Approximate equivalence of group actions

2017 ◽  
Vol 38 (4) ◽  
pp. 1201-1237 ◽  
Author(s):  
ANDREAS NÆS AASERUD ◽  
SORIN POPA
Keyword(s):  
Group Actions ◽  
The Other ◽  
Equivalence Relations ◽  
Orbit Equivalence ◽  
Usual Type ◽  
New Concepts ◽  
Probability Spaces ◽  
Measure Preserving Actions

We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining conditions. We compare them with the other existing equivalence relations between group actions, and study the usual type of rigidity questions around these new concepts (superrigidity, calculation of invariants, etc).

scholarly journals Weak containment of measure-preserving group actions

2019 ◽  
Vol 40 (10) ◽  
pp. 2681-2733 ◽  
Author(s):  
PETER J. BURTON ◽  
ALEXANDER S. KECHRIS
Keyword(s):  
Global Structure ◽  
Equivalence Classes ◽  
The Other ◽  
Unitary Representations ◽  
Weak Equivalence ◽  
Interesting Fact ◽  
Weak Containment ◽  
Probability Spaces ◽  
Measure Preserving Actions ◽  
Standard Probability

This paper concerns the study of the global structure of measure-preserving actions of countable groups on standard probability spaces. Weak containment is a hierarchical notion of complexity of such actions, motivated by an analogous concept in the theory of unitary representations. This concept gives rise to an associated notion of equivalence of actions, called weak equivalence, which is much coarser than the notion of isomorphism (conjugacy). It is well understood now that, in general, isomorphism is a very complex notion, a fact which manifests itself, for example, in the lack of any reasonable structure in the space of actions modulo isomorphism. On the other hand, the space of weak equivalence classes is quite well behaved. Another interesting fact that relates to the study of weak containment is that many important parameters associated with actions, such as the type, cost, and combinatorial parameters, turn out to be invariants of weak equivalence and in fact exhibit desirable monotonicity properties with respect to the pre-order of weak containment, a fact that can be useful in certain applications. There has been quite a lot of activity in this area in the last few years, and our goal in this paper is to provide a survey of this work.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

scholarly journals A rigidity result for crossed products of actions of Baumslag–Solitar groups

2015 ◽  
Vol 26 (14) ◽  
pp. 1550117
Author(s):  
Niels Meesschaert
Keyword(s):  
Probability Measure ◽  
Free Probability ◽  
Crossed Product ◽  
Crossed Products ◽  
Orbit Equivalence ◽  
Rigidity Result ◽  
Profinite Completions ◽  
Abelian Subgroups ◽  
Measure Equivalence ◽  
Measure Preserving Actions

Let [Formula: see text] and [Formula: see text] be two ergodic essentially free probability measure preserving actions of nonamenable Baumslag–Solitar groups whose canonical almost normal abelian subgroups act aperiodically. We prove that an isomorphism between the corresponding crossed product II1 factors forces [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text]. This improves an orbit equivalence rigidity result obtained by Houdayer and Raum in [Baumslag–Solitar groups, relative profinite completions and measure equivalence rigidity, J. Topol. 8 (2015) 295–313].

On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type

2013 ◽  
Vol 56 (1) ◽  
pp. 136-147
Author(s):  
Radu-Bogdan Munteanu
Keyword(s):  
Equivalence Relation ◽  
Product Type ◽  
Bratteli Diagram ◽  
Equivalence Relations ◽  
Orbit Equivalence ◽  
Property A

AbstractProduct type equivalence relations are hyperfinitemeasured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property A. This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper.

scholarly journals Validation as the Integral Part of a Knowledge Management Process

10.28945/2399 ◽  
2001 ◽  
Author(s):  
Maria A. Mach ◽  
Mieczyslaw L. Owoc
Keyword(s):  
Information Technology ◽  
Knowledge Management ◽  
Interdisciplinary Approach ◽  
The Other ◽  
Management Process ◽  
Theoretical Concepts ◽  
Whole Process ◽  
New Concepts ◽  
Organisational Knowledge ◽  
Knowledge Validation

Observing new concepts in information technology, we pay attention to its impact on more effective supporting human and organisational knowledge. Knowledge management (KM) is one of such promising and intriguing concepts. Its goals and infrastructures are defined in different ways, therefore interdisciplinary approach seems to be useful. We have presented a short survey of theoretical concepts in management, marketing and decision theory, which were adapted by the theory of KM. On the other hand, knowledge validation (KV), defined as two procedures: verification and evaluation any form of knowledge, is aimed on assuring its quality. The paper discusses the crucial interrelationships between knowledge validation and management. The main goal of this work is positioning KV activities in the context of knowledge management process, emphasising usability of KV techniques during the whole process.

Stochastic Theory of Human Slipping

2002 ◽  
Author(s):  
Ralph L. Barnett ◽  
Susanne A. Glowiak ◽  
Peter J. Poczynok
Keyword(s):  
Friction Coefficient ◽  
Duty Cycle ◽  
Stochastic Theory ◽  
The Other ◽  
Extreme Value Statistics ◽  
Conventional Theory ◽  
Low Friction ◽  
Friction Coefficients ◽  
Duty Cycles ◽  
New Concepts

The conventional approach to human slipping is essentially deterministic; it states that no slipping will occur when the average friction coefficient is greater than some critical friction criterion. Under this condition, pedestrians will not slip when they encounter the average friction coefficient. On the other hand, to successfully negotiate a walk of n-steps they must not slip when they encounter the smallest of the n friction coefficients. Consequently, a new slip theory has been formulated as a problem in extreme value statistics. An elegant relationship is obtained among the probability of slipping, the critical friction criterion, the number of steps taken by the walker, and the central measure, scatter, and asymmetry of the distribution of friction coefficients. The new theory reveals the structure of human slipping in a startling way that introduces completely new concepts: the go/no go nature of classical slip predictions is replaced by a probability of slipping; low friction floor/footwear couples may lead to fewer slips than high friction ones; slipping can occur in any case where conventional theory predicts “no slip”; and the number of slips depends on the distance traveled by a pedestrian. Finally, this paper develops the idea that the slipperiness of a real floor must be evaluated for a duty-cycle. Duty-cycles can be represented as frequency histograms when a floor is homogeneous and isotropic.

scholarly journals Orbit equivalence and rigidity of ergodic actions of Lie groups

1981 ◽  
Vol 1 (2) ◽  
pp. 237-253 ◽  
Author(s):  
Robert J. Zimmer
Keyword(s):  
Invariant Measure ◽  
Euclidean Space ◽  
Lie Groups ◽  
Homogeneous Spaces ◽  
The Other ◽  
Rigidity Theorem ◽  
Simple Groups ◽  
Orbit Equivalence ◽  
Finite Invariant Measure ◽  
Lattice Subgroups

AbstractThe rigidity theorem for ergodic actions of semi-simple groups and their lattice subgroups provides results concerning orbit equivalence of the actions of these groups with finite invariant measure. The main point of this paper is to extend the rigidity theorem on one hand to actions of general Lie groups with finite invariant measure, and on the other to actions of lattices on homogeneous spaces of the ambient connected group possibly without invariant measure. For example, this enables us to deduce non-orbit equivalence results for the actions of SL (n, ℤ) on projective space, Euclidean space, and general flag and Grassman varieties.

Development of a Family Vocational Guidance Potential as a Core Prerequisite to Successful Professional Self-Determination of Teenagers

10.12737/3080 ◽  
2014 ◽  
Vol 2 (1) ◽  
pp. 55-61
Author(s):  
Зеленкина ◽  
Tatyana Zelenkina
Keyword(s):  
Professional Education ◽  
Vocational Guidance ◽  
The Other ◽  
Self Determination ◽  
Vocational Choice ◽  
Pilot Testing ◽  
Other Hand ◽  
New Concepts ◽  
Professional Self

Optimized way to nurture parents’ readiness to guide vocational choice of their teenaged children is considered as a consistent element of vocational guidance potential and is scientifically proved. What makes the paper theoretically important, is the fact that the author clarifies the meaning for quite new concepts, as «family vocational guidance potential», «parents’ helpfulness», «successful vocational choice». Families are classified in terms of vocational guidance potential; several limitations in vocational choices of children in each category of families are outlined and illustrated by pictures and tables. Given the accented challenge of insufficient parents’ integration in vocational choices, made by their children, the idea of pilot testing described here, has been to use capabilities of additional professional education establishments to better preparing parents to the mission of facilitating the vocational choices of their children. As a result of parents-children cooperation, the parents are better prepared and eager to help their children in professional self-determination on one hand, while teenagers make more thoughtful vocational choices, on the other hand. Significant results and conclusions are provided, to prove reliability of researching hypothesis, put forward by the author.

Formulations about Dynamics of Mobile Robots

2010 ◽  
Vol 166-167 ◽  
pp. 309-314 ◽  
Author(s):  
Iuliu Negrean ◽  
Claudiu Schonstein ◽  
Kalman Kacso ◽  
Calin Negrean ◽  
Adina Duca
Keyword(s):  
Kinetic Energy ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Dynamic Control ◽  
Nonholonomic Constraints ◽  
The Other ◽  
Robot Motion ◽  
Mobile Platforms ◽  
Control Functions ◽  
New Concepts

In this paper the dynamics equations for a mobile robot, named PatrolBot, will be developed, using new concepts in advanced mechanics, based on important scientific researches of the main author, concerning the kinetic energy. In keeping the fact that the mathematical models of the mobile platforms are different besides the other robots types, due to nonholonomic constraints, these dynamic control functions, will be computed, according to these restrictions for robot motion.

Pan-Americanism and Imperialism

1938 ◽  
Vol 32 (2) ◽  
pp. 233-243 ◽  
Author(s):  
Joseph Lockey
Keyword(s):  
The Other ◽  
Formal Definition ◽  
Precise Meaning ◽  
New Concepts ◽  
Current Usage ◽  
The One ◽  
Pan Americanism ◽  
Made In

Pan-Americanism and imperialism appear to be mutually exclusive. Whether they are so in effect is a matter of definition. Neither term in current usage conveys a precise meaning. Pan-Americanism fails because it has not yet emerged into a distinct and easily recognizable form, and imperialism because it has evolved in the course of history through a variety of forms from which a doubtful choice must be made. In the one case the problem is to decide what meaning, and in the other, which meaning. The "what" is the more difficult to determine, since new concepts such as Pan Americanism acquire meaning with time and circumstance. It is not strange, therefore, that the attempts at formal definition have thus far proved unsatisfactory. Not even the genus to which Pan-Americanism belongs has been agreed upon. One author calls it an advocacy, another an idea, another a sentiment, and sti l others an aspiration, a tendency, or a doctrine. Obviously it does not fall indifferently into all these categories. If it is a sentiment merely, it is less than a doctrine; if it is a doctrine it is more than a tendency; and to call it a tendency is not the same as to say it is an aspiration or an idea. Moreover, none of these classifications when considered separately seems to fit the case.

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