Inverse Complexity Lab

Organisms, ecosystems, climates, information systems, and societies are examples of complex systems: they exhibit rich behavior emerging from a large number of individual components following relatively simple local rules, based on a network of direct interactions.

Complexity science is traditionally devoted to solving the forward problem: Given known local rules of interaction, what is the unknown large-scale organization that emerges from it?

Our research group focuses on the inverse problem: Given an empirically observed large-scale organization, what are the local rules of interaction that caused it?

With this aim, our group develops mathematical and computational models to explain the structure and function of complex network systems, and the algorithms to reconstruct the structure of these models from available empirical data.

We are particularly interested in problems related to:

  1. Statistically principled pattern identification in complex networks.
  2. Inverse problems and reconstruction of large-scale systems from indirect data.
  3. Uncertainty quantification for complex system data.
  4. Generative models that characterize modular hierarchies, ranks, and latent spaces.
  5. Temporality, higher-order organization, and multivariate annotation of complex data.
  6. Scalable network algorithms.
  7. Scientific software development and dataset curation.

In our work, we employ theory and methods from several disciplines, including statistical physics, computational statistics, information theory, Bayesian inference, and machine learning.

For more information see our research and publications pages.

The graph-tool library

Most of the methods developed in our group are made available as part of the graph-tool library, which is extensively documented.
For a practical introduction to many inference and reconstruction algorithms, please refer to the HOWTO.

Open positions

Interested PhD candidates are encouraged to apply for the “PhD Program in Computational X at IT:U”.

Prospective post-doc researchers should refer to the joining the group page.

Group news

  • 01/10/2024 — The group has moved to IT:U, Linz!
  • 21/06/2024 — Sebastian Kusch has been awarded the “best talk by an early-career researcher” at NetSci 2024 in Québec!
  • 06/05/2024 — A new version of graph-tool was released!
  • 02/05/2024 — New pre-print: “Network reconstruction via the minimum description length principle” [1]
  • 12/04/2024 — Upcoming talk at NetSI, Boston.
  • 09/04/2024 — Bukyoung Jhun has been awarded the Young Statistical Physicist Award by Korean Physical Society!
  • 01/03/2024 — Martina Contisciani has joined the group as a post-doc!
  • 04/01/2024 — New arxiv paper: “Scalable network reconstruction in subquadratic time” [2]
  • 01/01/2024 — Thomas Robiglio has joined the group as a PhD student!
  • 15/12/2023 — Silvia Guerrini defended her MSc thesis!
  • 01/09/2023 — Bukyoung Jhun has joined the group as a post-doc!

References

[1]
[2]
T. P. Peixoto, Scalable Network Reconstruction in Subquadratic Time, arXiv:2401.01404 (2024).

Tiago de Paula Peixoto
Univ.-Prof. of Complex Systems and Network Science
IT:U, Linz, Austria

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Short bio

I am a Professor of Complex Systems and Network Science at IT:U, Linz, Austria.

I have received my habilitation in theoretical physics at the University of Bremen in 2017. Previously, I have been an Associate Professor at the Central European University (2019-2024), Assistant Professor in Applied Mathematics at the University of Bath (2016-2019), External Researcher at the ISI Foundation (2015-2020), and post-doc researcher at the University of Bremen (2011-2016) and Technical University of Darmstadt (2008-2011).

I have received my PhD in Physics at the University of São Paulo in 2008.

My research group works at the interface between statistical physics, computational statistics, information theory, Bayesian inference, and machine learning, and has as its main focus the study of inverse problems in network science and complex systems.

My work was recognized with the Erdős–Rényi Prize from the Network Science Society in 2019.

I also received a Alexander von Humbolt Foundation fellowship in 2008.

And most importantly, I’m the proud 6th recipient of the distinguished Karate Club Club prize. 🥋🏆

Me (left) receiving the notorious Karate Club Club trophy from Travis Martin (right), on behalf of the 5th recipient, Mark Newman, in 2015.