Fractional residual series for conformable time‐fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations of seventh order

2021 ◽  
Author(s):  
Mohammed Al‐Smadi
Keyword(s):  
Residual Series ◽  
Seventh Order

scholarly journals A Sequential Autoencoder for Teleconnection Analysis

2020 ◽  
Vol 12 (5) ◽  
pp. 851 ◽  
Author(s):  
Jiena He ◽  
J. Ronald Eastman
Keyword(s):  
Time Series ◽  
Neural Representation ◽  
Strongly Correlated ◽  
Atmospheric Sciences ◽  
Teleconnection Patterns ◽  
The Earth ◽  
Unsupervised Neural Network ◽  
Residual Series ◽  
Components Analysis ◽  
Computationally Intensive

Many aspects of the earth system are known to have preferred patterns of variability, variously known in the atmospheric sciences as modes or teleconnections. Approaches to discovering these patterns have included principal components analysis and empirical orthogonal teleconnection (EOT) analysis. The latter is very effective but is computationally intensive. Here, we present a sequential autoencoder for teleconnection analysis (SATA). Like EOT, it discovers teleconnections sequentially, with subsequent analyses being based on residual series. However, unlike EOT, SATA uses a basic linear autoencoder as the primary tool for analysis. An autoencoder is an unsupervised neural network that learns an efficient neural representation of input data. With SATA, the input is an image time series and the neural representation is a unidimensional time series. SATA then locates the 0.5% of locations with the strongest correlation with the neural representation and averages their temporal vectors to characterize the teleconnection. Evaluation of the procedure showed that it is several orders of magnitude faster than other approaches to EOT, produces teleconnection patterns that are more strongly correlated to well-known teleconnections, and is particularly effective in finding teleconnections with multiple centers of action (such as dipoles).

scholarly journals Gravitational scattering at the seventh order in G : Nonlocal contribution at the sixth post-Newtonian accuracy

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Donato Bini ◽  
Thibault Damour ◽  
Andrea Geralico ◽  
Stefano Laporta ◽  
Pierpaolo Mastrolia
Keyword(s):  
Seventh Order ◽  
Gravitational Scattering
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