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Spherical harmonic correlation.
Middle: Spherical Harmonic Correlation Analysis between the 'true' model and the model estimated with (blue) and without (red) polar gap post-processing.
Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation.
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In this study the multivalent interactions of CTB and PnA to GM1 doped into a planar supported lipid bilayer (PSLB) are investigated by second-harmonic correlation spectroscopy (SHCS).
Binding kinetics of the multivalent proteins peanut agglutinin (PnA) and cholera toxin B subunit (CTB) to a GM1-doped 1,2-dioleoyl sn-glycero-3-phosphocholine (DOPC) lipid bilayer were investigated by both second-harmonic correlation spectroscopy (SHCS) and a traditional equilibrium binding isotherm.
In the multi-frequency harmonic wave correlation method (MHCM) as proposed in this work, for speckle patterns before and after the displacement, correlation calculations were performed on corresponding sets of data matrices assembled by amplitudes/intensities obtained from harmonic waves with different frequencies.
The set of tonality features is based on the calculation of the chromagram as described in[20, 21] and includes features like key, major/minor classification, chroma flatness, consonant strength, chroma eccentricity in a circle of fifths and harmonic strangeness (correlation between long- and short-term chroma).
By analogy with the spherical harmonics, the degree correlation between two spherical cap harmonic analyses can be estimated by (e.g., Langel and Hinze, 1998; section 4.5.2) (9)with and the estimated and 'true' local parameters of the Legendre basis function.
Hence, the choice for the reconstruction of non-overlapping harmonics whose presence is energetically similar to the energy of the overlapping harmonic suggests that the correlation factor between the involved partials will be higher.
Individual frequency components depend on the power production in different ways: characteristic harmonics are independent of power; interharmonics show a strong correlation with power; other harmonic and interharmonic components present various patterns.
The intensities of both harmonic and stochastic excitations and correlation time of stochastic excitations are assumed to be small in order to obtain approximate analytical results.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com