scholarly journals On the Reliability of Initial Conditions for Dissipationless Cosmological Simulations

2003 ◽  
Vol 20 (2) ◽  
pp. 173-183 ◽  
Author(s):  
Alexander Knebe ◽  
Alvaro Domínguez
Keyword(s):  
Power Spectrum ◽  
Fundamental Mode ◽  
Initial Conditions ◽  
Interparticle Distance ◽  
Particle Distributions ◽  
The Mean ◽  
Internal Properties ◽  
Correlation Properties ◽  
Random Nature ◽  
Simulation Volume

AbstractWe present the study of ten random realisations of a density field characterised by a cosmological power spectrum P(k) at redshift z = 50. The reliability of such initial conditions for N-body simulations is tested with respect to their correlation properties. The power spectrum P(k) and the mass variance σM(r) do not show detectable deviations from the desired behaviour in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for ξ(r) is too noisy to detect any reliable signal at the initial redshift z = 50. The particle distributions are then evolved forward until z = 0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realisation of the stochastic initial conditions whereas the real Universe contains many realisations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode.

scholarly journals Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

2020 ◽  
Vol 496 (3) ◽  
pp. 3862-3869 ◽  
Author(s):  
Anatoly Klypin ◽  
Francisco Prada ◽  
Joyce Byun
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Initial Conditions ◽  
Cosmological Parameters ◽  
Average Density ◽  
Covariance Matrices ◽  
Acoustic Oscillations ◽  
Galaxy Clustering ◽  
The Mean ◽  
Statistical Noise

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.

scholarly journals Spherically Restricted Random Hyperbolic Diffusion

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 217 ◽  
Author(s):  
Philip Broadbridge ◽  
Alexander Kolesnik ◽  
Nikolai Leonenko ◽  
Andriy Olenko ◽  
Dareen Omari
Keyword(s):  
Power Spectrum ◽  
Random Fields ◽  
Spectral Measure ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Angular Power Spectrum ◽  
Numerical Studies ◽  
Random Initial Conditions ◽  
Mean Square Convergence ◽  
The Mean

This paper investigates solutions of hyperbolic diffusion equations in R 3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere S 2 are studied. All assumptions are formulated in terms of the angular power spectrum or the spectral measure of the random initial conditions. Approximations to the exact solutions are given. Upper bounds for the mean-square convergence rates of the approximation fields are obtained. The smoothness properties of the exact solution and its approximation are also investigated. It is demonstrated that the Hölder-type continuity of the solution depends on the decay of the angular power spectrum. Conditions on the spectral measure of initial conditions that guarantee short- or long-range dependence of the solutions are given. Numerical studies are presented to verify the theoretical findings.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

scholarly journals Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using 150 MHz GMRT observations

2020 ◽  
Author(s):  
Srijita Pal ◽  
Somnath Bharadwaj ◽  
Abhik Ghosh ◽  
Samir Choudhuri
Keyword(s):  
Power Spectrum ◽  
Unbiased Estimate ◽  
Power Spectra ◽  
Neutral Hydrogen ◽  
Statistical Error ◽  
Temperature Fluctuations ◽  
Radio Frequency Interference ◽  
Rectangular Region ◽  
Angular Power Spectrum ◽  
The Mean

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

scholarly journals A modified fluctuation test for elucidating drug resistance in microbial and cancer cells

2020 ◽  
Author(s):  
Pavol Bokes ◽  
Abhyudai Singh
Keyword(s):  
Drug Resistance ◽  
Cancer Cells ◽  
Colony Size ◽  
Random Number ◽  
Initial Conditions ◽  
Fano Factor ◽  
Persister Cells ◽  
Efficient Treatment ◽  
Fluctuation Test ◽  
The Mean

AbstractClonal populations of microbial and cancer cells are often driven into a drug-tolerant persister state in response to drug therapy, and these persisters can subsequently adapt to the new drug environment via genetic and epigenetic mechanisms. Estimating the frequency with which drug-tolerance states arise, and its transition to drug-resistance, is critical for designing efficient treatment schedules. Here we study a stochastic model of cell proliferation where drug-tolerant persister cells transform into a drug-resistant state with a certain adaptation rate, and the resistant cells can then proliferate in the presence of the drug. Assuming a random number of persisters to begin with, we derive an exact analytical expression for the statistical moments and the distribution of the total cell count (i.e., colony size) over time. Interestingly, for Poisson initial conditions the noise in the colony size (as quantified by the Fano factor) becomes independent of the initial condition and only depends on the adaptation rate. Thus, experimentally quantifying the fluctuations in the colony sizes provides an estimate of the adaptation rate, which then can be used to infer the starting persister numbers from the mean colony size. Overall, our analysis introduces a modification of the classical Luria–Delbrück experiment, also called the “Fluctuation Test”, providing a valuable tool to quantify the emergence of drug resistance in cell populations.

LONG RANGE CORRELATION PROPERTIES OF AFTERSHOCK RELAXATION SIGNALS

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 839-847 ◽  
Author(s):  
A. VESPIGNANI ◽  
A. PETRI ◽  
A. ALIPPI ◽  
G. PAPARO ◽  
M. COSTANTINI
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Statistical Analysis ◽  
Power Spectrum ◽  
Power Law ◽  
Amplitude Distribution ◽  
Relaxation Processes ◽  
Critical Dynamics ◽  
Range Correlation ◽  
Correlation Properties

Relaxation processes taking place after microfracturing of laboratory samples give rise to ultrasonic acoustic emission signals. Statistical analysis of the resulting time series has revealed many features which are characteristic of critical phenomena. In particular, the autocorrelation functions obey a power-law behavior, implying a power spectrum of the kind 1/f. Also the amplitude distribution N(V) of such signals follows a power law, and the obtained exponents are consistent with those found in other experiments: N(V) dV≃V–γ dV, with γ=1.7±0.2. We also analyzed the distribution N(τ) of the delay time τ between two consecutive acoustic emission events. We found that a N(τ) distribution rather close to a power law constitutes a common feature of all the recorded signals. These experimental results can be considered as a striking evidence for a critical dynamics underlying the microfracturing processes.

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 The information content of Cosmic Infrared Background anisotropies

2019 ◽  
Author(s):  
Robert Reischke ◽  
Vincent Desjacques ◽  
Saleem Zaroubi
Keyword(s):  
Power Spectrum ◽  
Cosmological Parameters ◽  
Model Parameters ◽  
Mass Relation ◽  
Infrared Background ◽  
Cross Correlations ◽  
The Mean ◽  
Cosmic Infrared Background ◽  
Almost All ◽  
Halo Occupation Distribution

Abstract We use analytic computations to predict the power spectrum as well as the bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis we use wavelengths in eight frequency channels between 200 and 900 GHz with survey specifications given by Planck and LiteBird. We explore the sensitivity to the model parameters up to multipoles of ℓ = 1000 using auto- and cross-correlations between the different frequency bands. With this setting, cosmological, HOD and CIB parameters can be constrained to a few percent. Galactic dust is modeled by a power law and the shot noise contribution as a frequency dependent amplitude which are marginalized over. We find that dust residuals in the CIB maps only marginally influence constraints on standard cosmological parameters. Furthermore, the bispectrum yields tighter constraints (by a factor four in 1σ errors) on almost all model parameters while the degeneracy directions are very similar to the ones of the power spectrum. The increase in sensitivity is most pronounced for the sum of the neutrino masses. Due to the similarity of degeneracies a combination of both analysis is not needed for most parameters. This, however, might be due to the simplified bias description generally adopted in such halo model approaches.

The Service Time Properties of an Unreliable Server Characterize the Exponential Distribution

1994 ◽  
Vol 26 (01) ◽  
pp. 172-182 ◽  
Author(s):  
Z. Khalil ◽  
B. Dimitrov
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Initial Conditions ◽  
Mean Values ◽  
Unreliable Server ◽  
Service Disciplines ◽  
The Mean ◽  
Server Reliability ◽  
Preemptive Repeat Different

Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

Sign in / Sign up

Export Citation Format

Share Document