Homotopy of gauge groups over high-dimensional manifolds

2021 ◽  
pp. 1-27
Author(s):  
Ruizhi Huang
Keyword(s):  
Homotopy Theory ◽  
High Dimensional ◽  
Gauge Groups ◽  
Classical Work

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high-dimensional manifolds. To be more specific, we study gauge groups of bundles over (n − 1)-connected closed 2n-manifolds, the classification of which was determined by Wall and Freedman in the combinatorial category. We also investigate the gauge groups of the total manifolds of sphere bundles based on the classical work of James and Whitehead. Furthermore, other types of 2n-manifolds are also considered. In all the cases, we show various homotopy decompositions of gauge groups. The methods are combinations of manifold topology and various techniques in homotopy theory.

scholarly journals Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals

2020 ◽  
Vol 10 (5) ◽  
pp. 1797 ◽  
Author(s):  
Mera Kartika Delimayanti ◽  
Bedy Purnama ◽  
Ngoc Giang Nguyen ◽  
Mohammad Reza Faisal ◽  
Kunti Robiatul Mahmudah ◽  
...  
Keyword(s):  
Machine Learning ◽  
Sleep Stage ◽  
Machine Learning Algorithms ◽  
High Dimensional ◽  
Sleep Stages ◽  
Eeg Signals ◽  
Stage Classification ◽  
Sleep Stage Classification ◽  
Low Dimensional

Manual classification of sleep stage is a time-consuming but necessary step in the diagnosis and treatment of sleep disorders, and its automation has been an area of active study. The previous works have shown that low dimensional fast Fourier transform (FFT) features and many machine learning algorithms have been applied. In this paper, we demonstrate utilization of features extracted from EEG signals via FFT to improve the performance of automated sleep stage classification through machine learning methods. Unlike previous works using FFT, we incorporated thousands of FFT features in order to classify the sleep stages into 2–6 classes. Using the expanded version of Sleep-EDF dataset with 61 recordings, our method outperformed other state-of-the art methods. This result indicates that high dimensional FFT features in combination with a simple feature selection is effective for the improvement of automated sleep stage classification.

CLASSIFICATION OF HIGH-DIMENSIONAL MICROARRAY DATA WITH A TWO-STEP PROCEDURE VIA A WILCOXON CRITERION AND MULTILAYER PERCEPTRON

2011 ◽  
Vol 10 (01) ◽  
pp. 1-14
Author(s):  
VLADIMIR NIKULIN ◽  
TIAN-HSIANG HUANG ◽  
GEOFFREY J. MCLACHLAN
Keyword(s):  
Data Mining ◽  
Feature Selection ◽  
High Dimensional ◽  
Second Step ◽  
Support Vector ◽  
Step Procedure ◽  
Leave One Out ◽  
Natural Combination ◽  
Feature Selection Techniques

The method presented in this paper is novel as a natural combination of two mutually dependent steps. Feature selection is a key element (first step) in our classification system, which was employed during the 2010 International RSCTC data mining (bioinformatics) Challenge. The second step may be implemented using any suitable classifier such as linear regression, support vector machine or neural networks. We conducted leave-one-out (LOO) experiments with several feature selection techniques and classifiers. Based on the LOO evaluations, we decided to use feature selection with the separation type Wilcoxon-based criterion for all final submissions. The method presented in this paper was tested successfully during the RSCTC data mining Challenge, where we achieved the top score in the Basic track.

scholarly journals Methodology Proposal of ADHD Classification of Children Based on Cross Recurrence Plots

2021 ◽  
Author(s):  
Marco Aceves-Fernandez
Keyword(s):  
Machine Learning ◽  
Spectral Distribution ◽  
High Dimensional ◽  
Control Group ◽  
Machine Learning Method ◽  
Learning Method ◽  
Recurrence Plots ◽  
Eeg Signals ◽  
Power Spectral

Abstract Dealing with electroencephalogram signals (EEG) are often not easy. The lack of predicability and complexity of such non-stationary, noisy and high dimensional signals is challenging. Cross Recurrence Plots (CRP) have been used extensively to deal with detecting subtle changes in signals even when the noise is embedded in the signal. In this contribution, a total of 121 children performed visual attention experiments and a proposed methodology using CRP and a Welch Power Spectral Distribution have been used to classify then between those who have ADHD and the control group. Additional tools were presented to determine to which extent the proposed methodology is able to classify accurately and avoid misclassifications, thus demonstrating that this methodology is feasible to classify EEG signals from subjects with ADHD. Lastly, the results were compared with a baseline machine learning method to prove experimentally that this methodology is consistent and the results repeatable.

Classification of high-dimensional evolving data streams via a resource-efficient online ensemble

2017 ◽  
Vol 31 (5) ◽  
pp. 1242-1265 ◽  
Author(s):  
Tingting Zhai ◽  
Yang Gao ◽  
Hao Wang ◽  
Longbing Cao
Keyword(s):  
Data Streams ◽  
High Dimensional ◽  
Evolving Data
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