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Synchrony and Desynchrony in IntegrateandFire Oscillators
 NEURAL COMPUTATION
, 1999
"... Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coup ..."
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Cited by 24 (1 self)
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Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrateandfire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrateandfire oscillators. We illustrate that a LEGION architecture with integrateandfire oscillators can be similarly used to address image analysis.
SelfOrganization in PeertoPeer Systems
 In Proceedings of the 2002 SIGOPS European Workshop, St. Emilion
, 2002
"... This paper addresses the problem of forming groups in peertopeer (P2P) systems and examines what dependability means in decentralized distributed systems. Much of the literature in this field assumes that the participants form a local picture of global state, yet little research has been done disc ..."
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Cited by 22 (2 self)
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This paper addresses the problem of forming groups in peertopeer (P2P) systems and examines what dependability means in decentralized distributed systems. Much of the literature in this field assumes that the participants form a local picture of global state, yet little research has been done discussing how this state remains stable as nodes enter and leave the system. We assume that nodes remain in the system long enough to benefit from retaining state, but not sufficiently long that the dynamic nature of the problem can be ignored. We look at the components that describe a system's dependability and argue that nextgeneration decentralized systems must explicitly delineate the information dispersal mechanisms (e.g., probe, eventdriven, broadcast), the capabilities assumed about constituent nodes (bandwidth, uptime, reentry distributions), and distribution of information demands (needles in a haystack vs. hay in a haystack [13]). We evaluate two systems based on these criteria: Chord [22] and a heterogeneousnode hierarchical grouping scheme [11]. The former gives a failed request rate under normal P2P conditions and a prototype of the latter a similar rate under more strenuous conditions with an order of magnitude more organizational messages. This analysis suggests several methods to greatly improve the prototype.
Mapping SelfOrganized Criticality onto Criticality
, 1995
"... : We present a general conceptual framework for selforganized criticality (SOC), based on the recognition that it is nothing but the expression, "unfolded" in a suitable parameter space, of an underlying unstable dynamical critical point. More precisely, SOC is shown to result from the tuning of th ..."
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Cited by 13 (0 self)
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: We present a general conceptual framework for selforganized criticality (SOC), based on the recognition that it is nothing but the expression, "unfolded" in a suitable parameter space, of an underlying unstable dynamical critical point. More precisely, SOC is shown to result from the tuning of the order parameter to a vanishingly small, but positive value, thus ensuring that the corresponding control parameter lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the very slow driving rate common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forestfires, which have been proposed as examples of SOC. R'esum'e : Nous proposons une strat'egie g'en'erale pour identifier le m'ecanisme responsable des ph'enom`enes critiques autoorganis'es, bas'ee sur l'id'ee qu'ils sont simplement la traduction, dans un espace de param`etres choisis, d'un point critique d...
Symmetry and phaselocking in a ring of pulsecoupled oscillators with distributed delays
 Physica D
, 1999
"... Phaselocking in a ring of pulsecoupled integrateandfire oscillators with distributed delays is analysed using group theory. The period of oscillation of a solution and those related by symmetry is determined selfconsistently. Numerical continuation of maximally symmetric solutions in characteri ..."
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Cited by 11 (4 self)
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Phaselocking in a ring of pulsecoupled integrateandfire oscillators with distributed delays is analysed using group theory. The period of oscillation of a solution and those related by symmetry is determined selfconsistently. Numerical continuation of maximally symmetric solutions in characteristic system length and timescales yields bifurcation diagrams with spontaneous symmetry breaking. The stability of phaselocked solutions is determined via a linearisation of the oscillator firing map. In the weakcoupling regime, averaging leads to an effective phasecoupled model with distributed phaseshifts and the analysis of the system is considerably simplified. In particular, the collective period of a solution is now slaved to the relative phases. For odd numbered rings, spontaneous symmetry breaking can lead to a change of stability of a travelling wave state via a simple Hopf bifurcation. The resulting nonphaselocked solutions are constructed via numerical continuation at these bifurcation points. The corresponding behaviour in the integrateandfire system is explored with simulations showing bifurcations to
Selforganization without conservation: true or just apparent scaleinvariance?
, 905
"... Abstract. The existence of true scaleinvariance in slowly driven models of selforganized criticality without a conservation law, as forestfires or earthquake automata, is scrutinized in this paper. By using three different levels of description (i) a simple mean field, (ii) a more detailed meanf ..."
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Cited by 2 (0 self)
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Abstract. The existence of true scaleinvariance in slowly driven models of selforganized criticality without a conservation law, as forestfires or earthquake automata, is scrutinized in this paper. By using three different levels of description (i) a simple mean field, (ii) a more detailed meanfield description in terms of a (selforganized) branching processes, and (iii) a full stochastic representation in terms of a Langevin equation, it is shown on general grounds that nonconserving dynamics does not lead to bona fide criticality. Contrarily to conserving systems, a parameter, which we term “recharging ” rate (e.g. the treegrowth rate in forestfire models), needs to be finetuned in nonconserving systems to obtain criticality. In the infinite size limit, such a finetuning of the loading rate is easy to achieve, as it emerges by imposing a second separation of timescales but, for any finite size, a precise tuning is required to achieve criticality and a coherent finitesize scaling picture. Using the approaches above, we shed light on the common mechanisms by which “apparent criticality ” is observed in nonconserving systems, and explain in detail (both qualitatively and quantitatively) the difference with respect to true criticality obtained in conserving systems. We
PACS: 64.60.Ht: Dynamical critical phenomena
, 1994
"... 05.40+j: Fluctuations phenomena, random processes and brownian motion Abstract: We present a general conceptual framework for selforganized criticality (SOC), based on the recognition that it is nothing but the expression, ”unfolded” in a suitable parameter space, of an underlying unstable dynamica ..."
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05.40+j: Fluctuations phenomena, random processes and brownian motion Abstract: We present a general conceptual framework for selforganized criticality (SOC), based on the recognition that it is nothing but the expression, ”unfolded” in a suitable parameter space, of an underlying unstable dynamical critical point. More precisely, SOC is shown to result from the tuning of the order parameter to a vanishingly small, but positive value, thus ensuring that the corresponding control parameter lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the very slow driving rate common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forestfires, which have been proposed as examples of SOC. Résumé: Nous proposons une stratégie générale pour identifier le mécanisme responsable des phénomènes critiques autoorganisés, basée sur l’idée qu’ils sont simplement la traduction, dans un espace de paramètres choisis, d’un point critique dynamique instable standart. La criticalité autoorganisé résulte du contrôle du paramètre d’ordre ajusté à une valeur positive tendant vers zéro, ce qui assure automatiquement que le paramètre de contrôle correspondant se cale exactement sur sa valeur critique de la transition de critique sousjacente. Ce résultat explique le rôle particulier joué par le forçage infiniment lent qui est un caractère commun à tous les systèmes critiques autoorganisés. Nous appliquons ces idées aux modèles de tas de sable, aux modèles de tremblements de terre, de feux de forêts, aux transitions de décrochage et aux modèles de croissance fractale, qui ont été proposés comme autant d’exemples caractéristiques de la criticalité autoorganisée. 1 1
ADAPTATION AND NONLINEAR PARAMETRIZATION: NONLINEAR DYNAMICS PROSPECTIVE
, 2004
"... Abstract: We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often necessary to use such energy inefficient compensators i ..."
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Abstract: We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often necessary to use such energy inefficient compensators it in wide range of applications. In particular, we show that recently introduced adaptive control algorithms in finite form which are applicable to monotonic parameterized systems can be extended to general smooth nonmonotonic parametrization. These schemes do not require any damping or domination in control inputs.
TIME SYNCHRONIZATION IN LARGESCALE NETWORKS
, 2007
"... Network time synchronization is an important aspect of sensor network operation. It is often achieved by synchronizing the clock of each node in the network to the clock of some reference node. However, it is well known that synchronization error accumulates over multiple hops. This scalability prob ..."
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Network time synchronization is an important aspect of sensor network operation. It is often achieved by synchronizing the clock of each node in the network to the clock of some reference node. However, it is well known that synchronization error accumulates over multiple hops. This scalability problem presents a challenge for largescale, multihop sensor networks with a large number of nodes distributed over wide areas. In this thesis we develop the use of spatial averaging as an approach to mitigating the effects of the scalability problem. We first develop a cooperative synchronization technique using spatial averaging that can achieve “perfect ” synchronization in the limit of an infinitely dense network. We show that it is possible to maintain a perfect timing signal with equispaced zerocrossings that occur at integer values of the reference time. Second, we study the benefits of cooperative time synchronization using spatial averaging in networks of finite density. We present a protocol that uses spatial averaging to reduce error accumulation in largescale networks and show that synchronization performance can be significantly improved by increasing network density.
Synchrony and Desynchrony in IntegrateandFire Oscillators
"... Due to many experimental reports of synchronized neural activity in the brain, there is much interest in understanding synchronization in networks of oscillators and using these systems for perceptual organization. We examine locally coupled networks of integrateandre oscillators and, contrary t ..."
Abstract
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Due to many experimental reports of synchronized neural activity in the brain, there is much interest in understanding synchronization in networks of oscillators and using these systems for perceptual organization. We examine locally coupled networks of integrateandre oscillators and, contrary to a recent report by Hop$eld and Herz [2], we$nd that they can quickly synchrony. Moreover; we$nd that time to achieve synchrony increases logarithmically with the system size. Inspired by LEGION dynamics with relaxation oscillators, we are able to reliably desynchronize different oscillator groups in a network of integrateandJire oscillators using a global inhibitor 1.