Application of Reconstructed Phase Space in Autism Intervention

2019 ◽  
Author(s):  
Piyush Saxena ◽  
Devansh Saxena ◽  
Xiao Nie ◽  
Aaron Helmers ◽  
Nithin Ramachandran ◽  
...  
Keyword(s):  
Phase Space ◽  
Autism Intervention ◽  
Reconstructed Phase Space

Exterior Ballistic Data Processing by SVD and Wavelet Transform

2012 ◽  
Vol 562-564 ◽  
pp. 1394-1397
Author(s):  
Yu Hua Dong ◽  
Hai Chun Ning
Keyword(s):  
Wavelet Transform ◽  
Phase Space ◽  
Data Processing ◽  
Wavelet Decomposition ◽  
Hankel Matrix ◽  
Singular Value ◽  
Experimental Data Processing ◽  
Abnormal Detection ◽  
Reconstructed Phase Space ◽  
Trajectory Measurement

This paper proposes a method of wavelet transform combined with SVD (Singular Value Extracting), and the abnormal data elimination in its trajectory measurement is studied. After the wavelet decomposition of the observed data, combining the approximate component and the detail component, the phase space is reconstructed. The increment criterion of singular entropy is used for the input observed matrix of SVD, and the singular value is selected. Then the original signal is reconstructed by SVD inverse transform. This method overcomes the distortion problem of data end in phase space reconstruction by Hankel matrix. The reconstructed phase space by components of wavelet decomposition is orthogonal. So it further improves the accuracy of noise reduction and abnormal detection by SVD. The results of experimental data processing show the effectiveness of this method proposed in the paper.

The association between reconstructed phase space and Artificial Neural Networks for vectorcardiographic recognition of myocardial infarction

2018 ◽  
Vol 51 (3) ◽  
pp. 443-449 ◽  
Author(s):  
Cecília M. Costa ◽  
Ittalo S. Silva ◽  
Rafael D. de Sousa ◽  
Renato A. Hortegal ◽  
Carlos Danilo M. Regis
Keyword(s):  
Myocardial Infarction ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Phase Space ◽  
Reconstructed Phase Space ◽  
Artificial Neural

Dynamics of Thermoacoustic Oscillations Leading to Lean Flame Blowout

2012 ◽  
Author(s):  
Lipika Kabiraj ◽  
R. I. Sujith
Keyword(s):  
Time Series ◽  
Steady State ◽  
Phase Space ◽  
Dynamical Systems ◽  
Nonlinear Oscillation ◽  
Bifurcation Analysis ◽  
Nonlinear Time Series Analysis ◽  
Pressure Oscillations ◽  
Reconstructed Phase Space ◽  
Thermoacoustic Oscillations

Lean flame blowout induced by thermoacoustic oscillations is a serious problem faced by the power and propulsion industry. We analyze a prototypical thermoacoustic system through systematic bifurcation analysis and find that starting from a steady state, this system exhibits successive bifurcations resulting in complex nonlinear oscillation states, eventually leading to flame blowout. To understand the observed bifurcations, we analyze the oscillation states using nonlinear time series analysis, particularly through the representation of pressure oscillations on a reconstructed phase space. Prior to flame blowout, a bursting phenomenon is observed in pressure oscillations. These burst oscillations are found to exhibit similarities with the phenomenon known as intermittency in the dynamical systems theory. This investigation based on nonlinear analysis of experimentally acquired data from a thermoacoustic system sheds light on how thermoacoustic oscillations lead to flame blowout.

scholarly journals Complexity of COVID-19 Dynamics

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 50
Author(s):  
Bellie Sivakumar ◽  
Bhadran Deepthi
Keyword(s):  
Phase Space ◽  
Infectious Diseases ◽  
Nearest Neighbor ◽  
Respiratory Illness ◽  
Temporal Dynamic ◽  
Dynamic Complexity ◽  
Dimensional Phase Space ◽  
The World ◽  
Medium Level ◽  
Reconstructed Phase Space

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

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