• Scheffran J.  "Integrated Modelling of Viable Complex Networks in Sustainability Transitions" (Abstract)
• Gerhard Petschel-Held Sustainability Science : requirements for and some experiences with Complex System Theories (Abstract)
• Ioannides Y. "Toplogies of Social Interactions"  Abstract (doc)  Paper (pdf)
• Fagiolo G, Coordination, Local Interactions and Endogenous Neighborhood Formation Abstract (doc)  Paper (pdf)
• Fagiolo G  (with L. Marengo and M. Valente): "Endogenous Networks in Random Population Games"Abstract (doc)  Paper (pdf)
• Bonneuil N. Making Ecosystem Models Viable (Abstract)
• Manolova P., Lai Tong C. and  Deissenberg C. "Money and exchange in an economy with spatially differentiated agents"(Abstract)
• Françoise J.-P. Bursting Oscillations, coupled oscillators and neural networks (Abstract)
• Klaus Eisenack,  Management and Decision-Making for Sustainable Fisheries:A Qualitative Multi-Agent Approach to Viable Control (Abstract)
• Aubin J.-P.  Regulation of the Evolution of the Architecture of a Connectionist Network by Tensors Operating on Coalitions of Actors (paper)
• Aubin J.-P. (1998) Connectionist Complexity and its Evolution, in Equations aux dérivées partielles, Articles dédiés à J.-L. Lions (paper)
• Saint-Pierre P.,  An introduction to the Viability Kernel Algorithm
• Aubin J.-P.,  An introduction to Viability Theory (paper)
• Guzzi R., Approche de l'urbanisme par modèles complexes
• Guillaume Deffuant, Frédéric Amblard, Gérard Weisbuch and Thierry Faure (2002)   How can extremism prevail? A study based on the relative agreement

 interaction model (paper)
• Gérard Weisbuch and al. Meet, discuss and segregate   (paper)
• Olivier Dordan Dynamique qualitaitve simulation : from a particular genetic model to a general abstrac model (paper)
• Denise Pumain,  Simulating the evolution of a system of cities (Abstract)

 

Name	e-mail
Iannis Ionnides	yioannid@emerald.tufts.edu
Juergen Scheffran	scheffran@pik-potsdam.de
Christophe Deissenberg	deissenb@univ-aix.fr
Jean-Pierre Françoise	jpf@ccr.jussieu.fr
Paul Bourgine	bourgine@poly.polytechnique.fr
Denise Pumain	pumain@parisgeo.cnrs.fr
Olivier Dordan	dordan@viete.sm.u-bordeaux2.fr
Hermann Held	held@pik-potsdam.de
Noel Bonneuil	bonneuil@ined.fr
Patrick Saint-Pierre	saint-pierre@viab.dauphine.fr
Gerhard Petschel-Held	gerhard@pik-potsdam.de
Pierre-Yves Boelle	boelle@u444.jussieu.fr
Giorgio Fagiolo	fagiolo@sssup.it
Klaus Eisenack	eisenack@pik-potsdam.de
Jean-Pierre Aubin	J.P.Aubin@wanadoo.fr

 Objectives

The project explores the evolution, stability and control of complex dynamic networks in natural, socio-economic and information systems, and develops methods to connect a large number of subsystems into a viable integrated architecture. One expected result will be an advisory tool based on an integrated software platform that allows to choose and apply appropriate instruments for the analysis of different types of complex nertworks.
Besides the scientific plea to assess complexity in a fruitful and concise manner, it is of utmost importance from the viewpoint of real world problems to develop feasible concepts and operational methods for the management of complex systems under uncertainty. Within this proposal the goal of control is related to the concept of viability, i.e., undesirable domains in the state space of the system under consideration are sought to be avoided. In particular, we want to focus on “connectionist complexity'' of dynamically evolving networks where the coupling between individual parts of the system is described by connectivity operators. These are used as regulators for controlling the viability of the system and also account for concepts of stability to be induced by coupling. This applies for more rigid designed complexity, as in the natural Earth System, and for more flexible designed networks as socio-economic systems, as well as biomedical systems in between.
There are numerous definitions and measures of complexity which in some or the other way express the difficulty to understand or explain something. An important meaning of complexity is the connectivity of a system which is represented by the network of links connecting many parts in a way that together they form an integrated whole. While George Cowan, the founder of the Santa Fe Institute, suggests that in the universe everything is connected with everything, the question is to which degree. A network with too little connectivity may not able to perform a given task or stay within a viability domain, while a network with too much connectivity is overwhelmed with the task of coordinating the various parts and the information flows between them.
Finding adequate network organizations and designs which are efficient, stable and viable at minimum complexity is the main purpose of this project. Within an integrating framework for cross-disciplinary research, mathematical and computational tools are to be developed and applied to four different cases studies of networks. The expected outcome will be used to develop an advisory tool for the assessment, design and management of complex dynamic networks.
Such an approach is of great interest in many fields of complex networks: computer networks (internet, intranet); communication networks (fixed and mobile phones); socio-economic networks (transport, energy, demography, technology, production and distribution networks); neural and cognitive networks (human brain, artificial intelligence); gene networks (spread of infectious diseases, metabolic circuits); environmental networks (pollution, climate system, population dynamics, resource management). Some of these networks play a prominent role in the project as cases to study the emergence and viability of complex network organization. The ultimate overall objectives of the project are:
1. the development of a taxonomy of problems, questions and criteria for the assessment, design and management of complex networks,
2. the design and application of a set of methods and tools to allow efficient analytical and numerical computation of solutions of different viability problems for various classes of complex networks according to the taxonomy of (1), and
3. to gain insights into the viability properties of exemplary cases, with a focus on issues of Earth System analysis, bio-medicine, resource management and economic networks. In order to achieve these ultimate objectives, major methodological progress towards an  integrative framework is required. In real-world systems quantities such as the flow of matter, energy and information are the glue that hold networks together. Communication signals transmit messages required to coordinate the activities of the individual parts, forming aggregated ensembles (coalitions) to improve the viability of the whole system. At the same time, the actions, the messages, the coalitions of actors and the connectionist operators do evolve, consistent with the constraints, objectives and inter-temporal viability criteria, often referred to as “quality” or “fitness”. Yet, collective constraints are not necessarily satisfied at each instant by the evolution of the individual units, due to uncertainties and stochastic disturbances. This leads to the question of how to correct the interaction between individual systems to re-establish this consistency. This problem is at the heart of the theoretical framework of the project. We thus seek to find answers to the following, methodologically inspired questions:

4. How are systems characterized by means of connectionist complexity?

5. How can viability theory of complex networks be applied to real world systems and what extensions or modifications are necessary to optimise its utilisation?

6. Which numerical algorithms and software tools are best suited to implement the theoretical results?
A major benefit of the COMPLEXNET project is to bridge the wide gap between mathematical theory and concrete applications in specific systems. On the one hand, this raises concrete, application-oriented questions for mathematics as just stated. On the other hand, as the project aims to provide basic and robust answers for these systems, the following application-specific  questions within its case studies come up, each closely related to the issue of viability in dynamically evolving networks:

7. The natural Earth System: To what extent is coupling between different sub-components of the system, i.e., atmosphere, oceans and hydrosphere, biosphere, lithosphere, etc., responsible for the stability and viability of the Earth’s climate? What types of viable coupling actually have evolved in the natural Earth System?

8. Biomedical networks: How robust against uncertainties and perturbations should metabolic genetic or neuronal networks be to ensure the viability of its functioning? We need to define the domain of viability of antibiotic resistant organisms to define optimal use of antibiotics at the population level.

9. Resource networks: What are least-cost strategies for a sustainable management of renewable resources? We need to identify crucial couplings within and between action spheres to minimize control and complexity.

10. Socio-economic actor networks: To what extent can the development of the size of actor groups and the topology of their network be endogenized by obtaining viability constraints in connectionist complex networks? Which distribution networks would ensure viable links between producers and consumers on global markets?
The answers to these application-specific questions require computational tools and approaches which shall be generalized beyond the specific systems investigated. This generalization then paves the way towards the ultimate objectives (1-3) of the project.

Modern society is marked by a variety of complex networks, including networks of actors, computers or even states that are highly interdependent and forming systems with positive and negative feedback loops. On a common theoretical ground the issues faced by modern society can be condensed to: How can dynamically evolving networks be managed and how does information technology affect this task? What can network design and management contribute to information society? Addressing these questions the present project seeks to provide methodological foundations to this issue in terms of  mathematical theory, computational and numerical tools as well as concrete applications in selected fields related to sustainable development, resource management, bio-medicine and industrial development.
 

The project’s approach to design management strategies for complex systems promises new and efficient advances. It does so by two means:
1. Concrete applications of theoretical and mathematical concepts to real world systems which are under close scrutiny at the time being. Though they abstract from detailed aspects of technology, the systems investigated are of utmost relevance for the future of modern society under the guiding principle of sustainable development. The management of these problems needs interdisciplinary research and new emerging methods of integration and analysis.
2. The generality of the computation tools and mathematical approaches to be developed guarantee the transferability of the project’s results to other systems characterized by connectionist complexity. Therefore the project can contribute to a major breakthrough in various societal issues, e.g. computer, communication, socio-economic networks, or political (like the EU itself) networks just to mention a few.

In the project adequate network structures, viablity criteria, as well as operational methods and concepts will be developed to facilitate an efficient, stable and viable evolution of different systems at minimum complexity. The outcomes of the four case studies will be used to develop a taxonomy of criteria and questions for the assessment, design and management of complex networks. This allows to choose adequate programming tools from the software library that will be developed. By taking the risk of a highly interdisciplinary team involving several scientific fields of applications, the project can achieve unexpected insights due to parallel structures in the different case studies, which can be revealed by the common theoretical framework. As a fallback, the project can be expected to provide a new and deeper understanding in the case studies (by applying new methodologies), as well as an expansion of the mathematical research in viability theory (motivated by and based on real-world problems).
 

The main innovative impulse in the project stems from merging three important roots. The first is the broad stream of complexity theory, which is specified in a concise way for the project as connectionist complexity. This formalization allows to compare a broad field of applications, which are the second root, as expertise from different fields and cases can be integrated in a  fruitful manner. Third, the notion of connectionist complexity is combined with knowledge from viability theory, which gives additional impulses to the case studies. This unique approach, bringing together these three parts for the first time, will result in a theoretical framework of viable complex networks theory and an integrated software platform, including an advisory tool  to choose methods appropriate for different types of complex networks.
 

1. General aspects

To analyse and discuss the cross-disciplinary aspects of dynamic networks, the unifying methodological approach plays the key role. It rigorously addresses the questions how dynamically coupled sub-models can be stabilised, and how stable coupled systems are. To the best of our knowledge, the proposed approach to investigate adaptation and to search for classes of dynamical systems satisfying the required properties has not been pursued so far and is, in fact, original. The approach differs strongly from the quasi-exclusive use of simulation methods as in other countries, as well as from the main stream of modelling by studying static networks with graph theory and dynamical complex systems by ordinary or partial differential equations, a difficult task outside the physical sciences.
By cross-fertilizing and integrating case studies, we expect an inspiring cooperation in this project. The common ground is promising and will allow profound learning by comparing the different applications. At the same time, the methodological framework is tested by the applications and improved with the challenges from the case studies.
Viability theory and the concept of connectionist complexity will be used in a rigorous way for the first time to analyse the interaction between environmental, economic and political spheres, the Earth System, the energy system, market structures, molecular and genetic networks. Heterogeneous sub-systems exhibiting strong uncertainty and different degrees of rigidity in design are analysed, and their coupling is investigated from the same dynamical perspective. Thus, important structural principles, design concepts and control strategies can be identified for different areas.
The project will develop new mathematical and computational tools. The modules will be applied and integrated to a common platform. Thus, the new approach of viable complex networks becomes available to a broader community of users. Additionally, a taxonomy of criteria and typical properties to categorize complex networks under the perspective of viability control will be compiled and integrated in the software platform. In this sense one optional category refers to underlying assumptions of specific mathematical methods and/or theorems. This helps to choose the appropriate modelling tool from the box that will be provided by the project. The toolbox with integrated advisory facilities will also be valuable for other users dealing with complex networks.

2. Case studies

Advances in developing the different case studies are fostered by applying mathematical theories of viability in dynamic coupling and control as well as practical implementation. They are based on programming tools, empirical facts and the estimation of uncertainty. The case studies and methodological developments will be cross-fertilizing and beneficial for further research.

2.1. Model coupling and uncertainty propagation in the natural Earth System

This case study will offer a new impulse to the Earth System modelling community (in particular to climate modelling), where at present the implicit master strategy of successive model coupling is pursued. While each of the models is designed to represent a subsystem (atmosphere, vegetation, ocean, etc.), it is assumed that in this way the complex system under investigation can be digitally represented. Along such a modelling avenue, process knowledge for adequate model coupling is crucial. A main obstacle for making progress along those lines stems from the fact that the knowledge on real-world coupling processes is rather limited. The modelling community typically responds to the obstacle by means of pragmatic strategies selecting model couplings which result in a “reasonable” performance of the coupled model. Quite on the contrary, our proposed project plans to utilise viability theory in order to replace the above trial-and-error strategy for model coupling with a mathematically founded classification, hence, pre-selection of possible tensorial coupling functions.
This application of viability theory is novel within Earth System science and can serve as a conceptually new basis for the interplay of data and the development of modules designed for coupling. It should be pointed out that the method envisaged can be thought of as an inverse mode: due to the fact that the coupling of the Earth System’s components is “prescribed by reality”, the question of viability theory turned around: to what extent is the given coupling responsible for the long lasting stability of the Earth System? While this extension of the standard mode to the inverse mode is straightforward we would like to stress that it is novel not only with respect to the above application but also within viability theory itself.

2.2. Robustness of biomedical networks

This topic will contribute to the framework project by extending the domain of investigation to the viability and non-viability of intrinsically complex bio-medical networks.  Increasingly, the complex nature of biological systems is considered essential to its good functioning, because it provides a set-up to understand how internal or external fluctuations sometimes strongly influence a given system, or, on the contrary, fail to perturb it. In biological situations, complexity stems first from the nature of the interacting agents, such as molecules, neurons and populations. In medical applications, complexity for example arises from the variety of structures found in social networks. The methods developed within this project should therefore provide means to explore highly important questions such as the persistence of infection within populations, the stability of cognitive and metabolic functions in the face of uncertainty and environmental changes, the robustness of gene networks and metabolic functions. In sharp contrast to biomedical applications on the micro level, the new approach in the study of disease spread in population networks – linking micro and macro levels - arises mainly from the fact that we are really motivated by the search for “non viability” of organisms that fail to emerge or to spread infectious diseases. Investigating these three problem areas within the framework of viability theory is a novel approach which offers new insights.

2.3. Managing complex resource networks

The last decade has seen growing concern on the sustainable utilization of natural resources. For instance, due to the absence or failure of adequate management more than 70% of the world's fish resources are assumed to be heavily exploited or overexploited. The world’s growing energy consumption gets in conflict with declining availability of traditional energy sources and the impact of emissions on climate change. The task of sustainable resource management suffers from the intricately complex interaction between natural and socio-economic systems which hampers adequate resource assessment and forecasting as well as easy solutions of the problem.
To tackle the challenge, our novel approach is the integration of dynamically evolving interactions between subsystems in economic, environmental and political action spheres of resource management into the framework of viability theory. Each of the sub-systems exhibits uncertainties and different degrees of rigidity against perturbations. Up to now, viability theory has only been applied in a rudimentary fashion in the areas of sustainable fisheries and climate change. With the proposed approach, the effect of different types of resource management and environmental policy strategies on the dynamic coupling and the uncertainty of outcomes can be analysed. Moreover, the methodology opens up a common ground for comparison of different resource networks and offers new insights for the development of adequate management frameworks in a field of high importance for a society facing global change and degrading resources, such as fishery and energy. Thus, identifying principles, design concepts and control strategies for complex resource management will be a major expected output from this case study. The innovative methodological framework offers new possibilities for deriving integrated sustainability strategies, based on dynamic network analysis.

2.4. Production, distribution and consumption in viable economic networks

Focusing on the dynamics of markets and industries in economic networks, special attention will be given to the evolution of market structures driven by strategic alliances or network coalitions, by patent, brand names and other forms of intellectual property rights, or by the introduction of new technologies like e-marketing, in the battle for market access and power. The economic dynamics is the aggregate outcome of a dispersed set of interactions, whose "neighbourhood" or "niche" structure constitutes one of the main objects of the analysis.  Interactions in market networks are generally not controlled by a centralized entity, but are shaped by mechanisms of both competition and coordination among firms. Thus, strategies, behaviours and actions continuously evolve as agents accumulate experience in their attempt to cope with a permanently changing landscape. In such settings heterogeneity is indeed a fundamental source of innovation and drives the evolution of economic networks. The development of techniques that allow to correctly deal with the notion of heterogeneity and evolving networks is one of the challenges not rigorously addressed before.
Increasingly production and consumption of economic goods are dependent on global distribution chains, based on transport networks for energy and materials as well as virtual networks for information flow. The abuse of monopsony power in international distribution chains might have a detrimental effect on the long term viability of markets and raises concern about fair competition. Since the organisation of distribution networks has profound effects on the way the production is organized in a worldwide scale and, at the same time, often localized, research on a viable network designs provides new principles and criteria usable for definition and implementation of anti-trust policies.

3. Methodological development

In parallel to new insights in the domains of the case studies fostered by the common theoretical framework, their demands and observations will in turn contribute to the transfer of the general concept of viable complex networks (VCN) into a well-established theory. This effect will be twofold: first, theoretical concepts are refined or newly developed and mathematical theorems about their interconnections will be proved. Second, these theoretical improvements will coagulate to software tools that can be directly applied to the case studies as well as forthcoming applications. Only few numerical tools of this kind are available at present.
The wide spectrum of motivating applications and case studies requires a coherent interdisciplinary approach for abstracting the relevant features common to these systems in order to assess, design and manage evolving complex networks. Although many physicists and system engineers do tackle some of the above problems with existing tools, few applied mathematicians are engaged in designing new tools dedicated to these questions. A group of applied mathematicians is strongly involved in the multidisciplinary team in charge of this project, to master the challenge of developing an integrated theoretical framework of viable complex networks, developing a set of formal tools and innovative mathematical techniques based on non-linear dynamics, qualitative differential equations, viability theory, differential inclusions and hybrid control.
The project follows an innovative yet risky path in order to develop the envisioned framework for complex system analysis, management and control. Most likely, the project is expected to enhance state-of-the-art knowledge in the case studies and to improve the efficiency of numerical methods that implement viability theory. The approach that we have chosen is highly promising to achieve the ambitious goals and generate benefits, both for the project partners and other users of the results as well.