Estimating interdependences in networks of weakly coupled deterministic systems

The extraction of information from measured data about the interactions taking place in a network of systems is a key topic in modern applied sciences. This topic has been traditionally addressed considering bivariate time series, providing methods that are sometimes difficult to extend to multivariate data, the limiting factor being the computational complexity. Here, we present a computationally viable method based on black-box modeling which, whilst theoretically applicable only when a deterministic hypothesis about the processes behind the recordings is plausible, proves to work also when this assumption is severely affected. Conceptually, the method is very simple and is composed of three independent steps: in the first step a state-space reconstruction is performed separately on each measured signal; in the second step, a local model, i.e. a nonlinear dynamical system, is fitted separately on each (reconstructed) measured signal; afterwards, a linear model of the dynamical interactions is obtained cross-relating the (reconstructed) measured variables to the dynamics unexplained by the local models. The method is successfully validated on numerically generated data. An assessment of its sensitivity to data length and modeling and measurement noise intensity, and of its applicability to large scale systems, is also provided.

Assessing cooperative behavior in dynamical networks with applications to brain data

Cristian Carmeli

Capturing the collective coherent spatiotemporal activity from measured data in large ensembles of coupled nonlinear sub-systems has revealed to be a key topic in many areas of applied sciences. Currently, this topic is addressed by considering multivariate time series analysis tools. They provide methods whose limiting factors are the amount and quality of data, or the restricted applicability to the class of narrow-band signals. In this study, we propose three new methods to infer cooperativeness from broad-band multivariate signals that also cope with the constraints due to amount and quality of data. Successfully, we validated all the methods on prototypical models of dynamical networks. Also, we tested their sensitiveness upon amount of data, endogenous and exogenous noises intensity, and number of sub-systems. The first two methods rely on statistical properties of the multivariate signals by using an entropy-like formula from the correlation matrix estimated from the data. They compute the amount of cooperativeness among the sub-systems by estimating the amount of shrinking of the network embedded space relative to the uncoupled case. The second method of them, based on the partial correlation matrix, may account for cooperation marginalizing third confounder systems. Furthermore, both methods may be applied to embedded and not embedded data, and may be used to estimate (partial) cooperativeness among communities of sub-systems. The third method follows a deterministic dynamical modeling approach. By means of a suitably decomposed identification of dynamical systems, it can detect interactions among signals both in strength and direction. The method allows the adaptability of the algorithmic setup on the specific applications, and provides a model of local behavior. In parallel to the methodological development, we applied the first method to two brain data sets in order to assess visual stimuli induced interhemispheric cooperativeness. According to the neuroscientist's interpretation, our results gave new insights about brain functioning. We have been able to assay flexible stimulus-dependent modulation (i.e. behavior) of neuronal cooperativeness over two brain spatial scales: macroscopic by analyzing EEG recordings, and mesoscopic by analyzing LFP recordings. The analysis on EEGs has extended previous results highlighting that the stimuli induced arrangement of cooperativeness goes beyond the one addressable by narrow-band analysis. The analysis on LFPs allowed us to describe a new kind of inter-hemispheric integration. We assayed that inter-hemispheric connections modulate in a flexible, stimulus-dependent way, the cooperation in neuronal populations likely to be involved in stimulus detection and/or categorization. Finally, contrary to current belief in neuroscience, our results showed that simple relations between frequencies and brain functions are unlikely to be true and that stimulus-driven cortical dynamics may change in a way still far from being fully understood.

EPFL2006

Object-oriented approach for dynamic system modelling and simulation

Adel Besrour

Software engineering always cares to provide solutions for building applications as close as possible to what they should be, according to the requirements and the final users needs. Systems behavior simulation is a very common application to virtually reproduce and often predict the real-world behavior. Simulation is one of the most operational research tool in a large variety of engineering and scientific domains: Transport, telecommunication, medicine, chemical processes, physics, etc. The complexity of such application is relative to the increasing complexity of the systems. In this context, it is relevant to bring together different tools and formalisms such as markovian chain, Petri nets, etc., to improve the existent approaches and so to answer the simulations performances needs. The principle objective of this thesis is to bring together techniques from software engineering and safety engineering in order to improve the state of the art of modeling and simulation of dynamic systems in the industrial context. In addressing this objective, this work initially involves defining the essential limitations of the used formalisms, methods and tools regarding from one hand the software engineering modeling and simulation techniques and from the other hand the existent risk analysis methodologies. This work is conducted with respect to the problem of danger identification, considering the context of the complex systems behavior and their interaction with the human operator. In software engineering, it is well known that Petri/high-level nets have attractive characteristics to be used in systems simulation and behavior prediction such as the natural graphical representation, and their well-defined semantic. They are well-suited for the description of complex situations with concurrency (interleaving and true concurrency depending on the underlying semantics), conflict and confusion. However, the absence of structuring capabilities has been one of the main criticisms raised against Petri nets/high-level nets. Thus, there have been many attempts to introduce structuring principles in nets of this kind [BCM88] [Kie89] [JR91]. The attractive characteristics of Petri/high-level nets have prompted researchers to enrich these formalisms with object-oriented features. CO-OPN (Concurrent Object-Oriented Petri Net) approach, brings together the power of both Petri/high-level nets and object-orientation techniques, it has been devised so as to offer an adequate framework for the specification and design of large scale concurrent system [BG91]. CO-OPN, as a powerful modeling tool, has been used in a limited way to simulate systems. This work aims to provide a CO-OPN extension to allow a more realistic systems' simulation. Actually, its simulator semantic uses to be a suitable approach for modeling near closed systems and software components, because they need to loose coupling with external world. But, when we model more realistic problems like industrial processes, where human interaction is a relevant event, this approach is not sufficient to catch all system activity attributes. Moreover, the CO-OPN interpretation process does not allow interaction with the object internal states. This work provides a new solution to overcome CO-OPN simulation limitations and a set of prototypes to assist dynamic systems simulations. Furthermore, this work has been conducted in a Risk Analysis (RA) context, a domain where computer-based simulations research are of utmost interest. Actually, classical approaches used to address complex workplace hazard in a limited way, using checklists or sequence models. Moreover, the use of single oriented methods, such as AEA (man-oriented), FMEA (machine oriented) or HAZOP (process oriented), is not satisfactory to overcome the increasing sophistication of industrial processes. The automation of a part of the analysis process as well as the multiple-oriented approach allowed by dynamic modeling may indeed enhance significantly the analysis completeness and reduce the time analyzing time. This work, based on Object Oriented Petri net formalism (CO-OPN), propose an alternative multi-oriented approach where existent methods limitations have been criticized to develop a dynamic model, MORM (Man-machine Occupational Risk Modeling). A real industrial system (metal wire making process) has been specified to implement the different approach steps (system identification, model application, system simulation, system analysis).

EPFL2005

Accuracy and Stability of The Continuous-Time 3DVAR Filter for The Navier-Stokes Equation

The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems, such as those arising in weather forecasting. To gain understanding of filters in applications such as these, it is hence of interest to study their behaviour when applied to infinite dimensional dynamical systems. This motivates study of the problem of accuracy and stability of 3DVAR filters for the Navier- Stokes equation. We work in the limit of high frequency observations and derive continuous time filters. This leads to a stochastic partial differential equation (SPDE) for state estimation, in the form of a dampeddriven Navier-Stokes equation, with mean-reversion to the signal, and spatially-correlated time-white noise. Both forward and pullback accuracy and stability results are proved for this SPDE, showing in particular that when enough low Fourier modes are observed, and when the model uncertainty is larger than the data uncertainty in these modes (variance inflation), then the filter can lock on to a small neighbourhood of the true signal, recovering from order one initial error, if the error in the observations modes is small. Numerical examples are given to illustrate the theory.