CLASSIFICATION OF APPROXIMATELY INNER ACTIONS OF DISCRETE AMENABLE GROUPS ON STRONGLY AMENABLE SUBFACTORS

2005 ◽  
Vol 16 (10) ◽  
pp. 1193-1206 ◽  
Author(s):  
TOSHIHIKO MASUDA
Keyword(s):  
Classification Theorem ◽  
Type Ii ◽  
Amenable Groups ◽  
Characteristic Invariant

We give the classification theorem of approximately inner actions of discrete amenable groups on strongly amenable subfactor of type II1by means of the characteristic invariant and ν invariant. To prove this theorem, we also give the classification theorem when the inner part and the centrally trivial part of actions coincide.

A NOTE ON COMMUTING SQUARES ARISING FROM AUTOMORPHISMS ON SUBFACTORS

1999 ◽  
Vol 10 (02) ◽  
pp. 207-214 ◽  
Author(s):  
PHAN H. LOI
Keyword(s):  
Finite Index ◽  
Simple Proof ◽  
Classification Theorem ◽  
Type Ii ◽  
Finitely Generated ◽  
Amenable Groups ◽  
Finite Set ◽  
Commuting Squares ◽  
Special Case

Using an idea due to Popa, we can associate a commuting square of factors to any given finite set of automorphisms acting on an inclusion of factors of finite index. We use this setting to obtain a simple proof of Popa's classification theorem of strongly outer actions of finitely generated discrete strongly amenable groups on a strongly amenable inclusion of type II 1 factors. We also obtain a new complete outer conjugacy invariant for arbitrary automorphisms, which contains the higher obstruction of Kawahigashi and the standard invariant as a special case.

CLASSIFICATION OF ACTIONS OF DISCRETE AMENABLE GROUPS ON AMENABLE SUBFACTORS OF TYPE II

2010 ◽  
Vol 21 (12) ◽  
pp. 1663-1695 ◽  
Author(s):  
SORIN POPA
Keyword(s):  
Type Ii ◽  
Classification Result ◽  
Amenable Groups ◽  
Type Iii

We prove a classification result for properly outer actions σ of discrete amenable groups G on strongly amenable subfactors of type II, N ⊂ M, a class of subfactors that were shown to be completely classified by their standard invariant [Formula: see text], in [27]. The result shows that the action σ is completely classified in terms of the action it induces on [Formula: see text]. As an application of this, we obtain that inclusions of type III λ factors, 0 < λ < 1, having discrete decomposition and strongly amenable graph, are completely classified by their standard invariant.

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

Morphological types of spermatheca in Coreidae: bearing on intra-familial classification and tribal-groupings (Hemiptera: Heteroptera)

Zootaxa ◽  
2020 ◽  
Vol 4834 (4) ◽  
pp. 451-501
Author(s):  
DOMINIQUE PLUOT-SIGWALT ◽  
PIERRE MOULET
Keyword(s):  
Western Hemisphere ◽  
Type I ◽  
Type Ii ◽  
Type Iii ◽  
Spermathecal Duct ◽  
Eastern Hemisphere ◽  
Intermediate Part ◽  
Muscular Pump ◽  
Familial Classification

The morphology of the spermatheca is described in 109 species of 86 genera representing all four currently recognised subfamilies of Coreidae, covering the undivided Hydarinae, both tribes of Pseudophloeinae, all three tribes of Meropachyinae and 27 of the 32 tribes of Coreinae. Three types of spermatheca are recognised. Type I is bipartite, consisting only of a simple tube differentiated into distal seminal receptacle and proximal spermathecal duct and lacks the intermediate part present in most Pentatomomorpha, in which it serves as muscular pump. Type II is also bipartite but more elaborate in form with the receptacle generally distinctly wider than the duct. Type III is tripartite, with receptacle, duct and an often complex intermediate part. Four subtypes are recognised within type III. Type I is found only in Hydarinae and type II only in Pseudophloeinae. Type III is found in both Coreinae and Meropachyinae. Subtype IIIA (“Coreus-group”) unites many tribes from the Eastern Hemisphere and only one (Spartocerini) from the Western Hemisphere. Subtypes IIIB (“Nematopus-group”) and IIID (“Anisoscelis-group”) are confined to taxa from the Western Hemisphere and subtype IIIC (“Chariesterus-group”) is found in tribes from both hemispheres. The polarity of several characters of the intermediate part and some of the spermathecal duct is evaluated, suggesting autapomorphies or apomorphies potentially relevant to the classification of Coreidae at the sufamilial and tribal levels. Characters of the intermediate part strongly indicate that the separation of Meropachyinae and Coreinae as currently constituted cannot be substantiated. The tribes Anisoscelini, Colpurini, Daladerini and Hyselonotini are heterogeneous, each exhibiting two subtypes of spermatheca, and probably polyphyletic. Two tribes, Cloresmini and Colpurini, requiring further investigation remain unplaced. This study demonstrates the great importance of characters of the spermatheca, in particular its intermediate part, for research into the phylogeny and taxonomy of Pentatomomorpha. 

Split spinal cord malformations in children

1998 ◽  
Vol 88 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Yusuf Ersşahin ◽  
Saffet Mutluer ◽  
Sevgül Kocaman ◽  
Eren Demirtasş
Keyword(s):  
Spinal Cord ◽  
Neurological Deficits ◽  
Single Type ◽  
Type I ◽  
Type Ii ◽  
Content Type ◽  
Spinal Lesion ◽  
The Mean ◽  
Fine Print

Object. The authors reviewed and analyzed information on 74 patients with split spinal cord malformations (SSCMs) treated between January 1, 1980 and December 31, 1996 at their institution with the aim of defining and classifying the malformations according to the method of Pang, et al. Methods. Computerized tomography myelography was superior to other radiological tools in defining the type of SSCM. There were 46 girls (62%) and 28 boys (38%) ranging in age from less than 1 day to 12 years (mean 33.08 months). The mean age (43.2 months) of the patients who exhibited neurological deficits and orthopedic deformities was significantly older than those (8.2 months) without deficits (p = 0.003). Fifty-two patients had a single Type I and 18 patients a single Type II SSCM; four patients had composite SSCMs. Sixty-two patients had at least one associated spinal lesion that could lead to spinal cord tethering. After surgery, the majority of the patients remained stable and clinical improvement was observed in 18 patients. Conclusions. The classification of SSCMs proposed by Pang, et al., will eliminate the current chaos in terminology. In all SSCMs, either a rigid or a fibrous septum was found to transfix the spinal cord. There was at least one unrelated lesion that caused tethering of the spinal cord in 85% of the patients. The risk of neurological deficits resulting from SSCMs increases with the age of the patient; therefore, all patients should be surgically treated when diagnosed, especially before the development of orthopedic and neurological manifestations.

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.

scholarly journals A FURTHER STUDY ON THE BIOLOGIC CLASSIFICATION OF PNEUMOCOCCI

1915 ◽  
Vol 22 (6) ◽  
pp. 804-819 ◽  
Author(s):  
Oswald T. Avery
Keyword(s):  
The Other ◽  
Type Ii ◽  
Respective Group ◽  
Immune Reactions ◽  
Subgroup Ii ◽  
Typical Type ◽  
Immunity Reaction ◽  
Pneumococcus Type

1. At least three subgroups of Pneumococcus Type II may be recognized by specific immune reactions. They have been called Subgroups II A, II B, and II X. 2. That the organisms of these three subgroups are biologically related to Pneumococcus Type II is shown by the following facts: (a) Agglutination with Antipneumococcus Serum II. (b) Protection with Antipneumococcus Serum II, except Subgroup II X. (c) Absorption of Antipneumococcus Serum II with typical Type II pneumococcus removes the antibodies for all subgroups, (d) Absorption of Antipneumococcus Serum II with a member of Subgroups II A or II B removes only the antibodies for the homologous subgroup. Absorption of Antipneumococcus Serum II with any given member of Subgroup II X removes the antibodies for that particular strain only. 3. That the three subgroups, although biologically related to Pneumococcus Type II, possess, nevertheless, specific differential characterswhich separate them one from another, is evidenced by thefollowing facts: (a) The organisms of any subgroup are not agglutinated bythe antisera of the other two subgroups. (b) They are not protected against by the sera of the other subgroups. (c) They do not absorb from Antipneumococcus Serum II the specific immune bodies of the other subgroups. 4. Subgroups II A and II B are characterized by immunity reactions identical within the respective group. 5. Subgroup II X consists of heterogeneous strains which do not cross in their immunity reaction with each other or with Subgroups II A or II B.

scholarly journals NCOG-02. PROGNOSTIC VALIDATION OF THE EANO ESMO CLASSIFICATION OF LEPTOMENINGEAL METASTASIS

2020 ◽  
Vol 22 (Supplement_2) ◽  
pp. ii129-ii129
Author(s):  
Emilie Le Rhun ◽  
Patrick Devos ◽  
Johannes Weller ◽  
Katharina Seystahl ◽  
Francesca Mo ◽  
...  
Keyword(s):  
Tumor Cells ◽  
Leptomeningeal Metastasis ◽  
Rank Test ◽  
Type I ◽  
Type Ii ◽  
Primary Tumors ◽  
Kaplan Meier ◽  
Negative Prognostic Factor ◽  
Choice Of Treatment

Abstract BACKGROUND The EANO ESMO guidelines have proposed a classification of leptomeningeal metastases (LM) based on clinical (typical/atypical), cytological (positive/negative/equivocal) and MRI (A linear, B nodular, C linear and nodular, D normal or hydrocephalus only) presentation. Type I LM is defined by the presence of tumor cells in the cerebrospinal fluid (CSF) (confirmed LM) whereas type II LM is defined by typical clinical and MRI signs (probable or possible LM). Here we explored the clinical utility of these EANO ESMO LM subtypes for choice of treatment and outcome. PATIENTS AND METHODS We retrospectively assembled data from 254 patients with newly diagnosed LM from different solid tumors, including as main primary tumors breast cancer (n=98, 45%), lung cancer (n=65, 25.5%) and melanoma (n=51, 13.5%). Survival curves were estimated using the Kaplan-Meier method and compared by Log-rank test. RESULTS Median age at LM diagnosis was 56.5 years (range 20-82 years). Typical clinical LM symptoms or signs were noted in 225 patients (88.5%); only 13 patients (5%) were clinically asymptomatic. The most common MRI subtype was A seen in 117 patients (46%). Types B (n=33, 13%), C (n=54, 21%) and D (n=50, 19.5%) were less common. Tumor cells in the CSF were observed in 186 patients (73%) whereas the CSF was equivocal in 24 (9.5%) and negative in 44 (17.5%) patients. Patients with confirmed LM had inferior outcome than patients with probable or possible LM (p=0.0063). Type I patients had inferior outcome than type II patients (p=0.0019). Nodular disease was a negative prognostic factor in type II LM, but not in type I LM (p=0.0138). CONCLUSION The EANO ESMO LM subtypes are highly prognostic and should be considered for stratification and overall design of clinical trials.

scholarly journals Abductive Networks For Two-Group Classification: A Comparison With Neural Networks

2011 ◽  
Vol 15 (2) ◽  
pp. 1 ◽  
Author(s):  
Anurag Agarwal
Keyword(s):  
Neural Networks ◽  
Linear Mapping ◽  
Group Classification ◽  
Type Ii ◽  
Artificial Intelligence Technique ◽  
Empirical Tests ◽  
Multivariate Discriminant ◽  
Better Than

<span>In this study, a new Artificial Intelligence technique for non-linear mapping called Abductive Networks is used for two-group classification of firms. The results are compared with Neural Networks, another AI technique, which has been shown to perform better than the traditional statistical techniques such as multivariate discriminant analysis and logit. In empirical tests, Abductive Networks perform as well or better than Neural Networks on various criteria of measurement such as Type 1 / Type II accuracy criteria and Distance Between Centroids.</span>

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