Showing papers on "Spectral density published in 2000"

MAXIMA-1: A measurement of the cosmic microwave background anisotropy on angular scales of 10′-5°

Abstract: We present a map and an angular power spectrum of the anisotropy of the cosmic microwave background (CMB) from the first flight of MAXIMA. MAXIMA is a balloon-borne experiment with an array of 16 bolometric photometers operated at 100 mK. MAXIMA observed a 124 deg region of the sky with 10' resolution at frequencies of 150, 240 and 410 GHz. The data were calibrated using in-flight measurements of the CMB dipole anisotropy. A map of the CMB anisotropy was produced from three 150 and one 240 GHz photometer without need for foreground subtractions. Analysis of this CMB map yields a power spectrum for the CMB anisotropy over the range 36 {le} {ell} {le} 785. The spectrum shows a peak with an amplitude of 78 {+-} 6 {mu}K at {ell} {approx_equal} 220 and an amplitude varying between {approx} 40 {mu}K and {approx} 50 {mu}K for 400 {approx}< {ell} {approx}< 785.

The Anisotropy of MHD Alfv\'{e}nic Turbulence

Abstract: We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.

Velocity Modification of H I Power Spectrum

Abstract: The distribution of atomic hydrogen in the Galactic plane is usually mapped using the Doppler shift of 21 cm emission line, and this causes the modification of the observed emission spectrum. We calculate the emission spectrum in velocity slices of data (channel maps) and derive its dependence on the statistics of velocity and density fields. We find that, (1) if the density spectrum is steep, i.e., n < -3, the large k asymptotics of the emissivity spectrum are dominated by the velocity fluctuations; and (2) the velocity fluctuations make the emission spectra shallower, provided that the data slices are sufficiently thin. In other words, turbulent velocity creates small-scale structure that can erroneously be identified as clouds. The effect of thermal velocity is very similar to the change of the effective slice thickness, but the difference is that, while an increase of the slice thickness increases the amplitude of the signal, the increase of the turbulent velocity leaves the measured intensities intact while washing out fluctuations. The contribution of fluctuations in warm H I is suppressed relative to those in the cold component when the velocity channels used are narrower than the warm H I thermal velocity and small angular scale fluctuations are measured. We calculate how the spectra vary with the change of velocity slice thickness and show that the observational 21 cm data is consistent with the explanation that the intensity fluctuations within individual channel maps are generated by turbulent velocity fields. As the thickness of velocity slices increases, density fluctuations begin to dominate emissivity. This allows us to disentangle velocity and density statistics. The application of our technique to Galactic and SMC data reveals spectra of density and velocity with power law indexes close to -11/3. This is a Kolmogorov index, but the explanation of the spectrum as due to the Kolmogorov-type cascade faces substantial difficulties. We generalize our treatment for the case of a statistical study of turbulence inside individual clouds. The mathematical machinery developed is applicable to other emission lines.

Power spectrum and detrended fluctuation analysis: Application to daily temperatures

Abstract: The variability measures of fluctuation analysis (FA) and detrended fluctuation analysis (DFA) are expressed in terms of the power spectral density and of the autocovariance of a given process. The diagnostic potential of these methods is tested on several model power spectral densities. In particular we find that both FA and DFA reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance. A scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by DFA than by FA. We apply FA and DFA to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential. As a third possible model we suggest a Weibull distribution. However, it turns out that neither FA nor DFA can reliably distinguish between the proposed models.

Deriving the nonlinear cosmological power spectrum and bispectrum from analytic dark matter halo profiles and mass functions

Abstract: We present an analytic model for the fully nonlinear two- and three-point correlation functions of the cosmological mass density field, and their Fourier transforms, the mass power spectrum and bispectrum. The model is based on physical properties of dark matter halos, with the three main model inputs being analytic halo density profiles, halo mass functions, and halo-halo spatial correlations, each of which has been well studied in the literature. We demonstrate that this new model can reproduce the power spectrum and bispectrum computed from cosmological simulations of both an n = -2 scale-free model and a low-density cold dark matter model. To enhance the dynamic range of these large simulations, we use the synthetic-halo replacement technique of Ma & Fry, in which the original halos with numerically softened cores are replaced by synthetic halos of realistic density profiles. At high wavenumbers, our model predicts a slope for the nonlinear power spectrum different from the often-used fitting formulas in the literature based on the stable-clustering assumption. Our model also predicts a three-point amplitude, Q, that is scale dependent, in contrast to the popular hierarchical clustering assumption. This model provides a rapid way to compute the mass power spectrum and bispectrum over all length scales where the input halo properties are valid. It also provides a physical interpretation of the clustering properties of matter in the universe.

The Observed Probability Distribution Function, Power Spectrum, and Correlation Function of the Transmitted Flux in the Lyα Forest*

Abstract: A sample of eight quasars observed at high resolution and signal-to-noise ratio is used to determine the transmitted flux probability distribution function (TFPDF), and the power spectrum and correlation function of the transmitted flux in the Lyα forest, in three redshift bins centered at z = 2.41, 3.00, and 3.89. All the results are presented in tabular form, with full error covariance matrices, to allow for comparisons with any numerical simulations and with other data sets. The observations are compared with a numerical simulation of the Lyα forest of a ΛCDM model with Ω = 0.4, known to agree with other large-scale structure observational constraints. There is excellent agreement for the TFPDF if the mean transmitted flux is adjusted to match the observations. A small difference between the observed and predicted TFPDF is found at high fluxes and low redshift, which may be due to the uncertain effects of fitting the spectral continuum. Using the numerical simulation, we show how the flux power spectrum can be used to recover the initial power spectrum of density fluctuations. From our sample of eight quasars, we measure the amplitude of the mass power spectrum to correspond to a linear variance per unit ln k of Δ(k) = 0.72 ± 0.09 at k = 0.04(km s-1)-1 and z = 3, and the slope of the power spectrum near the same k to be np = -2.55 ± 0.10 (statistical error bars). The results are statistically consistent with those of Croft et al., although our value for the rms fluctuation is lower by a factor of 0.75. For the ΛCDM model we use, the implied primordial slope is n = 0.93 ± 0.10, and the normalization is σ8 = 0.68 + 1.16(0.95 - n) ± 0.04.

Ray-tracing Simulations of Weak Lensing by Large-Scale Structure

Abstract: We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high-resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from ~1' to a few degrees. Various aspects of the weak-lensing approximation are also tested. We show that the nonscalar component of the shear generated by the multiple deflections is small. For fields a few degrees on a side, the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power-spectrum estimates are investigated by comparing several ray-tracing realizations of a given model. For survey areas smaller than 1° on a side, the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method that uses this effect to estimate Ωm from the scatter in power-spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately on scales corresponding to 1-10 h-1 Mpc with realistic number densities of source galaxies with large intrinsic ellipticities. Non-Gaussian features in the one-point distribution function of the weak-lensing convergence (reconstructed from the shear) are also sensitive to Ωm. We suggest several techniques for estimating Ωm in the presence of noise and compare their statistical power, robustness, and simplicity. With realistic number densities of source galaxies, Ωm can be determined to within 0.1-0.2 from a deep survey of several square degrees.

Radical Compression of Cosmic Microwave Background Data

Abstract: Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with 104 pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., "band-powers," as inputs. We identify a bias which results if one approximates the probability distribution of the band-power errors as Gaussian—as is the usual practice. This bias can be eliminated by using specific approximations to the non-Gaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximum-likelihood band-power and variance. We use this non-Gaussian form to estimate the power spectrum of the CMB in 11 bands from multipole moment l = 2 (the quadrupole) to l = 3000 from all published band-power data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.

Uncorrelated modes of the non-linear power spectrum

Abstract: Non-linear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that pre-whitening the power spectrum – transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix – greatly narrows the covariance of power. The eigenfunctions of the covariance of the pre-whitened non-linear power spectrum provide a set of almost uncorrelated non-linear modes somewhat analogous to the Fourier modes of the power spectrum itself in the linear, Gaussian regime. These almost uncorrelated modes make it possible to construct a near-minimum variance estimator and Fisher matrix of the pre-whitened non-linear power spectrum analogous to the Feldman–Kaiser–Peacock (FKP) estimator of the linear power spectrum. The paper concludes with summary recipes, in gourmet, fine and fastfood versions, of how to measure the pre-whitened non-linear power spectrum from a galaxy survey in the FKP approximation. An appendix presents FFTLog, a code for taking the fast Fourier or Hankel transform of a periodic sequence of logarithmically spaced points, which proves useful in some of the manipulations.

Multifrequency complementary phase-coded radar signal

Abstract: A multifrequency radar signal is considered It uses M subcarriers simultaneously The subcarriers are phase modulated by M different sequences that constitute a complementary set Such a set can be constructed, for example, from the M cyclic shifts of a perfect phase-coded sequence of length M (eg P4) The subcarriers are separated by the inverse of the duration of a phase element t/sub b/, yielding orthogonal frequency division multiplexing (OFDM), well known in communications A single pulse of such a signal exhibits a thumbtack ambiguity function with delay resolution of t/sub b//M The power spectrum is relatively flat, with width of M/t/sub b/ The signal can be constructed by power combining M fixed-amplitude signals The resulting signal, however, is of variable amplitude The peak-to-mean envelope power ratio can be maintained below 2 A train of complementary pulses and a weight function along the frequency axis are useful for further sidelobe reduction

Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes

Abstract: Stochastic fractal signals can be characterized by the Hurst coefficient $H,$ which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate $H$ are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integral transform. Numerical simulations confirm this relationship for ideal synthesized fractal signals. Their performance as estimators of $H$ is compared based on a mean square error criterion and found to be similar. DFA measures are derived for physiological signals of heartbeat $R\ensuremath{-}R$ intervals through the integral transform of a spectral density estimate. These agree with directly calculated DFA estimates, indicating that the relationship holds for signals with nonideal fractal properties. It is concluded that DFA and spectral measures provide equivalent characterizations of stochastic signals with long-term correlation.

A new approach to spectral estimation: a tunable high-resolution spectral estimator

Abstract: Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitable choices of filter bank poles and spectral zeros, the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum.

Force and EMG power spectrum during eccentric and concentric actions.

Abstract: KOMI, P. V., V. LINNAMO, P. SILVENTOINEN, and M. SILLANPAA. Force and EMG power spectrum during eccentric and concentric actions. Med. Sci. Sports Exerc., Vol. 32, No. 10, pp. 1757–1762, 2000.IntroductionThis study was designed to examine the force and activation levels of elbow flexor muscles durin

Searching for periodic sources with LIGO. II: Hierarchical searches

Abstract: The detection of quasi-periodic sources of gravitational waves requires the accumulation of signal to noise over long observation times. This represents the most difficult data analysis problem facing experimenters with detectors such as those at LIGO. If not removed, Earth-motion induced Doppler modulations and intrinsic variations of the gravitational-wave frequency make the signals impossible to detect. These effects can be corrected (removed) using a parametrized model for the frequency evolution. In a previous paper, we introduced such a model and computed the number of independent parameter space points for which corrections must be applied to the data stream in a coherent search. Since this number increases with the observation time, the sensitivity of a search for continuous gravitational-wave signals is computationally bound when data analysis proceeds at a similar rate to data acquisition. In this paper, we extend the formalism developed by Brady et al. [Phys. Rev. D 57, 2101 (1998)], and we compute the number of independent corrections ${N}_{p}(\ensuremath{\Delta}T,N)$ required for incoherent search strategies. These strategies rely on the method of stacked power spectra---a demodulated time series is divided into N segments of length $\ensuremath{\Delta}T,$ each segment is Fourier transformed, a power spectrum is computed, and the N spectra are summed up. This method is incoherent; phase information is lost from segment to segment. Nevertheless, power from a signal with fixed frequency (in the corrected time series) is accumulated in a single frequency bin, and amplitude signal to noise accumulates as $\ensuremath{\sim}{N}^{1/4}$ (assuming the segment length $\ensuremath{\Delta}T$ is held fixed). For fixed available computing power, there are optimal values for N and $\ensuremath{\Delta}T$ which maximize the sensitivity of a search in which data analysis takes a total time $N\ensuremath{\Delta}T.$ We estimate that the optimal sensitivity of an all-sky search that uses incoherent stacks is a factor of $2\ensuremath{-}4$ better than achieved using coherent Fourier transforms, assuming the same available computing power; incoherent methods are computationally efficient at exploring large parameter spaces. We also consider a two-stage hierarchical search in which candidate events from a search using short data segments are followed up in a search using longer data segments. This hierarchical strategy yields a further $20\ensuremath{-}60%$ improvement in sensitivity in all-sky (or directed) searches for old (\ensuremath{\geqslant}1000 yr) slow (\ensuremath{\leqslant}200 Hz) pulsars, and for young (\ensuremath{\geqslant}40 yr) fast (\ensuremath{\leqslant}1000 Hz) pulsars. Assuming enhanced LIGO detectors (LIGO-II) and ${10}^{12}$ flops of effective computing power, we examine the sensitivity to sources in three specialized classes. A limited area search for pulsars in the Galactic core would detect objects with gravitational ellipticities of $\ensuremath{\epsilon}\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 200 Hz; such limits provide information about the strength of the crust in neutron stars. Gravitational waves emitted by unstable r-modes of newborn neutron stars would be detected out to distances of $\ensuremath{\sim}8$ Mpc, if the r-modes saturate at a dimensionless amplitude of order unity and an optical supernova provides the position of the source on the sky. In searches targeting low-mass x-ray binary systems (in which accretion-driven spin up is balanced by gravitational-wave spin down), it is important to use information from electromagnetic observations to determine the orbital parameters as accurately as possible. An estimate of the difficulty of these searches suggests that objects with x-ray fluxes exceeding $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8} {\mathrm{erg}\mathrm{}\mathrm{cm}}^{\ensuremath{-}2}{\mathrm{s}}^{\ensuremath{-}1}$ would be detected using the enhanced interferometers in their broadband configuration. This puts Sco X-1 on the verge of detectability in a broadband search; the amplitude signal to noise would be increased by a factor of order $\ensuremath{\sim}5\ensuremath{-}10$ by operating the interferometer in a signal-recycled, narrow-band configuration. Further work is needed to determine the optimal search strategy when limited information is available about the frequency evolution of a source in a targeted search.

Scattering of energetic particles by anisotropic magnetohydrodynamic turbulence with a goldreich-sridhar power spectrum

Abstract: Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors nearly perpendicular to the background magnetic field, scattering is too weak to provide either the mean-free paths commonly used in Galactic cosmic-ray propagation models or the mean-free paths required for acceleration of cosmic rays at quasiparallel shocks. Where strong pitch-angle scattering occurs, it is due to fluctuations not described by the GS spectrum, such as fluctuations generated by streaming cosmic rays.

Lyman-alpha Forest Constraints on the Mass of Warm Dark Matter and the Shape of the Linear Power Spectrum

Abstract: High resolution N-body simulations of cold dark matter (CDM) models predict that galaxies and clusters have cuspy halos with excessive substructure. Observations reveal smooth halos with central density cores. One possible resolution of this conflict is that the dark matter is warm (WDM); this will suppress the power spectrum on small scales. The Lyman-alpha forest is a powerful probe of the linear power spectrum on these scales. We use collisionless N-body simulations to follow the evolution of structure in WDM models, and analyze artificial Lyman-alpha forest spectra extracted from them. By requiring that there is enough small-scale power in the linear power spectrum to reproduce the observed properties of the Lyman-alpha forest in quasar spectra, we derive a lower limit to the mass of the WDM particle of 750 eV. This limit is robust to reasonable uncertainties in our assumption about the temperature of the mean density gas (T0) at z=3. We argue that any model that suppresses the CDM linear theory power spectrum more severely than a 750 eV WDM particle cannot produce the Lyman-alpha forest.

Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models

Abstract: For a long time, it has been known that the power spectrum of Barkhausen noise had a power-law decay at high frequencies. Up to now, the theoretical predictions for this decay have been incorrect, or have only applied to a small set of models. In this paper, we describe a careful derivation of the power spectrum exponent in avalanche models, and in particular, in variations of the zero-temperature random-field Ising model. We find that the naive exponent, $(3\ensuremath{-}\ensuremath{\tau})/\ensuremath{\sigma}\ensuremath{ u}z,$ which has been derived in several other papers, is in general incorrect for small $\ensuremath{\tau},$ when large avalanches are common. $(\ensuremath{\tau}$ is the exponent describing the distribution of avalanche sizes, and $\ensuremath{\sigma}\ensuremath{ u}z$ is the exponent describing the relationship between avalanche size and avalanche duration.) We find that for a large class of avalanche models, including several models of Barkhausen noise, the correct exponent for $\ensuremath{\tau}l2$ is $1/\ensuremath{\sigma}\ensuremath{ u}z.$ We explicitly derive the mean-field exponent of $2.$ In the process, we calculate the average avalanche shape for avalanches of fixed duration and scaling forms for a number of physical properties.

Clustering of Galaxy Clusters in CDM Universes

Abstract: We use very large cosmological N--body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ($\tau$CDM) and a flat low density model with a cosmological constant ($\Lambda$CDM). Our simulations each use $10^9$ particles to follow the mass distribution within cubes of side $2h^{-1}$Gpc ($\tau$CDM) and $3h^{-1}$Gpc ($\Lambda$CDM) with a force resolution better than $10^{-4}$ of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from $r_0=12$ -- 13$h^{-1}$Mpc for samples with mean separation $d_{\rm c}=30h^{-1}$Mpc to $r_0=22$-- 27$h^{-1}$Mpc for samples with $d_{\rm c}=100h^{-1}$Mpc. The lower value here corresponds to $\tau$CDM and the upper to $\Lambda$CDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10% using the simple model of Sheth, Mo & Tormen (2000). This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the APM cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for $\Lambda$CDM. The observed power spectrum (for a cluster sample of mean separation $d_{\rm c}=31h^{-1}$Mpc) lies significantly above the predictions of both models.

Direct strain estimation in elastography using spectral cross-correlation.

Abstract: Spectral estimation of tissue strain has been performed previously by using the centroid shift of the power spectrum or by estimating the variation in the mean scatterer spacing in the spectral domain. The centroid shift method illustrates the robustness of the direct, incoherent strain estimator. In this paper, we present a strain estimator that uses spectral cross-correlation of the pre- and postcompression power spectrum. The centroid shift estimator estimates strain from the mean center frequency shift, while the spectral cross-correlation estimates the shift over the entire spectrum. Spectral cross-correlation is shown to be more sensitive to small shifts in the power spectrum and, thus, provides better estimation for smaller strains when compared to the spectral centroid shift. Spectral cross-correlation shares all the advantages gained using the spectral centroid shift, in addition to providing accurate and precise strain estimation for small strains. The variance and noise properties of the spectral strain estimators quantified by their respective strain filters are also presented.

Spectral Analysis and Filter Theory in Applied Geophysics

Abstract: I Spectral Analysis of Deterministic Processes.- 1 Fourier Series Representation of Periodic Functions.- 2 Spectral Representation of Nonperiodic Processes.- 3 The Dirac Delta Function and its Fourier Transform.- 4 Spectral Analysis of Time-Limited Observations of Infinitely Long Processes.- 5 Spectral Analysis of Discrete Functions.- 6 z-Transform Representation of Time Series.- 7 Examples of the Use of the Fourier Transform in Applied Seismics.- II Spectral Analysis of Random Processes.- 8 Characterization of Random Processes in the Time and Frequency Domains.- 9 Estimation of the Power Spectral Density Function.- 10 Evaluation of Magnetotelluric Survey Data.- III Spectral Analysis of Random Processes by Model Fitting.- 11 Spectral Estimation by Model Fitting.- 12 Estimating Power Spectra using Criteria from Information Theory.- IV Fundamentals of Filter Theory.- 13 Filtering from the Viewpoint of System Theory.- 14 Filtering in the Frequency Domain.- V Digital Filtering.- 15 Basics of Digital Filtering.- 16 Filtering using Simple Mathematical Operations.- 17 Designing Nonrecursive Digital Filters of Finite Length.- 18 Synthesis of Recursive Digital Filters.- VI Fundamentals of Optimum Filtering.- 19 Designing Analog and Digital Optimum Filters.- 20 Application of Optimum Filters to Reflection Seismic Data.- 21 Kalman Filters.- VII Fundamentals of Deconvolution and their Application to Reflection Seismic Data.- 22 Mathematical Basis of Deconvolution.- 23 Deconvolution: Problems and Approaches in Reflection Seismics.- VIII Multidimensional and Multichannel Filters.- 24 Multidimensional Filters.- 25 Two-Dimensional Filters for Gravity and Magnetic Data.- 26 Multichannel Filtering of Seismic Data.- Author Index.

Variability and noise in continuous force production.

Abstract: In the present 3 experiments, the authors examined the hypothesis, derived from information theory, that increases in the variability of motor responses result from increases in perceptual-motor noise Three different groups of participants (Ns = 10, 9, and 10, respectively, in Experiments 1, 2, and 3) produced continuous isometric force under either low, intermediate, or high target force levels When considered together, the results showed that force variability (SD) increased exponentially as a function of force level However, an index of information transmission (M/SD), as well as measures of noise in both the time (approximate entropy) and the frequency (power spectrum) domains, changed according to an inverted-U-shaped function over the range of force levels The findings provide further evidence that increased information transmission is related to increases, and not to decreases, in the noisiness of the structure of force output

Power spectrum of the Sunyaev-Zel’dovich effect

Abstract: The hot gas in the IGM produces anisotropies in the cosmic microwave background (CMB) through the thermal Sunyaev-Zel'dovich (SZ) effect. The SZ effect is a powerful probe of large-scale structure in the universe, and must be carefully subtracted from measurements of the primary CMB anisotropies. We use moving-mesh hydrodynamical simulations to study the 3-dimensional statistics of the gas, and compute the mean Comptonization parameter y and the angular power spectrum of the SZ fluctuations, for different cosmologies. We compare these results with predictions using the Press-Schechter formalism. We find that the two methods agree approximately, but differ in details. We discuss this discrepancy, and show that resolution limits the reliability of our results to the $200\ensuremath{\lesssim}l\ensuremath{\lesssim}2000$ range. For cluster normalized CDM models, we find a mean y-parameter of the order of ${10}^{\ensuremath{-}6},$ one order of magnitude below the current observational limits from the COBE-FIRAS instrument. For these models, the SZ power spectrum is comparable to the primordial power spectrum around $l=2000.$ It is well below the projected noise for the upcoming MAP satellite, and should thus not be a limitation for this mission. It should be easily detectable with the future Planck Surveyor mission. We show that groups and filaments (kT\ensuremath{\lesssim}5 keV) contribute about 50% of the SZ power spectrum at $l=500.$ About half of the SZ power spectrum on these scales are produced at redshifts $z\ensuremath{\lesssim}0.1,$ and can thus be detected and removed using existing catalogs of galaxies and x-ray clusters.

A Wavelet‐Based Test for Stationarity

Abstract: We develop a test for stationarity of a time series against the alternative of a time-changing covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time-varying spectral density. Coefficients w.r.t. a Haar wavelet series expansion of such a time-varying periodogram are a possible indicator whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.

Back reaction of inhomogeneities on the expansion: The evolution of cosmological parameters

Abstract: Averaging and evolving inhomogeneities are noncommuting operations. This implies the existence of deviations of an averaged model from the standard Friedmann-Lema\^{\i}tre cosmologies. We quantify these deviations, encoded in a back reaction parameter, in the framework of Newtonian cosmology. We employ the linear theory of gravitational instability in the Eulerian and Lagrangian approaches, as well as the spherically and plane-symmetric solutions as standards of reference. We propose a model for the evolution of the average characteristics of a spatial domain for generic initial conditions that contains the spherical top-hat model and the planar collapse model as exact subcases. A central result is that the back reaction term itself, calculated on sufficiently large domains, is small but, still, its presence can drive the cosmological parameters on the averaging domain far away from their global values of the standard model. We quantify the variations of these parameters in terms of the fluctuations in the initial data as derived from the power spectrum of initial cold dark matter density fluctuations. For example, in a domain with a radius of 100 Mpc today and initially one-\ensuremath{\sigma} fluctuations, the density parameters deviate from their homogeneous values by 15%; three-\ensuremath{\sigma} fluctuations lead to deviations larger than 100%.

Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps

Abstract: We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to its self-organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of the components have non-Gaussian distributions. We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100GHz) used by the Low Frequency Instrument of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissions, and extragalactic radio sources. The effects of the angular response functions of the detectors and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1per cent for the CMB, and 10per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to .0.7sCMB, where sCMB is the rms level of the CMB fluctuations. The signal recovered has equal quality on all scales larger than the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recovered with per cent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.

Lensing of the CMB: Non-Gaussian aspects

Abstract: We study the generation of cosmic microwave background (CMB) anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between the large scale gradient and the small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point functions of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the $S/N.$

Spectral compression of the electromyographic signal due to decreasing muscle fiber conduction velocity

Abstract: Spectral compression of the electromyographic (EMG) signal, due largely to decreasing muscle fiber conduction velocity, is commonly used as an indication of muscle fatigue. Current methods of estimating conduction velocity using characteristic frequencies such as the median frequency of the power spectrum, are based on an assumption of uniform spectral compression. To examine changes in the EMG frequency spectrum during fatigue, muscle fiber conduction velocity was measured during sustained, isometric contractions of the biceps brachii. Compression of the EMG power and amplitude spectra was simultaneously examined using the median frequency and-an alternative method-the spectral distribution technique. The spectral distribution technique consistently gave a better estimate of the relative change in muscle fiber conduction velocity than either of the median frequencies. This was further examined using a physiologically based EMG simulation model, which confirmed these findings. The model indicated that firing statistics can significantly influence spectral compression, particularly the behavior of characteristic frequencies in the vicinity of the firing rates. The relative change in the median frequency, whether of the amplitude or frequency spectrum, was consistently greater than the relative change in conduction velocity. The most accurate indication of the relative change in conduction velocity was obtained by calculating the mean shift in the midfrequency region of the EMG amplitude spectrum using the spectral distribution technique.

Spectral Energy Balance of Breaking Waves within the Surf Zone

Abstract: The spectral energy balance of ocean surface waves breaking on a natural beach is examined with field observations from a cross-shore array of pressure sensors deployed between the shoreline and the outer edge of the surf zone near Duck, North Carolina. Cross-shore gradients in wave energy flux were estimated from spectral changes observed between closely spaced sensors. Direct, empirical estimates of nonlinear energy exchanges between different frequency components of the wave spectrum were obtained from observed bispectra using Boussinesq theory for near-resonant triad wave–wave interactions. The large decrease in energy flux observed across the surf zone in the energetic part of the wave spectrum is balanced closely by the estimated nonlinear energy transfers from the spectral peak to higher frequencies. In the high-frequency tail of the spectrum, observed energy flux gradients are small and do not balance the nonlinear energy transfers. This analysis indicates that the observed decay of wave ...

Perturbations in a coupled scalar field cosmology

Abstract: I analyse the density perturbations in a cosmological model with a scalar field coupled to ordinary matter, such as one obtains in string theory and in conformally transformed scalar–tensor theories. The spectrum of multipoles on the last scattering surface and the power spectrum at the present epoch are compared with observations to derive bounds on the coupling constant and on the exponential potential slope. It is found that the acoustic peaks and the power spectrum are strongly sensitive to the model parameters. The models that best fit the galaxy spectrum and satisfy the cluster abundance normalization have field energy density Ω≃0.05–0.15 and a scalefactor expansion law a∼t p, p≃0.67–0.69.