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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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