Showing papers on "Spectral density published in 2007"

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak

Abstract: The baryon acoustic oscillations are a promising route to the precision measure of the cosmological distance scale and hence the measurement of the time evolution of dark energy. We show that the nonlinear degradation of the acoustic signature in the correlations of low-redshift galaxies is a correctable process. By suitable reconstruction of the linear density field, one can sharpen the acoustic peak in the correlation function or, equivalently, restore the higher harmonics of the oscillations in the power spectrum. With this, one can achieve better measurements of the acoustic scale for a given survey volume. Reconstruction is particularly effective at low redshift, where the nonlinearities are worse but where the dark energy density is highest. At z = 0.3, we find that one can reduce the sample variance error bar on the acoustic scale by at least a factor of 2 and in principle by nearly a factor of 4. We discuss the significant implications our results have for the design of galaxy surveys aimed at measuring the distance scale through the acoustic peak.

On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter

Abstract: We discuss the effects of nonlinear structure formation on the signature of acoustic oscillations in the late-time galaxy distribution. We argue that the dominant nonlinear effect is the differential motion of pairs of tracers separated by 150 Mpc. These motions are driven by bulk flows and cluster formation and are much smaller than the acoustic scale itself. We present a model for the nonlinear evolution based on the distribution of pairwise Lagrangian displacements that provides a quantitative model for the degradation of the acoustic signature, even for biased tracers in redshift space. The Lagrangian displacement distribution can be calibrated with a significantly smaller set of simulations than would be needed to construct a precise power spectrum. By connecting the acoustic signature in the Fourier basis with that in the configuration basis, we show that the acoustic signature is more robust than the usual Fourier-space intuition would suggest, because the beat frequency between the peaks and troughs of the acoustic oscillations is a very small wavenumber that is well inside the linear regime. We argue that any possible shift of the acoustic scale is related to infall on a scale of 150 Mpc, which is O(0.5%) fractionally at first order, even at z = 0. For the matter, there is a first-order cancellation such that the mean shift is O(10-4). However, galaxy bias can circumvent this cancellation and produce a subpercent systematic bias.

The clustering of luminous red galaxies in the Sloan Digital Sky Survey imaging data

Abstract: We present the 3D real-space clustering power spectrum of a sample of ∼600 000 luminous red galaxies measured by the Sloan Digital Sky Survey, using photometric redshifts. These galaxies are old, elliptical systems with strong 4000-A breaks, and have accurate photometric redshifts with an average error of Δz= 0.03. This sample of galaxies ranges from redshift z= 0.2 to 0.6 over 3528 deg2 of the sky, probing a volume of 1.5 h−3 Gpc3, making it the largest volume ever used for galaxy clustering measurements. We measure the angular clustering power spectrum in eight redshift slices and use well-calibrated redshift distributions to combine these into a high-precision 3D real-space power spectrum from k= 0.005 to k= 1 h Mpc−1. We detect power on gigaparsec scales, beyond the turnover in the matter power spectrum, at a ∼2σ significance for k < 0.01 h Mpc−1, increasing to 5.5σ for k < 0.02 h Mpc−1. This detection of power is on scales significantly larger than those accessible to current spectroscopic redshift surveys. We also find evidence for baryonic oscillations, both in the power spectrum, as well as in fits to the baryon density, at a 2.5 σ confidence level. The large volume and resulting small statistical errors on the power spectrum allow us to constrain both the amplitude and the scale dependence of the galaxy bias in cosmological fits. The statistical power of these data to constrain cosmology is ∼1.7 times better than previous clustering analyses. Varying the matter density and baryon fraction, we find ΩM= 0.30 ± 0.03, and Ωb/ΩM= 0.18 ± 0.04, for a fixed Hubble constant of 70 km s−1 Mpc−1 and a scale-invariant spectrum of initial perturbations. The detection of baryonic oscillations also allows us to measure the comoving distance to z= 0.5; we find a best-fitting distance of 1.73 ± 0.12 Gpc, corresponding to a 6.5 per cent error on the distance. These results demonstrate the ability to make precise clustering measurements with photometric surveys.

Cosmology of f ( R ) gravity in the metric variational approach

Abstract: We consider the cosmologies that arise in a subclass of $f(R)$ gravity with $f(R)=R+{\ensuremath{\mu}}^{2n+2}/(\ensuremath{-}R{)}^{n}$ and $n\ensuremath{\in}(\ensuremath{-}1,0)$ in the metric (as opposed to the Palatini) variational approach to deriving the gravitational field equations. The calculations of the isotropic and homogeneous cosmological models are undertaken in the Jordan frame and at both the background and the perturbation levels. For the former, we also discuss the connection to the Einstein frame in which the extra degree of freedom in the theory is associated with a scalar field sharing some of the properties of a ``chameleon'' field. For the latter, we derive the cosmological perturbation equations in general theories of $f(R)$ gravity in covariant form and implement them numerically to calculate the cosmic microwave background (CMB) temperature and matter power spectra of the cosmological model. The CMB power is shown to reduce at low $l$'s, and the matter power spectrum is almost scale independent at small scales, thus having a similar shape to that in standard general relativity. These are in stark contrast with what was found in the Palatini $f(R)$ gravity, where the CMB power is largely amplified at low $l$'s and the matter spectrum is strongly scale dependent at small scales. These features make the present model more adaptable than that arising from the Palatini $f(R)$ field equations, and none of the data on background evolution, CMB power spectrum, or matter power spectrum currently rule it out.

Scale Dependence of Halo and Galaxy Bias: Effects in Real Space

Abstract: We examine the scale dependence of dark matter halo and galaxy clustering on very large scales ($0.01lk[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]l0.15$), due to nonlinear effects from dynamics and halo bias. We pursue a two line offensive: high-resolution numerical simulations are used to establish some old and some new results, and an analytic model is developed to understand their origins. Our simulations show: (i) that the $z=0$ dark matter power spectrum is suppressed relative to linear theory by $\ensuremath{\sim}5%$ on scales $0.05lk[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]l0.075$; (ii) that, indeed, halo bias is nonlinear over the scales we probe and that the scale dependence is a strong function of halo mass. High mass haloes show no suppression of power on scales $kl0.07[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]$, and only show amplification on smaller scales, whereas low mass haloes show strong, $\ensuremath{\sim}5%--10%$, suppression over the range $0.05lk[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]l0.15$. These results were primarily established through the use of the cross-power spectrum of dark matter and haloes, which circumvents the thorny issue of shot-noise correction. The halo-halo power spectrum, however, is highly sensitive to the shot-noise correction; we show that halo exclusion effects make this sub-Poissonian and a new correction is presented. Our results have special relevance for studies of the baryon acoustic oscillation features in the halo power spectra. Nonlinear mode-mode coupling: (i) damps these features on progressively larger scales as halo mass increases; (ii) produces small shifts in the positions of the peaks and troughs which depend on halo mass. We show that these effects on halo clustering are important over the redshift range relevant to such studies $(0lzl2)$, and so will need to be accounted for when extracting information from precision measurements of galaxy clustering. Our analytic model is described in the language of the ``halo model.'' The halo-halo clustering term is propagated into the nonlinear regime using ``1-loop'' perturbation theory and a nonlinear halo bias model. Galaxies are then inserted into haloes through the halo occupation distribution. We show that, with nonlinear bias parameters derived from simulations, this model produces predictions that are qualitatively in agreement with our numerical results. We then use it to show that the power spectra of red and blue galaxies depend differently on scale, thus underscoring the fact that proper modeling of nonlinear bias parameters will be crucial to derive reliable cosmological constraints. In addition to showing that the bias on very large scales is not simply linear, the model also shows that the halo-halo and halo-dark matter spectra do not measure precisely the same thing. This complicates interpretation of clustering in terms of the stochasticity of bias. However, because the shot-noise correction is nontrivial, evidence for this in the simulations is marginal.

Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum

Abstract: Statistical isotropy of primordial perturbations is a common assumption in cosmology, but it is an assumption that should be tested. To this end, we develop cosmic microwave background statistics for a primordial power spectrum that depends on the direction, as well as the magnitude, of the Fourier wave vector. We first consider a simple estimator that searches in a model-independent way for anisotropy in the square of the temperature (and/or polarization) fluctuation. We then construct the minimum-variance estimators for the coefficients of a spherical-harmonic expansion of the directional dependence of the primordial power spectrum. To illustrate, we apply these statistics to an inflation model with a quadrupole dependence of the primordial power spectrum on direction and find that a power quadrupole as small as 2.0% can be detected with the Planck satellite.

Spectral Exponents of Kinetic and Magnetic Energy Spectra in Solar Wind Turbulence

Abstract: Kinetic and magnetic energy spectra in the ecliptic plane near 1 AU are found to exhibit different power-law behaviors in the inertial range, with the magnetic spectrum often having a power-law exponent near 5/3 and the kinetic energy spectrum often having a power-law exponent near 3/2 (the inertial range extends from approximately 5 × 10-4 to 10-1 Hz). The total energy, kinetic plus magnetic, has a power-law exponent that lies between 3/2 and 5/3, with a value near 1.6. The Alfven ratio, the ratio of kinetic to magnetic energy, is found to be a slowly increasing function of frequency in the inertial range, increasing from roughly 0.5 to 0.9 in the frequency range from 10-3 to 10-1 Hz. These conclusions are based on the analysis of four distinct time intervals of solar wind magnetic field and plasma data obtained by the Wind spacecraft near the end of solar cycle 22 and at different times throughout solar cycle 23. Three 54 day intervals and one 81 day interval are used to compute power spectra in the range from 10-5 to 1.7 × 10-1 Hz. Power-law exponents are estimated from linear least-squares fits to the logarithm of the power spectral density versus the logarithm of the frequency over the frequency interval from 10-3 to 10-2 Hz. To prevent errors due to spectral aliasing, the last decade of the spectrum is omitted from the calculation of the power-law exponents. The results show that a measurable difference exists between the power-law exponents of velocity and magnetic field fluctuations and that this difference persists throughout the solar cycle.

Joint Bayesian component separation and CMB power spectrum estimation

Abstract: We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are 1) conditional sampling of foreground spectral parameters, and 2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground-CMB posterior distribution, and therefore all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multi-resolution observations. To verify the method, we analyse simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3-yr WMAP data, downgraded to a common resolution of 3 degree FWHM. The results from the actual 3-yr WMAP temperature analysis are presented in a companion Letter.

Simulation of Nonstationary Stochastic Processes by Spectral Representation

Abstract: This paper presents a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly's evolutionary spectral representation theory. Applying this formula, sample functions can be generated with great computational efficiency. The simulated stochastic process is asymptotically Gaussian as the number of terms tends to infinity. This paper shows that (1) these sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number of terms in the cosine series is large, i.e., the ensemble averaged evolutionary power spectral density function (PSDF) or autocorrelation function approaches the corresponding target function as the sample size increases, and (2) the simulation formula, under certain conditions, can be reduced to that for nonstationary white noise process or Shinozuka's spectral representation of stationary process. In addition to derivation of simulation formula, three methods are developed in this paper to estimate the evolutionary PSDF of a given time-history data by means of the short-time Fourier transform (STFT), the wavelet transform (WT), and the Hilbert-Huang transform (HHT). A comparison of the PSDF of the well-known El Centro earthquake record estimated by these methods shows that the STFT and the WT give similar results, whereas the HHT gives more concentrated energy at certain frequencies. Effectiveness of the proposed simulation formula for nonstationary sample functions is demonstrated by simulating time histories from the estimated evolutionary PSDFs. Mean acceleration spectrum obtained by averaging the spectra of generated time histories are then presented and compared with the target spectrum to demonstrate the usefulness of this method.

Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence

Abstract: Atmospheric turbulence induces significant variation on the angle-of-arrival of laser beams used in free space laser communication. Angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture can be described in terms of the phase structure function that already has been calculated by Kolmogorov's power spectral density model. Unfortunately several experiments showed that Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly. In this paper, for horizontal path and weak turbulence, we carry out analysis of angle-of-arrival fluctuations using a non Kolmogorov power spectrum which uses a generalized exponent factor instead of constant standard exponent value 11/3 and a generalized amplitude factor instead of constant value 0.033. Also our non Kolmogorov spectrum includes both inner scale and outer scale effects.

Asymptotic spectral theory for nonlinear time series

Abstract: We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.

Dark matter clustering: a simple renormalization group approach

Abstract: I compute a renormalization group (RG) improvement to the standard beyond-linear-order Eulerian perturbation theory (PT) calculation of the power spectrum of large-scale density fluctuations in the Universe. At $z=0$, for a power spectrum matching current observations, lowest order RGPT appears to be as accurate as one can test using existing numerical simulation-calibrated fitting formulas out to at least $k\ensuremath{\simeq}0.3h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$; although inaccuracy is guaranteed at some level by approximations in the calculation (which can be improved in the future). In contrast, standard PT breaks down virtually as soon as beyond-linear corrections become non-negligible, on scales even larger than $k=0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. This extension in range of validity could substantially enhance the usefulness of PT for interpreting baryonic acoustic oscillation surveys aimed at probing dark energy, for example. I show that the predicted power spectrum converges at high $k$ to a power law with index given by the fixed-point solution of the RG equation. I discuss many possible future directions for this line of work. The basic calculation of this paper should be easily understandable without any prior knowledge of RG methods, while a rich background of mathematical physics literature exists for the interested reader.

Blind Calibration of Timing Offsets for Four-Channel Time-Interleaved ADCs

Abstract: In this paper, we describe a blind calibration method for timing mismatches in a four-channel time-interleaved analog-to-digital converter (ADC). The proposed method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the four ADC subchannels contain only three alias components, instead of four. Then the matrix power spectral density (PSD) of the ADC subchannels is rank deficient over this frequency band. Accordingly, when the timing offsets are known, we can construct a filter bank that nulls the vector signal at the ADC outputs. We employ a parametrization of this filter bank to develop an adaptive null steering algorithm for estimating the ADC timing offsets. The null steering filter bank employs seven fixed finite-impulse response filters and three unknown timing offset parameters which are estimated by using an adaptive stochastic gradient technique. A convergence analysis is presented for the blind calibration method. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed technique

21 cm angular-power spectrum from the dark ages

Abstract: At redshifts z > or approx. 30 neutral hydrogen gas absorbs cosmic microwave background radiation at the 21 cm spin-flip frequency. In principle this is observable and a high-precision probe of cosmology. We calculate the linear-theory angular-power spectrum of this signal and cross correlation between redshifts on scales much larger than the linewidth. In addition to the well-known redshift distortion and density perturbation sources, a full linear analysis gives additional contributions to the power spectrum. On small scales there is a percent-level linear effect due to perturbations in the 21 cm optical depth, and perturbed recombination modifies the gas temperature perturbation evolution (and hence spin temperature and 21 cm power spectrum). On large scales there are several post-Newtonian and velocity effects; although negligible on small scales, these additional terms can be significant at l < or approx. 100 and can be nonzero even when there is no background signal. We also discuss the linear effect of reionization rescattering, which damps the entire spectrum and gives a very small polarization signal on large scales. On small scales we also model the significant nonlinear effects of evolution and gravitational lensing. We include full results for numerical calculation and also various approximate analyticmore » results for the power spectrum and evolution of small-scale perturbations.« less

Fluctuations and Rheology in Active Bacterial Suspensions

Abstract: We probe nonequilibrium properties of an active bacterial bath through measurements of correlations of passive tracer particles and the response function of a driven, optically trapped tracer. These measurements demonstrate violation of the fluctuation-dissipation theorem and enable us to extract the power spectrum of the active stress fluctuations. In some cases, we observe $1/\sqrt{\ensuremath{\omega}}$ scaling in the noise spectrum which we show can be derived from a theoretical model incorporating coupled stress, orientation, and concentration fluctuations of the bacteria.

Multiple inflation and the WMAP 'glitches' II. Data analysis and cosmological parameter extraction

Abstract: Detailed analyses of the WMAP data indicate possible oscillatory features in the primordial curvature perturbation, which moreover appears to be suppressed beyond the present Hubble radius. Such deviations from the usual inflationary expectation of an approximately Harrison-Zeldovich spectrum are expected in the supergravity-based ``multiple inflation'' model wherein phase transitions during inflation induce sudden changes in the mass of the inflaton, thus interrupting its slow roll. In a previous paper we calculated the resulting curvature perturbation and showed how the oscillations arise. Here we perform a Markov chain Monte Carlo fitting exercise using the 3-year WMAP data to determine how the fitted cosmological parameters vary when such a primordial spectrum is used as an input, rather than the usually assumed power-law spectrum. The concordance $\ensuremath{\Lambda}\mathrm{CDM}$ model is still a good fit when there is just a step in the spectrum. However, if there is a bump in the spectrum (due e.g. to two phase transitions in rapid succession), the precision cosmic microwave background data can be well fitted by a flat Einstein-de Sitter cosmology without dark energy. This however requires the Hubble constant to be $h\ensuremath{\simeq}0.44$ which is lower than the locally measured value. To fit the Sloane Digital Sky Survey data on the power spectrum of galaxy clustering requires a $\ensuremath{\sim}10%$ component of hot dark matter, as would naturally be provided by 3 species of neutrinos of mass $\ensuremath{\sim}0.5\text{ }\text{ }\mathrm{eV}$. This $\mathrm{\text{cold}}+\mathrm{\text{hot dark matter}}$ model cannot however fit the position of the baryon acoustic peak in the luminous red galaxies redshift two-point correlation function. It may be possible to overcome these difficulties in an inhomogeneous Lema\^{\i}tre-Tolman-Bondi cosmological model with a local void, which can potentially also account for the SN Ia Hubble diagram without invoking cosmic acceleration.

Fourier transform wavefront control with adaptive prediction of the atmosphere

Abstract: Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48×48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2×109 floating-point operations/s.

Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere.

Abstract: We report analytic formulas for the elements of the e 2 X2 cross-spectral density matrix of a stochastic electromagnetic anisotropic beam propagating through the turbulent atmosphere with the help of vector integration. From these formulas the changes in the spectral density (spectrum), in the spectral degree of polarization, and in the spectral degree of coherence of such a beam on propagation are determined. As an example, these quantities are calculated for a so-called anisotropic electromagnetic Gaussian Schell-model beam propagating in the isotropic and homogeneous atmosphere. In particular, it is shown numerically that for a beam of this class, unlike for an isotropic electromagnetic Gaussian Schell-model beam, its spectral degree of polarization does not return to its value in the source plane after propagating at sufficiently large distances in the atmosphere. It is also shown that the spectral degree of coherence of such a beam tends to zero with increasing distance of propagation through the turbulent atmosphere, in agreement with results previously reported for isotropic beams.

Probing dark energy with cluster counts and cosmic shear power spectra: including the full covariance

Abstract: Several dark energy experiments are available from a single large-area imaging survey and may be combined to improve cosmological parameter constraints and/or test inherent systematics. Two promising experiments are cosmic shear power spectra and counts of galaxy clusters. However, the two experiments probe the same cosmic mass density field in large-scale structure, therefore the combination may be less powerful than first thought.We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance, as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l~103 and the cluster counts containing halos with masses M1014 M⊙. Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise (S/N) ratios up to ~±20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss the fact that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold ((S/N)cluster~6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone.

Minimum-Variance Multitaper Spectral Estimation on the Sphere

Abstract: We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when only a portion of the data are available for analysis, or estimating the power spectrum from local data under the assumption that the data are locally stationary in a specified region. Restricting a global function to a spatial subdomain—whether by necessity or by design—is a windowing operation, and an equation like a convolution in the spectral domain relates the expected value of the windowed power spectrum to the underlying global power spectrum and the known power spectrum of the localization window. The best windows for the purpose of localized spectral analysis have their energy concentrated in the region of interest while possessing the smallest effective bandwidth as possible. Solving an optimization problem in the sense of Slepian (1960) yields a family of orthogonal windows of diminishing spatiospectral localization, the best concentrated of which we propose to use to form a weighted multitaper spectrum estimate in the sense of Thomson (1982). Such an estimate is both more representative of the target region and reduces the estimation variance when compared to estimates formed by any single bandlimited window. We describe how the weights applied to the individual spectral estimates in forming the multitaper estimate can be chosen such that the variance of the estimate is minimized.

Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization

Abstract: We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior, data likelihood, and numerical inverse extra-regularization schemes are derived and classified. The Bayesian methodology presented in this paper tries to unify and extend the following methods: Wiener-filtering, Tikhonov regularization, Ridge regression, Maximum Entropy, and inverse regularization techniques. The inverse techniques considered here are the asymptotic regularization, the Jacobi, Steepest Descent, Newton-Raphson, Landweber-Fridman, and both linear and non-linear Krylov methods based on Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The structures of the up-to-date highest-performing algorithms are presented, based on an operator scheme, which permits one to exploit the power of fast Fourier transforms. Using such an implementation of the generalized Wiener-filter in the novel ARGO-software package, the different numerical schemes are benchmarked with 1-, 2-, and 3-dimensional problems including structured white and Poissonian noise, data windowing and blurring effects. A novel numerical Krylov scheme is shown to be superior in terms of performance and fidelity. These fast inverse methods ultimately will enable the application of sampling techniques to explore complex joint posterior distributions. We outline how the space of the dark-matter density field, the peculiar velocity field, and the power spectrum can jointly be investigated by a Gibbs-sampling process. Such a method can be applied for the redshift distortions correction of the observed galaxies and for time-reversal reconstructions of the initial density field.

Astrophysical effects of scalar dark matter miniclusters

Abstract: We model the formation, evolution and astrophysical effects of dark compact Scalar Miniclusters (``ScaMs''). These objects arise when a scalar field, with an axion-like or Higgs-like potential, undergoes a second-order phase transition below the QCD scale. Such a scalar field may couple too weakly to the standard model to be detectable directly through particle interactions, but may still be detectable by gravitational effects, such as lensing and baryon accretion by large, gravitationally bound miniclusters. The masses of these objects are shown to be constrained by the $\mathrm{Ly}\ensuremath{\alpha}$ power spectrum to be less than $\ensuremath{\sim}{10}^{4}{M}_{\ensuremath{\bigodot}}$, but they may be as light as classical axion miniclusters, of the order of ${10}^{\ensuremath{-}12}{M}_{\ensuremath{\bigodot}}$. We simulate the formation and nonlinear gravitational collapse of these objects around matter-radiation equality using an $N$-body code, estimate their gravitational lensing properties, and assess the feasibility of studying them using current and future lensing experiments. Future MACHO-type variability surveys of many background sources can reveal either high-amplification, strong-lensing events, or measure density profiles directly via weak-lensing variability, depending on ScaM parameters and survey depth. However, ScaMs, due to their low internal densities, are unlikely to be responsible for apparent MACHO events already detected in the Galactic halo. As a result, in the entire window between ${10}^{\ensuremath{-}7}{M}_{\ensuremath{\bigodot}}$ and ${10}^{2}{M}_{\ensuremath{\bigodot}}$ covered by the galactic scale lensing experiments, ScaMs may in fact compose all the dark matter. A simple estimate is made of parameters that would give rise to early structure formation; in principle, early stellar collapse could be triggered by ScaMs as early as recombination, and significantly affect cosmic reionization.

Equilibrium and Nonequilibrium Dynamics of the Sub-Ohmic Spin-Boson Model

Abstract: Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density $J(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, $s\ensuremath{\ll}1$, weakly damped coherent oscillations on short time scales are possible even in the localized phase---this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.

The multifrequency angular power spectrum of the epoch of reionization 21-cm signal

Abstract: Observations of redshifted 21cm radiation from neutral hydrogen (HI) at high redshifts is an important future probe of reionization. We consider the Multi-frequency Angular Power Spectrum (MAPS) to quantify the statistics of the HI signal as a joint function of the angular multipole l and frequency separation �ν. The signal at two different frequencies is expected to decorrelate as �ν is increased, and quantifying this is particularly importa nt in deciding the frequency resolution for future HI observations. This is al so expected to play a very crucial role in extracting the signal from foregrounds as the signal is expected to decorrelate much faster than the foregrounds (which are largely continuum sources) with increasing �ν. In this paper we develop formulae relating MAPS to different components of the three dimensional HI power spectrum taking into account HI peculiar velocities. We show that the flat-sky approximation provides a very good representation over the angular scales of interest, and a final expression which is very simple to calculate and in terpret. We present results for z = 10 assuming a neutral hydrogen fraction of 0.6 considering two models for the HI distribution, namely, (i) DM: where the HI traces the dark matter and (ii) PR: where the effects of patchy reionization are incorporated through two parameters which are the bubble size and the clustering of the bubble centers relative to the dark mat ter (bias) respectively. We find that while the DM signal is largely featureless, the PR signal peaks at the angular scales of the individual bubbles where it is Poisson fluctuation dominate d, and the signal is considerably enhanced for large bubble size. For most cases of interest at l � 100 the signal is uncorrelated beyond �ν � 1MHz or even less, whereas this occurs around � 0.1MHz at l � 10 3 . The �ν dependence also carries an imprint of the bubble size and the bias, and is expected to be an important probe of the reionization scenario. Finally we find that the l range 10 3 10 4 is optimum for separating out the cosmological HI signal from the foregrounds, while this will be extremely demanding at l < 100 where it is necessary to characterize the �ν dependence of the foreground MAPS to an accuracy better than 1%.

A Nonstationary Model of Newborn EEG

Abstract: The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and nonstationary nature. The model consists of background and seizure submodels. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models have a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively)

Upper Limit map of a background of gravitational waves

Abstract: We searched for an anisotropic background of gravitational waves using data from the LIGO S4 science run and a method that is optimized for point sources. This is appropriate if, for example, the gravitational wave background is dominated by a small number of distinct astrophysical sources. No signal was seen. Upper limit maps were produced assuming two different power laws for the source strain power spectrum. For an f^(−3) power law and using the50 Hz to 1.8 kHz band the upper limits on the source strain power spectrum vary between 1.2×10^(−48) Hz^(−1) (100 Hz/f)^3 and 1.2×10^(−47) Hz^(−1) (100 Hz/f)^3, depending on the position in the sky. Similarly, in the case of constant strain power spectrum, the upper limits vary between 8.5×10−49 Hz−1 and 6.1×10^(−48) Hz^(−1). As a side product a limit on an isotropic background of gravitational waves was also obtained. All limits are at the 90% confidence level. Finally, as an application, we focused on the direction of Sco-X1, the brightest low-mass x-ray binary. We compare the upper limit on strain amplitude obtained by this method to expectations based on the x-ray flux from Sco-X1.

Prospects of inflation in delicate D-brane cosmology

Abstract: We study D-brane inflation in a warped conifold background that includes brane-position dependent corrections for the nonperturbative superpotential. Instead of stabilizing the volume modulus $\ensuremath{\chi}$ at instantaneous minima of the potential and studying the inflation dynamics with an effective single field (radial distance between a brane and an antibrane) $\ensuremath{\phi}$, we investigate the multifield inflation scenario involving these two fields. The two-field dynamics with the potential $V(\ensuremath{\phi},\ensuremath{\chi})$ in this model is significantly different from the effective single-field description in terms of the field $\ensuremath{\phi}$ when the field $\ensuremath{\chi}$ is integrated out. The latter picture underestimates the total number of e-foldings even by 1 order of magnitude. We show that a correct single-field description is provided by a field $\ensuremath{\psi}$ obtained from a rotation in the two-field space along the background trajectory. This model can give a large number of e-foldings required to solve flatness and horizon problems at the expense of fine-tunings of model parameters. We also estimate the spectra of density perturbations and show that the slow-roll parameter ${\ensuremath{\eta}}_{\ensuremath{\psi}\ensuremath{\psi}}={M}_{\mathrm{pl}}^{2}{V}_{,\ensuremath{\psi}\ensuremath{\psi}}/V$ in terms of the rotated field $\ensuremath{\psi}$ determines the spectral index of scalar metric perturbations. We find that it is generally difficult to satisfy, simultaneously, both constraints of the spectral index and the cosmic background explorer normalization, while the tensor to scalar ratio is sufficiently small to match with observations.

Statistical properties of dust far-infrared emission

Abstract: Context. Far-infrared dust emission has a self-similar structure which reveals the complex dynamical processes that shape the interstellar medium. The description of the statistical properties of this emission gives important constraints on the physics of the interstellar medium but it is also a useful way to estimate the contamination of diffuse interstellar emission in the cases where it is considered a nuisance. Aims. The main goals of this analysis of the power spectrum and non-Gaussian properties of far-infrared dust emission are 1) to estimate the power spectrum of interstellar matter density in three dimensions; 2) to review and extend previous estimates of the cirrus noise due to dust emission; and 3) to produce simulated dust emission maps that reproduce the observed statistical properties. Methods. To estimate the statistical properties of dust emission we analyzed the power spectrum and wavelet decomposition of 100 μ m IRIS data (an improved version of the IRAS data) over 55% of the sky. The simulation of realistic infrared emission maps is based on modified Gaussian random fields. Results. The main results are the following. 1) The cirrus noise level as a function of brightness has been previously overestimated. It is found to be proportional to $\langle I\rangle $ instead of $\langle I\rangle^{1.5}$, where $\langle I\rangle $ is the local average brightness at 100 μ m. This scaling is in accordance with the fact that the brightness fluctuation level observed at a given angular scale on the sky is the sum of fluctuations of increasing amplitude with distance on the line of sight. 2) The spectral index of dust emission at scales between 5 arcmin and 12.5° is $\langle\gamma\rangle=-2.9$ on average but shows significant variations over the sky. Bright regions have systematically steeper power spectra than diffuse regions. 3) The skewness and kurtosis of brightness fluctuations are high, indicative of strong non-Gaussianity. Unlike the standard deviation of the fluctuations, the skewness and kurtosis do not depend significantly on brightness, except in bright regions (>10 MJy sr -1 ) where they are systematically higher, probably due to contrasted structures related to star formation activity. 4) Based on our characterization of the 100 μ m power spectrum we provide a prescription of the cirrus confusion noise as a function of wavelength and scale. 5) Finally we present a method based on a modification of Gaussian random fields to produce simulations of dust maps which reproduce the power spectrum and non-Gaussian properties of interstellar dust emission.

Features in the Primordial Spectrum from WMAP: A Wavelet Analysis

Abstract: Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [A. Shafieloo and T. Souradeep, Phys. Rev. D 70, 043523 (2004).], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, 'best fit' scale free spectra ({delta}lnL{approx_equal}25 with respect to the Harrison-Zeldovich spectrum, and, {delta}lnL{approx_equal}11 with respect to the power law spectrum with n{sub s}=0.95). In this paper we use the discrete wavelet transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infrared cutoff at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.