REVIEW OF CHAOS COMMUNICATION BY FEEDBACK CONTROL OF SYMBOLIC DYNAMICS

This paper is meant to serve as a tutorial describing the link between symbolic dynamics as a description of a chaotic attractor, and how to use control of chaos to manipulate the corresponding symbolic dynamics to transmit an information bearing signal. We use the Lorenz attractor, in the form of the discrete successive maxima map of the z-variable time-series, as our main example. For the first time, here, we use this oscillator as a chaotic signal carrier. We review the many previously developed issues necessary to create a working control of symbol dynamics system. These include a brief review of the theory of symbol dynamics, and how they arise from the flow of a differential equation. We also discuss the role of the (symbol dynamics) generating partition, the difficulty of finding such partitions, which is an open problem for most dynamical systems, and a newly developed algorithm to find the generating partition which relies just on knowing a large set of periodic orbits. We also discuss the importance of using a generating partition in terms of considering the possibility of using some other arbitrary partition, with discussion of consequences both generally to characterizing the system, and also specifically to communicating on chaotic signal carriers. Also, of practical importance, we review the necessary feedback-control issues to force the flow of a chaotic differential equation to carry a desired message.

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The Origins of the Re Hastings-Bass Rule

Trustee Decision Making ◽

10.1093/oso/9780198727316.003.0003 ◽

2015 ◽

Author(s):

Michael Ashdown

Keyword(s):

Supreme Court ◽

Present State ◽

Practical Importance ◽

Future Application ◽

Precise Nature ◽

The Supreme Court ◽

The Future ◽

The Law ◽

The Many ◽

Court Of Appeal

The present state of the law must now be treated as authoritatively set out by Lord Walker in Pitt v Holt, and to a lesser but still important extent by the earlier judgment of Lloyd LJ in the Court of Appeal in the same case. This chapter, however, is concerned with the earlier development of the Re Hastings-Bass doctrine. Its purpose is to establish the doctrinal legitimacy of the rule in Re Hastings-Bass as an aspect of the English law of trusts. Whilst this is primarily of academic and theoretical concern, in view of the Supreme Court’s reformulation of the law into its present shape, it is also of practical importance. In particular, the future application of the doctrine to novel situations will depend upon understanding the precise nature and scope of the rule propounded by the Supreme Court. That decision cannot simply be divorced from the many decided cases which preceded it, and from its place in the wider compass of the law of trusts.

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Minding the Mechanisms: A Discussion of How Mindfulness Leads to Positive Outcomes at Work

Industrial and Organizational Psychology ◽

10.1017/iop.2015.89 ◽

2015 ◽

Vol 8 (4) ◽

pp. 620-629 ◽

Cited By ~ 2

Author(s):

Dexter Miksch ◽

Meghan I. H. Lindeman ◽

Lebena Varghese

Keyword(s):

Theoretical Model ◽

Empirical Research ◽

Practical Importance ◽

Work Outcomes ◽

Future Research ◽

Positive Outcomes ◽

Mindfulness Practices ◽

Mediating Mechanisms ◽

The Many ◽

Positive Work

Hyland, Lee, and Mills (2015) asserted that the many benefits of mindfulness practices have been underutilized and understudied at work. We agree with the focal article's stance that more research is needed on mindfulness at work. We extend this argument to include a request that future research pays attention to the mechanisms responsible for the effects of mindfulness at work. In this commentary, we (a) briefly discuss the practical importance of understanding the mechanisms by which mindfulness practices lead to positive outcomes, (b) outline the mediating mechanisms proposed by the leading theoretical model of mindfulness effects and how those mediators apply to work, and (c) argue that more rigorous, empirical research is needed to understand the mechanisms through which mindfulness practices lead to positive work outcomes.

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A Deep Wide Field Survey from Digitally Stacked Schmidt Plates

International Astronomical Union Colloquium ◽

10.1017/s0252921100021904 ◽

1995 ◽

Vol 148 ◽

pp. 192-199

Author(s):

M. R. S. Hawkins

Keyword(s):

Field Survey ◽

Wide Field ◽

Large Set ◽

Proper Motions ◽

Brown Dwarf ◽

Schmidt Telescope ◽

Expected Gain ◽

Low Mass ◽

The Many

AbstractA large set of exposures of a single UK Schmidt Telescope field has been obtained, covering five colour bands over 18 years. Techniques have been developed for combining digitised data from many plates. The results of adding 64 exposures in Bj and R are demonstrated showing that the expected gain of ~ 2.5 magnitudes in limiting magnitude are achieved. By combining various subsets of the data, proper motions and variability can be determined. Two examples of the many possible uses of the dataset are given: the discovery of low mass brown dwarf candidates using colours and proper motions, and of quasars using variability and colours.

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Lorenz knots are prime

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700002339 ◽

1984 ◽

Vol 4 (1) ◽

pp. 147-163 ◽

Cited By ~ 23

Author(s):

R. F. Williams

Keyword(s):

Differential Equation ◽

Periodic Orbits ◽

Lorenz Attractor ◽

The Real ◽

Geometric Lorenz Attractor

AbstractLorenz knots are the periodic orbits of a certain geometrically defined differential equation in ℝ3. This is called the ‘geometric Lorenz attractor’ as it is only conjecturally the real Lorenz attractor. These knots have been studied by the author and Joan Birman via a ‘knot-holder’, i.e. a certain branched two-manifold H. To show such knots are prime we suppose the contrary which implies the existence of a splitting sphere, S2. The technique of the proof is to study the intersection S2∩H. A novelty here is that S2∩H is likewise branched.

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On dynamical input reconstruction in a distributed second order equation

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2021-0004 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Yury S. Osipov ◽

Vyacheslav I. Maksimov

Keyword(s):

Differential Equation ◽

Feedback Control ◽

Control Theory ◽

Nonlinear Differential Equation ◽

Order Equation ◽

Second Order ◽

Ill Posed ◽

Computational Errors ◽

Input Reconstruction ◽

Feedback Control Theory

Abstract A second order nonlinear differential equation is considered. An algorithm for reconstructing an input from inaccurate measurements of the solution at discrete times is designed. The algorithm based on the constructions of feedback control theory and theory of ill-posed problems is stable with respect to informational noises and computational errors.

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A Comprehensive Stability Criterion for Forced Vibrations in Nonlinear Systems

Journal of Applied Mechanics ◽

10.1115/1.4010586 ◽

1953 ◽

Vol 20 (1) ◽

pp. 9-12

Author(s):

K. Klotter ◽

E. Pinney

Keyword(s):

Differential Equation ◽

Nonlinear Systems ◽

Stability Criterion ◽

Practical Importance ◽

Nonlinear Function ◽

Forced Vibrations ◽

Maximum Value ◽

The Stability

Abstract This paper deals with the forced vibrations described by the differential equation a q .. + c q + c Φ ( q , q . ) = P cos Ω t wherein Φ denotes a nonlinear function of q and/or q̇. It presents a criterion for determining their stability. It is shown that under very weak restrictions, which equivalently means, for a large variety of cases (including all of practical importance) the stability depends on the sign of ∂q*/∂P (q* denoting the maximum value of q(t) within a period). The motion is stable if this derivative is positive; it is unstable if it is negative.

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Theory of Itinerant Electron Magnetism, 2nd Edition

10.1093/oso/9780192895639.001.0001 ◽

2021 ◽

Author(s):

Jürgen Kübler

Keyword(s):

Density Functional ◽

Giant Magnetoresistance ◽

Permanent Magnets ◽

Practical Importance ◽

Magnetic Ordering ◽

Weak Ferromagnetism ◽

Large Field ◽

Itinerant Electron ◽

The Many ◽

Magnetic Skyrmions

The book, in the broadest sense, is an application of quantum mechanics and statistical mechanics to the field of magnetism. Under certain well-described conditions, an immensely large number of electrons moving in the solid will collectively produce permanent magnetism. Permanent magnets are of fundamental interest, and magnetic materials are of great practical importance as they provide a large field of technological applications. The physical details describing the many-electron problem of magnetism are presented in this book on the basis of the density-functional approximation. The emphasis is on realistic magnets, for which the equations describing properties of the many-electron problem can only be solved by using computers. The great recent and continuing improvements are, to a very large extent, responsible for the progress in this field. Along with an introduction to the density-functional theory, the book describes representative computational methods and detailed formulas for physical properties of magnets, which include among other things the computation of magnetic ordering temperatures, the giant magnetoresistance, magneto-optical effects, weak ferromagnetism, the anomalous Hall and Nernst effects, and novel quasiparticles, such as Weyl fermions and magnetic skyrmions.

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COMPUTATIONAL TECHNIQUE FOR MODELING AND CLUSTERING OF FEEDBACK CONTROL IN GALAXIES USING GRAVITATIONAL THERMODYNAMICS

Asian Journal of Pharmaceutical and Clinical Research ◽

10.22159/ajpcr.2017.v10s1.19983 ◽

2017 ◽

Vol 10 (13) ◽

pp. 431

Author(s):

Ankush Rai ◽

Jagadeesh Kannan R

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Equation Of State ◽

Feedback Control ◽

Gravitational Interaction ◽

Computational Technique ◽

Expanding Universe ◽

Mass System ◽

Gravitational Thermodynamics ◽

Thermodynamic Equations

A model for clustering of galaxies through relativistic gravitational thermodynamics is laid on. Unlike the theories presented which consists of point mass system in expanding universe we presented the methodology in which partial differential equation & thermodynamic equations with the equation of state in accord with gravitational interaction between particles in order to study extended structures of universe.

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