TOPDRIM aims to provide methods driven by the topology of data for describing the dynamics of multi-level complex systems. Professor Mario Rasetti presents TopDrim – a global vision of data. The tale, philosophy, motivations of an ambitious, difficult project.
Topdrim partners Rick Quax and Peter Sloot (with co-author Andrea Apolloni), just published a paper where they develop a information-theoretical method to distinguish the contribution of each individual unit of the complex system to the collective out-of-equilibrium dynamics. They show that highly connected units have less impact on the system’s dynamics when compared to intermediately connected units.
Abstract: It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.
The paper was published in the J. R. Soc. Interface – doi: 10.1098/rsif.2013.0568 and is available for download
Rick Quax and Omri Har-Shemesh attended the “3rd European Summer School for Mathematical Modeling of Complex Systems”, which was held in Heraklion, Crete between the 15th and 27th of July 2013. The lectures in the summer school covered the foundations of complexity science, complex networks (theory and application), complex quantum systems and complexity in the social and biological sciences. The school also included a practical computer lab where they could explore non-linear systems first-hand.
In addition to the science covered, the program also included a talk by a PRL editor about publishing in PRL and the new PRX journal, and different aspects of Cretan culture. A visit to the Faistos palace with Prof. Gareth Owens which explained about the Minoan civilisation and the Faistos Disc, a pottery festival in the village of Thrapsano and even some Cretan dancing lessons.
The software developed by Topdrim members Petri, G., Scolamiero, M., Donato I. & Vaccarino, F. from ISI, for their work on the “Topological strata of weighted complex networks” has been made available for download and was published online at github. The software named “Holes” is a a Python module for detecting, analysing and visualising persistent homological features of complex networks according to the methodology presented in the PLoS paper earlier this year.
Mario Rasetti gave the introductory talk on “The Mapping Class Group in Big Data” to the Topdrim partners in the meeting the consortium held in San Benedetto del Tronto, Italy on July 30-31.
The meeting was the opportunity for partners to present their latest developments and to coordinate next tasks and collaborations as the project first year draws to a close. The two day meeting also allowed the partners to work in parallel sessions to advance their respective collaborations.
Topdrim partner Francesco Vaccarino wrote a news story on how topology is impacting the way start-ups make money when applied to big data analysis. The story was published on July 17, in the Italian newspaper La Stampa Tuttoscienze.
TOPDRIM partner Francesco Vaccarino and his colleagues jut published in PLOS.One a paper entitled Topological Strata of Weighted Complex Networks where they tackle the mesoscopic structure of complex networks, and where they introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods.
Their research is of most importance as this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.
Topdrim held a team meeting in Florence, June 5, with the aim of discuss and challenge partners to cooperate among each other. The two main objectives of the meeting where:
From this workshop some cross research opportunities emerged and topdrim aims to bring together the partners’ ideas at future TOPDRIM Grand Challenge Workshops.
Topdrim partners Emanuela Merelli and Mario Rasetti just published a paper entitled Non locality, Topology, Formal languages: New Global Tools to Handle Large Data Sets in which the authors state “that large sets of data can be handled through an organised set of mathematical and computational tools rooted in a global geometric vision of data space allowing to explore the structure and hidden information patterns thereof”.
This paper was presented at the ICCS’2013 conference, held in Barcelona June 5-7, and organised by Topdrim partner Peter Sloot from UvA. The work was also disseminated within the workshop Modeling and Computing Multiscale Systems Subtopic: Distributed Computing chaired by Alfons Hoekstra, coordinator of the Sophocles project.
Links:
Non locality, Topology, Formal languages: New Global Tools to Handle Large Data Sets
Emanuela Merelli(a(), Mario Rasetti(b)
a) School of Science and Technology, University of Camerino, Via del Bastione,1, Camerino 62032, italy
b) ISI Foundation, Via Alassio 11-C, Torino 10126, Italy
Topological Methods in Complexity Science @ECCS’13
Where:
Barcelona, September 18th 2013. Co-located with ECCS’13
Important dates:
Organizers:
Primoz Skraba , Francesco Vaccarino
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 is expected to promote rapid progress in these areas, even though the nature of the data varies. Given the heterogeneity of the data, topological features often clearly convey important qualitative features of a system, while retaining the quantitative rigour.
This workshop aims at offering an up-to-date view on the study of complex multi-level systems via topological methods such as persistent (co)homology and techniques from topological dynamics.
We invite contributions in the form of extended abstracts not exceeding 4 pages (excluding references).
The topics include but are not limited to:
The workshop welcomes any relevant contribution in the area of computational/applied topology and applications of topological techniques to understanding complex systems. These include new application areas, new techniques to specific applications or new interpretations of existing results.
There will be no formal proceedings though the abstracts will be made available online.
Link for contribution:
https://www.easychair.org/conferences/?conf=tmcs2013