- Topology Driven Methods for Complex Systems

Call 8 - DyM-CS - Dynamics of Multi-Level Complex Systems
GA N. 318121

University of Camerino

Emanuela Merelli

TOPDRIM : Topology Driven Methods for Complex Systems slides
Many complex systems are characterized by multi-level properties that make the study of their dynamics and of their emerging phenomena a daunting task. The huge amount of data available in modern sciences can be expected to support great progress in these studies, even though the nature of the data varies. Given that, it is crucial to extract as much as possible features from data, including qualitative (topological) ones. The goal of this project is to provide methods driven by the topology of data for describing the dynamics of multi-level complex systems. To this end the project will develop new mathematical and computational formalisms accounting for topological effects. To pursue these objectives the project brings together scientists from many diverse fields including as topology and geometry, statistical physics and information theory, computer science and biology. The proposed methods, obtained through concerted efforts, will cover different aspects of the science of complexity ranging from foundations, to simulations through modelling and analysis, and are expected to constitute the building blocks for a new generalized theory of complexity.
The partner institutions are:

  1. University of Camerino (ITALY) Coordinator - Emanuela MERELLI
  2. University of Southern Denmark (DENMARK) - Christian REIDYS
  3. University of Amsterdam (THE NETHERLAND)- Peter SLOOT
  4. Open University (UNITED KINGDOM) - Jeff JOHNSON
  5. ISI Foundation (ITALY) - Mario RASETTI
  6. Aix-Marseille University (FRANCE) - Marco PETTINI

Related Projects

  • TOPOSYS : Topological Complex Systems slides
    In dynamics, local behaviour is often very unstable, while global behaviour often is immensely hard to derive from local knowledge. Traditionally, topology has been used in abstracting the local behaviour into qualitative classes of behaviour — while we cannot describe the path a particular flow will take around a strange attractor in a chaotic system, we can often say meaningful things about the trajectory as an entirety, and its abstract properties.
    We propose to use computational topology, which takes notions from algebraic topology and adapts and extends them into more algorithmic forms, to enrich the study of the dynamics of multi-scale complex systems. With the algorithmic approach, we are able to consider inverse problems, such as reconstructing dynamical behaviorus from discrete point samples. This is the right approach to take for complex systems, where the precise behaviour is difficult if not impossible to analyse analytically. In particular we will extend the technique of persistence to include ideas from dynamical systems, as well as incorporating category theory and statistics. Persistence is inherently multi-scale, and provides a framework that will support the analysis of multi-scale systems, category theory provides a platform for a unified theory and joint abstraction layers, and statistics allows us to provide quality measures, inferences, and provide confidence intervals and variance measures for our analyses.
    The combination of category theory, statistics, and dynamical systems with computational topology serving as the joint platform for the other areas, will allow for a mathematically rigorous description of the dynamics of a system from a local to a global scale. In this framework, multi-scale features have a natural place, and the focus on computation and algorithmics means we can easily verify and validate our theory. We propose to do this on two datasets, capturing robot configuration spaces and social media.
    The partner institutions are:

    1. Jozef Stefan Institute (SLOVENIA) Coordinator - Primoz SKRABA
    2. Institute of Science and Technology Austria (AUSTRIA) - Herbert Edelsbrunner
    3. KTH - Royal Institute of Technology (SWEDEN) - Danica Kragic
    4. Jagiellonian University (POLAND) - Marian Mrozek
    5. Israel Institute of Technology Technion (ISRAEL) - Robert Adler

  • Sophocles: Self-Organised information PrOcessing, CriticaLity and Emergence in multilevel Systems slides
    We will contribute to a theory of dynamics of multi level complex systems by developing mathematical and computational formalisms for information processing in such multi level systems. We will develop the formalism in the context of criticality, emergence, and tipping points in multi level systems and apply it to real data. This should lead to a better understanding, but more important, to an improvement in predictive power for early warning. Can we observe tell-tales of things to happen in the (near) future? We will relate the emergence of structures and collective effects to the existence of an information-driven phase transition. Emergent structures may mean selection of preferred scales, creation of new levels or annihilation of existing levels, or occurrence of tipping points leading to extreme phenomena. We believe that these transitions are often self-organized because they appear in a spontaneous way, driven only by the dynamics of the system and the co-evolving topology of the interactions. We will create an experimental facility, a Computational Exploratory, which allows to implement our theoretical framework of information processing in multilevel complex systems, and to apply this to real life data. The theory will be validated on real world applications involving large, heterogeneous multi level datasets from the Socio-Economic domain (high frequency FX data, datasets on interest rates, and social media data) and applied to study the question of emergence of scales, and the detection and prediction of tipping points in real-life datasets. We contribute to the questions if and why Nature has preferred scales, and if so, if such emerging scales can be detected in real data sets. The impact of our theory on understanding of emergence of multilevel systems due to critical information processing is expected to be substantial. Our theory will offer new tools for critical transitions and extreme events prediction in real-life datasets.
    The partner institutions are:

    1. University of Amsterdam (TEH NETEHRLAND) Coordinator - Alfons HOEKSTRA
    2. University of Geneva (SWITZERLAND) -
    3. Warsaw University of Technology (POLAND) -
    4. Universitat de les Illes Balears (SPAIN) -
    5. Olsen Ltd. -
    6. Jozef Stefan Institute (SLOVENIA) -

  • LASAGNE: multi-LAyer SpAtiotemporal Generalized NEtworks slides
    Thanks to modern ICT, a new generation of large data sets of social, biological, and man-made systems are now available. Many more will be produced at an ever–increasing rate in the near future. Such data contain high precision and integrated information on the nature and the evolution -in space and time- of the state of each single component, together with information on different types of interactions between them. Unfortunately, it is extremely difficult to extract meaningful information from this new generation of high-integrated data, since current network theory provides not much more than a static description of single, independent networks. The aim of this proposal is to provide a novel and coherent theoretical framework for analyzing and modeling these dynamic and multi-layer networks in terms of multi-graphs embedded in space and time. To do this, we will treat time, space and the nature of interactions not as additional dimensions of the problem, but as natural, inherent components of the very same generalized network (GNE) description. The first goal of the project is to devise novel metrics and models, able to capture the interactions between different layers and across different spatio-temporal scales. The second goal is to understand the combined role of spatial distance, time and inter-layer interactions on the dynamics of processes running on GNEs, and on the emergence of collective behaviors, such as synchronization. The third goal is to investigate cases where GNEs are co-evolving with the processes they facilitate. The theory will be validated on real-world applications involving large and heterogeneous data sets of brain networks, on- and off-line social systems, healthcare systems, and transportation flows in cities. Our project will provide new quantitative opportunities in different fields, ranging from the prediction of pathologies to the diffusion of ideas and trends in societies, and for the management of socio-technological systems.
    The partner institutions are:

    1. Medical University of Vienna MUW (AUSTRIA) Coordinator
    2. Queen Mary University of London QMUL (UNITED KINGDOM)
    3. Universitat de Barcelona UB (SPAIN)
    4. Universitat de les Illes Balears UIB (SPAIN)
    5. University of Cambridge UCAM (UNITED KINGDOM)
    6. University of Birmingham UoB (UNITED KINGDOM)
    7. Conseil National de la Recherche Scientifique CNRS (FRANCE)
  • PLEXMATH: slides
    Complex systems are made up by many interacting, non-identical components, whose individual dynamics are usually governed by simple rules that operate at multiple levels. The structure of interactions between the system’s components is defined through networks, the study of which represent one of the most fascinating topics in modern science. Network science has revolutionized our classical understanding of physical, biological, social and technological systems. Nevertheless, there are several challenges hindering significant advances in the theoretical and computational characterization of complex networks, the most important one being the lack of a mathematical formalism for coping with the multi-level (both in space and time) nature of many real systems. The vision of PLEXMATH relies on formulating a brand new mathematical framework for the analysis of multi-level networks in terms of tensors, in particular rank-four tensors that represent with four indices the most general structure of possible connections. We therefore will accommodate current and future theoretical and algorithmic needs by adopting a radically new point of view. Capitalizing on tensorial algebra we will reformulate all network descriptors and will propose dynamical equations to represent diffusive processes on multiplex networks. In doing this, we will generate new mathematical models that will be validated on unparalleled amounts of ICT data that describe relevant socioeconomic and techno-social systems. PLEXMATH constitutes a vital step towards a more general formalism for real-world networks, as the generated knowledge will substantially improve our understanding of complex systems, and will directly impact the way we deal with structural and dynamical patterns in many systems, including ICT.
    The partner institutions are:

    1. Universitat Rovira i Virgili (SPAIN) Coordinator
    2. University of Limerick (IRELAND)
    3. Institute of Theoretical Physics CEA, CNRS-URA (FRANCE)
    4. University of Oxford (UNITED KINGDOM)
    5. Universidad de Zaragoza (SPAIN)

  • MATHEMACS: Mathematics for Multilevel Anticipatory Complex Systems slides
    The MATHEMACS project aims to develop a mathematical theory of complex multi-level systems and their dynamics. In addition to considering systems with respect to a given level structure, as is natural in certain applications or dictated by available data, the project has the unique goal of identifying additional meaningful levels for understanding multi-level systems. This is done through a general formulation based on the mathematical tools of information and dynamical systems theories.
    To ensure that the theoretical framework is at the same time practically applicable, three key application areas are represented within the project, namely neurobiology, human communication, and economics. These areas not only provide us with some of the best-known epitomes of complex multi-level systems, but also constitute a challenging test bed for validating the generality of the theory since they span a vast range of spatial and temporal scales.
    Furthermore, they have an important common aspect; namely, their complexity and self-organizational character is partly due to the anticipatory and predictive actions of their constituent units. The MATHEMACS project contends that the concepts of anticipation and prediction are particularly relevant for multi-level systems since they often involve different levels. Thus, as a further unique feature, the project includes the mathematical representation and modeling of anticipation in its agenda for understanding complex multi-level systems.
    For validating the theory on large heterogeneous data sets, the project has a specific component with exclusive access to a wide range of data from human movement patterns to complex urban environments. In this way, MATHEMACS provides a well-rounded approach to lay the foundations of a mathematical theory of the dynamics of complex multi-level systems.
    The partner institutions:

    1. Max Planck Institute for Mathematics in the Sciences, (GERMANY) Coordinator - Fatihcan Atay
    2. University of Bielefeld, (GERMANY)
    3. Chalmers University of Technology, (SWEDEN)
    4. Ca' Foscari University, Venezia, (ITALY)
    5. INRIA Sophia Antipolis, (FRANCE)
    6. Universita' Politecnica dela Marche, (ITALY)

  • CONGAS: Dynamics and Coevolution in Multi Level Strategic iNteraction Games slides
    Many real world systems possess a rich multi-level structure and exhibit complex dynamics that are the result of a web of interwoven interactions among elements with autonomous decision-making capabilities. CONGAS will develop new mathematical models and tools, rooted in game theory, for the analysis, prediction and control of dynamical processes in such complex systems.
    CONGAS will provide a coherent theoretical framework for understanding the emergence of structure and patterns in complex systems, accounting for interactions spanning various scales in time and space, and acting at different structural and aggregation levels. This framework will be built around game theoretical concepts, in particular evolutionary and multi-resolution games, and will include also techniques drawn from graph theory, statistical mechanics, control and optimization theory. Specific attention will be devoted to systems that are prone to intermittency and catastrophic events due to the effect of collective dynamics. The theory developed in the project will be validated by considering three use cases, one on the growth of the Internet, one on business ecosystems and one on viral marketing dynamics in Internet marketplaces.
    The CONGAS Consortium comprises seven universities and research institution and includes leading scientists in game theory, evolutionary games, complex systems science, network science and data-driven analysis of socio-technical systems.

  • HIERATIC: Hierarchical Analysis of Complex Dynamical Systems slide
    The central aim of HIERATIC is to develop a new framework for understanding complex systems as a multi-level hierarchy of sub-systems using non-linear decompositions.
    To achieve this goal, HIERATIC is structured in three interlinked sets of activities: theoretical work, deriving the novel mathematics required to identify suitable non-linear state space reductions of complex systems; software development of efficient multi-scale simulation and prediction libraries; demonstrators, illustrating the power of our results – network dynamics, cell cycle simulations, social interactions in animals.
    The theoretical work will use unconventional approaches from topology and dynamical systems theory to derive an algorithmic approach to identifying “coarse-grainings” of large complex systems. These algorithms will be used to develop highly efficient simulation and prediction tools, integrated with the world-leading software libraries MASON and PRISM. The demonstrators will show the potential application of these techniques, in a range of applications, including validation on large empirical data sets.
    The project brings together leading researchers in complex systems theory, biosystems, multi-agent simulation, and experimental ecology, from around the EU and USA.
    The partner institutions are:

    1. University of Birmingham, (UNITED KINGDOM) Coordinator
    2. Chalmers University of Technology, (SWEDEN)
    3. Friedrich Schiller University, Jena, (GERMANY)
    4. University of Sheffield, (UNITED KINGDOM)

    with external advisors:
    • George Mason University, (USA)
    • Princeton University, (USA)
  • MULTIPLEX: Foundational Research on MULTIlevel comPLEX networks and systems slides
    The Science of Complex Systems is regarded as a success story among the emerging fields of science. However, further progress in the ICT domain is hampered by the lack of deeper knowledge about how multi-level complex systems function. Preliminary findings indicate that interactions in a multi-level system cannot be treated as interactions in a single-level system. For example, multi-level dependencies may amplify cascade failures or make more sudden the collapse of the entire system, as indeed was observed in recent large-scale blackouts resulting from cascades in the power-grid coupled to the control communication system. A better understanding of multi-level systems is essential for future ICT’s and for improving life quality and security in an increasingly interconnected and interdependent world. In this respect, complex networks science is particularly suitable for the many challenges that we face today, from critical infrastructures and communication systems, to techno-social and socio-economic networks. MULTIPLEX proposes a substantial paradigm shift for the development of a mathematical, computational and algorithmic framework for multi-level complex networks. Firstly, this will lead to a significant progress in the understanding and the prediction of complex multi-level systems. Secondly, it will enable a better control, and optimization of their dynamics. By combining mathematical analyses, modelling approaches and the use of massive heterogeneous data sets, we shall address several prominent aspects of multi-level complex networks, i.e. their topology, dynamical organization and evolution. On the empirical side, the theories, models and algorithms developed by MULTIPLEX will be tested and validated in relevant economic, technological and societal contexts. The long-term objective of the project is to bring the newly developed formalisms to other areas of complexity and to supply new conceptual tools for EU policy makers, stakeholders and citizens.
    The partner institutions are:


The list of project acronyms, topic and coordinator are:

proposes to use computational topology to enrich the study of the dynamics of multi-scale complex systems.
Coordinator: Primoz Skraba

is to provide a theoretical framework for multi-layer networks in terms of multi-graphs embedded in space and time.
Coordinator: Stefan Thurner

will develop a formalism in the context of criticality, emergence, and tipping points in multi level systems.
Coordinator: Alfons Hoekstra

will develop a mathematical framework for the analysis of multi-level networks in terms of rank four tensors.
Coordinator: Alex Arenas

will provide methods driven by the topology of data for describing the dynamics of multi-level complex systems.
Coordinator: Emanuela Merelli

will work around concepts of anticipation and prediction in multi-level systems.
Coordinator: Fatihcan Atay

will deal with the emergence of structure and patterns in complex systems acting at different structural and aggregation levels and built around evolutionary and multi-resolution games.
Coordinator: Francesco De Pellegrini

will derive the novel mathematics required to identify suitable non-linear state space reductions of complex systems.
Coordinator: Jonathan Rowe

proposes a network of networks paradigm shift for the development of a mathematical, computational and algorithmic framework for multi-level complex networks
Coordinator: Guido Caldarelli

Finally, keep in mind we are in a process of negotiation, so the contracts are not yet signed.



DyM-CS objective coordinator