scholarly journals Validation of a power-law noise model for simulating small-scale breast tissue

2013 ◽  
Vol 58 (17) ◽  
pp. 6011-6027 ◽  
Author(s):  
I Reiser ◽  
A Edwards ◽  
R M Nishikawa
Keyword(s):  
Power Law ◽  
Breast Tissue ◽  
Noise Model ◽  
Small Scale ◽  
Power Law Noise

Breast tissue characterization based on modeling of ultrasonic echoes using the power-law shot noise model

2003 ◽  
Vol 24 (4-5) ◽  
pp. 741-756 ◽  
Author(s):  
M.Alper Kutay ◽  
Athina P Petropulu ◽  
Catherine W Piccoli
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Breast Tissue ◽  
Tissue Characterization ◽  
Noise Model

Mean amplitudes of the signal in the seasonal and shorter period length of day time series computed by the frequency-dependent autocovariance

2021 ◽  
Author(s):  
Wieslaw Kosek
Keyword(s):  
Time Series ◽  
Power Law ◽  
Amplitude Spectrum ◽  
Noise Model ◽  
Prediction Errors ◽  
Length Of Day ◽  
Frequency Dependent ◽  
Filter Bandwidth ◽  
Power Law Noise ◽  
The Mean

<p>The frequency-dependent autocovariance (FDA) function is defined in this paper as the autocovariance function of a wideband oscillation filtered by the Fourier transform bandpass filter (FTBPF). It was shown that the FDA estimation is a useful algorithm to detect mean amplitudes of oscillations in a very noisy time series. In this paper the least-squares polynomial harmonic model was used to remove the trend, low frequency as well as the annual and semi-annual oscillations from the IERS eopc04R_IAU2000_daily length of day (LOD) time series to compute their residuals. Next, the mean amplitudes of the signal as a function of frequency were determined from the difference between the FDA of LOD residuals and FDA of power-law noise model similar to the noise present in LOD residuals.  Several power-law noise model data were generated with a similar spectral index and variance as the noise in LOD data to estimate the mean amplitude spectrum in the seasonal and shorter period frequency band.  It was shown that the mean amplitudes of the oscillations in LOD residuals are very small compared to the noise standard deviation and do not depend on the filter bandwidth of the FTBPF. These small amplitudes explain why LOD prediction errors increase rapidly with the prediction length.</p>

NONLINEAR TIME SERIES PREDICTION BASED ON A POWER-LAW NOISE MODEL

2007 ◽  
Vol 18 (12) ◽  
pp. 1839-1852 ◽  
Author(s):  
FRANK EMMERT-STREIB ◽  
MATTHIAS DEHMER
Keyword(s):  
Time Series ◽  
Power Law ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Logistic Map ◽  
Optimization Procedure ◽  
Nonlinear Time Series ◽  
Noise Model ◽  
Annual Number ◽  
Power Law Noise

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

scholarly journals Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

2021 ◽  
Vol 10 (3) ◽  
pp. 157
Author(s):  
Paul-Mark DiFrancesco ◽  
David A. Bonneau ◽  
D. Jean Hutchinson
Keyword(s):  
Computational Geometry ◽  
Surface Reconstruction ◽  
Power Law ◽  
Point Cloud ◽  
Point Clouds ◽  
Volume Estimation ◽  
Estimation Methods ◽  
Small Scale ◽  
Reconstruction Methods ◽  
3D Volume

Key to the quantification of rockfall hazard is an understanding of its magnitude-frequency behaviour. Remote sensing has allowed for the accurate observation of rockfall activity, with methods being developed for digitally assembling the monitored occurrences into a rockfall database. A prevalent challenge is the quantification of rockfall volume, whilst fully considering the 3D information stored in each of the extracted rockfall point clouds. Surface reconstruction is utilized to construct a 3D digital surface representation, allowing for an estimation of the volume of space that a point cloud occupies. Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology. In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls. The database was derived from a 5-year LiDAR monitoring campaign of an active rock slope in interior British Columbia, Canada. Each method resulted in a different magnitude-frequency distribution of rockfall. The implications of 3D volume estimation were demonstrated utilizing surface mesh visualization, cumulative magnitude-frequency plots, power-law fitting, and projected annual frequencies of rockfall occurrence. The 3D volume estimation methods caused a notable shift in the magnitude-frequency relations, while the power-law scaling parameters remained relatively similar. We determined that the optimal 3D volume calculation approach is a hybrid methodology comprised of the Power Crust reconstruction and the Alpha Solid reconstruction. The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions.

scholarly journals Transient brightenings in the quiet Sun detected by ALMA at 3 mm

2020 ◽  
Vol 638 ◽  
pp. A62 ◽  
Author(s):  
A. Nindos ◽  
C. E. Alissandrakis ◽  
S. Patsourakos ◽  
T. S. Bastian
Keyword(s):  
Solar Atmosphere ◽  
Power Law ◽  
Small Scale ◽  
Solar Chromosphere ◽  
Average Intensity ◽  
Quiet Sun ◽  
Brightness Temperatures ◽  
Weak Preference ◽  
Thermal Origin ◽  
First Time

Aims. We investigate transient brightenings, that is, weak, small-scale episodes of energy release, in the quiet solar chromosphere; these episodes can provide insights into the heating mechanism of the outer layers of the solar atmosphere. Methods. Using Atacama Large Millimeter/submillimeter Array (ALMA) observations, we performed the first systematic survey for quiet Sun transient brightenings at 3 mm. Our dataset included images of six 87″ × 87″ fields of view of the quiet Sun obtained with angular resolution of a few arcsec at a cadence of 2 s. The transient brightenings were detected as weak enhancements above the average intensity after we removed the effect of the p-mode oscillations. A similar analysis, over the same fields of view, was performed for simultaneous 304 and 1600 Å data obtained with the Atmospheric Imaging Assembly. Results. We detected 184 3 mm transient brightening events with brightness temperatures from 70 K to more than 500 K above backgrounds of ∼7200 − 7450 K. All events showed light curves with a gradual rise and fall, strongly suggesting a thermal origin. Their mean duration and maximum area were 51.1 s and 12.3 Mm2, respectively, with a weak preference of appearing at network boundaries rather than in cell interiors. Both parameters exhibited power-law behavior with indices of 2.35 and 2.71, respectively. Only a small fraction of ALMA events had either 304 or 1600 Å counterparts but the properties of these events were not significantly different from those of the general population except that they lacked their low-end energy values. The total thermal energies of the ALMA transient brightenings were between 1.5 × 1024 and 9.9 × 1025 erg and their frequency distribution versus energy was a power law with an index of 1.67 ± 0.05. We found that the power per unit area provided by the ALMA events could account for only 1% of the chromospheric radiative losses (10% of the coronal ones). Conclusions. We were able to detect, for the first time, a significant number of weak 3 mm quiet Sun transient brightenings. However, their energy budget falls short of meeting the requirements for the heating of the upper layers of the solar atmosphere and this conclusion does not change even if we use the least restrictive criteria possible for the detection of transient brightenings.

scholarly journals The Dynamics of Baroclinic Zonal Jets*

2015 ◽  
Vol 72 (3) ◽  
pp. 1137-1151 ◽  
Author(s):  
Paul D. Williams ◽  
Christopher W. Kelsall
Keyword(s):  
Root Mean Square ◽  
Power Law ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Square ◽  
Initial State ◽  
Zonal Jets ◽  
Rotation Periods ◽  
Inverse Energy Cascade ◽  
Geostrophic Turbulence

Abstract Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

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