Estimation of parameters in nonlinear systems using balanced synchronization

Abarbanel, Henry D. I.; Creveling, Daniel R.; Jeanne, James M.

doi:10.1103/physreve.77.016208

Cited by 49 publications

(44 citation statements)

References 19 publications

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“…This is work by Abarbanel et al [45][46][47] The basic idea is similar to Parlitz' above, but more care is taken to avoid mathematical difficulties and the method is generalized to more complex situations, including those involving time series and data using sophisticated regularization approaches. We do not have sufficient space here to even crudely cover all the ideas in this work, but we note that it sets the tone for much more development of the use of synchronization for parameter estimation and system analysis.…”

Section: More Sophisticated Approachesmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

431

326

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We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.

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Section: More Sophisticated Approachesmentioning

confidence: 99%

Synchronization of chaotic systems

Pecora

Carroll

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

431

326

View full text Add to dashboard Cite

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“…However, if the coupling between the observations and the model is too strong, the variation of synchronization with respect to the parameters is too small to permit optimization. This leads to the notion of balanced synchronization that requires that the CLE ''remain negative but small in magnitude'' [65]. In other words, we want the synchronization between the causes of sensory input and neuronal representations to be strong but not too strong.…”

Section: R = φ(ψ) Is Stablementioning

confidence: 99%

Critical Slowing and Perception

Friston

Breakspear

Deco

2014

Criticality in Neural Systems

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It is generally assumed that criticality and metastability underwrite the brain's dynamic repertoire of responses to an inconstant world. From perception to behavior, the ability to respond sensitively to changes in the environment -and to explore alternative hypotheses and policies -seems inherently linked to selforganized criticality. This chapter addresses the relationship between perception and criticality -using recent advances in the theoretical neuroscience of perceptual inference. In short, we will see that (Bayes) optimal inference -on the causes of sensations -necessarily entails a form of criticality -critical slowing -and a balanced synchronization between the sensorium and neuronal dynamics. This means that the optimality principles describing our exchanges with the world may also account for dynamical phenomena that characterize self-organized systems such as the brain.This chapter considers the formal basis of self-organized instabilities that enable perceptual transitions during Bayes-optimal perception. We will consider the perceptual transitions that lead to conscious ignition [1] and how they depend on dynamical instabilities that underlie chaotic itinerancy [2, 3] and self-organized criticality [4][5][6]. We will try to understand these transitions using a dynamical formulation of perception as approximate Bayesian inference. This formulation suggests that perception has an inherent tendency to induce dynamical instabilities that enable the brain to respond sensitively to sensory perturbations. We review the dynamics of perception, in terms of Bayesian optimization (filtering), present a formal conjecture about self-organized instability, and then test this conjecture, using neuronal simulations of perceptual categorization. Perception and Neuronal DynamicsPerceptual categorization speaks to two key dynamical phenomena: transitions from one perceptual state to another and the dynamical mechanisms that permit Criticality in Neural Systems, First Edition. Edited by Dietmar Plenz and Ernst Niebur.

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“…(See [39] for a somewhat related physics-based optimization approach for fitting dynamical systems models.) In many cases S(x; θ) is a jointly concave function of (x, θ); since S(x; θ) and its derivatives may be computed quite easily, this significantly simplifies the computation ofθ.…”

Section: Laplace Approximationmentioning

confidence: 99%

Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

Koyama

Paninski

2009

J Comput Neurosci

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A number of important data analysis problems in neuroscience can be solved using state-space models. In this article, we describe fast methods for computing the exact maximum a posteriori (MAP) path of the hidden state variable in these models, given spike train observations. If the state transition density is log-concave and the observation model satisfies certain standard assumptions, then the optimization problem is strictly concave and can be solved rapidly with Newton-Raphson methods, because the Hessian of the loglikelihood is block tridiagonal. We can further exploit this block-tridiagonal structure to develop efficient parameter estimation methods for these models. We describe applications of this approach to neural decoding problems, with a focus on the classic integrate-and-fire model as a key example.

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Estimation of parameters in nonlinear systems using balanced synchronization

Cited by 49 publications

References 19 publications

Synchronization of chaotic systems

Synchronization of chaotic systems

Critical Slowing and Perception

Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

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