On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports

2021 ◽  
Vol 16 (1) ◽  
pp. 1-40
Author(s):  
Lan Nguyen
Keyword(s):  
Characteristic Zero ◽  
Functional Equations ◽  
Classification Problem ◽  
Rational Field ◽  
Maximal Solutions ◽  
All Solutions ◽  
Classification Of Solutions

Abstract In this paper, we classify all solutions with cyclic and semi-cyclic semigroup supports of the functional equations arising from multiplication of quantum integers with fields of coefficients of characteristic zero. This also solves completely the classification problem proposed by Melvyn Nathanson and Yang Wang concerning the solutions, with semigroup supports which are not prime subsemigroups of ℕ, to these functional equations for the case of rational field of coefficients. As a consequence, we obtain some results for other problems raised by Nathanson concerning maximal solutions and extension of supports of solutions to these functional equations in the case where the semigroup supports are not prime subsemigroups of ℕ.

Classification of Solutions for Harmonic Functions With Neumann Boundary Value

2018 ◽  
Vol 61 (2) ◽  
pp. 438-448 ◽  
Author(s):  
Tao Zhang ◽  
Chunqin Zhou
Keyword(s):  
Harmonic Functions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
All Solutions ◽  
Classification Of Solutions

AbstractIn this paper, we classify all solutions ofwith the finite conditionsHere c is a positive number and β > −1.

scholarly journals ON ASYMPTOTIC CLASSIFICATION OF SOLUTIONS TO FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH SINGULAR POWER NONLINEARITY

2016 ◽  
Vol 21 (4) ◽  
pp. 502-521 ◽  
Author(s):  
Irina Astashova
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
All Solutions ◽  
Classification Of Solutions ◽  
Type Differential Equation

The asymptotic behavior of all solutions to the fourth-order Emden– Fowler type differential equation with singular nonlinearity is investigated. The equation is transformed into a system on the three-dimensional sphere. By investigation of the asymptotic behavior of all possible trajectories of this system an asymptotic classification of all solutions to the equation is obtained.

A COMPLETE DESCRIPTION OF MAXIMAL SOLUTIONS OF FUNCTIONAL EQUATIONS ARISING FROM MULTIPLICATION OF QUANTUM INTEGERS

2011 ◽  
Vol 07 (01) ◽  
pp. 9-56 ◽  
Author(s):  
LAN NGUYEN
Keyword(s):  
Characteristic Zero ◽  
Functional Equations ◽  
Maximal Solutions

In this paper, we resolve a problem raised by Nathanson concerning the maximal solutions to functional equations naturally arising from multiplication of quantum integers ([4]). Together with our results obtained in [11], which treats the case where the field of coefficients is ℚ, this provides a complete description of the maximal solutions to these functional equations and their support bases P in characteristic zero setting.

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.

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/.

FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES

2016 ◽  
Vol 95 (2) ◽  
pp. 209-213
Author(s):  
YUEYUE LI ◽  
JIE-TAI YU
Keyword(s):  
Associative Algebra ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Free Associative Algebra ◽  
Polynomial Algebras ◽  
Fixed Element ◽  
The Given

Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

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>

Sign in / Sign up

Export Citation Format

Share Document