMS experiment. They cover not the deployment for multiple sub-detectors and the operation of different processing and networking equipment as well as a distributed collaboration of users with different needs. The use of the software in various application scenarios demonstrated the viability of the approach. We discuss two applications, the tracker local DAQ system for front-end commissioning and the muon chamber validation system. The description is completed by a brief overview of XDAQ.Comment: Conference CHEP 2003 (Computing in High Energy and Nuclear Physics, La Jolla, CA