scholarly journals Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

2021 ◽  
Vol 10 (1) ◽  
pp. 166-179
Author(s):  
Peter J. Dukes ◽  
Xavier Martínez-Rivera
Keyword(s):  
Finite Fields ◽  
Coding Theory ◽  
Ramsey Theory ◽  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Characteristic Sequence ◽  
Combinatorial Properties ◽  
Recent Classification

Abstract The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽 n×n is defined as ℓ1ℓ2· · · ℓ n , where ℓ j ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author’s recent classification of the epr-sequences of symmetric matrices over the field 𝔽 = 𝔽2, we initiate a study of the case 𝔽= 𝔽3. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.

scholarly journals The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga
Keyword(s):  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Multiplicity ◽  
Necessary And Sufficient ◽  
Multiplicity Of An Eigenvalue

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.

scholarly journals The enhanced principal rank characteristic sequence over a field of characteristic 2

2017 ◽  
Vol 32 ◽  
pp. 273-290 ◽  
Author(s):  
Xavier Martínez-Rivera
Keyword(s):  
Symmetric Matrix ◽  
Complete Characterization ◽  
Symmetric Matrices ◽  
Characteristic Sequence ◽  
The Matrix ◽  
Characteristic 2

The enhanced principal rank characteristic sequence (epr-sequence) of an $n \times n$ symmetric matrix over a field $\F$ was recently defined as $\ell_1 \ell_2 \cdots \ell_n$, where $\ell_k$ is either $\tt A$, $\tt S$, or $\tt N$ based on whether all, some (but not all), or none of the order-$k$ principal minors of the matrix are nonzero. Here, a complete characterization of the epr-sequences that are attainable by symmetric matrices over the field $\Z_2$, the integers modulo $2$, is established. Contrary to the attainable epr-sequences over a field of characteristic $0$, this characterization reveals that the attainable epr-sequences over $\Z_2$ possess very special structures. For more general fields of characteristic $2$, some restrictions on attainable epr-sequences are obtained.

scholarly journals A57 THE USE AND INTERPRETATION OF HLA-DQ2/DQ8 GENOTYPING BY PEDIATRIC GASTROENTEROLOGISTS

2021 ◽  
Vol 4 (Supplement_1) ◽  
pp. 14-15
Author(s):  
B Moreau ◽  
E Robidoux
Keyword(s):  
Risk Groups ◽  
Risk Classification ◽  
Low Risk ◽  
Risk Alleles ◽  
Seronegative Patient ◽  
Espghan Guidelines ◽  
Recent Classification ◽  
American Society ◽  
Hla Dq2

Abstract Background A recent classification of high and low risk alleles associated with celiac disease (CD) shows that the presence of a single allele (DQA1*05 or DQB1*02; coding together for HLA-DQ2), without a positive genotype (HLA-DQ2 and or HLA-DQ8), represents a risk of developing the disease. Aims The aim of this study is to evaluate the use and interpretation of the HLA-DQ2/DQ8 genotyping by pediatric gastroenterologists, as there is no study on the matter and the latest guidelines do not address this risk classification. Methods A web-based survey was sent by email to all NASPGHAN (North American society of pediatric gastroenterolgy, hepatology and nutrition) members. Results Results 294 pediatric gastroenterologists sent a complete survey. 86,1% use the HLA-DQ2/DQ8 genotyping according mainly to the NASPGHAN and ESPGHAN guidelines. The main indications considered were to exclude CD in a patient on a gluten-free diet with a resolution of his symptoms and in a seronegative patient with equivocal biopsies. A minority would consider the genotyping for screening high risk groups or for making a diagnosis in children with high specific CD antibodies and strong clinical suspicion without performing biopsies, as suggested by the ESPGHAN guidelines. The alleles associated with CD are not well known, but 76,7% the participants are aware of the risk classification. While only 62,8% have access to the complete genotype, 47,8% consider it useful. Nevertheless, 82,6% would still want to know the presence of a low risk allele. Conclusions The risk classification of alleles related to CD warrants a modification of the genotyping result with access to the alleles and an adaptation of the guidelines. Funding Agencies None

scholarly journals Neuropathology of Temporal Lobe Epilepsy

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Fahd Al Sufiani ◽  
Lee Cyn Ang
Keyword(s):  
Temporal Lobe Epilepsy ◽  
Temporal Lobe ◽  
Focal Cortical Dysplasia ◽  
Cortical Dysplasia ◽  
Wide Range ◽  
Pathologic Findings ◽  
Pathologic Lesions ◽  
Recent Classification ◽  
Associated Tumors

Pathologic findings in surgical resections from patients with temporal lobe epilepsy include a wide range of diagnostic possibilities that can be categorized into different groups on the basis of etiology. This paper outlines the various pathologic entities described in temporal lobe epilepsy, including some newly recognized epilepsy-associated tumors, and briefly touch on the recent classification of focal cortical dysplasia. This classification takes into account coexistent pathologic lesions in focal cortical dysplasia.

A Global Phylogenomic Study of the Thelypteridaceae

2021 ◽  
Vol 46 (4) ◽  
pp. 891-915
Author(s):  
Susan Fawcett ◽  
Alan R. Smith ◽  
Michael Sundue ◽  
J. Gordon Burleigh ◽  
Emily B. Sessa ◽  
...  
Keyword(s):  
Morphological Characters ◽  
Morphological Evidence ◽  
Phylogenetic Studies ◽  
The Family ◽  
Likelihood Analysis ◽  
Single Genus ◽  
The Subject ◽  
Recent Classification ◽  
Phylogenomic Study

Abstract— The generic classification of the Thelypteridaceae has been the subject of much controversy. Proposed taxonomic systems have varied from recognizing the approximately 1200 species in the family within the single genus Thelypteris, to systems favoring upwards of 30 genera. Insights on intrafamilial relationships, especially for neotropical taxa, have been gained from recent phylogenetic studies; however, in the most recent classification, 10 of 30 recognized genera are either non-monophyletic or untested. We sequenced 407 nuclear loci for 621 samples, representing all recognized genera and approximately half the known species diversity. These were analyzed using both maximum likelihood analysis of a concatenated matrix and multi-species coalescent methods. Our phylogenomic results, informed by recently published morphological evidence, provide the foundation for a generic classification which recircumscribed 14 genera and recognized seven new genera. The 37 monophyletic genera sampled demonstrate greater geographic coherence than previous taxonomic concepts suggested. Additionally, our results demonstrate that certain morphological characters, such as frond division, are evolutionarily labile and are thus inadequate for defining genera.

An Efficient Algorithm for Automating Classification of Chemical Reactions into Classes in Ugi’s Reaction Scheme

2013 ◽  
pp. 285-296
Author(s):  
Sanjay Ram ◽  
Somnath Pal
Keyword(s):  
Chemical Reactions ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Symmetric Matrix ◽  
Reaction Scheme ◽  
Space Complexity ◽  
Average Case ◽  
Model Driven ◽  
Reaction Matrix

There are two approaches for classification of chemical reactions: Model-Driven and Data-Driven. In this paper, the authors develop an efficient algorithm based on a model-driven approach developed by Ugi and co-workers for classification of chemical reactions. The authors’ algorithm takes reaction matrix of a chemical reaction as input and generates its appropriate class as output. Reaction matrices being symmetric, matrix implementation of Ugi’s scheme using upper/lower tri-angular matrix is of O(n2) in terms of space complexity. Time complexity of similar matrix implementation is O(n4), both in worst case as well as in average case. The proposed algorithm uses two fixed size look-up tables in a novel way and requires constant space complexity. Time complexity both in worst and average cases of the algorithm is linear.

SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS

1992 ◽  
Vol 06 (13) ◽  
pp. 773-784 ◽  
Author(s):  
R. HILFER
Keyword(s):  
Phase Transitions ◽  
Statistical Physics ◽  
Thermodynamic Description ◽  
Classification Theory ◽  
Nonequilibrium Phase Transitions ◽  
Critical Limit ◽  
Scaling Hypothesis ◽  
Recent Classification ◽  
Thermodynamics And Statistical Mechanics

The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transitions by orders less than unity and by the fact that equilibrium thermodynamics and statistical mechanics become inapplicable at the critical point. The latter fact requires a change in the Gibbs assumption underlying the canonical and grandcanonical ensembles in order to recover the thermodynamic description in the critical limit.

scholarly journals Finding roots in with the successive resultants algorithm

2014 ◽  
Vol 17 (A) ◽  
pp. 203-217 ◽  
Author(s):  
Christophe Petit
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Finite Fields ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Polynomial Equations ◽  
Preliminary Results ◽  
Characteristic Case ◽  
Practical Security

AbstractThe problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. In this paper, we consider polynomial equations over a ‘large’ finite field with a ‘small’ characteristic. We introduce a new algorithm for solving this type of equations, called the successive resultants algorithm (SRA). SRA is radically different from previous algorithms for this problem, yet it is conceptually simple. A straightforward implementation using Magma was able to beat the built-in Roots function for some parameters. These preliminary results encourage a more detailed study of SRA and its applications. Moreover, we point out that an extension of SRA to the multivariate case would have an important impact on the practical security of the elliptic curve discrete logarithm problem in the small characteristic case.Supplementary materials are available with this article.

scholarly journals On Turnbull identity for skew-symmetric matrices

2000 ◽  
Vol 43 (2) ◽  
pp. 379-393 ◽  
Author(s):  
Tôru Umeda ◽  
Takeshi Hirai
Keyword(s):  
Differential Operators ◽  
Symmetric Matrix ◽  
Point Of View ◽  
Symmetric Matrices ◽  
Invariant Differential Operators ◽  
Type Identity ◽  
Central Elements ◽  
Theoretic Point ◽  
Invariant Differential ◽  
Matrix Spaces

AbstractIn the last six lines of Turnbull's 1948 paper, he left an enigmatic statement on a Capelli-type identity for skew-symmetric matrix spaces. In the present paper, on Turnbull's suggestion, we show that certain Capelli-type identities hold for this case. Our formulae connect explicitly the central elements inU(gln) to the invariant differential operators, both of which are expressed with permanent. This also clarifies the meaning of Turnbull's statement from the Lie-theoretic point of view.

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