TOPOSYS
Topological Complex Systems
| Coordinatore | INSTITUT JOZEF STEFAN
Organization address
address: Jamova 39 contact info |
| Nazionalità Coordinatore | Slovenia [SI] |
| Totale costo | 3˙449˙204 € |
| EC contributo | 2˙635˙000 € |
| Programma | FP7-ICT
Specific Programme "Cooperation": Information and communication technologies |
| Code Call | FP7-ICT-2011-8 |
| Funding Scheme | CP |
| Anno di inizio | 2012 |
| Periodo (anno-mese-giorno) | 2012-10-01 - 2015-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
INSTITUT JOZEF STEFAN
Organization address
address: Jamova 39 contact info |
SI (LJUBLJANA) | coordinator | 0.00 |
| 2 |
Institute of Science and Technology Austria
Organization address
address: Am Campus contact info |
AT (Klosterneuburg) | participant | 0.00 |
| 3 |
KUNGLIGA TEKNISKA HOEGSKOLAN
Organization address
address: Valhallavaegen contact info |
SE (STOCKHOLM) | participant | 0.00 |
| 4 |
TECHNION ISRAEL INSTITUTE OF TECHNOLOGY
Organization address
address: Technion City-Senate Building contact info |
IL (HAIFA) | participant | 0.00 |
| 5 |
UNIWERSYTET JAGIELLONSKI
Organization address
address: Ul. Golebia contact info |
PL (KRAKOW) | participant | 0.00 |
Mappa
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Obiettivo del progetto (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.nnWe 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.nnIn 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.nnThe 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.