scholarly journals Reliable cryo-EM resolution estimation with modified Fourier shell correlation

IUCrJ ◽  
2020 ◽  
Vol 7 (6) ◽  
pp. 995-1008 ◽  
Author(s):  
Pawel A. Penczek
Keyword(s):  
Adverse Effect ◽  
Input Data ◽  
Degrees Of Freedom ◽  
Strong Influence ◽  
Real Space ◽  
Reciprocal Space ◽  
Helical Structures ◽  
Gaussian Window ◽  
Resolution Estimation ◽  
Secondary Element

A modified Fourier shell correlation (mFSC) methodology is introduced that is aimed at addressing two fundamental problems that mar the use of the FSC: the strong influence of mask-induced artifacts on resolution estimation and the lack of assessment of FSC uncertainties stemming from the inability to determine the associated number of degrees of freedom. It is shown that by simply changing the order of the steps in which the FSC is computed, the correlations induced by masking of the input data can be eliminated. In addition, to further reduce artifacts, a smooth Gaussian window function is used to outline the regions of reciprocal space within which the mFSC is computed. Next, it is shown that the number of degrees of freedom (ndf) of the system is approximated well by combining the ndf associated with the Gaussian window in reciprocal space with further reduction of the ndf owing to the use of the mask in real space. It is demonstrated through the application of the mFSC to both single-particle and helical structures that the mFSC yields reliable, mask-induced artifact-free results as a result of the introduced modifications. Since the adverse effect of the mask is eliminated, it also becomes possible to compute robust local resolutions both per voxel of a 3D map as well as, in a newly developed approach, per functional subunit, segment or even larger secondary element of the studied complex.

scholarly journals Surveying the higher dimensions of the aperiodic composite nonadecane/urea

2014 ◽  
Vol 70 (a1) ◽  
pp. C171-C171
Author(s):  
Garry McIntyre ◽  
Marie-Hélène Lemée-Cailleau ◽  
Bertrand Toudic
Keyword(s):  
Degrees Of Freedom ◽  
Structural Changes ◽  
Dynamic Range ◽  
Real Space ◽  
Reciprocal Space ◽  
Neutron Spectrometer ◽  
Weak Intensity ◽  
Key Factor ◽  
Lower Temperature ◽  
First Time

We recently observed for the first time that there exist phase transitions where the structural changes correspond just to degrees of freedom hidden in the internal (super)space of an aperiodic material, here the composite nonadecane/urea [1]. A key factor in the discovery of this type of transition [2] was the examination of the diffraction pattern in 3D, only possible at the time on a four-circle triple-axis neutron spectrometer, the analyzer used in zero-energy transfer to reduce the background and improve resolution. Despite the greater accessibility in reciprocal space, the weak intensity of the superlattice reflections limited the volume of reciprocal space that could be explored. Modern neutron Laue diffractometers with large image-plate detectors permit rapid and extensive exploration of reciprocal space with high resolution in the two-dimensional projection and a wide dynamic range with negligible bleeding of intense diffraction spots [3]. Surveying nonadecane/urea with neutron Laue diffraction from 300K to 4K reveals further detail of the superspace-driven phase transition, notably an increase in misorientation in the plane perpendicular to the composite misfit axis, as well as a first-order transition to a new phase at lower temperature. These new observations shed further light on how nature can use the degrees of freedom hidden in the internal superspace to form states that cannot be envisaged in the usual 3D real space.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

2003 ◽  
Vol 218 (1) ◽  
Author(s):  
K. Chowdhury ◽  
S. Ghosh ◽  
M. Mukherjee
Keyword(s):  
Cytochrome C ◽  
Ab Initio ◽  
Structure Determination ◽  
Direct Method ◽  
Real Space ◽  
Reciprocal Space ◽  
Cytochrome C6 ◽  
Ab Initio Structure ◽  
Space Approach

AbstractThe direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c

“Cartography” in 7-Dimensions at CHESS: Mapping of Structure in Real Space, Reciprocal Space, and Time Using High-Energy X-rays

2020 ◽  
Vol 33 (6) ◽  
pp. 11-16
Author(s):  
K. E. Nygren, ◽  
D. C. Pagan, ◽  
J. P. C. Ruff ◽  
E. Arenholz ◽  
J. D. Brock
Keyword(s):  
High Energy ◽  
Real Space ◽  
Reciprocal Space ◽  
X Rays ◽  
Space And Time

scholarly journals Synthetic Gauge Structures in Real Space in a Ring lattice

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Kunal K. Das ◽  
Miroslav Gajdacz
Keyword(s):  
Degrees Of Freedom ◽  
Real Space ◽  
Physical Motion ◽  
Physical Universe ◽  
Subatomic Particles ◽  
Internal States ◽  
Synthetic Gauge Fields ◽  
Fundamental Forces ◽  
Spatially Varying ◽  
Internal Degrees Of Freedom

Abstract Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we propose a way to realize and study gauge structures in real space, manifest in external degrees of freedom of quantum states. We present a model based on a ring-shaped lattice potential, which allows for both Abelian and non-Abelian constructs. Non trivial Wilson loops are shown possible via physical motion of the system. The underlying physics is based on the close analogy of geometric phase with gauge potentials that has been utilized to create synthetic gauge fields with internal states of ultracold atoms. By scaling up to an array with spatially varying parameters, a discrete gauge field can be realized in position space, and its dynamics mapped over macroscopic size and time scales.

scholarly journals Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains

Science ◽  
2020 ◽  
Vol 367 (6474) ◽  
pp. 186-189 ◽  
Author(s):  
Jayadev Vijayan ◽  
Pimonpan Sompet ◽  
Guillaume Salomon ◽  
Joannis Koepsell ◽  
Sarah Hirthe ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Separation ◽  
Real Space ◽  
Quantum Gas ◽  
Interacting Particles ◽  
Time Resolved ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Charge Correlations ◽  
The Individual

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

Orientation Relationships and Interfaces Between Low Symmetry Phases in The Yttria-Alumina System

1994 ◽  
Vol 357 ◽  
Author(s):  
R. S. Hay
Keyword(s):  
Monoclinic Phase ◽  
Three Dimensional ◽  
Real Space ◽  
Reciprocal Space ◽  
High Symmetry ◽  
Orientation Relationships ◽  
Yttrium Aluminum ◽  
High Resolution Tem ◽  
Interphase Boundaries ◽  
Definition Of

AbstractInterphase boundaries and orientation relationships for yttria - yttrium-aluminum monoclinic and yttrium-aluminum monoclinic - yttrium-aluminum perovskite eutectics were observed by standard and high resolution TEM techniques. Three and five orientation relationships were found for each system, respectively. These eutectics all had a monoclinic phase and therefore had little potential for high symmetry overlap. In many cases low index planes with similer spacings or spacing multiples were parallel. However, presence of a monoclinic phase made definition of a three-dimensional low index near-CSL very difficult, so a combination of planes corresponding to reciprocal-space directions and zones corresponding to real-space directions were often needed for a geometric description of the orientation relationship. In general, two planes and the real-space direction corresponding to the zone for these planes described the orientation relationships. The disregistry between reciprocal-space coincidence sites was not localized by dislocations large enough to be visible.

Abinitiostructure solution of nucleic acids and proteins by direct methods: reciprocal-space and real-space approach

2005 ◽  
Vol 38 (1) ◽  
pp. 217-222 ◽  
Author(s):  
Krishna Chowdhury ◽  
Soma Bhattacharya ◽  
Monika Mukherjee
Keyword(s):  
Nucleic Acids ◽  
Direct Method ◽  
Heavy Atom ◽  
Direct Methods ◽  
Disulfide Bridge ◽  
Real Space ◽  
Reciprocal Space ◽  
Space Groups ◽  
Data Resolution ◽  
Modification Procedure

Anab initiomethod for solving macromolecular structures is described. The heavy atom(s) or some disulfide bridge in the structure are located from the phase sets selected on the basis of a figure of merit of a reciprocal-space-based multiple-solution direct method. Subsequent weighted Fourier recycling reveals recognizable structures for two nucleic acids where data resolution is 1.3 Å or better. With lower than 1.3 Å data resolution or sulfur as the heaviest atom in the structure, the phase refinement has been carried out using the density modification procedure (PERP) operating in direct space. The resulting electron density map can readily be interpreted. The methodology has been illustrated with six known nucleic acids and proteins crystallizing in different space groups. It has proved to be fast, simple to use and a very effective tool for solving macromolecular structures with data resolution up to 1.7 Å.

scholarly journals Real-Space and Reciprocal-Space Berry Phases in the Hall Effect ofMn1−xFexSi

2014 ◽  
Vol 112 (18) ◽  
Author(s):  
C. Franz ◽  
F. Freimuth ◽  
A. Bauer ◽  
R. Ritz ◽  
C. Schnarr ◽  
...  
Keyword(s):  
Hall Effect ◽  
Real Space ◽  
Reciprocal Space ◽  
Berry Phases

An eigenstate formulation of the magnetotelluric impedance tensor

Geophysics ◽  
1982 ◽  
Vol 47 (8) ◽  
pp. 1204-1214 ◽  
Author(s):  
Dwight E. Eggers
Keyword(s):  
Electric Fields ◽  
Degrees Of Freedom ◽  
Homogeneous Medium ◽  
Real Space ◽  
Conventional Approach ◽  
Impedance Tensor ◽  
Electric And Magnetic Fields ◽  
Coordinate Rotation ◽  
Rotation Methods ◽  
Transverse Electromagnetic

An important step in the interpretation of magnetotelluric (MT) data is the extraction of scalar parameters from the impedance tensor Z, the transfer function which relates the observed horizontal magnetic and electric fields. The conventional approach defines parameters in terms of elements of a coordinate‐rotated tensor. The rotation angle is chosen such that Z′(θ) approximates in some sense the form for a two‐dimensional (2-D) subsurface conductivity distribution, with zero elements on the diagonal. There are two major problems with this approach. (1) Apparent resistivities, defined from the off‐diagonal elements of the rotated tensor, are independent of the trace of Z. It is problematic that apparent resistivities, the parameters for which we have physical analogs and which are most heavily used in interpretation, are insensitive to the addition of an arbitrary constant on the diagonal of Z. (2) The conventional parameter set is incomplete; there are two degrees of freedom in Z which are transparent to all parameters. Through a variation of the classical eigenstate formulation of a matrix, it is shown that in general there exist two, and only two, polarization states for which the electric and magnetic fields have the same polarization at perpendicular orientations. For each eigenstate the magnetic and electric fields are related by a scalar, the eigenvalue for that state. This scalar relationship between fields is of identical form to the solution for transverse electromagnetic (TEM) waves in a homogeneous medium and thus provides a physically more satisfactory basis for defining apparent resistivity than the conventional approach using the off‐diagonal elements of the coordinate‐rotated impedance tensor. The eigenstate and coordinate‐rotation methods yield identical results in the limited cases of 1-D and 2-D subsurface conductivity distributions. The eigenstates provide the basis for new definitions of parameters as concise, closed expressions which are complete and more amenable to interpretational insight. The polarization ellipses defined by the eigenstates provide a concise display in real space of all the information contained in the impedance tensor.

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