scholarly journals Quasi-isometric classification of some high dimensional right-angled Artin groups

2010 ◽  
pp. 681-692 ◽  
Author(s):  
Jason Behrstock ◽  
Tadeusz Januszkiewicz ◽  
Walter Neumann
Keyword(s):  
High Dimensional ◽  
Artin Groups ◽  
Right Angled Artin Groups

On commensurability of right-angled Artin groups II: RAAGs defined by paths

2019 ◽  
pp. 1-50
Author(s):  
MONTSERRAT CASALS–RUIZ ◽  
ILYA KAZACHKOV ◽  
ALEXANDER ZAKHAROV
Keyword(s):  
Integer Programming ◽  
Artin Groups ◽  
Linear Integer Programming ◽  
Right Angled Artin Groups

Abstract In this paper we continue the study of right-angled Artin groups up to commensurability initiated in [CKZ]. We show that RAAGs defined by different paths of length greater than 3 are not commensurable. We also characterise which RAAGs defined by paths are commensurable to RAAGs defined by trees of diameter 4. More precisely, we show that a RAAG defined by a path of length n > 4 is commensurable to a RAAG defined by a tree of diameter 4 if and only if n ≡ 2 (mod 4). These results follow from the connection that we establish between the classification of RAAGs up to commensurability and linear integer-programming.

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.

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

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.

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