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Stochastic parametrization of short-scale processes is revisited in an idealized setting in which the short scales are manifested as small-amplitude deterministic forcings acting on the evolution laws of the resolved variables. Conditions under which the invariant probability density of the original deterministic system tends to that induced by the action of appropriately parametrized Gaussian white noise are identified. On the other hand, substantial differences are revealed between the deterministic description and its stochastic substitute when time-dependent properties are considered such as short-time behaviour of the variance, recurrence and first passage time statistics. Illustrations and explicit evaluations are provided on low-order model systems., SCOPUS: ar.j, DecretOANoAutActif, info:eu-repo/semantics/published

Stochastic resonance is analyzed in an array of nonlinear spatially coupled subsystems. Analytic expressions for the different steady-state solutions, for the rates of transitions between them in the presence of noise, and for the response to a weak external periodic forcing are derived. It is shown that the presence of spatial degrees of freedom modifies considerably the mechanisms of transitions between states and is responsible for a marked sensitivity of the response on the coupling constant and on the system size., SCOPUS: ar.j, info:eu-repo/semantics/published

The classical setting of stochastic resonance is extended to account for parameter variations leading to transitions between a unique stable state, bistability, and multistability regimes, across singularities of various kinds. Analytic expressions for the amplitude and the phase of the response in terms of key parameters are obtained. The conditions for optimal responses are derived in terms of the bifurcation parameter, the driving frequency, and the noise strength., SCOPUS: ar.j, info:eu-repo/semantics/published

A class of complex self-organizing systems subjected to fluctuations of environmental or intrinsic origin and to nonequilibrium constraints in the form of an external periodic forcing is analyzed from the standpoint of information theory. Conditions under which the response of information entropy and related quantities to the nonequilibrium constraint can be optimized via a stochastic resonance-type mechanism are identified, and the role of key parameters is assessed., SCOPUS: ar.j, info:eu-repo/semantics/published

Symbolic sequences arising from the coarse graining of deterministic dynamical systems continuous in phase space are considered. The extent to which signatures of the time irreversibility and of the nonequilibrium constraints at the level of the original system, such as fluxes or dissipation, can be identified at the coarse-grained level is analyzed. The roles of the partition, of the time window, and of time averaging in distinguishing in a clear-cut way the equilibrium versus nonequilibrium character of the sequence are brought out., SCOPUS: ar.j, info:eu-repo/semantics/published

The principal signatures of deterministic dynamics in the probabilistic properties of extremes are identified. Analytical expressions for n-fold cumulative distributions and their associated densities are derived. Substantial differences from the classical statistical theory of extreme values are found and illustrated on generic classes of dynamical systems giving rise to fully developed chaos and to quasi-periodic behavior., SCOPUS: re.j, info:eu-repo/semantics/published

The principal signatures of deterministic dynamics in the probabilistic properties of extremes are identified in this chapter. Analytical expressions for n-fold cumulative distributions and their associated densities, for the exceedance probabilities and spatial propagation of extremes, are derived and complemented by numerical simulations. Substantial differences from the classical statistical theory are found and illustrated on generic classes of dynamical systems, giving rise to fully developed chaos, intermittent chaos, and quasi-periodic behavior., SCOPUS: ch.b, info:eu-repo/semantics/published

A linear response theory of systems of interest in atmospheric and climate dynamics taking fully into account the nonlinearities of the underlying processes is developed. Under the assumption that the source of intrinsic variability can be modeled as a white-noise process, a Fokker-Planck equation approach leads to fluctuation-dissipation-type expressions in the form of time cross-correlation functions, linking the perturbation-induced shift of an observable to the statistical and dynamical properties of the reference system. These expressions feature a generalized potential function and enable one to go systematically beyond the Gaussian approximation usually adopted in the literature. Full solutions and explicit expressions are derived for different subclasses of systems, including a global climate model giving rise to oscillatory behavior., SCOPUS: ar.j, info:eu-repo/semantics/published

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ2 tests shows that DNA can not be described as a low order Markov chain of order up to r=6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details. © 2014 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

Complexity measures are used to compare the genomic characteristics of five organisms belonging to distinct classes spanning the evolutionary tree: higher eukaryotes, amoebae, unicellular eukaryotes and bacteria. The comparisons are undertaken using the full four-letter alphabet and the coarse grained two-letter alphabets AG-CT and AT-CG. We show that the conditional probability matrix for the four-letter and AT-CG alphabet is markedly asymmetric in eukaryotes while it is nearly symmetric in bacterial genomes. Spatial asymmetry is revealed in the four-letter alphabet, signifying that the probability fluxes are nonvanishing and thus the reading sense of a sequence is irreversible for all organisms. Calculations of the block entropy and excess entropy demonstrate that the human genome accommodates better all possible block configurations, especially for long blocks. With respect to point-to-point details and to spatial arrangement of blocks the exit distance distributions from a particular letter demonstrate long distance characteristics in the eukaryotic sequences for all three alphabets, while the bacterial (prokaryotic) genomes deviate indicating short range characteristics. Overall, the conditional probability, the fluxes, the block entropy content and the exit distance distributions can be used as markers, discriminating between eukaryotic and prokaryotic DNA, allowing in many cases to discern details related to finer classes. In all cases the reduction from four letters to two masks some important statistical and spatial properties, with the AT-CG alphabet having higher ability of discrimination than the AG-CT one. In particular, the AT-CG alphabet reduction accentuates the CpG related properties (conditional probabilities w32, long ranged exit distance distribution for A and T nucleotides), but masks sequence asymmetry and irreversibility in all examined organisms., SCOPUS: ar.j, info:eu-repo/semantics/published

The response of a dynamical system to systematic variations of a control parameter in time in the presence of noise is analyzed by a reduction of the multivariate dynamics to a normal form in the vicinity of bifurcations of the pitchfork and of the limit point type. Mean-field responses, mean values, second- and fourth-order cumulants, probability densities, and entropy-like quantities are evaluated as the system sweeps across the bifurcation point, moving forward toward a multiple state region or moving backward out of this region. Depending on the case stabilization of unstable states, delays and slowing down are found and their signatures on particular observables are identified with an emphasis on the role of noise and on global properties beyond linearized theory. © 2014 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

The response of a dynamical system to systematic variations of a control parameter in time in the presence of noise is analyzed by a reduction of the multivariate dynamics to a normal form in the vicinity of bifurcations of the pitchfork and of the limit point type. Mean-field responses, mean values, second- and fourth-order cumulants, probability densities, and entropy-like quantities are evaluated as the system sweeps across the bifurcation point, moving forward toward a multiple state region or moving backward out of this region. Depending on the case stabilization of unstable states, delays and slowing down are found and their signatures on particular observables are identified with an emphasis on the role of noise and on global properties beyond linearized theory. © 2014 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

Complexity measures are used to compare the genomic characteristics of five organisms belonging to distinct classes spanning the evolutionary tree: higher eukaryotes, amoebae, unicellular eukaryotes and bacteria. The comparisons are undertaken using the full four-letter alphabet and the coarse grained two-letter alphabets AG-CT and AT-CG. We show that the conditional probability matrix for the four-letter and AT-CG alphabet is markedly asymmetric in eukaryotes while it is nearly symmetric in bacterial genomes. Spatial asymmetry is revealed in the four-letter alphabet, signifying that the probability fluxes are nonvanishing and thus the reading sense of a sequence is irreversible for all organisms. Calculations of the block entropy and excess entropy demonstrate that the human genome accommodates better all possible block configurations, especially for long blocks. With respect to point-to-point details and to spatial arrangement of blocks the exit distance distributions from a particular letter demonstrate long distance characteristics in the eukaryotic sequences for all three alphabets, while the bacterial (prokaryotic) genomes deviate indicating short range characteristics. Overall, the conditional probability, the fluxes, the block entropy content and the exit distance distributions can be used as markers, discriminating between eukaryotic and prokaryotic DNA, allowing in many cases to discern details related to finer classes. In all cases the reduction from four letters to two masks some important statistical and spatial properties, with the AT-CG alphabet having higher ability of discrimination than the AG-CT one. In particular, the AT-CG alphabet reduction accentuates the CpG related properties (conditional probabilities w32, long ranged exit distance distribution for A and T nucleotides), but masks sequence asymmetry and irreversibility in all examined organisms., SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.k, info:eu-repo/semantics/published

SCOPUS: ar.k, info:eu-repo/semantics/published

SCOPUS: ar.k, info:eu-repo/semantics/published

The probabilistic properties of extreme values in multivariate deterministic dynamical systems are analyzed. It is shown that owing to the intertwining of unstable and stable modes the effect of dynamical complexity on the extremes tends to be masked, in the sense that the cumulative probability distribution of typical variables is differentiable and its associated probability density is continuous. Still, there exist combinations of variables probing the dominant unstable modes displaying singular behavior in the form of nondifferentiability of the cumulative distributions of extremes on certain sets of phase space points. Analytic evaluations and extensive numerical simulations are carried out for characteristic examples of Kolmogorov-type systems, for low-dimensional chaotic flows, and for spatially extended systems. © 2012 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

We present a comparative analysis of sequential versus hierarchical mechanisms of self-assembly in supramolecular architectures. The analysis is multifaceted, drawing on and inter-relating insights from a kinetic mean-field analysis and one based on the theory of finite Markov processes, complemented by Monte Carlo calculations. We give explicit results for two reaction pathways that are likely to dominate in early stages of self-assembly, and draw attention to experimental studies to which our results pertain: crystallization of zeolites from the bulk phase and aggregation of surface-supported supramolecular structures. Among the several conclusions that can be drawn from the theory and the simulations is a crossover from one mechanism to another, depending on the values of system parameters. © 2012 Copyright Taylor and Francis Group, LLC., SCOPUS: ar.j, info:eu-repo/semantics/published

We present a comparative analysis of sequential versus hierarchical mechanisms of self-assembly in supramolecular architectures. The analysis is multifaceted, drawing on and inter-relating insights from a kinetic mean-field analysis and one based on the theory of finite Markov processes, complemented by Monte Carlo calculations. We give explicit results for two reaction pathways that are likely to dominate in early stages of self-assembly, and draw attention to experimental studies to which our results pertain: crystallization of zeolites from the bulk phase and aggregation of surface-supported supramolecular structures. Among the several conclusions that can be drawn from the theory and the simulations is a crossover from one mechanism to another, depending on the values of system parameters. © 2012 Copyright Taylor and Francis Group, LLC., SCOPUS: ar.j, info:eu-repo/semantics/published

The probabilistic properties of extreme values in multivariate deterministic dynamical systems are analyzed. It is shown that owing to the intertwining of unstable and stable modes the effect of dynamical complexity on the extremes tends to be masked, in the sense that the cumulative probability distribution of typical variables is differentiable and its associated probability density is continuous. Still, there exist combinations of variables probing the dominant unstable modes displaying singular behavior in the form of nondifferentiability of the cumulative distributions of extremes on certain sets of phase space points. Analytic evaluations and extensive numerical simulations are carried out for characteristic examples of Kolmogorov-type systems, for low-dimensional chaotic flows, and for spatially extended systems. © 2012 American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.k, info:eu-repo/semantics/published

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science., SCOPUS: bk.b, info:eu-repo/semantics/published

The formalism of irreversible thermodynamics is extended to include the effect of random perturbations and applied to representative systems giving rise to instabilities and to complex nonlinear behaviours. The extent to which dissipation as measured by the entropy production exhibits variational properties that can be linked to key indicators of the dynamical behaviour is explored with emphasis on the conjecture of the climate system as a system of maximum dissipation. © 2010 Royal Meteorological Society., SCOPUS: ar.j, FLWIN, info:eu-repo/semantics/published

The formalism of irreversible thermodynamics is extended to include the effect of random perturbations and applied to representative systems giving rise to instabilities and to complex nonlinear behaviours. The extent to which dissipation as measured by the entropy production exhibits variational properties that can be linked to key indicators of the dynamical behaviour is explored with emphasis on the conjecture of the climate system as a system of maximum dissipation. © 2010 Royal Meteorological Society., SCOPUS: ar.j, FLWIN, info:eu-repo/semantics/published

The propagation of extreme events in space is analyzed for a class of dynamical systems giving rise to spatiotemporal chaos. It is shown that this process can be mapped into a generalized random walk, whereby the mean square displacement increases linearly in time and there is a nonvanishing probability for jumps beyond first neighbors. The relative roles of the local dynamics and of the spatial coupling are identified.

A dynamical approach to recurrent and extreme events is developed focusing on the role of correlations and memory in the structure of the probability distributions and their low-order moments. The procedure is illustrated on homogeneous first and second order Markov chains, non-Markovian and nonhomogeneous processes and deterministic dynamical systems. Substantial differences with classical statistical theory as applied to independent identically distributed random variables are identified. © 2009 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

An approach to Complexity from the perspective of fundamental science is outlined, drawing on the cross-fertilization of concepts and tools from nonlinear dynamics, statistical physics, probability and information theories, data analysis and numerical simulation. Emphasis is placed on the intertwining between different levels of description and on the probabilistic dimension of complex systems, in connection with the issue of prediction. © 2009 Academia Europaea., SCOPUS: ar.j, info:eu-repo/semantics/published

An approach to Complexity from the perspective of fundamental science is outlined, drawing on the cross-fertilization of concepts and tools from nonlinear dynamics, statistical physics, probability and information theories, data analysis and numerical simulation. Emphasis is placed on the intertwining between different levels of description and on the probabilistic dimension of complex systems, in connection with the issue of prediction. © 2009 Academia Europaea., SCOPUS: ar.j, info:eu-repo/semantics/published

A dynamical approach to recurrent and extreme events is developed focusing on the role of correlations and memory in the structure of the probability distributions and their low-order moments. The procedure is illustrated on homogeneous first and second order Markov chains, non-Markovian and nonhomogeneous processes and deterministic dynamical systems. Substantial differences with classical statistical theory as applied to independent identically distributed random variables are identified. © 2009 The American Physical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

The extreme value statistics of systems possessing a two-hump probability density of the relevant variable, in which the left peak is more pronounced than the right one, is studied. It is shown that systems of this type display a nontrivial transient behavior in the form of anomalous fluctuations around the mean, for certain (finite) ranges of observational time windows. The results are illustrated on independent identically distributed random variables, systems possessing two locally stable states and subjected to additive white noise, and dynamical systems in the regime of deterministic chaos.

Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level., SCOPUS: bk.b, info:eu-repo/semantics/published

We study two important aspects of the diffusion of a free particle in the presence of a time-dependent control parameter. The latter is represented by a friction coefficient that is a given function of time. We solve the stochastic Liouville equation (the Fokker-Planck equation) for the probability density of the particle in phase space, i. e. in both position and velocity. The exact solution is then used to analyze the behavior of (i) the variance in the position, a global characterizer of the system; and (ii) the mean rate of crossings of an arbitrary threshold in the position, a local characterizer. The former is the more conventional descriptor of diffusive processes, but the latter provides valuable complementary information on the dynamical behavior. Depending on the long-time behavior of the friction coefficient, the asymptotic behaviors of both these char-acterizers vary, and exhibit several cross-overs. This helps elucidate the nature of the interplay between the destabilizing effects of the noise and the stabilizing tendency of the damping, as the latter undergoes a controlled variation in time., SCOPUS: cp.p, info:eu-repo/semantics/published

A microscopic model of warm clouds involving input of water droplets, dropletdroplet aggregation, droplet breakup, and precipitation is presented. Numerical simulations and analytical arguments indicate that after the stage of growth and just before precipitation sets in, a warm cloud is characterized by a droplet-size distribution which follows from an inverse power law as a function of the droplet size. When precipitation is taken into account, the above distribution is transformed into a distribution decaying exponentially with the droplet size, in agreement with field observations. It is suggested that the initiation of rainfall in a precipitating warm cloud can be viewed as an instability triggered by the presence of a power-law distribution. © 1994 Plenum Publishing Corporation., SCOPUS: ar.j, info:eu-repo/semantics/published

A microscopic model of warm clouds involving input of water droplets, dropletdroplet aggregation, droplet breakup, and precipitation is presented. Numerical simulations and analytical arguments indicate that after the stage of growth and just before precipitation sets in, a warm cloud is characterized by a droplet-size distribution which follows from an inverse power law as a function of the droplet size. When precipitation is taken into account, the above distribution is transformed into a distribution decaying exponentially with the droplet size, in agreement with field observations. It is suggested that the initiation of rainfall in a precipitating warm cloud can be viewed as an instability triggered by the presence of a power-law distribution. © 1994 Plenum Publishing Corporation., SCOPUS: ar.j, info:eu-repo/semantics/published

An analysis of the West European climate over short time scales is performed by means of time series of the 500 mb geopotential height at nine different meteorological stations. The characterization of the dynamics is based on the computation of the dimensions of manifolds on which the systems evolve. For this purpose several embedding techniques are used and compared. All methods give similar results, namely, that the data in different stations seem to derive from a single dynamical system of a few degrees of freedom possessing a low-dimensional attractor. The authors have estimated some average properties of the attractor such as its dimension and the dominant Lyapounov exponents. Furthermore, they have explored its local structure and found a relation between the rate of divergence on it and the corresponding heights of geopotential., Anglais

A chaotic dynamics model creating Markovian strings of symbols as well as sequences of "words" is presented, and its possible relevance to Zipf's law is discussed. © 1989 Plenum Publishing Corporation., SCOPUS: ar.j, info:eu-repo/semantics/published

A chaotic dynamics model creating Markovian strings of symbols as well as sequences of "words" is presented, and its possible relevance to Zipf's law is discussed. © 1989 Plenum Publishing Corporation., SCOPUS: ar.j, info:eu-repo/semantics/published

Recent progress in nonlinear dynamics provides the means for the characterisation of the behavior of natural systems from time series. The analysis of electroencephalogram data from the human brain during the sleep cycle reveals the existence of chaotic attractors for sleep stages two and four. The onset of sleep is followed by increasing "coherence" towards deterministic dynamics involving a limited set of variables. © 1985., SCOPUS: ar.j, info:eu-repo/semantics/published

The entropy balance associated with a Budyko‐Sellers climatic model is developed. It is shown that different regimes, associated with decreasing, as well as increasing values of entropy production (which measures the rate of dissipation in the system) in the course of time are possible. This immediately poses the problem of stability of steady states of the climatic system. An explicit criterion of climatic stability is thus derived, which is expressed in terms of thermodynamic quantities related to excess entropy production. The results are illustrated on simple cases involving diffusive energy transport. A comparison with Paltridge's minimum entropy exchange principle is also attempted. Copyright © 1980 Royal Meteorological Society, SCOPUS: ar.j, info:eu-repo/semantics/published

Doctorat en Sciences, info:eu-repo/semantics/nonPublished