scholarly journals 016 Characteristic Dimension: A Novel Adjunct to Analyzing Species Composition in Digitized Photos of Turfgrass Plots

HortScience ◽  
1999 ◽  
Vol 34 (3) ◽  
pp. 443D-443
Author(s):  
Steven C. Wiest
Keyword(s):  
Power Spectrum ◽  
Tall Fescue ◽  
Fourier Transforms ◽  
Power Spectra ◽  
Characteristic Dimension ◽  
The Other ◽  
Average Spacing ◽  
Photographic Images ◽  
Buffalo Grass ◽  
Radial Plot

Digitized photographic images of turf plots composed of bermudagrass, buffalo grass, tall fescue, and zoysiagrass were taken at a height of about 150 cm with a 28-mm lens. Fast Fourier transforms of these images were performed, and a radial plot of the power spectrum was obtained from each image. Hurst plots (log frequency vs. log intensity) were used to subtract “background” from the power spectra, so peaks would be more evident. The peak of the power spectrum occurs at the average spacing between leaves (more precisely, between areas of the canopy that reflects a significant amount of light) and defines the characteristic dimension. Zoysiagrass had the lowest characteristic dimension, while tall fescue had the highest. The width of the power spectrum is indicative of the variability of the characteristic dimension within the canopy. The minimum characteristic dimension (occurring at the highest frequency) was less than 1.7 cm, whereas all the other species had about the same minimum characteristic dimension of ≈1.9 cm. The maximum characteristic dimension was greatest for fescue (6.9 cm), followed by buffalo grass (3.8 cm), bermudagrass (3.3 cm), and zoysiagrass (2.8 cm). These results indicate that the characteristic dimension can be a useful tool for discriminating between turfgrass species in digitized images.

scholarly journals Computing the small-scale galaxy power spectrum and bispectrum in configuration space

2019 ◽  
Vol 492 (1) ◽  
pp. 1214-1242 ◽  
Author(s):  
Oliver H E Philcox ◽  
Daniel J Eisenstein
Keyword(s):  
Power Spectrum ◽  
Configuration Space ◽  
Fourier Transforms ◽  
Cosmological Parameters ◽  
Power Spectra ◽  
Small Scale ◽  
High K ◽  
Cross Covariance ◽  
Small Scales ◽  
Point Correlation

ABSTRACT We present a new class of estimators for computing small-scale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim 100\, h^{-1}\, \mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\mathcal {O}(NnR_0^3)$ (or $\mathcal {O}(Nn^2R_0^6)$ for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artefacts, making them ideal for high-k analysis. Unlike conventional Fourier-transform-based approaches, our algorithm becomes more efficient on small scales (since a smaller R0 may be used), thus we may efficiently estimate spectra across k-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.

Changes in electromyogram power spectra of facial and jaw-elevator muscles during fatigue

1983 ◽  
Vol 54 (1) ◽  
pp. 51-58 ◽  
Author(s):  
A. van Boxtel ◽  
P. Goudswaard ◽  
G. M. van der Molen ◽  
W. E. van den Bosch
Keyword(s):  
Power Spectrum ◽  
Masseter Muscle ◽  
Power Spectra ◽  
Spectral Shift ◽  
The Other ◽  
Median Frequency ◽  
Corrugator Supercilii ◽  
Static Contraction ◽  
Exponential Decrease ◽  
Zygomaticus Major

Endurance and changes in electromyogram (EMG) power spectra were investigated during a fatiguing static contraction at 50% of the maximum EMG amplitude in two jaw-elevator muscles (masseter and temporalis) and five facial muscles (frontalis, corrugator supercilii, zygomaticus major, orbicularis oris, and buccinator). Relatively high endurance was found in orbicularis oris, frontalis, and corrugator supercilii muscles; intermediate endurance was found in zygomaticus major, buccinator, and temporalis muscles; and low endurance was found in the masseter muscle. The last muscle showed a relatively fast linear decrease of the median frequency of the power spectrum. The other muscles showed a much slower, exponential decrease. The median frequency appeared to reflect reliably the changes in the shape of the power spectra during fatigue. Large differences between the shape of power spectra of different muscles in the unfatigued state were found. These, however, were unrelated to endurance and degree of spectral shift during fatigue.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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 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.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

Spectrum analysis of sympathetic nerve activity and blood pressure in conscious rats

1992 ◽  
Vol 263 (5) ◽  
pp. H1348-H1355 ◽  
Author(s):  
P. B. Persson ◽  
H. Stauss ◽  
O. Chung ◽  
U. Wittmann ◽  
T. Unger
Keyword(s):  
Blood Pressure ◽  
Power Spectrum ◽  
Sympathetic Nerve ◽  
Sympathetic Nerve Activity ◽  
Power Spectra ◽  
High Frequency Component ◽  
Bipolar Electrode ◽  
Phase Lag ◽  
Nerve Activity ◽  
Wistar Kyoto

This study tests whether the power spectrum of blood pressure (BP) provides information toward the sympathovagal balance of BP control by comparing the BP (femoral arterial catheter) spectrum with the spectrum of the efferent sympathetic nerve activity (SNA, bipolar electrode around splanchnic nerve). A remarkable resemblance between both spectra was found. A high-frequency component (HF) linked to respiration and a slower fluctuation type between 0.15 and 0.6 Hz (LF) were identified. There was a large and significant coherence only in the HF range of the BP and SNA power spectrum (P < 0.01). The phase lag of SNA and BP was roughly 200 ms. The recordings were repeated during pharmacological blockade in nine Wistar-Kyoto rats (WKY) and nine spontaneously hypertensive rats (SHR). alpha 1-Adrenoceptor blockade (prazosin) reduced the proportional LF power of BP in both rat strains (WKY P < 0.01, SHR P < 0.05) in favor of HF (WKY P < 0.01, SHR P < 0.01). Parasympathetic blockade (methylscopolamine) had no effect on proportions of power. Similarly, there were no significant differences in the proportional HF and LF power spectra of WKY and SHR. These data provide direct evidence for a relationship between the BP and SNA power spectra; however, only the acute changes in the sympathetic tone changed the LF-HF relationship.

Neuronal mechanisms underlying physiological tremor

1978 ◽  
Vol 41 (3) ◽  
pp. 557-571 ◽  
Author(s):  
J. H. Allum ◽  
V. Dietz ◽  
H. J. Freund
Keyword(s):  
Power Spectrum ◽  
Pathological Condition ◽  
Power Spectra ◽  
Motor Units ◽  
Physiological Tremor ◽  
Force Level ◽  
Force Output ◽  
Experimental Conditions ◽  
Single Motor Unit ◽  
Total Fusion

1. Tremor force was recorded during stationary isometric contractions of intrinsic hand muscles of normal subjects. Subjects maintained a steady force level between their thumb and forefinger for 30 s. The force level varied from weak (0.2 kg) to strong contractions (7 kg). These experimental conditions were the same as those in two preceding studies, where single motor-unit activity (14) and the correlation between the discharges of two simultaneously recorded motor units and physiological tremor (11) have been investigated. 2. Two alterations of the power spectra were observed at successively stronger contractions: increase of tremor amplitude and changes in the shape of the power spectrum. At all force levels, the power spectra of tremor force show the well-known decay of tremor amplitude from the lower to the higher frequencies with a local peak at 6--10 Hz. This peak does not show a significant change with respect to frequency when the force level is varied. It is shifted toward lower frequencies in a pathological condition (Parkinsonism) where the recruitment firing rates of the motor units are significantly lower than in the normal. 3. Higher frequencies (greater than 20 Hz) are barely present in the power spectrum during the very weak contractions. They become significant as the contractions become stronger. 4. The steep decay of the power spectrum toward higher frequencies has a similar slope (--43 dB/decade) as the reduction in amplitude of the unfused part of the muscle contractions with increasing stimulus rates (--38 dB/decade). The cutoff of the power spectrum above 25 Hz parallels the achievement of total fusion of muscle twitches above this rate. 5. The results are consistent with the hypothesis that the power spectrum over the range of 6--25 Hz is mainly caused by the unfused parts of the twitch contractions of motor units firing between recruitment (6--8/s) and total fusion of the twitches (25--30/s). The decline of the power spectrum toward higher frequencies can be explained by mechanical damping, which results from increasing fusion of the twitch contractions. The low-frequency part of the power spectrum is assumed to be the result of the slow force deviations produced by changes in the net output of the motoneuron pool. 6. These assumptions were supported by additional animal experiments where the number and rate of force-producing elements could be controlled. Bundles of ventral root filaments innervating cat soleus and gastrocnemius muscles were stimulated synchronously and asynchronously at a number of different rates. The force output of the strain gauge was recorded, filtered, and analyzed in the same way as the human force records. 7. Stimualtion of one nerve bundle at one fixed frequency led to a sharp peak in the power spectrum at that frequency plus peaks of decreasing height representing the harmonics of the stimulation frequency. The height of the peaks decreased at --37 dB/decade. 8...

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.

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