scholarly journals Shot noise in multitracer constraints on fNL and relativistic projections: Power spectrum

2020 ◽  
Vol 495 (1) ◽  
pp. 932-942
Author(s):  
Dimitry Ginzburg ◽  
Vincent Desjacques
Keyword(s):  
Power Spectrum ◽  
Shot Noise ◽  
Small Mass ◽  
High Mass ◽  
Small Scale ◽  
Number Density ◽  
Signal To Noise ◽  
Optimal Sample ◽  
Poissonian Noise ◽  
Dipole Term

ABSTRACT Multiple tracers of the same surveyed volume can enhance the signal-to-noise on a measurement of local primordial non-Gaussianity and the relativistic projections. Increasing the number of tracers comparably increases the number of shot noise terms required to describe the stochasticity of the data. Although the shot noise is white on large scales, it is desirable to investigate the extent to which it can degrade constraints on the parameters of interest. In a multitracer analysis of the power spectrum, a marginalization over shot noise does not degrade the constraints on fNL by more than ∼30 per cent so long as haloes of mass $M\lesssim 10^{12}\, \mathrm{M}_\odot$ are resolved. However, ignoring cross shot noise terms induces large systematics on a measurement of fNL at redshift z < 1 when small mass haloes are resolved. These effects are less severe for the relativistic projections, especially for the dipole term. In the case of a low and high mass tracer, the optimal sample division maximizes the signal-to-noise on fNL and the projection effects simultaneously, reducing the errors to the level of ∼10 consecutive mass bins of equal number density. We also emphasize that the non-Poissonian noise corrections that arise from small-scale clustering effects cannot be measured with random dilutions of the data. Therefore, they must either be properly modelled or marginalized over.

scholarly journals Extracting H i astrophysics from interferometric Intensity Mapping

2021 ◽  
Author(s):  
Zhaoting Chen ◽  
Laura Wolz ◽  
Marta Spinelli ◽  
Steven G Murray
Keyword(s):  
Galaxy Formation ◽  
Shot Noise ◽  
Large Scale ◽  
Neutral Hydrogen ◽  
Mass Function ◽  
Small Scale ◽  
Number Density ◽  
Model Framework ◽  
Intensity Mapping ◽  
Cent Level

Abstract We present a new halo model of neutral hydrogen (H i) calibrated to galaxy formation simulations at redshifts z ∼ 0.1 and z ∼ 1.0 which we employ to investigate the constraining power of interferometric H i Intensity Mapping on H i astrophysics. We demonstrate that constraints on the small-scale H i power spectrum can break the degeneracy between the H i density $\Omega _{\rm H\, \rm \small {I}}$ and the H i bias $b_{\rm H\, \rm \small {I}}$. For z ∼ 0.1, we forecast that an accurate measurement of $\Omega _{\rm H\, \rm \small {I}}$ up to 6 per cent level precision and the large scale H i bias $b_{\rm H\, \rm \small {I}}^0$ up to 1 per cent level precision can be achieved using Square Kilometre Array (SKA) pathfinder data from MeerKAT and ASKAP. We also propose a new description of the H i shot noise in the halo model framework in which a scatter of the relation between the H i mass of galaxies and their host halo mass is taken into account. Furthermore, given the number density of H i galaxies above a certain H i mass threshold, future surveys will also be able to constrain the H i Mass Function using only the H i shot noise. This will lead to constraints at the 10 per cent level using the standard Schechter function. This technique will potentially provide a new way of measuring the H i Mass Function, independent from existing methods. We predict that the SKA will be able to further improve the low redshift constraints by a factor of three, as well as pioneering measurements of H i astrophysics at higher redshifts.

scholarly journals Anti-symmetric clustering signals in the observed power spectrum

2021 ◽  
Vol 2021 (12) ◽  
pp. 003
Author(s):  
José Fonseca ◽  
Chris Clarkson
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Euler Equation ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Power Spectra ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Signal To Noise ◽  
Peculiar Velocities

Abstract In this paper, we study how to directly measure the effect of peculiar velocities in the observed angular power spectra. We do this by constructing a new anti-symmetric estimator of Large Scale Structure using different dark matter tracers. We show that the Doppler term is the major component of our estimator and we show that we can measure it with a signal-to-noise ratio up to ∼ 50 using a futuristic SKAO HI galaxy survey. We demonstrate the utility of this estimator by using it to provide constraints on the Euler equation.

Study on Fast Algorithm for SNR and Method for Threshold Confirmation

2013 ◽  
Vol 427-429 ◽  
pp. 1718-1722
Author(s):  
Lin Sun ◽  
Ran Wei ◽  
Fu Ting Bao ◽  
Xian Zhang Tian
Keyword(s):  
Power Spectrum ◽  
Fast Algorithm ◽  
Human Gene ◽  
Signal To Noise Ratio ◽  
Average Power ◽  
Threshold Value ◽  
Computational Experiments ◽  
Rigorous Derivation ◽  
Signal To Noise ◽  
Average Power Spectrum

To reduce the amount of computing resources, a fast algorithm of the average power spectrum and signal-to-noise ratio was presented based on rigorous derivation of the formula. Also, it proved the rule gained from computational experiments. Besides, a method called fitting-optimization to determine the classification threshold value was proposed. It improves the accuracy by about 7% for human gene.

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

Power spectral analysis of the diaphragm electromyogram

1983 ◽  
Vol 54 (6) ◽  
pp. 1579-1584 ◽  
Author(s):  
T. K. Aldrich ◽  
J. M. Adams ◽  
N. S. Arora ◽  
D. F. Rochester
Keyword(s):  
Power Spectrum ◽  
Signal To Noise Ratio ◽  
Normal Subjects ◽  
Chronic Obstructive ◽  
Signal To Noise ◽  
Low Frequencies ◽  
Mean Values ◽  
The Mean ◽  
Noise Ratio ◽  
Diaphragm Fatigue

We studied the power spectrum of the diaphragm electromyogram (EMG) at frequencies between 31 and 246 Hz in four young normal subjects and five patients with chronic obstructive lung disease (COPD). Diaphragm EMGs were analyzed during spontaneous breathing and maximum inspiratory efforts to determine the effect of signal-to-noise ratio on the power spectrum and if treadmill exercise to dyspnea was associated with diaphragm fatigue. We found that the centroid frequencies of the power spectra (fc) were strongly correlated (r = 0.93) with ratios of power at high frequencies to power at low frequencies (H/L) for all subjects. Of the two indices, H/L had the largest standard deviation expressed as a percentage of the mean. The mean values of both of these decreased significantly after exercise, fc from 100.2 to 97.3 and H/L from 1.07 to 0.97. Signal-to-noise ratios were higher in maximal inspiratory efforts and after exercise in normal subjects and higher in COPD patients. The signal-to-noise ratio was correlated negatively with fc and H/L, indicating that these indices of the shape of the power spectrum are influenced by signal strength and noise levels as well as muscle function. We conclude that the fc and H/L index similar qualities of the power spectrum, that they are partially determined by the signal-to-noise ratio, and that, in some cases, exercise to dyspnea is associated with apparently mild diaphragm fatigue.

scholarly journals A duality between curvature and torsion

2018 ◽  
Vol 27 (14) ◽  
pp. 1847008 ◽  
Author(s):  
Swanand Khanapurkar ◽  
Tejinder P. Singh
Keyword(s):  
Scale Effects ◽  
Gravitational Interaction ◽  
Large Mass ◽  
Small Mass ◽  
Teleparallel Gravity ◽  
Einstein Equations ◽  
Small Scale ◽  
Underlying Theory ◽  
Newman Black Hole ◽  
Curvature And Torsion

Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an underlying theory which includes torsion. We show that in this underlying theory, the gravitational interaction between small masses is weaker than in Newtonian gravity. We explain as to why the Kerr–Newman black hole and the electron both have the same nonclassical gyromagnetic ratio. We propose a duality between curvature and torsion and show that general relativity and teleparallel gravity are respectively the large mass and small mass limit of the ECSK theory. We demonstrate that small scale effects of torsion can be tested with current technology.

Small-Scale Power Spectrum and Correlations in Lambda + Cold Dark Matter Models

1996 ◽  
Vol 466 ◽  
pp. 13 ◽  
Author(s):  
Anatoly Klypin ◽  
Joel Primack ◽  
Jon Holtzman
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Cold Dark Matter ◽  
Small Scale
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