Project title: Towards an Information Topological Theory of Emergence
We are seeking a highly motivated and ambitious PhD candidate to carry out interdisciplinary theoretical research on the development of a fundamental theory of emergence from an information theoretic perspective.
You will work on a new mathematical framework to identify and characterize emergent information structures in multivariate data. The theory will build upon ideas from information topology, information geometry, and statistical modeling. We will aim to address the question: ‘How can one detect and characterize emergent properties of real systems in a model-independent way?’
You will work at the University of Amsterdam starting as soon as possible and before the 15th of September 2024, where you will enjoy a stimulating multi-disciplinary research environment. You will be part of the research program ‘Foundations and Applications of Emergence’ (FAEME) of the Dutch Institute for Emergent Phenomena (DIEP), and will work under the supervision of an interdisciplinary team of researchers: Dr. Clélia de Mulatier at the Institute for Theoretical Physics, Prof. Jo Ellis-Monaghan at the Korteweg-de Vries Institute for Mathematics, and Dr. Patrick Forré at the Informatics Institute. Depending on the evolution of the project, there will also be opportunities for international collaborations.
More details about the project: The main challenge in developing a general theory of emergence is to understand how the complex behaviors of many interacting units can give rise to a simpler macroscopic behaviour while abstracting away the mechanistic details of the complex interactions. Over the past century, the research on complex systems has focused on identifying the microscopic interactions that may lead to such emergent behavior, and emergence has been mainly studied on a case-by-case basis. However, the last decades have seen fast development in experimental techniques that have enabled recording data from complex systems at both large scales and high resolutions. This opens up the possibility to understand emergent phenomena in real systems through the lens of data analysis, instead of systems modeling.
During your PhD, you will explore a new approach to a theory of emergence, by studying the structure of information in data from a topological perspective and tackling the question of how simpler information structures emerge. The project will build upon recent developments in two different lines of research: on the topological structure of information and statistical models on one hand, and on the information-theoretic characterisation of what simplicity means on the other hand. We will study in more detail the case of binary data, for which there exists a well-understood complete family of statistical models (the physics-inspired spin models with high-order interactions). To illustrate our approach, we finally aim to apply it to artificial and real-world datasets.
More details about application procedure can be found here.