Linear stability of Perelman's ν-entropy on symmetric spaces of compact type

2015 ◽  
Vol 2015 (709) ◽  
Author(s):  
Huai-Dong Cao ◽  
Chenxu He
Keyword(s):  
Linear Stability ◽  
Symmetric Spaces ◽  
Ricci Solitons ◽  
Einstein Manifolds ◽  
Compact Type ◽  
Positive Ricci Curvature ◽  
The Stability ◽  
Hilbert Action ◽  
Full Classification

AbstractFollowing [`Gaussian densities and stability for some Ricci solitons', preprint 2004], in this paper we study the linear stability of Perelman's ν-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the linear stability (also called ν-stability in this paper) restricted to the transversal traceless symmetric 2-tensors and the stability of Einstein manifolds with respect to the Hilbert action. As a main application, we give a full classification of linear stability of the ν-entropy on symmetric spaces of compact type. In particular, we exhibit many more ν-stable and ν-unstable examples than previously known and also the first ν-stable examples, other than the standard spheres, whose second variations are negative definite.

scholarly journals Stability of Einstein metrics on symmetric spaces of compact type

2021 ◽  
Author(s):  
Paul Schwahn
Keyword(s):  
Linear Stability ◽  
Stability Problem ◽  
Symmetric Spaces ◽  
Einstein Metrics ◽  
Compact Type ◽  
The Stability ◽  
Hilbert Action

AbstractWe prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $${\text {SU}}(n)$$ SU ( n ) , $$n\ge 3$$ n ≥ 3 , and $$E_6/F_4$$ E 6 / F 4 . Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.

scholarly journals On the symmetries of three-dimensional generalized symmetric spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 451-462
Author(s):  
Lakehal Belarbi
Keyword(s):  
Symmetric Spaces ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Riemannian Metric ◽  
Killing Vector Fields ◽  
Generalized Symmetric Space ◽  
Generalized Symmetric Spaces ◽  
Full Classification

In this work we consider the three-dimensional generalized symmetric space, equipped with the left-invariant pseudo-Riemannian metric. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations

scholarly journals On the symmetries of Lorentzian four-dimensional generalized symmetric spaces of type C

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 133-147
Author(s):  
Lakehal Belarbi
Keyword(s):  
Ricci Curvature ◽  
Symmetric Spaces ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Lorentzian Metric ◽  
Generalized Symmetric Spaces ◽  
Type C ◽  
Full Classification

We consider the four-dimensional generalized symmetric spaces of type C, equipped with a left-invariant Lorentzian metric. We completely describe its affine, homothetic and Killing vector fields. We also obtain a full classification of its Ricci, curvature and matter collineations.

Influence of internal and external risks on sustainability of financial system of Аltai krai

2018 ◽  
Vol 35 (4) ◽  
pp. 133-136
Author(s):  
R. N. Ibragimov
Keyword(s):  
Sustainable Development ◽  
Financial Stability ◽  
Management Strategy ◽  
Financial System ◽  
Risk Management Strategy ◽  
The Sustainable Development ◽  
The Stability ◽  
The Impact

The article examines the impact of internal and external risks on the stability of the financial system of the Altai Territory. Classification of internal and external risks of decline, affecting the sustainable development of the financial system, is presented. A risk management strategy is proposed that will allow monitoring of risks, thereby these measures will help reduce the loss of financial stability and ensure the long-term development of the economy of the region.

DEVELOPMENT OF THE BASIC CRITERIA FOR RUSSIAN COASTS TYPIFICATION

2017 ◽  
Author(s):  
Рубен Косян ◽  
Ruben Kosyan ◽  
Viacheslav Krylenko ◽  
Viacheslav Krylenko
Keyword(s):  
Coastal Zone ◽  
Coastal Area ◽  
Economic Activity ◽  
Basic Information ◽  
Dynamic Features ◽  
Static State ◽  
Evolutionary Features ◽  
Coastal Features ◽  
The Stability

There are many types of coasts classifications that indicate main coastal features. As a rule, the "static" state of the coasts is considered regardless of their evolutionary features and ways to further transformation. Since the most part of the coastal zone studies aimed at ensuring of economic activity, it is clear that the classification of coast types should indicate total information required by the users. Accordingly, the coast classification should include the criterion, characterizing as dynamic features of the coast and the conditions and opportunities of economic activity. The coast classification, of course, should be based on geomorphological coast typification. Similar typification has been developed by leading scientists from Russia and can be used with minimal modifications. The authors propose to add to basic information (geomorphological type of coast) the evaluative part for each coast sector. It will include the estimation of the coast changes probability and the complexity of the coast stabilization for economic activity. This method will allow to assess the dynamics of specific coastal sections and the processes intensity and, as a result – the stability of the coastal area.

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Can Vaccination Trigger Autoimmune Disorders? A Meta-Analysis

Vaccines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 821
Author(s):  
Marek Petráš ◽  
Ivana Králová Lesná ◽  
Jana Dáňová ◽  
Alexander M. Čelko
Keyword(s):  
Meta Analysis ◽  
Autoimmune Disorders ◽  
Risk Of Bias ◽  
Extensive Literature ◽  
Primary Analysis ◽  
Measures Of Association ◽  
Assessment Development ◽  
Extensive Literature Search ◽  
The Stability

Vaccination as an important tool in the fight against infections has been suggested as a possible trigger of autoimmunity over the last decades. To confirm or refute this assumption, a Meta-analysis of Autoimmune Disorders Association With Immunization (MADAWI) was conducted. Included in the meta-analysis were a total of 144 studies published in 1968–2019 that were available in six databases and identified by an extensive literature search conducted on 30 November 2019. The risk of bias classification of the studies was performed using the Newcastle–Ottawa Quality Assessment Scale. The strength of evidence was assessed using the Grading of Recommendations Assessment, Development, and Evaluation. While our primary analysis was conducted in terms of measures of association employed in studies with a low risk of bias, the robustness of the MADAWI outcome was tested using measures independent of each study risk of bias. Additionally, subgroup analyses were performed to determine the stability of the outcome. The pooled association of 0.99 (95% confidence interval, 0.97–1.02), based on a total of 364 published estimates, confirmed an equivalent occurrence of autoimmune disorders in vaccinated and unvaccinated persons. The same level of association reported by studies independently of the risk of bias was supported by a sufficient number of studies, and no serious limitation, inconsistency, indirectness, imprecision, and publication bias. A sensitivity analysis did not reveal any discrepancy in the primary result. Current common vaccination is not the cause of any of the examined autoimmune disorders in the medium and long terms.

scholarly journals An Ensemble Feature Selection Approach to Identify Relevant Features from EEG Signals

2021 ◽  
Vol 11 (15) ◽  
pp. 6983
Author(s):  
Maritza Mera-Gaona ◽  
Diego M. López ◽  
Rubiel Vargas-Canas
Keyword(s):  
Feature Selection ◽  
Sensitivity And Specificity ◽  
Eeg Signals ◽  
Specificity And Sensitivity ◽  
Selection Approach ◽  
Feature Selection Approach ◽  
The Stability ◽  
Selection Algorithms ◽  
Epileptiform Events

Identifying relevant data to support the automatic analysis of electroencephalograms (EEG) has become a challenge. Although there are many proposals to support the diagnosis of neurological pathologies, the current challenge is to improve the reliability of the tools to classify or detect abnormalities. In this study, we used an ensemble feature selection approach to integrate the advantages of several feature selection algorithms to improve the identification of the characteristics with high power of differentiation in the classification of normal and abnormal EEG signals. Discrimination was evaluated using several classifiers, i.e., decision tree, logistic regression, random forest, and Support Vecctor Machine (SVM); furthermore, performance was assessed by accuracy, specificity, and sensitivity metrics. The evaluation results showed that Ensemble Feature Selection (EFS) is a helpful tool to select relevant features from the EEGs. Thus, the stability calculated for the EFS method proposed was almost perfect in most of the cases evaluated. Moreover, the assessed classifiers evidenced that the models improved in performance when trained with the EFS approach’s features. In addition, the classifier of epileptiform events built using the features selected by the EFS method achieved an accuracy, sensitivity, and specificity of 97.64%, 96.78%, and 97.95%, respectively; finally, the stability of the EFS method evidenced a reliable subset of relevant features. Moreover, the accuracy, sensitivity, and specificity of the EEG detector are equal to or greater than the values reported in the literature.

scholarly journals On some recent progress in the classification of $$(P\hbox { and }Q)$$-polynomial association schemes

2019 ◽  
Author(s):  
Alexander L. Gavrilyuk ◽  
Jack H. Koolen
Keyword(s):  
Symmetric Spaces ◽  
Recent Progress ◽  
Association Schemes ◽  
Compact Symmetric Spaces ◽  
Expository Paper

AbstractThe problem of classification of $$(P\hbox { and }Q)$$(PandQ)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.

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