Detection of Stable Manifolds in High Dimensional Phase Space

1999 ◽  
pp. 440-443
Author(s):  
Tetsuro Konishi
Keyword(s):  
Phase Space ◽  
High Dimensional ◽  
Stable Manifolds ◽  
Dimensional Phase Space

scholarly journals Fractional Delay Time Embedding of EEG Signals into High Dimensional Phase Space

2014 ◽  
Vol 20 (8) ◽  
Author(s):  
R. Damasevicius ◽  
I. Martisius ◽  
V. Jusas ◽  
D. Birvinskas
Keyword(s):  
Phase Space ◽  
Delay Time ◽  
High Dimensional ◽  
Eeg Signals ◽  
Dimensional Phase Space ◽  
Fractional Delay

Low-dimensional chaos in high-dimensional phase space: how does it occur?

2003 ◽  
Vol 15 (2) ◽  
pp. 219-232 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Erik M. Bollt ◽  
Zonghua Liu
Keyword(s):  
Phase Space ◽  
High Dimensional ◽  
Dimensional Phase Space ◽  
Low Dimensional

The ADHD effect on the high-dimensional phase space trajectories of EEG signals

2019 ◽  
Vol 121 ◽  
pp. 39-49 ◽  
Author(s):  
Reza Yaghoobi Karimui ◽  
Sassan Azadi ◽  
Parviz Keshavarzi
Keyword(s):  
Phase Space ◽  
High Dimensional ◽  
Eeg Signals ◽  
Space Trajectories ◽  
Dimensional Phase Space ◽  
Phase Space Trajectories

scholarly journals Privacy-Preserving Data Sharing in High Dimensional Regression and Classification Settings

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Stephen E. Fienberg ◽  
Jiashun Jin
Keyword(s):  
Phase Diagram ◽  
Phase Space ◽  
Data Sharing ◽  
High Dimensional Data ◽  
Privacy Preserving ◽  
High Dimensional ◽  
Statistical Research ◽  
Higher Criticism ◽  
Dimensional Phase Space ◽  
Privacy Violation

We focus on the problem of multi-party data sharing in high dimensional data settings where the number of measured features (or the dimension) p is frequently much larger than the number of subjects (or the sample size) n, the so-called p >> n scenario that has been the focus of much recent statistical research. Here, we consider data sharing for two interconnected problems in high dimensional data analysis, namely the feature selection and classification. We characterize the notions of ``cautious", ``regular", and ``generous" data sharing in terms of their privacy-preserving implications for the parties and their share of data, with focus on the ``feature privacy" rather than the ``sample privacy", though the violation of the former may lead to the latter. We evaluate the data sharing methods using {\it phase diagram} from the statistical literature on multiplicity and Higher Criticism thresholding. In the two-dimensional phase space calibrated by the signal sparsity and signal strength, a phase diagram is a partition of the phase space and contains three distinguished regions, where we have no (feature)-privacy violation, relatively rare privacy violations, and an overwhelming amount of privacy violation.

Analysis of High-Dimensional Phase Space via Poincaré Section for Patient-Specific Seizure Detection

2016 ◽  
Vol 24 (3) ◽  
pp. 386-398 ◽  
Author(s):  
Morteza Zabihi ◽  
Serkan Kiranyaz ◽  
Ali Bahrami Rad ◽  
Aggelos K. Katsaggelos ◽  
Moncef Gabbouj ◽  
...  
Keyword(s):  
Phase Space ◽  
Seizure Detection ◽  
Patient Specific ◽  
High Dimensional ◽  
Poincaré Section ◽  
Poincare Section ◽  
Dimensional Phase Space

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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