19,786 research outputs found
Anticipated synchronization: a metaphorical linear view
We study the regime of anticipated synchronization recently described on a
number of dynamical systems including chaotic and noisy ones. We use simple
linear caricatures to show the minimal setups able to reproduce the basic facts
described.Comment: 7 pages,5 figure
Neural synchrony in cortical networks : history, concept and current status
Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies
Neural synchrony in cortical networks : history, concept and current status
Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies
A continuous-time analysis of distributed stochastic gradient
We analyze the effect of synchronization on distributed stochastic gradient
algorithms. By exploiting an analogy with dynamical models of biological quorum
sensing -- where synchronization between agents is induced through
communication with a common signal -- we quantify how synchronization can
significantly reduce the magnitude of the noise felt by the individual
distributed agents and by their spatial mean. This noise reduction is in turn
associated with a reduction in the smoothing of the loss function imposed by
the stochastic gradient approximation. Through simulations on model non-convex
objectives, we demonstrate that coupling can stabilize higher noise levels and
improve convergence. We provide a convergence analysis for strongly convex
functions by deriving a bound on the expected deviation of the spatial mean of
the agents from the global minimizer for an algorithm based on quorum sensing,
the same algorithm with momentum, and the Elastic Averaging SGD (EASGD)
algorithm. We discuss extensions to new algorithms which allow each agent to
broadcast its current measure of success and shape the collective computation
accordingly. We supplement our theoretical analysis with numerical experiments
on convolutional neural networks trained on the CIFAR-10 dataset, where we note
a surprising regularizing property of EASGD even when applied to the
non-distributed case. This observation suggests alternative second-order
in-time algorithms for non-distributed optimization that are competitive with
momentum methods.Comment: 9/14/19 : Final version, accepted for publication in Neural
Computation. 4/7/19 : Significant edits: addition of simulations, deep
network results, and revisions throughout. 12/28/18: Initial submissio
Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
Learning and decision making in the brain are key processes critical to
survival, and yet are processes implemented by non-ideal biological building
blocks which can impose significant error. We explore quantitatively how the
brain might cope with this inherent source of error by taking advantage of two
ubiquitous mechanisms, redundancy and synchronization. In particular we
consider a neural process whose goal is to learn a decision function by
implementing a nonlinear gradient dynamics. The dynamics, however, are assumed
to be corrupted by perturbations modeling the error which might be incurred due
to limitations of the biology, intrinsic neuronal noise, and imperfect
measurements. We show that error, and the associated uncertainty surrounding a
learned solution, can be controlled in large part by trading off
synchronization strength among multiple redundant neural systems against the
noise amplitude. The impact of the coupling between such redundant systems is
quantified by the spectrum of the network Laplacian, and we discuss the role of
network topology in synchronization and in reducing the effect of noise. A
range of situations in which the mechanisms we model arise in brain science are
discussed, and we draw attention to experimental evidence suggesting that
cortical circuits capable of implementing the computations of interest here can
be found on several scales. Finally, simulations comparing theoretical bounds
to the relevant empirical quantities show that the theoretical estimates we
derive can be tight.Comment: Preprint, accepted for publication in Neural Computatio
Revealing networks from dynamics: an introduction
What can we learn from the collective dynamics of a complex network about its
interaction topology? Taking the perspective from nonlinear dynamics, we
briefly review recent progress on how to infer structural connectivity (direct
interactions) from accessing the dynamics of the units. Potential applications
range from interaction networks in physics, to chemical and metabolic
reactions, protein and gene regulatory networks as well as neural circuits in
biology and electric power grids or wireless sensor networks in engineering.
Moreover, we briefly mention some standard ways of inferring effective or
functional connectivity.Comment: Topical review, 48 pages, 7 figure
Robust synchronization for 2-D discrete-time coupled dynamical networks
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under
Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
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