Francesco Calogero
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ...
More
A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the same, fixed period. Recently, a simple transformation has been introduced, featuring a real parameter ω and reducing to the identity for ω=0. This transformation is applicable to a quite large class of dynamical systems and it yields ω-modified autonomous systems which are isochronous, with period T = 2π/ω. This justifies the notion that isochronous systems are not rare. In this monograph—which covers work done over the last decade by its author and several collaborators—this technology to manufacture isochronous systems is reviewed. Many examples of such systems are provided, including many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs: Partial Differential Equations). This monograph shall be of interest to researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It shall also appeal to experimenters and practitioners interested in isochronous phenomena. It might be used as basic or complementary textbook for an undergraduate or graduate course.Less
A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the same, fixed period. Recently, a simple transformation has been introduced, featuring a real parameter ω and reducing to the identity for ω=0. This transformation is applicable to a quite large class of dynamical systems and it yields ω-modified autonomous systems which are isochronous, with period T = 2π/ω. This justifies the notion that isochronous systems are not rare. In this monograph—which covers work done over the last decade by its author and several collaborators—this technology to manufacture isochronous systems is reviewed. Many examples of such systems are provided, including many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs: Partial Differential Equations). This monograph shall be of interest to researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It shall also appeal to experimenters and practitioners interested in isochronous phenomena. It might be used as basic or complementary textbook for an undergraduate or graduate course.
Giovanna Colombetti
- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780262019958
- eISBN:
- 9780262318419
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262019958.003.0003
- Subject:
- Philosophy, Philosophy of Mind
In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical ...
More
In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical systems concepts have been used in “dynamical affective science” to model emotions. Although existing proposals apply at very different levels of description, they all characterize the organism as complex, self-organizing, open, and plastic, realizing emotional episodes that are softly assembled, context dependent, and highly variable, yet patterned and recurrent. I then elaborate on the implications of this dynamical conceptualization for the debate on the nature of the emotions discussed in the previous chapter. This dynamical conceptualization notably posits neither internal causes of emotional episodes and of their different aspects, nor a distinction between alleged basic and nonbasic emotions; rather, it treats all emotions as complex organismic patterns subject to both evolutionary and developmental pressures. I conclude with a discussion of how dynamical systems concepts also help characterize the relationship between emotions and moods.Less
In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical systems concepts have been used in “dynamical affective science” to model emotions. Although existing proposals apply at very different levels of description, they all characterize the organism as complex, self-organizing, open, and plastic, realizing emotional episodes that are softly assembled, context dependent, and highly variable, yet patterned and recurrent. I then elaborate on the implications of this dynamical conceptualization for the debate on the nature of the emotions discussed in the previous chapter. This dynamical conceptualization notably posits neither internal causes of emotional episodes and of their different aspects, nor a distinction between alleged basic and nonbasic emotions; rather, it treats all emotions as complex organismic patterns subject to both evolutionary and developmental pressures. I conclude with a discussion of how dynamical systems concepts also help characterize the relationship between emotions and moods.
Wolfgang Banzhaf and Lidia Yamamoto
- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9780262029438
- eISBN:
- 9780262329460
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029438.001.0001
- Subject:
- Public Health and Epidemiology, Public Health
The field of Artificial Life (ALife) is now firmly established in the scientific world, but it has yet to achieve one of its original goals: an understanding of the emergence of life on Earth. The ...
More
The field of Artificial Life (ALife) is now firmly established in the scientific world, but it has yet to achieve one of its original goals: an understanding of the emergence of life on Earth. The new field of Artificial Chemistries draws from chemistry, biology, computer science, mathematics, and other disciplines to work toward that goal. For if, as it has been argued, life emerged from primitive, prebiotic forms of self-organization, then studying models of chemical reaction systems could bring ALife closer to understanding the origins of life. In Artificial Chemistries (ACs), the emphasis is on creating new interactions rather than new materials. The results can be found both in the virtual world, in certain multiagent systems, and in the physical world, in new (artificial) reaction systems. This book offers an introduction to the fundamental concepts of ACs, covering both theory and practical applications. After a general overview of the field and its methodology, the book reviews important aspects of biology, including basic mechanisms of evolution; discusses examples of ACs drawn from the literature; considers fundamental questions of how order can emerge, emphasizing the concept of chemical organization (a closed and self-maintaining set of chemicals); and surveys a range of applications, which include computing, systems modeling in biology, and synthetic life. An appendix provides a Python toolkit for implementing ACs.Less
The field of Artificial Life (ALife) is now firmly established in the scientific world, but it has yet to achieve one of its original goals: an understanding of the emergence of life on Earth. The new field of Artificial Chemistries draws from chemistry, biology, computer science, mathematics, and other disciplines to work toward that goal. For if, as it has been argued, life emerged from primitive, prebiotic forms of self-organization, then studying models of chemical reaction systems could bring ALife closer to understanding the origins of life. In Artificial Chemistries (ACs), the emphasis is on creating new interactions rather than new materials. The results can be found both in the virtual world, in certain multiagent systems, and in the physical world, in new (artificial) reaction systems. This book offers an introduction to the fundamental concepts of ACs, covering both theory and practical applications. After a general overview of the field and its methodology, the book reviews important aspects of biology, including basic mechanisms of evolution; discusses examples of ACs drawn from the literature; considers fundamental questions of how order can emerge, emphasizing the concept of chemical organization (a closed and self-maintaining set of chemicals); and surveys a range of applications, which include computing, systems modeling in biology, and synthetic life. An appendix provides a Python toolkit for implementing ACs.
Francesco Calogero
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In Chapter 6—reporting very recent findings (although the main idea is not new)—autonomous dynamical systems are treated whose generic solutions approach asymptotically (at large time) isochronous ...
More
In Chapter 6—reporting very recent findings (although the main idea is not new)—autonomous dynamical systems are treated whose generic solutions approach asymptotically (at large time) isochronous evolutions, namely, all their dependent variables tend asymptotically to functions periodic with the same, fixed period. Two examples—associated to somewhat different mechanisms—are then discussed: the first is an integrable, indeed solvable many-body model of goldfish type, the second a rather large class of, generally nonintegrable, many-body problems.Less
In Chapter 6—reporting very recent findings (although the main idea is not new)—autonomous dynamical systems are treated whose generic solutions approach asymptotically (at large time) isochronous evolutions, namely, all their dependent variables tend asymptotically to functions periodic with the same, fixed period. Two examples—associated to somewhat different mechanisms—are then discussed: the first is an integrable, indeed solvable many-body model of goldfish type, the second a rather large class of, generally nonintegrable, many-body problems.
Martin Clayton
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199811328
- eISBN:
- 9780199369539
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199811328.003.0002
- Subject:
- Music, Ethnomusicology, World Music, Performing Practice/Studies
This chapter examines relationships between the empirical study of musical entrainment and an ethnographic research model. Moving beyond a description of the concept of entrainment (roughly speaking, ...
More
This chapter examines relationships between the empirical study of musical entrainment and an ethnographic research model. Moving beyond a description of the concept of entrainment (roughly speaking, synchronisation), its wider context—that is, dynamical systems theory—is introduced, and the implications of viewing musical ensembles as complex systems discussed. Such an approach presents a challenge to many proponents of an interpretative, humanistic approach who see scientific approaches as essentially reductionist: this critique is addressed head-on with a refutation of the notion that all scientific method is necessarily reductionist. The chapter argues that in order to understand musical interactions it is important to bring the unique insights of a dynamical systems approach into a productive dialogue with an ethnographic and interpretative framework alert to local contexts and meanings.Less
This chapter examines relationships between the empirical study of musical entrainment and an ethnographic research model. Moving beyond a description of the concept of entrainment (roughly speaking, synchronisation), its wider context—that is, dynamical systems theory—is introduced, and the implications of viewing musical ensembles as complex systems discussed. Such an approach presents a challenge to many proponents of an interpretative, humanistic approach who see scientific approaches as essentially reductionist: this critique is addressed head-on with a refutation of the notion that all scientific method is necessarily reductionist. The chapter argues that in order to understand musical interactions it is important to bring the unique insights of a dynamical systems approach into a productive dialogue with an ethnographic and interpretative framework alert to local contexts and meanings.
Mark Newman
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0017
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, ...
More
An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, fixed points, and limit cycles. Dynamical systems on networks are introduced, focusing initially on systems with only one variable per node and progressing to multi-variable systems. Linear stability analysis is developed in detail, leading to master stability conditions and the connection between stability and the spectral properties of networks. The chapter ends with a discussion of synchronization phenomena, the stability of limit cycles, and master stability conditions for synchronization.Less
An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, fixed points, and limit cycles. Dynamical systems on networks are introduced, focusing initially on systems with only one variable per node and progressing to multi-variable systems. Linear stability analysis is developed in detail, leading to master stability conditions and the connection between stability and the spectral properties of networks. The chapter ends with a discussion of synchronization phenomena, the stability of limit cycles, and master stability conditions for synchronization.
Wolfgang Banzhaf and Lidia Yamamoto
- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9780262029438
- eISBN:
- 9780262329460
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029438.003.0009
- Subject:
- Public Health and Epidemiology, Public Health
This chapter provides an overview of a large class of artificial chemistries, formal rewriting systems. A brief introduction explains the general concept of rewriting or production systems. We then ...
More
This chapter provides an overview of a large class of artificial chemistries, formal rewriting systems. A brief introduction explains the general concept of rewriting or production systems. We then explore the classical lambda calculus which was used as an early example of an AC. Further sections are devoted to an AC computer language, Gamma, and the chemical abstract machine formalism. Other examples of ACs follow, among them the chemical rewriting system on multisets, P systems, and MGS. The chapter concludes with a short discussion of other formal calculi inspired by a chemical metaphor and an explanation of how L systems and other rewriting systems would fit into the category of Artificial Chemistries.Less
This chapter provides an overview of a large class of artificial chemistries, formal rewriting systems. A brief introduction explains the general concept of rewriting or production systems. We then explore the classical lambda calculus which was used as an early example of an AC. Further sections are devoted to an AC computer language, Gamma, and the chemical abstract machine formalism. Other examples of ACs follow, among them the chemical rewriting system on multisets, P systems, and MGS. The chapter concludes with a short discussion of other formal calculi inspired by a chemical metaphor and an explanation of how L systems and other rewriting systems would fit into the category of Artificial Chemistries.
Xin Wei Sha
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262019514
- eISBN:
- 9780262318914
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262019514.003.0007
- Subject:
- Philosophy, Aesthetics
The motto "art all the way down," which harkens to the amodern working ethos of the preindustrial atelier, the Bauhaus fusion of craft and art, and the plenist ontological commitments driving our ...
More
The motto "art all the way down," which harkens to the amodern working ethos of the preindustrial atelier, the Bauhaus fusion of craft and art, and the plenist ontological commitments driving our object-free approach to ontogenesis, prompts us to examine how such art practice and the critical studies of media arts and sciences can be sustained in the sociocultural and capital economies of the arts and the academy. What sort of working ethos can one derive to sustain the work of atelier-studio-labs like the Topological Media Lab or FoAM and their kin? Chapter 7 derives practices that draw from the collectivist practices of the engineering laboratory and the theater, as well as the more solitary aesthetico-economic practices of the art studio.Less
The motto "art all the way down," which harkens to the amodern working ethos of the preindustrial atelier, the Bauhaus fusion of craft and art, and the plenist ontological commitments driving our object-free approach to ontogenesis, prompts us to examine how such art practice and the critical studies of media arts and sciences can be sustained in the sociocultural and capital economies of the arts and the academy. What sort of working ethos can one derive to sustain the work of atelier-studio-labs like the Topological Media Lab or FoAM and their kin? Chapter 7 derives practices that draw from the collectivist practices of the engineering laboratory and the theater, as well as the more solitary aesthetico-economic practices of the art studio.
Daniel D. Hutto and Erik Myin
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780262036115
- eISBN:
- 9780262339773
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262036115.003.0002
- Subject:
- Philosophy, Philosophy of Mind
Chapter 2 introduces REC’s Equal Partner Principle, according to which invoking neural, bodily, and environmental factors all make equally important contributions when it comes to explaining ...
More
Chapter 2 introduces REC’s Equal Partner Principle, according to which invoking neural, bodily, and environmental factors all make equally important contributions when it comes to explaining cognitive activity. In line with that principle, it is made clear how REC can accept that cognitive capacities depend on structural changes that occur inside organisms and their brains, without understanding such changes in information processing and representationalist terms.
This chapter explicates the Hard Problem of Content, aka the HPC, as basis for a compelling argument for REC. The HPC is a seemingly intractable theoretical puzzle for defenders of unrestricted CIC. A straight solution to the HPC requires explaining how it is possible to get from informational foundations that are noncontentful to a theory of mental content using only the resources of a respectable explanatory naturalism that calls on the resources of the hard sciences.
It is revealed how the need to deal with the HPC can be avoided by adopting REC’s revolutionary take on basic cognition, and why going this way has advantages over other possible ways of handling the HPC.Less
Chapter 2 introduces REC’s Equal Partner Principle, according to which invoking neural, bodily, and environmental factors all make equally important contributions when it comes to explaining cognitive activity. In line with that principle, it is made clear how REC can accept that cognitive capacities depend on structural changes that occur inside organisms and their brains, without understanding such changes in information processing and representationalist terms.
This chapter explicates the Hard Problem of Content, aka the HPC, as basis for a compelling argument for REC. The HPC is a seemingly intractable theoretical puzzle for defenders of unrestricted CIC. A straight solution to the HPC requires explaining how it is possible to get from informational foundations that are noncontentful to a theory of mental content using only the resources of a respectable explanatory naturalism that calls on the resources of the hard sciences.
It is revealed how the need to deal with the HPC can be avoided by adopting REC’s revolutionary take on basic cognition, and why going this way has advantages over other possible ways of handling the HPC.
Michael Silberstein
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262027236
- eISBN:
- 9780262322461
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027236.003.0017
- Subject:
- Philosophy, Philosophy of Mind
Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity ...
More
Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity often break down. Systems neuroscience has provided some reason to believe that the best explanation for this break down is in terms of the degradation of key brain subsymbolic network properties such as small-world graphical structures. It is argued that if such systems neuroscience explanations for failures of systematicity in schizophrenia are robust then this is a victory for network approaches over symbol-and-rule approaches that themselves provide little insight into said failures. Finally, there is speculation that the relevant dynamical and graphical relations in such cases extend beyond the brain to include body and environment.Less
Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity often break down. Systems neuroscience has provided some reason to believe that the best explanation for this break down is in terms of the degradation of key brain subsymbolic network properties such as small-world graphical structures. It is argued that if such systems neuroscience explanations for failures of systematicity in schizophrenia are robust then this is a victory for network approaches over symbol-and-rule approaches that themselves provide little insight into said failures. Finally, there is speculation that the relevant dynamical and graphical relations in such cases extend beyond the brain to include body and environment.
