French Complex Systems Roadmap 2007

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In general terms, a complex system is any system comprised of many, heterogeneous entities, in which strong interactions among those entities create multiple levels of collective structure and organization. Examples include natural systems, ranging from bio-molecules and living cells up through the ecosphere and human social systems, as well as sophisticated artificial systems such as the Internet, the electrical grid or any large-scale software system. What sets complex systems specificity either not addressed or largely under investigated by traditional science is the emergence of non-trivial superstructures that often dominate the system’s behavior and cannot in any easy way be traced to the properties of the constituent entities themselves. Not only higher emergent features of complex systems arise out of the lower level interactions but also the patterns they create act back on those lower levels. In many cases, complex systems possess an impressive robustness to even large scale or multi-dimensional perturbations and other disruptions; and they have an inherent ability to adapt or persist in a stable way. Because of their inherent complexity, which requires analysis at many scales of space and time, science faces novel challenges in learning to observe complex systems, to describe e them effectively, and to develop theories for their behavior and control or management.

Complex systems therefore need intrinsically an interdisciplinary approach: first, because all the questions they address appear in almost the same formulation on objects belonging to extremely different disciplines – from biology to computer networks to human societies; second, because the models and methods to tackle these questions also belong to different disciplines – mainly computer science, mathematics and physics; last, because standard specialized approaches rarely focus on multiple level approaches needed in the context of complex systems, and reachable through more integrated and interdisciplinary approaches.

Two types of interdisciplinary approaches are mainly possible. The first consists in working on an object of research that is intrinsically multidisciplinary, like for instance cognition: it results in raising various questions about the same object starting from viewpoints which can be very different, in contrast to more integrated and interdisciplinary approaches. The second consists in studying the same question in connection with different objects of research. It is this second approach that concerns a science of complex systems. However, the success of these two approaches, complementary one of the other, is intrinsically dependent on the design of new protocols, new models and formalisms for reconstructing emergent phenomena and dynamics at all scale. It is in this joint goal of massive data acquisition on the basis of a set of prior assumptions and their reconstruction by modeling that a science of complex systems can develop. There remains much to do in the theoretical domain to build concepts and models capable of providing elegant and meaningful explanations to the so-called “emergent phenomena characterizing complex systems.

The goal of this roadmap is to identify a set of wide thematic domains for complex systems research over the next five years. Each domain is organized either around a specific question or phenomenon and proposes relevant “grand challenges – clearly identifiable problems, the solution of which would stimulate significant progress in both theoretical methods and experimental strategies.
Theoretical questions are varied. An important aspect is to take into account the different levels of organization. In complex systems, individual behaviors lead to the emergence of collective organization and behavior at higher levels. These emergent structures influence individual behavior in return. This raises important questions: what are the various levels of organization and what are their characteristic scales of space and time? How do reciprocal influences operate between the individual and collective behavior? How can we simultaneously study multiple levels of organization, as is often required in problems in biology or social sciences? How can we efficiently characterize emergent structures? How can we understand the changing structures of emergent forms, their robustness or sensitivity to perturbations? Is it more important to study attractors of the dynamics or families of transients? How can we understand slow and fast dynamics in an integrated way? Which special emergent properties characterize complex systems that are particularly capable of adaptation in changing environments? During such adaptation, individual entities often appear and disappear, creating and destroying links in the graph of interactions. How can we understand the dynamics of these changing interactions and their relationship to the system’s functions?

Questions related to the reconstruction of dynamics from data play also a central role. These include questions related to the epistemic loop – the problem of moving from data to models and back to data, including model driven data production – that is the source of very hard inverse problems. Other fundamental questions arise around the constitution of databases, or the selection and extraction of stylized facts from distributed and heterogeneous databases, or the deep problem of reconstructing appropriate dynamical models from incomplete, incorrect or redundant data.

Finally, some questions are related to governance and design of complex systems. Complex systems engineering concerns a second class of inverse problems. On the basis of an incomplete reconstruction of dynamics starting from data, how can we steer system dynamics toward desirable consequences or at least keep the system away inside their viability constraints? How control can be distributed on many distinct hierarchical levels in either centralized or de-centralized ways – a so-called complex control. And finally, how is it possible to design complex artificial systems, integrating new way of studying their multilevel control?

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All these general questions are detailed in the roadmap. The first questions concern different aspects of emergent phenomena in the context of multi-scale systems. The question of reconstructing multi-scale dynamics addresses the problem of dealing with incomplete, badly organized and under qualified data sets. Another important aspect to consider is the importance played in complex systems by the reaction to perturbation: it can be at once weak in certain components or scales of the system and strong in others. These effects, central to the prediction and control of complex systems and models, must be specifically studied. In addition, it is also important to develop both strategies for representing and extracting pertinent parameters and formalisms for modeling morphodynamics. Learning to successfully predict multi-scale dynamics raises other important challenges, as the question of being able to go from controlled systems to governed systems in which the control is less centralized and more distributed among hierarchical levels. The last general question addressed in this roadmap concerns the conception of artificial complex systems.

Grand challenges for complex systems research draw their inspiration from different kinds of complex phenomena arising from different scientific fields. Their presentation follows the hierarchy of organizational levels of complex systems, either natural, social or artificial. Understanding this hierarchy is itself a primary aim of complex systems science.

In modern physics, the understanding of collective behavior and out-of-equilibrium fluctuations is increasingly important. Biology (in a wide meaning of the word – going from biological macromolecules to ecosystems) is one of the major fields of application in which complex behaviors must be tackled. Indeed, the question of gaining an integrated understanding of the different scales of biological systems is probably one of the most difficult and exciting tasks for researchers in the next decade. Before hoping to be able to integrate a total hierarchy of living systems, going from the bio-macromolecules to ecosystems, the integration between each level and the next one has to be studied. The first one concerns the cellular and subcellular spatio-temporal organization. At a higher level, the study of multicellular systems (integrating intracellular dynamics, such as regulation networks, with cell-cell interactions) is of great importance, as is the question of the impact of local perturbations in the stability and dynamics of multicellular organizations. Continuing on the way to larger scales raises the question of physiologic functions emerging from sets of cells and tissues in their interaction with a given environment. At the largest level, the understanding and control of ecosystems requires integrating interacting living organisms in a given biotope. In the context of human and social sciences also the complex systems approach is central – even if for the moment less developed than in biology. One important domain to be investigated is learning how the individual cognition of interacting agents leads to social cognition. An important situation requiring particular attention due to its potential societal consequences is related to innovation, its dynamical appearance and diffusion, frequency and coevolution with cognition. The complex systems approach can also help us to gain an integrated understanding of all components, hierarchical levels and time scales in a way that would help to move society toward sustainable development. In the context of globalisation and the growing importance of long distance interactions through a variety of networks, complex systems analysis (including direct observations and simulation experiments) can help us explore a variety of issues related to the environment, economic development or social cohesion at different geographical scales.

Finally, the growing influence of information technology in our societies and the decentralized networks based on it also demands a specific focus by complex systems research. In particular the movement going from processors to networks leads to the emergence of the so called ubiquitous intelligence that plays an increasing role in the way to design and manage the networks that will be fundamentally important for the future.

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