CORDIS
EU research results

CORDIS

English EN

Topological Complex Systems

Objective

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 these four areas: category theory, statistics, and dynamical systems with computational topology as the joint platform for the three other components, 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.
Leaflet | Map data © OpenStreetMap contributors, Credit: EC-GISCO, © EuroGeographics for the administrative boundaries

Coordinator

INSTITUT JOZEF STEFAN

Address

Jamova 39
1000 Ljubljana

Slovenia

Activity type

Research Organisations

EU Contribution

€ 642 813

Administrative Contact

Primoz Skraba (Dr.)

Participants (4)

Sort alphabetically

Sort by EU Contribution

Expand all

INSTITUTE OF SCIENCE AND TECHNOLOGYAUSTRIA

Austria

EU Contribution

€ 498 171

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY

Israel

EU Contribution

€ 497 864

UNIWERSYTET JAGIELLONSKI

Poland

EU Contribution

€ 495 576

KUNGLIGA TEKNISKA HOEGSKOLAN

Sweden

EU Contribution

€ 500 576

Project information

Grant agreement ID: 318493

Status

Closed project

  • Start date

    1 October 2012

  • End date

    30 September 2015

Funded under:

FP7-ICT

  • Overall budget:

    € 3 449 204

  • EU contribution

    € 2 635 000

Coordinated by:

INSTITUT JOZEF STEFAN

Slovenia