7,092 research outputs found
Global convergence of quorum-sensing networks
In many natural synchronization phenomena, communication between individual
elements occurs not directly, but rather through the environment. One of these
instances is bacterial quorum sensing, where bacteria release signaling
molecules in the environment which in turn are sensed and used for population
coordination. Extending this motivation to a general non- linear dynamical
system context, this paper analyzes synchronization phenomena in networks where
communication and coupling between nodes are mediated by shared dynamical quan-
tities, typically provided by the nodes' environment. Our model includes the
case when the dynamics of the shared variables themselves cannot be neglected
or indeed play a central part. Applications to examples from systems biology
illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages:
36
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
Shaping bursting by electrical coupling and noise
Gap-junctional coupling is an important way of communication between neurons
and other excitable cells. Strong electrical coupling synchronizes activity
across cell ensembles. Surprisingly, in the presence of noise synchronous
oscillations generated by an electrically coupled network may differ
qualitatively from the oscillations produced by uncoupled individual cells
forming the network. A prominent example of such behavior is the synchronized
bursting in islets of Langerhans formed by pancreatic \beta-cells, which in
isolation are known to exhibit irregular spiking. At the heart of this
intriguing phenomenon lies denoising, a remarkable ability of electrical
coupling to diminish the effects of noise acting on individual cells.
In this paper, we derive quantitative estimates characterizing denoising in
electrically coupled networks of conductance-based models of square wave
bursting cells. Our analysis reveals the interplay of the intrinsic properties
of the individual cells and network topology and their respective contributions
to this important effect. In particular, we show that networks on graphs with
large algebraic connectivity or small total effective resistance are better
equipped for implementing denoising. As a by-product of the analysis of
denoising, we analytically estimate the rate with which trajectories converge
to the synchronization subspace and the stability of the latter to random
perturbations. These estimates reveal the role of the network topology in
synchronization. The analysis is complemented by numerical simulations of
electrically coupled conductance-based networks. Taken together, these results
explain the mechanisms underlying synchronization and denoising in an important
class of biological models
Synchronization and Noise: A Mechanism for Regularization in Neural Systems
To learn and reason in the presence of uncertainty, the brain must be capable
of imposing some form of regularization. Here we suggest, through theoretical
and computational arguments, that the combination of noise with synchronization
provides a plausible mechanism for regularization in the nervous system. The
functional role of regularization is considered in a general context in which
coupled computational systems receive inputs corrupted by correlated noise.
Noise on the inputs is shown to impose regularization, and when synchronization
upstream induces time-varying correlations across noise variables, the degree
of regularization can be calibrated over time. The proposed mechanism is
explored first in the context of a simple associative learning problem, and
then in the context of a hierarchical sensory coding task. The resulting
qualitative behavior coincides with experimental data from visual cortex.Comment: 32 pages, 7 figures. under revie
Cooperative Adaptive Control for Cloud-Based Robotics
This paper studies collaboration through the cloud in the context of
cooperative adaptive control for robot manipulators. We first consider the case
of multiple robots manipulating a common object through synchronous centralized
update laws to identify unknown inertial parameters. Through this development,
we introduce a notion of Collective Sufficient Richness, wherein parameter
convergence can be enabled through teamwork in the group. The introduction of
this property and the analysis of stable adaptive controllers that benefit from
it constitute the main new contributions of this work. Building on this
original example, we then consider decentralized update laws, time-varying
network topologies, and the influence of communication delays on this process.
Perhaps surprisingly, these nonidealized networked conditions inherit the same
benefits of convergence being determined through collective effects for the
group. Simple simulations of a planar manipulator identifying an unknown load
are provided to illustrate the central idea and benefits of Collective
Sufficient Richness.Comment: ICRA 201
Realizing the physics of motile cilia synchronization with driven colloids
Cilia and flagella in biological systems often show large scale cooperative
behaviors such as the synchronization of their beats in "metachronal waves".
These are beautiful examples of emergent dynamics in biology, and are essential
for life, allowing diverse processes from the motility of eukaryotic
microorganisms, to nutrient transport and clearance of pathogens from mammalian
airways. How these collective states arise is not fully understood, but it is
clear that individual cilia interact mechanically,and that a strong and long
ranged component of the coupling is mediated by the viscous fluid. We review
here the work by ourselves and others aimed at understanding the behavior of
hydrodynamically coupled systems, and particularly a set of results that have
been obtained both experimentally and theoretically by studying actively driven
colloidal systems. In these controlled scenarios, it is possible to selectively
test aspects of the living motile cilia, such as the geometrical arrangement,
the effects of the driving profile and the distance to no-slip boundaries. We
outline and give examples of how it is possible to link model systems to
observations on living systems, which can be made on microorganisms, on cell
cultures or on tissue sections. This area of research has clear clinical
application in the long term, as severe pathologies are associated with
compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic
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