Invariance of Tameness under Stable Equivalence: Krause’s Theorem

2000 ◽  
pp. 405-418 ◽  
Author(s):  
Helmut Lenzing
Keyword(s):  
Stable Equivalence

A note on the stable equivalence conjecture

1996 ◽  
Vol 24 (9) ◽  
pp. 2793-2809 ◽  
Author(s):  
Aiping Tang
Keyword(s):  
Stable Equivalence

scholarly journals Classification of Symmetric Special Biserial Algebras With At Most One Non-Uniserial Indecomposable Projective

2015 ◽  
Vol 58 (3) ◽  
pp. 739-767 ◽  
Author(s):  
Nicole Snashall ◽  
Rachel Taillefer
Keyword(s):  
Natural Generalization ◽  
Stable Equivalence ◽  
Symmetric Algebras ◽  
Special Biserial Algebras ◽  
Weakly Symmetric ◽  
Dihedral Type ◽  
Indecomposable Projective Module ◽  
Algebras Of Dihedral Type ◽  
Euclidean Type

AbstractWe consider a natural generalization of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the weakly symmetric algebras of Euclidean type n, as studied by Bocian et al., as well as some algebras of dihedral type.

scholarly journals Validation of automatic passenger counting: introducing the t-test-induced equivalence test

2019 ◽  
Vol 47 (6) ◽  
pp. 3031-3045
Author(s):  
Michael Siebert ◽  
David Ellenberger
Keyword(s):  
Measurement Errors ◽  
T Test ◽  
Statistical Hypothesis ◽  
Type I ◽  
Equivalence Testing ◽  
Sample Sizes ◽  
Equivalence Test ◽  
Stable Equivalence ◽  
Student’S T ◽  
Type Ii Errors

Abstract Automatic passenger counting (APC) in public transport has been introduced in the 1970s and has been rapidly emerging in recent years. Still, real-world applications continue to face events that are difficult to classify. The induced imprecision needs to be handled as statistical noise and thus methods have been defined to ensure that measurement errors do not exceed certain bounds. Various recommendations for such an APC validation have been made to establish criteria that limit the bias and the variability of the measurement errors. In those works, the misinterpretation of non-significance in statistical hypothesis tests for the detection of differences (e.g. Student’s t-test) proves to be prevalent, although existing methods which were developed under the term equivalence testing in biostatistics (i.e. bioequivalence trials, Schuirmann in J Pharmacokinet Pharmacodyn 15(6):657–680, 1987) would be appropriate instead. This heavily affects the calibration and validation process of APC systems and has been the reason for unexpected results when the sample sizes were not suitably chosen: Large sample sizes were assumed to improve the assessment of systematic measurement errors of the devices from a user’s perspective as well as from a manufacturers perspective, but the regular t-test fails to achieve that. We introduce a variant of the t-test, the revised t-test, which addresses both type I and type II errors appropriately and allows a comprehensible transition from the long-established t-test in a widely used industrial recommendation. This test is appealing, but still it is susceptible to numerical instability. Finally, we analytically reformulate it as a numerically stable equivalence test, which is thus easier to use. Our results therefore allow to induce an equivalence test from a t-test and increase the comparability of both tests, especially for decision makers.

scholarly journals Stability of products of equivalence relations

2018 ◽  
Vol 154 (9) ◽  
pp. 2005-2019 ◽  
Author(s):  
Amine Marrakchi
Keyword(s):  
Probability Measure ◽  
Direct Product ◽  
Equivalence Relation ◽  
Equivalence Relations ◽  
Similar Question ◽  
Stable Equivalence ◽  
Local Characterization

An ergodic probability measure preserving (p.m.p.) equivalence relation ${\mathcal{R}}$ is said to be stable if ${\mathcal{R}}\cong {\mathcal{R}}\times {\mathcal{R}}_{0}$ where ${\mathcal{R}}_{0}$ is the unique hyperfinite ergodic type $\text{II}_{1}$ equivalence relation. We prove that a direct product ${\mathcal{R}}\times {\mathcal{S}}$ of two ergodic p.m.p. equivalence relations is stable if and only if one of the two components ${\mathcal{R}}$ or ${\mathcal{S}}$ is stable. This result is deduced from a new local characterization of stable equivalence relations. The similar question on McDuff $\text{II}_{1}$ factors is also discussed and some partial results are given.

Detecting Non-Triviality of Virtual Links

2003 ◽  
Vol 12 (06) ◽  
pp. 781-803 ◽  
Author(s):  
Teruhisa Kadokami
Keyword(s):  
Equivalence Classes ◽  
Geometric Method ◽  
Virtual Link ◽  
Virtual Knot ◽  
Stable Equivalence ◽  
Link Diagrams ◽  
Virtual Links ◽  
Algebraic Invariants ◽  
One To One

J. S. Carter, S. Kamada and M. Saito showed that there is one to one correspondence between the virtual Reidemeister equivalence classes of virtual link diagrams and the stable equivalence classes of link diagrams on compact oriented surfaces. Using the result, we show how to obtain the supporting genus of a projected virtual link by a geometric method. From this result, we show that a certain virtual knot which cannot be judged to be non-trivial by known algebraic invariants is non-trivial, and we suggest to classify the equivalence classes of projected virtual links by using the supporting genus.

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