On Classification of Filiform Leibniz Algebras

2015 ◽  
Vol 22 (spec01) ◽  
pp. 757-774 ◽  
Author(s):  
J.R. Gómez ◽  
B.A. Omirov
Keyword(s):  
Lie Algebra ◽  
Arbitrary Dimension ◽  
Classification Problem ◽  
Graded Algebra ◽  
Leibniz Algebras ◽  
Special Basis

In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.

Unitary representations of the maps S1 → su(N, 1)

1987 ◽  
Vol 102 (2) ◽  
pp. 259-272 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Andrew Pressley
Keyword(s):  
Lie Algebra ◽  
Classification Problem ◽  
Unitary Representations ◽  
Affine Algebra ◽  
Simple Lie Algebra ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Highest Weight Representations

For many questions, both in Mathematics and in Physics, the most important representations of a Lie algebra a are those which are unitarizable and highest weight (such representations are automatically irreducible). The classification of such representations when a is a finite-dimensional complex simple Lie algebra was completed only recently (see [3] for details and further references) and the corresponding question when a is an affine algebra was investigated by Jakobsen and Kac [5]. Theorem 3·1 of that paper contains a list of unitarizable highest weight representations which is claimed to be exhaustive. However, we shall show that this list is incomplete by constructing a further family of such representations. In fact, the classification problem in the affine case must be considered to be still open.

scholarly journals An aggregate method for thorax diseases classification

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bayu Adhi Nugroho
Keyword(s):  
Network Architecture ◽  
Classification Problem ◽  
Calculation Algorithm ◽  
Training Pattern ◽  
Deep Network ◽  
Network Training ◽  
Chest X Ray ◽  
Medical Image Classification ◽  
Positive Pattern

AbstractA common problem found in real-word medical image classification is the inherent imbalance of the positive and negative patterns in the dataset where positive patterns are usually rare. Moreover, in the classification of multiple classes with neural network, a training pattern is treated as a positive pattern in one output node and negative in all the remaining output nodes. In this paper, the weights of a training pattern in the loss function are designed based not only on the number of the training patterns in the class but also on the different nodes where one of them treats this training pattern as positive and the others treat it as negative. We propose a combined approach of weights calculation algorithm for deep network training and the training optimization from the state-of-the-art deep network architecture for thorax diseases classification problem. Experimental results on the Chest X-Ray image dataset demonstrate that this new weighting scheme improves classification performances, also the training optimization from the EfficientNet improves the performance furthermore. We compare the aggregate method with several performances from the previous study of thorax diseases classifications to provide the fair comparisons against the proposed method.

scholarly journals Classification of unlabeled online media

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sakthi Kumar Arul Prakash ◽  
Conrad Tucker
Keyword(s):  
Social Media ◽  
Real World ◽  
Graphical Model ◽  
Ground Truth ◽  
Classification Problem ◽  
Machine Learning Algorithms ◽  
Social Media Networks ◽  
Online Social Media ◽  
Wide Range

AbstractThis work investigates the ability to classify misinformation in online social media networks in a manner that avoids the need for ground truth labels. Rather than approach the classification problem as a task for humans or machine learning algorithms, this work leverages user–user and user–media (i.e.,media likes) interactions to infer the type of information (fake vs. authentic) being spread, without needing to know the actual details of the information itself. To study the inception and evolution of user–user and user–media interactions over time, we create an experimental platform that mimics the functionality of real-world social media networks. We develop a graphical model that considers the evolution of this network topology to model the uncertainty (entropy) propagation when fake and authentic media disseminates across the network. The creation of a real-world social media network enables a wide range of hypotheses to be tested pertaining to users, their interactions with other users, and with media content. The discovery that the entropy of user–user and user–media interactions approximate fake and authentic media likes, enables us to classify fake media in an unsupervised learning manner.

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

VirusTaxo: Taxonomic classification of virus genome using multi-class hierarchical classification by k-mer enrichment

2021 ◽  
Author(s):  
Rajan Saha Raju ◽  
Abdullah Al Nahid ◽  
Preonath Shuvo ◽  
Rashedul Islam
Keyword(s):  
Genome Sequence ◽  
Rna Viruses ◽  
Hierarchical Classification ◽  
Classification Problem ◽  
Virus Genome ◽  
Taxonomic Classification ◽  
Dna Viruses ◽  
Dna And Rna ◽  
Full Length Genome

AbstractTaxonomic classification of viruses is a multi-class hierarchical classification problem, as taxonomic ranks (e.g., order, family and genus) of viruses are hierarchically structured and have multiple classes in each rank. Classification of biological sequences which are hierarchically structured with multiple classes is challenging. Here we developed a machine learning architecture, VirusTaxo, using a multi-class hierarchical classification by k-mer enrichment. VirusTaxo classifies DNA and RNA viruses to their taxonomic ranks using genome sequence. To assign taxonomic ranks, VirusTaxo extracts k-mers from genome sequence and creates bag-of-k-mers for each class in a rank. VirusTaxo uses a top-down hierarchical classification approach and accurately assigns the order, family and genus of a virus from the genome sequence. The average accuracies of VirusTaxo for DNA viruses are 99% (order), 98% (family) and 95% (genus) and for RNA viruses 97% (order), 96% (family) and 82% (genus). VirusTaxo can be used to detect taxonomy of novel viruses using full length genome or contig sequences.AvailabilityOnline version of VirusTaxo is available at https://omics-lab.com/virustaxo/.

Classification of three-dimensional solvable p-adic Leibniz algebras

2010 ◽  
Vol 2 (3) ◽  
pp. 207-221 ◽  
Author(s):  
A. Kh. Khudoyberdiyev ◽  
T. K. Kurbanbaev ◽  
B. A. Omirov
Keyword(s):  
Three Dimensional ◽  
Leibniz Algebras

Classification of Filiform Leibniz Algebras in Low Dimensions

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov
Keyword(s):  
Low Dimensions ◽  
Leibniz Algebras

scholarly journals The Algebraic and Geometric Classification of Four Dimensional Superalgebras

2021 ◽  
Author(s):  
◽  
Aaron Armour
Keyword(s):  
Classification Problem ◽  
Associative Algebras ◽  
New Variety ◽  
Graded Algebras ◽  
Finite Representation ◽  
Algebraic Classification ◽  
Irreducible Components ◽  
Module Algebras ◽  
Sweedler’S Hopf Algebra

<p><b>The algebraic and geometric classification of k-algbras, of dimension fouror less, was started by Gabriel in “Finite representation type is open” [12].</b></p> <p>Several years later Mazzola continued in this direction with his paper “Thealgebraic and geometric classification of associative algebras of dimensionfive” [21]. The problem we attempt in this thesis, is to extend the resultsof Gabriel to the setting of super (or Z2-graded) algebras — our main effortsbeing devoted to the case of superalgebras of dimension four. Wegive an algebraic classification for superalgebras of dimension four withnon-trivial Z2-grading. By combining these results with Gabriel’s we obtaina complete algebraic classification of four dimensional superalgebras.</p> <p>This completes the classification of four dimensional Yetter-Drinfeld modulealgebras over Sweedler’s Hopf algebra H4 given by Chen and Zhangin “Four dimensional Yetter-Drinfeld module algebras over H4” [9]. Thegeometric classification problem leads us to define a new variety, Salgn —the variety of n-dimensional superalgebras—and study some of its properties.</p> <p>The geometry of Salgn is influenced by the geometry of the varietyAlgn yet it is also more complicated, an important difference being thatSalgn is disconnected. While we make significant progress on the geometricclassification of four dimensional superalgebras, it is not complete. Wediscover twenty irreducible components of Salg4 — however there couldbe up to two further irreducible components.</p>

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