Power Spectrum Of Data Research Articles

Putting the precision in precision cosmology: How accurate should your data covariance matrix be?

Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of parameter estimation is limited by the accuracy of the inverse data covariance matrix - the precision matrix. If the data covariance and precision matrices are estimated by sampling independent realisations of the data, their statistical properties are described by the Wishart and Inverse-Wishart distributions, respectively. Independent of any details of the survey, we show that the fractional error on a parameter variance, or a Figure-of-Merit, is equal to the fractional variance of the precision matrix. In addition, for the only unbiased estimator of the precision matrix, we find that the fractional accuracy of the parameter error depends only on the difference between the number of independent realisations and the number of data points, and so can easily diverge. For a 5% error on a parameter error and N_D << 100 data-points, a minimum of 200 realisations of the survey are needed, with 10% accuracy for the data covariance. If the number of data-points N_D >>100 we need N_S > N_D realisations and a fractional accuracy of <sqrt[2/N_D] in the data covariance. As the number of power spectra data points grows to N_D>10^4 -10^6 this approach will be problematic. We discuss possible ways to relax these conditions: improved theoretical modelling; shrinkage methods; data-compression; simulation and data resampling methods.

Experimental Validation of Roughness Power Spectrum-Based Theory of Anomalous Cottrell Response

We experimentally validate theoretical relation between the roughness power spectrum (PS) and electrochemical current transient for a reversible charge transfer system under a single potential step. Roughness features at the electrochemically roughened electrode are characterized using standard measurements such as scanning electron microscopy (SEM), atomic force microscopy (AFM) and cyclic voltammetry (CV). The PS obtained from AFM shows composite finite fractal and nonfractal nature in roughness, whereas the PS from SEM shows only a finite fractal nature. AFM or SEM measurements provide knowledge of fractal dimension (DH) and two fractal cutoff lengths (landL). Topothesy length (lτ) or the related proportionality factor (μ≡lτ2DH−3) from PS data of AFM requires extrapolation of data for unit wavenumber, but this method usually provides unphysical values of μ. We provide a novel method to determine the topothesy of electrodes from CV measurements of electroactive area in conjunction with SEM or AFM measur...

Neuronal avalanches in the resting MEG of the human brain.

What constitutes normal cortical dynamics in healthy human subjects is a major question in systems neuroscience. Numerous in vitro and in vivo animal studies have shown that ongoing or resting cortical dynamics are characterized by cascades of activity across many spatial scales, termed neuronal avalanches. In experiment and theory, avalanche dynamics are identified by two measures: (1) a power law in the size distribution of activity cascades with an exponent of -3/2 and (2) a branching parameter of the critical value of 1, reflecting balanced propagation of activity at the border of premature termination and potential blowup. Here we analyzed resting-state brain activity recorded using noninvasive magnetoencephalography (MEG) from 124 healthy human subjects and two different MEG facilities using different sensor technologies. We identified large deflections at single MEG sensors and combined them into spatiotemporal cascades on the sensor array using multiple timescales. Cascade size distributions obeyed power laws. For the timescale at which the branching parameter was close to 1, the power law exponent was -3/2. This relationship was robust to scaling and coarse graining of the sensor array. It was absent in phase-shuffled controls with the same power spectrum or empty scanner data. Our results demonstrate that normal cortical activity in healthy human subjects at rest organizes as neuronal avalanches and is well described by a critical branching process. Theory and experiment have shown that such critical, scale-free dynamics optimize information processing. Therefore, our findings imply that the human brain attains an optimal dynamical regime for information processing.

∊-Machine spectral reconstruction theory: a direct method for inferring planar disorder and structure from X-ray diffraction studies

In previous publications [Varn et al. (2002). Phys. Rev. B, 66, 174110; Varn et al. (2007). Acta Cryst. B63, 169-182] we introduced and applied a new technique for discovering and describing planar disorder in close-packed structures directly from their diffraction patterns. Here, we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. We show that the resulting statistical model of the stacking structure - called the ε-machine - allows the calculation of measures of memory, structural complexity and configurational entropy. The methods developed here can be adapted to a wide range of experimental systems in which power spectra data are available.

A global fit study on the new agegraphic dark energy model

We perform a global fit study on the new agegraphic dark energy (NADE) model in a non-flat universe by using the MCMC method with the full CMB power spectra data from the WMAP 7-yr observations, the SNIa data from Union2.1 sample, BAO data from SDSS DR7 and WiggleZ Dark Energy Survey, and the latest measurements of $H_0$ from HST. We find that the value of $\Omega_{k0}$ is greater than 0 at least at the 3$\sigma$ confidence levels (CLs), which implies that the NADE model distinctly favors an open universe. Besides, our results show that the value of the key parameter of NADE model, $n=2.673^{+0.053+0.127+0.199}_{-0.077-0.151-0.222}$, at the 1--3$\sigma$ CLs, where its best-fit value is significantly smaller than those obtained in previous works. We find that the reason leading to such a change comes from the different SNIa samples used. Our further test indicates that there is a distinct tension between the Union2 sample of SNIa and other observations, and the tension will be relieved once the Union2 sample is replaced by the Union2.1 sample. So, the new constraint result of the NADE model obtained in this work is more reasonable than before.

Constraints on primordial gravitational waves with variable sound speed from current CMB data

We make a comprehensive investigation of the observational effect of the inflation consistency relation. We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ from the Five-Year WMAP observations. We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When taking smaller values of $c_s$, the positive correlation between $r$ and $n_s$ also leads to slightly tighter constraint on the upper bound of $n_s$, while the running of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For the sound speed $c_s$, it is not well constrained if only the CMB power spectrum data is used, while the constraints are obtainable by taking $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ priors into account. With the constraining data of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$, we find that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$ case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL. In addition, the inclusion of $f_{\rm NL}^{\rm equil.}$ and $f_{\rm NL}^{\rm orth.}$ into the analysis can improve the constraints on $r$ and $n_s$. We further discuss the implications of our constraints on the test of inflation models.

The WiggleZ Dark Energy Survey: Final data release and cosmological results

This paper presents cosmological results from the final data release of the WiggleZ Dark Energy Survey. We perform full analyses of different cosmological models using the WiggleZ power spectra measured at z=0.22, 0.41, 0.60, and 0.78, combined with other cosmological datasets. The limiting factor in this analysis is the theoretical modelling of the galaxy power spectrum, including non-linearities, galaxy bias, and redshift-space distortions. In this paper we assess several different methods for modelling the theoretical power spectrum, testing them against the Gigaparsec WiggleZ simulations (GiggleZ). We fit for a base set of 6 cosmological parameters, {Omega_b h^2, Omega_CDM h^2, H_0, tau, A_s, n_s}, and 5 supplementary parameters {n_run, r, w, Omega_k, sum m_nu}. In combination with the Cosmic Microwave Background (CMB), our results are consistent with the LambdaCDM concordance cosmology, with a measurement of the matter density of Omega_m =0.29 +/- 0.016 and amplitude of fluctuations sigma_8 = 0.825 +/- 0.017. Using WiggleZ data with CMB and other distance and matter power spectra data, we find no evidence for any of the extension parameters being inconsistent with their LambdaCDM model values. The power spectra data and theoretical modelling tools are available for use as a module for CosmoMC, which we here make publicly available at http://smp.uq.edu.au/wigglez-data . We also release the data and random catalogues used to construct the baryon acoustic oscillation correlation function.

Frequency domain subspace-based identification of discrete-time singular power spectra

In this paper, we propose a subspace algorithm for the identification of linear-time-invariant discrete-time systems with more outputs than inputs from measured power spectrum data. The proposed identification algorithm is interpolatory and strongly consistent when the corruptions in the spectrum measurements have a bounded covariance function. Asymptotic performance and the interpolation properties of the proposed algorithm are illustrated by means of a numerical example.

Sleep Disturbance After Mild Traumatic Brain Injury: Indicator of Injury?

Mild traumatic brain injury (mTBI) is a complex entity with no known objective diagnostic markers. To test the hypothesis that sleep disturbances in the acute mTBI period can serve as an indicator of brain injury, the authors compared sleep polysomnograms (PSG) and sleep EEG power spectra (PS) data in seven mTBI subjects with seven age- and race-matched healthy-control subjects. The two groups differed significantly on PS measures, suggesting that mTBI can result in a disruption of sleep microarchitecture and, in theory, could be of use as a marker for brain injury. These pilot findings need to be replicated on larger samples.

Sleep Disturbance After Mild Traumatic Brain Injury: Indicator of Injury?

Mild traumatic brain injury (mTBI) is a complex entity with no known objective diagnostic markers. To test the hypothesis that sleep disturbances in the acute mTBI period can serve as an indicator of brain injury, the authors compared sleep polysomnograms (PSG) and sleep EEG power spectra (PS) data in seven mTBI subjects with seven age- and race-matched healthy-control subjects. The two groups differed significantly on PS measures, suggesting that mTBI can result in a disruption of sleep microarchitecture and, in theory, could be of use as a marker for brain injury. These pilot findings need to be replicated on larger samples.

The angular power spectra of photometric Sloan Digital Sky Survey luminous red galaxies

We construct new galaxy angular power spectra based on the extended, updated and final SDSS II Luminous Red Galaxy (LRG) photometric redshift survey: MegaZ DR7. Encapsulating 7746 deg^{2} we utilise 723,556 photometrically determined LRGs between 0.45 < z < 0.65 in a 3.3 (Gpc h^{-1})^3 spherical harmonic analysis of the galaxy distribution. By combining four photometric redshift bins we find preliminary parameter constraints of f_{b} = \Omega_{b}/\Omega_{m} = 0.173 +/- 0.046 and \Omega_{m} = 0.260 +/- 0.035 assuming H_{0} = 75 km s^{-1} Mpc^{-1}, n_{s}=1 and \Omega_{k} = 0. These limits are consistent with the CMB and the previous data release (DR4). The C_{\ell} are sensitive to redshift space distortions and therefore we also recast our constraints into a measurement of \beta ~ \Omega_{m}^{0.55}/b in different redshift shells. The robustness of these power spectra with respect to a number of potential systematics such as extinction, photometric redshift and ANNz training set extrapolation are examined. The latter includes a cosmological comparison of available photometric redshift estimation codes where we find excellent agreement between template and empirical estimation methods. MegaZ DR7 represents a methodological prototype to next generation surveys such as the Dark Energy Survey (DES) and, furthermore, is a photometric precursor to the spectroscopic BOSS survey. Our galaxy catalogue and all power spectra data can be found at http://zuserver2.star.ucl.ac.uk/~sat/MegaZ/MegaZDR7.tar.gz.

Frequency domain subspace-based identification of discrete-time power spectra from uniformly spaced measurements

In this paper, we revisit the problem of identifying multi-input/multi-output linear-time-invariant discrete-time systems from measured power spectrum data on uniform grids of frequencies studied by Van Overschee, De Moor, Dehandschutter, and Swevers (1997). We show that the algorithm proposed by these authors is not consistent. Then, we propose an interpolatory identification algorithm which is strongly consistent when the corruptions in the spectrum measurements have a bounded covariance function. The performance of the proposed algorithm is demonstrated in a simulation example.

Sunyaev-Zel’dovich galaxy clusters number counts: consequences of cluster scaling-law evolution

Galaxy cluster surveys based on the Sunyaev-Zeldovich effect (SZE) mapping are expected from ongoing experiments. Such surveys are anticipated to provide a significant amount of information relevant to cosmology from the number counts redshift distribution. We carry out an estimation of predicted SZE counts and their redshift distribution taking into account the current cosmological constraints and the X-ray cluster temperature distribution functions. Comparison between local and distant cluster temperature distribution functions provides evidence for an evolution in the abundance of X-ray clusters that is not consistent with the use of standard scaling relations of cluster properties in the framework of the current concordance model. The hypothesis of some evolution of the scaling law driven by non-gravitational processes is a natural solution to this problem. We perform a MCMC statistical study using COSMOMC, combining current CMB observations from WMAP, the SNIa Hubble diagram, the galaxy power spectrum data from SDSS and X-ray clusters temperature distributions to predict SZE cluster number counts. Models reproducing well the X-ray cluster temperature distribution function evolution lead to a significantly lower SZE clusters number counts with a distinctive redshift distribution. Ongoing microwave SZE surveys will therefore shed new light on intracluster gas physics and greatly help to identify the role of possible non-gravitational physics in the history of the hot gas component of x-ray clusters.

Cosmic microwave background with Brans-Dicke gravity. II. Constraints with the WMAP and SDSS data

Using the covariant formalism developed in a companion paper (paper I), we derive observational constraint on the Brans-Dicke model in a flat FLRW universe with cosmological constant and cold dark matter. The CMB observations we use include the WMAP five year data, the ACBAR 2007 data, the CBI polarization data, and the BOOMERanG 2003 flight data. For the large scale structure we use the matter power spectrum data measured with the LRG survey of the SDSS DR4. We parameterize the Brans-Dicke parameter $\omega$ with a new parameter $\zeta=\ln(1/\omega+1)$, and use the Markov-Chain Monte Carlo method to explore the parameter space. We find that using CMB data alone, one could place some constraint on positive $\zeta$ or $\omega$, but negative $\zeta$ or $\omega$ could not be constrained effectively. However, with additional large scale structure data, one could break the degeneracy at $\zeta<0$. The $2\sigma$ (95.5%) bound on $\zeta$ is $-0.00837<\zeta<0.01018$ (corresponding to $\omega < -120.0$ or $\omega > 97.8$). We also obtained constraint on $\dot{G}/G$, the rate of change of $G$ at present, as $-1.75 \times 10^{-12} \yr^{-1}<\dot{G}/G < 1.05 \times 10^{-12}\yr^{-1}$, and $\delta G/G$, the total variation of $G$ since the epoch of recombination, as $ -0.083 < \delta{G}/G < 0.095$ at $2\sigma$ confidence level.

Constraints on primordial non-Gaussianity from WMAP7 and luminous red galaxies power spectrum and forecast for future surveys

We place new constraints on the primordial local non-Gaussianity parameter ${f}_{\mathrm{NL}}$ using recent cosmic microwave background anisotropy and galaxy clustering data. We model the galaxy power spectrum according to the halo model, accounting for a scale-dependent bias correction proportional to ${f}_{\mathrm{NL}}/{k}^{2}$. We first constrain ${f}_{\mathrm{NL}}$ in a full 13 parameters analysis that includes 5 parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB data and the SDSS DR4 galaxy power spectrum, we find ${f}_{\mathrm{NL}}={171}_{\ensuremath{-}139}^{+140}$ at 68% C.L. and $\ensuremath{-}69&lt;{f}_{\mathrm{NL}}&lt;+492$ at 95% C.L. We discuss the degeneracies between ${f}_{\mathrm{NL}}$ and other cosmological parameters. Including SN-Ia data and priors on ${H}_{0}$ from Hubble Space Telescope observations we find a stronger bound: $\ensuremath{-}35&lt;{f}_{\mathrm{NL}}&lt;+479$ at 95%. We also fit the more recent SDSS DR7 halo power spectrum data finding, for a $\ensuremath{\Lambda}\mathrm{CDM}+{f}_{\mathrm{NL}}$ model, ${f}_{\mathrm{NL}}=\ensuremath{-}93\ifmmode\pm\else\textpm\fi{}128$ at 68% C.L. and $\ensuremath{-}327&lt;{f}_{\mathrm{NL}}&lt;+177$ at 95% C.L. We finally forecast the constraints on ${f}_{\mathrm{NL}}$ from future surveys as EUCLID and from CMB missions as Planck showing that their combined analysis could detect ${f}_{\mathrm{NL}}\ensuremath{\sim}5$.

Transient changes in frontal alpha asymmetry as a measure of emotional and physical distress during sleep

The aim of this project was to identify measurable physiological responses linked to the human experience of distress in a non-communicative state. Since sleep is a state of sensory-motor detachment in which subjects cannot report how they feel or what they experience, it can be considered a suitable model of non communicative states. A transitory distress-related response has consistently been reported in healthy awake subjects in the form of power spectrum alpha band changes in frontal brain areas. Hence, changes in frontal alpha asymmetry (FAA) were analysed in 16 volunteers before and after administration of distressful aversive stimuli during sleep. Transient physical or emotional distress was achieved by presentation of conditioned (to electroshocks or affective images) or directly-applied aversive stimuli (electroshocks). Frontal beta asymmetry (FBA) was also evaluated for comparisons. Power spectrum data were assessed from frontal electroencephalographic (EEG) leads (F3/F4). Galvanic skin response (GSR) and heart rate (HR) were also simultaneously monitored. To test the possibility that the short lasting stimulations would have long-term physiological effects, we included saliva cortisol sampling, evaluation of dream emotional valence and a standard assessment of sleep quality measurements. Aversive stimulation of diverse nature, compared to neutral valence stimuli, produced measurable changes in FAA (left>right) and in GSR evoked responses in both stage 2 (S2) and rapid eye movement (REM) sleep suggesting implicit processing of experiences with negative valence. Noticeably, dream content evaluation showed a trend towards increased negative emotionality. No FBA was observed, confirming the specificity of FAA responses. Saliva cortisol, and sleep parameters were not significantly affected by the protocol. This is, to our knowledge, the first time that an aversive imaging conditioning protocol has been successfully applied during sleep.

Viscous dark fluid universe

We investigate the cosmological perturbation dynamics for a universe consisting of pressureless baryonic matter and a viscous fluid, the latter representing a unified model of the dark sector. In the homogeneous and isotropic background the total energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically nonadiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS (DR7) data. A joint statistical analysis, using also Hubble-function and supernovae Ia data, shows that, different from other studies, there exists a maximum in the probability distribution for a negative present value ${q}_{0}\ensuremath{\approx}\ensuremath{-}0.53$ of the deceleration parameter. Moreover, while previous descriptions on the basis of generalized Chaplygin-gas models were incompatible with the matter power-spectrum data since they required a much too large amount of pressureless matter, the unified model presented here favors a matter content that is of the order of the baryonic matter abundance suggested by big-bang nucleosynthesis.

Anomalous parity asymmetry of WMAP 7-year power spectrum data at low multipoles: Is it cosmological or systematics?

We have investigated the odd-parity preference of the WMAP 7 year power spectrum. Comparison with simulation shows the odd-parity preference of WMAP data (2<= l <=22) is anomalous at 4-in-1000 level. We have investigated its origins, and ruled out some of non-cosmological origins such as asymmetric beams, noise and cut-sky effect. We also find primordial origin requires |Re[\Phi(\mathbf k)]|\ll|Im[\Phi(\mathbf k)]| for k\lesssim 22/\eta_0, where \eta_0 is the present conformal time. Multipoles associated with the odd-parity preference happen to coincide with some of other CMB anomalies. Therefore, there may exist a common origin, whether cosmological or not. Besides, we find it likely that low quadrupole power is the part of this odd-parity preference anomaly rather than an isolated one. The Planck surveyor, which possesses wide frequency coverage and systematics distinct from the WMAP, may allow us to resolve the mystery of the anomalous odd-parity preference.

Constraints on models with a break in the primordial power spectrum

One of the characteristics of the “Matter Bounce” scenario, an alternative to cosmological inflation for producing a scale-invariant spectrum of primordial adiabatic fluctuations on large scales, is a break in the power spectrum at a characteristic scale, below which the spectral index changes from ns=1 to ns=3. We study the constraints which current cosmological data place on the location of such a break, and more generally on the position of the break and the slope at length scales smaller than the break. The observational data we use include the WMAP five-year data set (WMAP5), other CMB data from BOOMERanG, CBI, VSA, and ACBAR, large-scale structure data from the Sloan Digital Sky Survey (SDSS, their luminous red galaxies sample), Type Ia Supernovae data (the “Union” compilation), and the Sloan Digital Sky Survey Lyman-α forest power spectrum (Lyα) data. We employ the Markov Chain Monte Carlo method to constrain the features in the primordial power spectrum which are motivated by the matter bounce model. We give an upper limit on the length scale where the break in the spectrum occurs.

Cosmological and astrophysical constraints from the Lyman α forest flux probability distribution function

Abstract We use the probability distribution function (PDF) of the Lyman α forest flux at z= 2–3, measured from high-resolution UVES/VLT data, and hydrodynamical simulations to obtain constraints on cosmological parameters and the thermal state of the intergalactic medium (IGM) at z∼ 2–3. The observed flux PDF at z= 3 alone results in constraints on cosmological parameters in good agreement with those obtained from the Wilkinson Microwave Anisotropy Probe (WMAP) data, albeit with about a factor of 2 larger errors. The observed flux PDF is best fit with simulations with a matter fluctuation amplitude of σ8= 0.8–0.85 ± 0.07 and an inverted IGM temperature–density relation (γ∼ 0.5–0.75), consistent with our previous results obtained using a simpler analysis. These results appear to be robust to uncertainties in the quasar (quasi-stellar object) continuum placement. We further discuss constraints obtained by a combined analysis of the high-resolution flux PDF and the power spectrum measured from the Sloan Digital Sky Survey (SDSS) Lyman α forest data. The joint analysis confirms the suggestion of an inverted temperature–density relation, but prefers somewhat higher values (σ8∼ 0.9) of the matter fluctuation amplitude than the WMAP data and the best fit to the flux PDF alone. The joint analysis of the flux PDF and power spectrum (as well as an analysis of the power spectrum data alone) prefers rather large values for the temperature of the IGM, perhaps suggesting that we have identified a not yet accounted for systematic error in the SDSS flux power spectrum data or that the standard model describing the thermal state of the IGM at z∼ 2–3 is incomplete.