scholarly journals Classification of Low Dimensional 3-Lie Superalgebras

2016 ◽  
pp. 1-12 ◽  
Author(s):  
Viktor Abramov ◽  
Priit Lätt
Keyword(s):  
Lie Superalgebras ◽  
Low Dimensional

scholarly journals A classification of low dimensional multiplicative Hom-Lie superalgebras

2016 ◽  
Vol 14 (1) ◽  
pp. 613-628 ◽  
Author(s):  
Chunyue Wang ◽  
Qingcheng Zhang ◽  
Zhu Wei
Keyword(s):  
Jacobi Identity ◽  
Complete Classification ◽  
Lie Superalgebras ◽  
Low Dimensions ◽  
Linear Map ◽  
Low Dimensional

Abstract We study a twisted generalization of Lie superalgebras, called Hom-Lie superalgebras. It is obtained by twisting the graded Jacobi identity by an even linear map. We give a complete classification of the complex multiplicative Hom-Lie superalgebras of low dimensions.

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

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 Primitive ideals, twisting functors and star actions for classical Lie superalgebras

2016 ◽  
Vol 2016 (718) ◽  
Author(s):  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Representation Theory ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Primitive Ideals

AbstractWe study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category

Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices

1992 ◽  
Vol 436 (1896) ◽  
pp. 55-68 ◽  
Keyword(s):  
Simple Formula ◽  
Three Dimensional ◽  
Voronoi Cell ◽  
Dimensional Lattice ◽  
Usual Treatment ◽  
Low Dimensional

The aim of this paper is to describe how the Voronoi cell of a lattice changes as that lattice is continuously varied. The usual treatment is simplified by the introduction of new parameters called the vonorms and conorms of the lattice. The present paper deals with dimensions n ≼ 3; a sequel will treat four-dimensional lattices. An elegant algorithm is given for the Voronoi reduction of a three-dimensional lattice, leading to a new proof of Voronoi’s theorem that every lattice of dimension n ≼ 3 is of the first kind, and of Fedorov’s classification of the three-dimensional lattices into five types. There is a very simple formula for the determinant of a three-dimensional lattice in terms of its conorms.

scholarly journals The local Universe in the era of large surveys – I. Spectral classification of S0 galaxies

2020 ◽  
Vol 495 (4) ◽  
pp. 4135-4157 ◽  
Author(s):  
J L Tous ◽  
J M Solanes ◽  
J D Perea
Keyword(s):  
Dimensional Space ◽  
Spectral Characteristics ◽  
Principal Component ◽  
Morphological Type ◽  
Physical Parameters ◽  
Star Forming ◽  
Interesting Possibility ◽  
Low Dimensional ◽  
Free Machine

ABSTRACT This is the first paper in a series devoted to review the main properties of galaxies designated S0 in the Hubble classification system. Our aim is to gather abundant and, above all, robust information on the most relevant physical parameters of this poorly understood morphological type and their possible dependence on the environment, which could later be used to assess their possible formation channel(s). The adopted approach combines the characterization of the fundamental features of the optical spectra of $68\, 043$ S0 with heliocentric z ≲ 0.1 with the exploration of a comprehensive set of their global attributes. A principal component analysis is used to reduce the huge number of dimensions of the spectral data to a low-dimensional space facilitating a bias-free machine-learning-based classification of the galaxies. This procedure has revealed that objects bearing the S0 designation consist, despite their similar morphology, of two separate subpopulations with statistically inconsistent physical properties. Compared to the absorption-dominated S0, those with significant nebular emission are, on average, somewhat less massive, more luminous with less concentrated light profiles, have a younger, bluer, and metal-poorer stellar component, and avoid high-galaxy-density regions. Noteworthy is the fact that the majority of members of this latter class, which accounts for at least a quarter of the local S0 population, show star formation rates and spectral characteristics entirely similar to those seen in late spirals. Our findings suggest that star-forming S0 might be less rare than hitherto believed and raise the interesting possibility of identifying them with plausible progenitors of their quiescent counterparts.

scholarly journals A Benign and Malignant Breast Tumor Classification Method via Efficiently Combining Texture and Morphological Features on Ultrasound Images

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mengwan Wei ◽  
Yongzhao Du ◽  
Xiuming Wu ◽  
Qichen Su ◽  
Jianqing Zhu ◽  
...  
Keyword(s):  
Breast Tumor ◽  
Texture Features ◽  
Morphological Features ◽  
High Dimensional ◽  
Svm Classifier ◽  
Ultrasound Images ◽  
Malignant Breast Tumor ◽  
Malignant Breast ◽  
Low Dimensional

The classification of benign and malignant based on ultrasound images is of great value because breast cancer is an enormous threat to women’s health worldwide. Although both texture and morphological features are crucial representations of ultrasound breast tumor images, their straightforward combination brings little effect for improving the classification of benign and malignant since high-dimensional texture features are too aggressive so that drown out the effect of low-dimensional morphological features. For that, an efficient texture and morphological feature combing method is proposed to improve the classification of benign and malignant. Firstly, both texture (i.e., local binary patterns (LBP), histogram of oriented gradients (HOG), and gray-level co-occurrence matrixes (GLCM)) and morphological (i.e., shape complexities) features of breast ultrasound images are extracted. Secondly, a support vector machine (SVM) classifier working on texture features is trained, and a naive Bayes (NB) classifier acting on morphological features is designed, in order to exert the discriminative power of texture features and morphological features, respectively. Thirdly, the classification scores of the two classifiers (i.e., SVM and NB) are weighted fused to obtain the final classification result. The low-dimensional nonparameterized NB classifier is effectively control the parameter complexity of the entire classification system combine with the high-dimensional parametric SVM classifier. Consequently, texture and morphological features are efficiently combined. Comprehensive experimental analyses are presented, and the proposed method obtains a 91.11% accuracy, a 94.34% sensitivity, and an 86.49% specificity, which outperforms many related benign and malignant breast tumor classification methods.

scholarly journals Equivariant Map Queer Lie Superalgebras

2016 ◽  
Vol 68 (2) ◽  
pp. 258-279 ◽  
Author(s):  
Lucas Calixto ◽  
Adriano Moura ◽  
Alistair Savage
Keyword(s):  
Finite Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Equivariant Map ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Regular Maps ◽  
A Finite Group ◽  
Special Case

AbstractAn equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Γ acting on X and q. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Γ is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Γ-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.

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