How does a choice of Markov partition affect the resultant symbolic dynamics?

Abstract This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

Download Full-text

D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽

10.1027/1614-2241/a000026 ◽

2011 ◽

Vol 7 (3) ◽

pp. 88-95 ◽

Cited By ~ 2

Author(s):

Jose A. Martínez ◽

Manuel Ruiz Marín

Keyword(s):

Symbolic Dynamics ◽

Scale Invariance ◽

Rating Scales ◽

Rating Scale ◽

Marketing Research ◽

Response Patterns ◽

Measurement Scales ◽

Improve Measurement ◽

Entropy Measures ◽

The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

Download Full-text

Exploring EMG pattern detection using symbolic dynamics during the performance of functional upper extremity tasks

PsycEXTRA Dataset ◽

10.1037/e591962009-001 ◽

2009 ◽

Author(s):

Dominic Nathan ◽

Stephen Guastello ◽

Dean Jeutter

Keyword(s):

Upper Extremity ◽

Symbolic Dynamics ◽

Pattern Detection

Download Full-text

Symbolic Dynamics and Orbital Decomposition

PsycEXTRA Dataset ◽

10.1037/e629492011-060 ◽

2011 ◽

Author(s):

David Pincus

Keyword(s):

Symbolic Dynamics ◽

Orbital Decomposition

Download Full-text

Topics in Stochastics, Symbolic Dynamics and Neural Networks

10.21236/ada336426 ◽

1996 ◽

Author(s):

Robert M. Burton ◽

Jr

Keyword(s):

Neural Networks ◽

Symbolic Dynamics

Download Full-text

Affective labour and class distinction in the night-time economy

The Sociological Review ◽

10.1177/00380261211006329 ◽

2021 ◽

pp. 003802612110063

Author(s):

Steven Threadgold ◽

David Farrugia ◽

Julia Coffey

Keyword(s):

Symbolic Dynamics ◽

Urban Areas ◽

Service Work ◽

Night Time ◽

Feminist Analysis ◽

Consumption Experience ◽

Gendered Politics ◽

The Aesthetic ◽

The Relationship ◽

Class Distinction

This article contributes to recent debates about the relationship between affective labour and class by exploring the classed distinctions enacted through affective labour in the urban night-time economy. Bringing theories of affective labour into a dialogue with Bourdieusian feminist analysis, the article explores the affective and symbolic dynamics of hospitality labour in a gentrified inner-urban neighbourhood of Melbourne, Australia. It shows how the practice of hospitality labour enacts classed distinctions and tensions emerging from the gentrification of inner-urban areas, and how the aesthetic and symbolic dimensions of class contribute to the valorisation of affect in hospitality venues. The valorisation of affect are processes in which the value attributed to an atmosphere or consumption experience is based on the forms of distinction practised within the venue, enacted in aesthetics, tastes and modes of embodiment. The article also shows how practices of class distinction – both ‘punching up’ and ‘managing down’ – are connected to the gendered politics of service work in the way that workers manage the threat of violence or sexual harassment in venues. In general, the article shows how the classed dynamics of gentrification are enacted in affective economies, and therefore how Bourdieusian analysis of class can be usefully deployed in theoretical debates about affective labour.

Download Full-text

Statistical Tests of Symbolic Dynamics

Mathematics ◽

10.3390/math9080817 ◽

2021 ◽

Vol 9 (8) ◽

pp. 817

Author(s):

Fernando López ◽

Mariano Matilla-García ◽

Jesús Mur ◽

Manuel Ruiz Marín

Keyword(s):

Monte Carlo ◽

Symbolic Dynamics ◽

Null Hypothesis ◽

Statistical Tests ◽

General Applicability ◽

Monte Carlo Experiments ◽

The Mean ◽

Theoretical Application ◽

New Statistics ◽

General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Download Full-text

The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2020.114 ◽

2020 ◽

pp. 1-26

Author(s):

SNIR BEN OVADIA

Keyword(s):

Symbolic Dynamics ◽

Full Measure ◽

Probability Measures ◽

Positive Entropy ◽

Surface Diffeomorphisms ◽

Srb Measures ◽

Hyperbolic Diffeomorphisms ◽

Set Of Points ◽

Math Phys ◽

Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

Download Full-text