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An interdisciplinary collaboration for deciphering the thermodynamic "arrow of time" in complex networks
  • Researchers from the Basque Center for Applied Mathematics, Hokkaido University and Kyoto University have deciphered the thermodynamic “arrow of time” in large-scale complex networks

  • This breakthrough is anchored in the Ising model, a cornerstone in statistical physics and machine learning

  • The result sheds light on recent findings in biological systems, like the emergence of an arrow of time in signals from the brain

  • The paper has been published in the journal Nature Communications

New research from the Basque Center for Applied Mathematics – BCAM, Hokkaido University and Kyoto University has found an innovative mathematical solution for the non-equilibrium thermodynamics of large-scale neuron networks based on their temporal asymmetry. This breakthrough helps to better understand the behavior of biological systems like networks of neurons, or the behavior of machine learning and AI tools. This research has been carried out by Dr. Miguel Aguilera Ikerbasque Research Fellow at BCAM and Professor Hideaki Shimazaki, associate professor at Kyoto University’s Graduate School of Informatics, and has been published in the research journal Nature Communications

Accompanied by the Councillor Jokin Bildarratz, the Lehendakari this morning received the heads of BCAM, BCBL and BC3 Basic Research and Excellence Centres, which make up the BERC (Basque Excellence Research Center) network of the Department of Education, on the occasion of their 15th Anniversary.

They highlighted the excellence of the research centres and the work they carry out for society. On the other hand, BCAM wanted to highlight their work during the pandemic.

  • Transmath seeks to promote research excellence and innovation from cross-border research in the Euskampus New Aquitaine-Euskadi-Navarre collaboration strategy


The Transmath Cross-border Cooperation Laboratory for Mathematics and its applications was set up in 2018 by the Euskampus – Bordeaux network of LTCs. The aim of this collaboration is to generate an institutional framework for research teams from the Basque Country and Bordeaux to work together. In Transmath LTC, Prof. David Lannes from the Centre National de la Recherche Scientifique (CNRS) in Bordeaux and Luis Vega, leader of the Linear and Non-Linear Waves group at the Basque Center for Applied Mathematics – BCAM in the Basque Country, are participating as principal investigators.

Santiago Mazuelas, Ramón y Cajal researcher in the Machine Learning group at the Basque Center for Applied Mathematics – BCAM, has been selected as a beneficiary of the Consolidation Research Grant 2022, awarded by the State Research Agency for his project “Supervised learning in environments affected by distribution shifts – SLEDS”.

The “Research Consolidation” grant is designed to consolidate the professional career of national and foreign researchers, so that they can develop their professional career within the Spanish Science, Technology and Innovation System and is financed by the European Union’s Resilience and Recovery Mechanism.  In addition, it strengthens the implementation of a research project and research careers or research groups. In this case, it will fund the work of Professor Santiago Mazuelas’ team including junior researchers and PhD students.