Post-Doctoral Research Visit F/M Topological and Stochastic Signatures of Brain Aging

Inria is the French National Institute for Research in Digital Science, of which the Inria Côte d'Azur University Center is a part. With strong expertise in computer science and applied mathematics, the research projects of the Inria Côte d'Azur University Center cover all aspects of digital science and technology and generate innovation. Based mainly in Sophia Antipolis, but also in Nice and Montpellier, it brings together 47 research teams and nine support services. It is active in the fields of artificial intelligence, data science, IT system security, robotics, network engineering, natural risk prevention, ecological transition, digital biology, computational neuroscience, health data, and more. The Inria Center at Université Côte d'Azur is a major player in terms of scientific excellence, thanks to the results it has achieved and its collaborations at both European and international level.

Every year Inria International Relations Department has a few postdoctoral positions in order to support Inria international collaborations. This particular project is designed to be part of the Inria Brazil program. Inria Brasil is an international program created in 2020 in the frame of the partnership with LNCC (Laboratório Nacional de Computação Cientifica- Brazilian Scientific Computing Laboratory) acting as Hub for Brazilian research and innovation ecosystem. The goal is to develop research collaborations between Inria, LNCC and Brazilian key players in R&D (universities, research centers and companies), in all scientific fields of interest of Inria.

The postdoctoral contract will have a duration of 24 months. The default start date is November 1st, 2026 and not later than January, 1st 2027. The postdoctoral fellow will be recruited by Inria Centre at Université Côte d'Azur, in the Inria Branch at the University of Montpellier, but it is recommended that the time is shared between France and Brazil.

This postdoctoral project is part of a triangular international collaboration between France and Brazil, bringing together complementary expertise in longitudinal brain imaging, stochastic processes, and topological signal processing. The postdoc will be based in France, at the Inria Branch of the University of Montpellier, working in the MathNeuro team, with access to a unique longitudinal aging dataset (containing in particular fMRI and PET scan) hosted by the NIH (USA), with whom we have signed a data transfer agreement. The project will involve a close collaboration with Prof. Gandhi Viswanathan (Universidade Federal do Rio Grande do Norte), a leading expert in Lévy dynamics applied to biological systems, and Prof. Fernando A. N. Santos (Universidade Federal de Pernambuco / University of Amsterdam), a specialist in topological signal processing. This project is part of a wider research programme on digital health applied to healthy and pathological aging, also involving neuroscientists (Prof. S. Rodrigues, Bilbao, Spain) and clinicians (Prof. T. Fülöp, Sherbrooke, Canada).

The originality of the project lies in combining topological and stochastic approaches to characterize brain dynamics across aging. By jointly analyzing the topological and geometrical invariances of brain-state trajectories, their associated phase transitions and their temporal transport properties, the project aims to uncover novel dynamical biomarkers of healthy and pathological aging. The 24-month project will include regular research stays in Brazil to interact with our main collaborators on this project.

Candidates for postdoctoral positions are recruited after the completion of their Ph.D. or a first postdoctoral period. To be eligible, candidates must have defended their Ph.D. no more than 3 years before the start date of the contract. As the start date will be between November 1, 2026 and January 1, 2027, the latest eligible Ph.D. defense date will vary accordingly (approximately between November 1, 2023 and January 1, 2024).

In order to encourage mobility, the postdoctoral position must take place in a scientific environment that is truly different from the one of the Ph.D. (and, if applicable, from the position held since the Ph.D.); particular attention is thus paid to French or international candidates who obtained their doctorate abroad.

The postdoctoral researcher will develop an integrative framework to analyze longitudinal brain imaging data using topological signal processing and stochastic modeling. The project will investigate whether aging is associated with changes in the topology of brain-state trajectories and with alterations in their temporal dynamics, including potential deviations from Lévy-like transport. A central objective is to identify biomarkers of aging based on topological reconfiguration events and their coupling with intermittent or constrained dynamical regimes. The approach will combine advanced data-driven methods, model-based inference, and validation using surrogate and simulated data.

• Construct time-resolved representations of brain states from longitudinal imaging data (e.g., sliding-window functional connectivity, latent embeddings);
• Develop and apply topological signal processing tools (persistent homology, dynamic topology, graph-based methods) to characterize brain-state organization over time;
• Quantify temporal transport properties of brain dynamics and assess the presence of Lévy-like or alternative stochastic regimes;
• Analyze the coupling between topological reconfiguration events and large dynamical transitions in brain-state space; Perform model comparison using simulated and surrogate data to validate candidate dynamical mechanisms;
• Identify and evaluate candidate biomarkers of aging and pathological trajectories, and disseminate results through publications and international collaborations.

• Strong programming skills in Python (or similar), with experience in scientific computing and data analysis;
• Background in at least one of the following fields: topological data analysis, topological signal processing, stochastic processes, statistical physics (knowledge of Lévy-type dynamics is a plus);
• Experience in machine learning, data science, or AI methods applied to complex datasets;
• Familiarity with neuroimaging data (e.g., fMRI, PET) and/or longitudinal data analysis is desirable;
• Ability to implement reproducible research practices (version control, documentation, open-source tools)
• Strong analytical thinking and ability to connect theoretical methods with applied research questions

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

Gross Salary: 2788 € per month