scholarly journals Infinite-Variate Extensions of Krawtchouk Polynomials and Zonal Spherical Functions over a Local Field

2021 ◽  
Vol 64 (1) ◽  
pp. 75-118
Author(s):  
Koei Kawamura
Keyword(s):  
Local Field ◽  
Spherical Functions ◽  
Krawtchouk Polynomials

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

Vagus Nerve Stimulation Induced Synchrony Modulation of Local Field Potential in the Rat Cerebral Cortex

2013 ◽  
Vol 133 (8) ◽  
pp. 1493-1500 ◽  
Author(s):  
Ryuji Kano ◽  
Kenichi Usami ◽  
Takahiro Noda ◽  
Tomoyo I. Shiramatsu ◽  
Ryohei Kanzaki ◽  
...  
Keyword(s):  
Cerebral Cortex ◽  
Vagus Nerve ◽  
Local Field ◽  
Nerve Stimulation ◽  
Local Field Potential ◽  
Vagus Nerve Stimulation ◽  
Field Potential ◽  
Rat Cerebral Cortex
Sign in / Sign up

Export Citation Format

Share Document