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Analysis of Dynamic Behavior

Domitilla Del Vecchio and Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0003
Subject:
Biology, Biochemistry / Molecular Biology

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the ... More


Synergy

Mark L. Latash

Published in print:
2008
Published Online:
May 2009
ISBN:
9780195333169
eISBN:
9780199864195
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195333169.001.0001
Subject:
Neuroscience, Sensory and Motor Systems, Techniques

This book discusses a general problem in biology: the lack of an adequate language for formulating biologically specific problems. This book describes recent progress in the control and coordination ... More


Anticipatory Control of Voluntary Action: Merging the Ideas of Equilibrium-point Control and Synergic Control

Mark L. Latash

in Motor Control: Theories, Experiments, and Applications

Published in print:
2010
Published Online:
January 2011
ISBN:
9780195395273
eISBN:
9780199863518
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195395273.003.0001
Subject:
Neuroscience, Sensory and Motor Systems

This chapter presents an overview of two major developments in the field of motor control: the referent configuration hypothesis (equilibrium-point hypothesis) and the theory of synergies (using the ... More


Uniform asymptotic stability, an initial treatment

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered ... More


Models and Beyond Motor Synergies

Mark L. Latash

in Synergy

Published in print:
2008
Published Online:
May 2009
ISBN:
9780195333169
eISBN:
9780199864195
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195333169.003.0008
Subject:
Neuroscience, Sensory and Motor Systems, Techniques

The final part of the book addresses two issues: modeling of synergies and possible synergic organization of non-motor functions such as the language and the sensory function. Within the first issue, ... More


Emilio Bizzi

Larry R. Squire

in The History of Neuroscience in Autobiography Volume 6

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195380101
eISBN:
9780199864362
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195380101.003.0002
Subject:
Neuroscience, History of Neuroscience

This chapter presents an autobiography of Emilio Bizzi. Bizzi's research formed the basis of a comprehensive theory—the equilibrium-point hypothesis—which accounts for how the central nervous system ... More


Neurophysiological Mechanisms

Mark L. Latash

in Synergy

Published in print:
2008
Published Online:
May 2009
ISBN:
9780195333169
eISBN:
9780199864195
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195333169.003.0007
Subject:
Neuroscience, Sensory and Motor Systems, Techniques

The seventh part of this book deals with possible neurophysiological mechanisms involved in motor synergies. It starts with a discussion of the structure-function controversy in neurophysiology. ... More


Small Vibrations About Equilibrium

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

A number of interesting mechanical systems have one or more essentially stable equilibrium configurations. When disturbed slightly, they vibrate about equilibrium in characteristic patterns called ... More


Games in Extensive Form

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0007
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a number of key concepts for extensive form game representation. It first considers a matrix that defines a zero-sum matrix game for which the minimizer has two actions and the ... More


Stochastic Policies for Games in Extensive Form

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses two types of stochastic policy for extensive form game representation as well as the existence and computation of saddle-point equilibrium. For games in extensive form, a mixed ... More


Mixed Policies

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions ... More


Zero-Sum Matrix Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0003
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome ... More


Computation of Mixed Saddle-Point Equilibrium Policies

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of mixed saddle-point equilibrium policies. In view of the Minimax Theorem, the mixed saddle-point equilibria can be determined by computing the mixed security ... More


State-Feedback Zero-Sum Differential Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0018
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum continuous time dynamic game in a state-feedback policy. It begins by considering the solution for two-player ... More


State-Feedback Zero-Sum Dynamic Games

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0017
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player ... More


Motor Routines

Dana H. Ballard

in Brain Computation as Hierarchical Abstraction

Published in print:
2015
Published Online:
September 2015
ISBN:
9780262028615
eISBN:
9780262323819
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262028615.003.0007
Subject:
Neuroscience, Research and Theory

The complexities of directing complicated high-degree of freedom interactions in the Newtonian world make the human motor system the most complicated of the brain’s large-scale systems. In particular ... More


Near-Equilibrium Oscillations

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, the theory of near-equilibrium oscillations is developed and normal mode analysis is performed. This topic requires a little bit of linear algebra when dealing with matrices, as well ... More


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