Taking advantage of multiplet structure for lineshape analysis in Fourier space

Three-dimensional reconstruction techniques using electron microscopy have been principally developed for application to 2-D arrays (i.e. monolayers) of biological molecules and symmetrical single particles (e.g. helical viruses). However many biological molecules that crystallise form multilayered microcrystals which are unsuitable for study by either the standard methods of 3-D reconstruction or, because of their size, by X-ray crystallography. The grid sectioning technique enables a number of different projections of such microcrystals to be obtained in well defined directions (e.g. parallel to crystal axes) and poses the problem of how best these projections can be used to reconstruct the packing and shape of the molecules forming the microcrystal.Given sufficient projections there may be enough information to do a crystallographic reconstruction in Fourier space. We however have considered the situation where only a limited number of projections are available, as for example in the case of catalase platelets where three orthogonal and two diagonal projections have been obtained (Fig. 1).

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The extended Fourier algorithm: Application in discrete optics and electron holography

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100172322 ◽

1994 ◽

Vol 52 ◽

pp. 918-919

Author(s):

E. Voelkl ◽

L. F. Allard

Keyword(s):

Fourier Transform ◽

Fourier Transforms ◽

Sampling Rate ◽

Electron Holography ◽

Optical Bench ◽

Fourier Space ◽

Ccd Cameras ◽

Simulated Image ◽

Initial Sampling ◽

Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010018135x ◽

1990 ◽

Vol 48 (1) ◽

pp. 520-521

Author(s):

Neng-Yu Zhang ◽

Bruce F. McEwen ◽

Joachim Frank

Keyword(s):

Function Space ◽

Convex Sets ◽

Electron Tomography ◽

Spinal Ganglion ◽

Fourier Space ◽

Missing Information ◽

Voltage Electron ◽

High Voltage Electron Microscope ◽

Energy Bound ◽

Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

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Fourier space time-stepping for option pricing with Lévy models

The Journal of Computational Finance ◽

10.21314/jcf.2008.178 ◽

2008 ◽

Vol 12 (2) ◽

pp. 1-29 ◽

Cited By ~ 94

Author(s):

Kenneth Jackson ◽

Sebastian Jaimungal ◽

Vladimir Surkov

Keyword(s):

Option Pricing ◽

Space Time ◽

Fourier Space ◽

Time Stepping

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Parallel Option Pricing with Fourier Space Time-Stepping Method on Graphics Processing Units

SSRN Electronic Journal ◽

10.2139/ssrn.1020207 ◽

2007 ◽

Cited By ~ 1

Author(s):

Vladimir Surkov

Keyword(s):

Option Pricing ◽

Graphics Processing Units ◽

Space Time ◽

Fourier Space ◽

Time Stepping ◽

Graphics Processing

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The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a multitracer analysis in Fourier space for measuring the cosmic structure growth and expansion rate

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab849 ◽

2021 ◽

Vol 504 (1) ◽

pp. 33-52

Author(s):

Gong-Bo Zhao ◽

Yuting Wang ◽

Atsushi Taruya ◽

Weibing Zhang ◽

Héctor Gil-Marín ◽

...

Keyword(s):

Growth Rate ◽

Power Spectrum ◽

Confidence Level ◽

Expansion Rate ◽

Fourier Space ◽

Redshift Range ◽

Significance Level ◽

Data Product ◽

New Development ◽

Cross Power Spectrum

ABSTRACT We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of z ∈ [0.6, 1.1], and detect an RSD signal from the cross-power spectrum at a ∼4σ confidence level, i.e., fσ8 = 0.317 ± 0.080 at zeff = 0.77. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measure the BAO distances and growth rate simultaneously at two effective redshifts, namely, DM/rd (z = 0.70) = 17.96 ± 0.51, DH/rd (z = 0.70) = 21.22 ± 1.20, fσ8 (z = 0.70) = 0.43 ± 0.05, and DM/rd (z = 0.845) = 18.90 ± 0.78, DH/rd (z = 0.845) = 20.91 ± 2.86, fσ8 (z = 0.845) = 0.30 ± 0.08. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-α sample, our measurement has raised the significance level of a non-zero ΩΛ to ∼11σ. The data product of this work is publicly available at https://github.com/icosmology/eBOSS_DR16_LRGxELG and https://www.sdss.org/science/final-bao-and-rsd-measurements/.

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