Bohm's Mysterious 'Quantum Force' and 'Active Information': Alternative Interpretation and Statistical Properties

2001 ◽  
Vol 56 (1-2) ◽  
pp. 205-207 ◽  
Author(s):  
Boon Leong Lan
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Important Implication ◽  
Alternative Interpretation ◽  
Quantum States ◽  
Statistical Properties ◽  
Numerical Evidence ◽  
Stationary Quantum ◽  
Non Gaussian ◽  
Quantum Force

AbstractAn alternative interpretation to Bohm’s ‘quantum force’ and ‘active information’ is proposed. Numerical evidence is presented, which suggests that the time series of Bohm’s ‘quantum force’ evaluated at the Bohmian position for non-stationary quantum states are typically non-Gaussian stable distributed with a flat power spectrum in classically chaotic Hamitonian systems. An important implication of these statistical properties is briefly mentioned

Simulating Quadratically Nonlinear Random Processes

1997 ◽  
Vol 07 (06) ◽  
pp. 1367-1374 ◽  
Author(s):  
Barry Vanhoff ◽  
Steve Elgar
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Ocean Waves ◽  
Original Time Series ◽  
Third Order ◽  
Target Power ◽  
Non Gaussian ◽  
Original Time ◽  
Gaussian Time ◽  
Gaussian Time Series

A technique to generate realizations of quadratically nonlinear non-Gaussian time series with a desired ("target") power spectrum and bispectrum is presented. Specifically, by generating a Gaussian time series (using amplitude information from the target power spectrum and random phases) and passing it through a quadratic filter (that uses phase information from the target bispectrum), a realization of a quadratically nonlinear random process with a specified power spectrum and bispectrum can be produced. Second- and third-order statistics from many realizations of simulated nonlinear time series compare well to those from the original time series providing the target power spectrum and bispectrum, with deviations consistent with theory. The simulation technique is shown to simulate accurately ocean waves in shallow water, which are well known to be quadratically nonlinear.

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

scholarly journals Cosmological model parameter dependence of the matter power spectrum covariance from the DEUS-PUR Cosmo simulations

2020 ◽  
Vol 500 (2) ◽  
pp. 2532-2542
Author(s):  
Linda Blot ◽  
Pier-Stefano Corasaniti ◽  
Yann Rasera ◽  
Shankar Agarwal
Keyword(s):  
Dark Energy ◽  
Power Spectrum ◽  
Cold Dark Matter ◽  
Matter Density ◽  
Density Fluctuations ◽  
Matrix Analysis ◽  
Model Parameter ◽  
Matter Power Spectrum ◽  
Non Gaussian ◽  
The Impact

ABSTRACT Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require one to accurately model the imprint of non-linearities of the matter density field. In particular, these induce a non-Gaussian contribution to the data covariance that needs to be properly taken into account to realize unbiased cosmological parameter inference analyses. Here, we study the cosmological dependence of the matter power spectrum covariance using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation–Parallel Universe Runs (DEUS-PUR) Cosmo. These consist of 512 realizations for 10 different cosmologies where we vary the matter density Ωm, the amplitude of density fluctuations σ8, the reduced Hubble parameter h, and a constant dark energy equation of state w by approximately $10{{\ \rm per\ cent}}$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial Λ-cold dark matter cosmology. We find that the variations can be as large as $150{{\ \rm per\ cent}}$ depending on the scale, redshift, and model parameter considered. By performing a Fisher matrix analysis we explore the impact of different choices in modelling the cosmological dependence of the covariance. Our results suggest that fixing the covariance to a fiducial cosmology can significantly affect the recovered parameter errors and that modelling the cosmological dependence of the variance while keeping the correlation coefficient fixed can alleviate the impact of this effect.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

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