scholarly journals Fourier transformation in spherical systems as a tool of structural biology

Author(s):  
A. V. Batyanovskii ◽  
V. A. Namiot ◽  
I. V. Filatov ◽  
V. G. Tumanyan ◽  
N. G. Esipova ◽  
...  

Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.

2021 ◽  
Author(s):  
Scott A. Stone ◽  
Quinn A Boser ◽  
T Riley Dawson ◽  
Albert H Vette ◽  
Jacqueline S Hebert ◽  
...  

Assessing gaze behaviour during real-world tasks is difficult; dynamic bodies moving through dynamic worlds make finding gaze fixations challenging. Current approaches involve laborious coding of pupil positions overlaid on video. One solution is to combine eye tracking with motion tracking to generate 3D gaze vectors. When combined with tracked or known object locations, fixation detection can be automated. Here we use combined eye and motion tracking and explore how linear regression models generate accurate 3D gaze vectors. We compare spatial accuracy of models derived from four short calibration routines across three data types: the performance of calibration routines were assessed using calibration data, a validation task that demands short fixations on task-relevant locations, and an object interaction task we used to bridge the gap between laboratory and "in the wild" studies. Further, we generated and compared models using spherical and cartesian coordinate systems and monocular (Left or Right) or binocular data. Our results suggest that all calibration routines perform similarly, with the best performance (i.e., sub-centimeter errors) coming from the task (i.e., the most "natural") trials when the participant is looking at an object in front of them. Further, we found that spherical coordinate systems generate more accurate gaze vectors with no differences in accuracy when using monocular or binocular data. Overall, we recommend recording one-minute calibration datasets, using a binocular eye tracking headset (for redundancy), a spherical coordinate system when depth is not considered, and ensuring data quality (i.e., tracker positioning) is high when recording datasets.


2002 ◽  
Vol 12 (2) ◽  
pp. 185-202 ◽  
Author(s):  
Imre Bertfai

The well-known methodology of the Fourier analysis is put against the background in the 2nd half of the century parallel to the development of the time-domain approach in the analysis of mainly economical time series. However, from the author's point of view, the former possesses some hidden analytical advantages which deserve to be re-introduced to the toolbox of analysts. This paper, through several case studies, reports research results for computer algorithm providing a harmonic model for time series. The starting point of the particular method is a harmonic analysis (Fourier-analysis or Lomb-periodogram). The results are optimized in a multifold manner resulting in a model which is easy to handle and able to forecast the underlying data. The results provided are particularly free from limitations characteristic for that methods. Furthermore, the calculated results are easy to interpret and use for further decisions. Nevertheless, the author intends to enhance the procedure in several ways. The method shown seems to be very effective and useful in modeling time series consisting of periodic terms. An additional advantage is the easy interpretation of the obtained parameters.


Author(s):  
M.A.A.M. Faham ◽  
H.M. Nasir

In a recent paper (Nasir, 2007), a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. In this work, we explore some linear relations between these two sets of spherical harmonics. Moreover, a power representation for the set of weakly orthogonal spherical harmonics corresponding to a mode is presented. We also determine the norm of the orthogonal spherical harmonics and hence the inner products for the weakly orthogonal spherical harmonics. As an immediate application of these properties, we present a Fourier series formulation of spherical functions defined on the cubed-sphere.  


2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Krishna Prasad Madasu

The effect of a closed boundary on the hydrodynamic drag of a nonconcentric semipermeable sphere in an incompressible viscous fluid is investigated. Darcy’s law holds in the permeable region and Stokes flow used inside the spherical cavity. Suitable boundary conditions are used on the surface of a semipermeable sphere and spherical cavity. Two spherical coordinate systems are used to solve the problem. By superposition principle, a general solution is constructed from the solutions based on the semipermeable sphere and spherical cavity. Numerical results for the hydrodynamic drag force exerted on the particle is obtained with good convergence for various values of the relative distance between the centers of the inner sphere and spherical cavity, permeability parameter and the separation parameter. The numerical values of the hydrodynamic drag force generalize the results obtained for an eccentric solid sphere.


Sign in / Sign up

Export Citation Format

Share Document