Author
Nicolas Tabareau
Other affiliations: Collège de France, University of Paris, Paris Diderot University ...read more
Bio: Nicolas Tabareau is an academic researcher from French Institute for Research in Computer Science and Automation. The author has contributed to research in topics: Type theory & Mathematical proof. The author has an hindex of 21, co-authored 80 publications receiving 1304 citations. Previous affiliations of Nicolas Tabareau include Collège de France & University of Paris.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of any two stochastically contracting systems.
Abstract: We investigate the incremental stability properties of Ito stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of nonlinear observers design and stochastic synchronization.
165 citations
01 Jan 2009
TL;DR: Tabareau et al. as discussed by the authors showed that under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization, which then allows reliable computations to be carried out even in the presence of significant noise.
Abstract: The functional role of synchronization has attracted much interest and debate: in particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore may play a role in temporal binding, in attention or in sensory-motor integration mechanisms. In this article, we study another role for synchronization: the socalled ‘‘collective enhancement of precision’’. We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations—intrinsic neuronal noise—which affect all neurons in the nervous system. More precisely, our main contribution is a mathematical proof that, under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization. This property then allows reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates). This in turn is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Similar concepts may be applicable to questions of noise and variability in systems biology. Citation: Tabareau N, Slotine J-J, Pham Q-C (2010) How Synchronization Protects from Noise. PLoS Comput Biol 6(1): e1000637. doi:10.1371/journal.pcbi.1000637 Editor: Michael Breakspear, The University of New South Wales, Australia Received June 18, 2009; Accepted December 8, 2009; Published January 15, 2010 Copyright: 2010 Tabareau et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported in part by EC—contract number FP6-IST-027140, action line: Cognitive Systems. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: nicolas.tabareau@inria.fr
98 citations
TL;DR: It is argued, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations—intrinsic neuronal noise—which affect all neurons in the nervous system.
Abstract: The functional role of synchronization has attracted much interest and debate: in particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore may play a role in temporal binding, in attention or in sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called “collective enhancement of precision”. We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations—intrinsic neuronal noise—which affect all neurons in the nervous system. More precisely, our main contribution is a mathematical proof that, under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization. This property then allows reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates). This in turn is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Similar concepts may be applicable to questions of noise and variability in systems biology.
89 citations
TL;DR: A multi-disciplinary approach at the convergence of neuroscience, dynamical system theory and autonomous robotics, in order to propose an efficient action selection mechanism based on a new model of the basal ganglia, which exhibits valuable dithering avoidance and energy-saving properties, when compared with a simple if-then-else decision rule.
63 citations
03 Jul 2009
TL;DR: This article explains how to compute the free commutative comonoid !
Abstract: The exponential modality of linear logic associates a commutative comonoid !A to every formula A in order to duplicate it. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We then apply this general recipe to two familiar models of linear logic, based on coherence spaces and on Conway games. This algebraic approach enables to unify for the first time apparently different constructions of the exponential modality in spaces and games. It also sheds light on the subtle duplication policy of linear logic. On the other hand, we explain at the end of the article why the formula does not work in the case of the finiteness space model.
59 citations
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TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects
3,424 citations
Journal Article•
TL;DR: AspectJ as mentioned in this paper is a simple and practical aspect-oriented extension to Java with just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns.
Abstract: Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.
2,947 citations
TL;DR: Recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components.
Abstract: A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.
503 citations
01 Jan 2002
TL;DR: This chapter presents the basic concepts of term rewriting that are needed in this book and suggests several survey articles that can be consulted.
Abstract: In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.
501 citations
TL;DR: It is found that endogenous brain activity can causally affect neural function through field effects under physiological conditions, and extracellular fields induced ephaptically mediated changes in the somatic membrane potential that were less than 0.5 mV under subthreshold conditions.
Abstract: The electrochemical processes that underlie neural function manifest themselves in ceaseless spatiotemporal field fluctuations. However, extracellular fields feed back onto the electric potential across the neuronal membrane via ephaptic coupling, independent of synapses. The extent to which such ephaptic coupling alters the functioning of neurons under physiological conditions remains unclear. To address this question, we stimulated and recorded from rat cortical pyramidal neurons in slices with a 12-electrode setup. We found that extracellular fields induced ephaptically mediated changes in the somatic membrane potential that were less than 0.5 mV under subthreshold conditions. Despite their small size, these fields could strongly entrain action potentials, particularly for slow (<8 Hz) fluctuations of the extracellular field. Finally, we simultaneously measured from up to four patched neurons located proximally to each other. Our findings indicate that endogenous brain activity can causally affect neural function through field effects under physiological conditions.
489 citations