scholarly journals Classification of External Zonotopal Algebras

10.37236/8299 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Gleb Nenashev
Keyword(s):  
Hyperplane Arrangements ◽  
One To One ◽  
Power Algebras

In this paper we work with power algebras associated to hyperplane arrangements. There are three main types of these algebras, namely, external, central, and internal zonotopal algebras. We classify all external algebras up to isomorphism in terms of zonotopes. Also, we prove that unimodular external zonotopal algebras are in one to one correspondence with regular matroids. For the case of central algebras we formulate a conjecture.

scholarly journals Classification of fused links

2016 ◽  
Vol 25 (14) ◽  
pp. 1650076 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Symmetric Group ◽  
Equivalence Classes ◽  
One To One ◽  
Text Component

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of [Formula: see text]-component fused links is in one-to-one correspondence with the set of elements of the abelization [Formula: see text] up to conjugation by elements from the symmetric group [Formula: see text].

Translation semantic variability: How semantic relatedness affects learning of translation-ambiguous words

2016 ◽  
Vol 20 (4) ◽  
pp. 783-794 ◽  
Author(s):  
JENNIFER BRACKEN ◽  
TAMAR DEGANI ◽  
CHELSEA EDDINGTON ◽  
NATASHA TOKOWICZ
Keyword(s):  
Language Learning ◽  
Word Learning ◽  
Ambiguous Word ◽  
Semantic Relatedness ◽  
Continuous Measure ◽  
Unique Variance ◽  
Ambiguous Words ◽  
One To One ◽  
Dichotomous Classification

Translations often do not align directly across languages, and indirect mappings reduce the accuracy of language learning. To facilitate examination of this issue, we developed a new continuous measure for quantifying the semantic relatedness of words with more than one translation (hereafter translation-ambiguous words). Participants rated the similarity of each translation to every other translation, yielding a Translation Semantic Variability (TSV) score, ranging from 1.00 (unrelated) to 7.00 (related). Then, we determined how relatedness between translations affects translation-ambiguous word learning from German to English. German words with low TSV scores were recognized as translations more slowly and less accurately than German words with high TSV scores. TSV explains unique variance beyond the previously-used dichotomous classification of words as form vs. meaning ambiguous. We propose that the relatedness of the translation alternatives influences learning because it affects the ease with which a one-to-one mapping can be established between form and meaning.

AN ALGEBRAIC THEORY FOR REGULAR LANGUAGES OF FINITE AND INFINITE WORDS

1993 ◽  
Vol 03 (04) ◽  
pp. 447-489 ◽  
Author(s):  
THOMAS WILKE
Keyword(s):  
Algebraic Theory ◽  
Algebraic Approach ◽  
Regular Languages ◽  
Cantor Space ◽  
Infinite Words ◽  
Finite Semigroups ◽  
Borel Hierarchy ◽  
Algebraic Description ◽  
One To One

An algebraic approach to the theory of regular languages of finite and infinite words (∞-languages) is presented. It extends the algebraic theory of regular languages of finite words, which is based on finite semigroups. Their role is taken over by a structure called right binoid. A variety theorem is proved: there is a one-to-one correspondence between varieties of ∞-languages and pseudovarieties of right binoids. The class of locally threshold testable languages and several natural subclasses (such as the class of locally testable languages) as well as classes of the Borel hierarchy over the Cantor space (restricted to regular languages) are investigated as examples for varieties of ∞-languages. The corresponding pseudovarieties of right binoids are characterized and in some cases defining equations are derived. The connections with the algebraic description and classification of regular languages of infinite words in terms of finite semigroups are pointed out.

Hyperplane arrangements for the fast matching and classification of visual landmarks

2014 ◽  
Vol 19 (3) ◽  
pp. 621-629
Author(s):  
Martin Stommel ◽  
Otthein Herzog ◽  
Weiliang Xu
Keyword(s):  
Hyperplane Arrangements ◽  
Visual Landmarks

AROUND DOT-DEPTH ONE

2012 ◽  
Vol 23 (06) ◽  
pp. 1323-1339 ◽  
Author(s):  
MANFRED KUFLEITNER ◽  
ALEXANDER LAUSER
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Membership Problem ◽  
First Order ◽  
Language Classes ◽  
One To One ◽  
Quantifier Alternation

The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider subclasses of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of alternation-free first-order logic without min- or max-predicate, respectively. For all fragments, we obtain effective algebraic characterizations. Moreover, we give new proofs for the decidability of the membership problem for dot-depth 1/2 and dot-depth 1.

Big data analysis with artificial intelligence technology based on machine learning algorithm

2020 ◽  
Vol 39 (5) ◽  
pp. 6733-6740
Author(s):  
Zeliang Zhang
Keyword(s):  
Machine Learning ◽  
Big Data ◽  
Data Analysis ◽  
Statistical Data ◽  
Big Data Analysis ◽  
Data Set ◽  
Artificial Intelligence Technology ◽  
One To One ◽  
Multi Classification

Artificial intelligence technology has been applied very well in big data analysis such as data classification. In this paper, the application of the support vector machine (SVM) method from machine learning in the problem of multi-classification was analyzed. In order to improve the classification performance, an improved one-to-one SVM multi-classification method was creatively designed by combining SVM with the K-nearest neighbor (KNN) method. Then the method was tested using UCI public data set, Statlog statistical data set and actual data. The results showed that the overall classification accuracy of the one-to-many SVM, one-to-one SVM and improved one-to-one SVM were 72.5%, 77.25% and 91.5% respectively in the classification of UCI publication data set and Statlog statistical data set, and the total classification accuracy of the neural network, decision tree, basic one-to-one SVM, directed acyclic graph improved one-to-one SVM and fuzzy decision method improved one-to-one SVM and improved one-to-one SVM proposed in this study was 83.98%, 84.55%, 74.07%, 81.5%, 82.68% and 92.9% respectively in the classification of fault data of transformer, which demonstrated the improved one-to-one SVM had good reliability. This study provides some theoretical bases for the application of methods such as machine learning in big data analysis.

scholarly journals Regular dessins uniquely determined by a nilpotent automorphism group

2018 ◽  
Vol 21 (3) ◽  
pp. 397-415 ◽  
Author(s):  
Na-Er Wang ◽  
Roman Nedela ◽  
Kan Hu
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Upper Bound ◽  
Automorphism Groups ◽  
Nilpotency Class ◽  
Isomorphism Classes ◽  
One To One

Abstract It is well known that the automorphism group of a regular dessin is a two-generator finite group, and the isomorphism classes of regular dessins with automorphism groups isomorphic to a given finite group G are in one-to-one correspondence with the orbits of the action of {{\mathrm{Aut}}(G)} on the ordered generating pairs of G. If there is only one orbit, then up to isomorphism the regular dessin is uniquely determined by the group G and it is called uniquely regular. In this paper we investigate the classification of uniquely regular dessins with a nilpotent automorphism group. The problem is reduced to the classification of finite maximally automorphic p-groups G, i.e., the order of the automorphism group of G attains Hall’s upper bound. Maximally automorphic p-groups of nilpotency class three are classified.

scholarly journals Maximally mutable Laurent polynomials

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Tom Coates ◽  
Alexander M. Kasprzyk ◽  
Giuseppe Pitton ◽  
Ketil Tveiten
Keyword(s):  
Mirror Symmetry ◽  
Three Dimensional ◽  
Computer Assisted ◽  
Del Pezzo Surfaces ◽  
Fano Varieties ◽  
Laurent Polynomials ◽  
Fano Manifold ◽  
One To One ◽  
Del Pezzo

We introduce a class of Laurent polynomials, called maximally mutable Laurent polynomials (MMLPs), which we believe correspond under mirror symmetry to Fano varieties. A subclass of these, called rigid, are expected to correspond to Fano varieties with terminal locally toric singularities. We prove that there are exactly 10 mutation classes of rigid MMLPs in two variables; under mirror symmetry these correspond one-to-one with the 10 deformation classes of smooth del Pezzo surfaces. Furthermore, we give a computer-assisted classification of rigid MMLPs in three variables with reflexive Newton polytope; under mirror symmetry these correspond one-to-one with the 98 deformation classes of three-dimensional Fano manifolds with very ample anti-canonical bundle. We compare our proposal to previous approaches to constructing mirrors to Fano varieties, and explain why mirror symmetry in higher dimensions necessarily involves varieties with terminal singularities. Every known mirror to a Fano manifold, of any dimension, is a rigid MMLP.

scholarly journals COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p3

2012 ◽  
Vol 11 (05) ◽  
pp. 1250100 ◽  
Author(s):  
DYLENE AGDA SOUZA DE BARROS ◽  
ALEXANDER GRISHKOV ◽  
PETR VOJTĚCHOVSKÝ
Keyword(s):  
Automorphism Group ◽  
Abelian Groups ◽  
Three Dimensional ◽  
Isomorphism Classes ◽  
Trivial Center ◽  
One To One ◽  
Nilpotent Class

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by [Formula: see text] the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z ≅ ℤp such that Q/Z ≅ ℤp × ℤp. Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop Fp in the variety of loops whose elements have order dividing p2 and whose associators have order dividing p, we show that every loop of [Formula: see text] is a quotient of Fp by a central subloop of order p3. The automorphism group of Fp induces an action of GL 2(p) on the three-dimensional subspaces of Z(Fp) ≅ (ℤp)4. The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from [Formula: see text]. We describe the orbits, and hence we classify the loops of [Formula: see text] up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing [Formula: see text] up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p3. There are precisely seven commutative automorphic loops of order p3 for every prime p, including the three abelian groups of order p3.

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