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Korteweg-de Vries Institute for Mathematics Korteweg-de Vries Institute for Mathematics

Dr. F.A. (Fernando) Nobrega Santos

I am an Assistant Professor in Interdisciplinary Mathematics at the Korteweg-de Vries Institute for Mathematics (KdVI), and an RPA PSI Fellow at the Dutch Institute for Emergent Phenomena (DIEP), within the University of Amsterdam research priority area on Emergent Phenomena in Society: Polarisation, Segregation and Inequality.

My research integrates theoretical physics, applied mathematics and data science, bridging computational topology, geometry and statistical mechanics with network neuroscience and artificial intelligence. Recent work centres on higher-order interactions in complex systems — from high-order hubs in the human connectome to curvature-based descriptions of brain, epidemic and urban networks — and on the link between imaging and behaviour.

Before joining the KdVI in February 2025, I was a Research Fellow at DIEP and at the Institute for Advanced Studies (IAS) of the University of Amsterdam, and a visiting fellow at the Department of Anatomy and Neurosciences at VUmc. Earlier I was a Research Associate at Amsterdam UMC and an Assistant Professor in the Department of Mathematics of the Federal University of Pernambuco in Recife, Brazil. I have also held visiting fellowships at the Wolfson Centre for Mathematical Biology at the University of Oxford, the International Centre for Theoretical Physics in Trieste, and the Institut Jean Lamour at the Université de Lorraine.

Faculty of Science
KDV
Area of expertise: Applied topology and geometry, discrete mathematics, network (neuro)science, complex systems, higher-order interactions, topological data analysis, statistical mechanics, brain networks, emergent phenomena
Visiting address
  • Science Park 107
Postal address
  • Postbus 94248
    1090 GE Amsterdam
Contact details
  • Profile

    I am an Assistant Professor in Interdisciplinary Mathematics at the Korteweg-de Vries Institute for Mathematics (KdVI), and an RPA PSI Fellow at the Dutch Institute for Emergent Phenomena (DIEP), within the University of Amsterdam research priority area on Emergent Phenomena in Society: Polarisation, Segregation and Inequality. My research integrates theoretical physics, applied mathematics and data science, bridging computational topology, geometry and statistical mechanics with network neuroscience and artificial intelligence. Recent work centres on higher-order interactions in complex systems — from high-order hubs in the human connectome to curvature-based descriptions of brain, epidemic and urban networks — and on the link between imaging and behaviour. Before joining the KdVI in February 2025, I was a Research Fellow at DIEP and at the Institute for Advanced Studies (IAS) of the University of Amsterdam, and a visiting fellow at the Department of Anatomy and Neurosciences at VUmc. Earlier, I was a Research Associate at Amsterdam UMC and an Assistant Professor in the Department of Mathematics of the Federal University of Pernambuco in Recife, Brazil. I have also held visiting fellowships at the Wolfson Centre for Mathematical Biology at the University of Oxford, the International Centre for Theoretical Physics in Trieste, and the Institut Jean Lamour at the Université de Lorraine.

    Personal website:

    https://www.fansantos.com
    Google Scholar:
    ORCID
    GitHub
    DIEP

  • Publications

    2026

    • Bispo, B. C., de Oliveira Neto, J. R., Lima, J. B., & Santos, F. A. N. (2026). From pairwise to higher-order brain community detection: A hypergraph signal processing approach on brain functional connectivity analysis. Computers in Biology and Medicine, 201, Article 111409. https://doi.org/10.1016/j.compbiomed.2025.111409 [details]
    • Breedt, L. C., MAGNIMS study group, Pontillo, G., Santos, F. A. N., Vriend, C., Prados, F., Wink, A. M., Bisecco, A., Cagol, A., Calabrese, M., Castellaro, M., Collorone, S., Cortese, R., De Stefano, N., Enzinger, C., Filippi, M., Foster, M. A., Gallo, A., Gonzalez-Escamilla, G., ... Douw, L. (2026). Structure–function multilayer network integration and cognition in multiple sclerosis. Network Neuroscience, 10(2), 400-417. https://doi.org/10.1162/NETN.a.545
    • Carvalho, A. M. S., Duarte-Filho, G. C., & Santos, F. A. N. (2026). Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors. Physical Review E, 113(3), Article 034308. https://doi.org/10.1103/cby1-s3gz
    • Merbis, W., Santos, F. A. N., Armas, J., Pijpers, F., & Lees, M. (2026). Hyperscaling of spatial fluctuations constrains the development of urban populations. Manuscript submitted for publication. http://adsabs.harvard.edu/abs/2026arXiv260401969M
    • dos Santos, T. C., de Araujo, D. B., Felippe, H., Miranda, J. G. V., Palhano-Fontes, F., Silva do Rosário, R., Onias, H., Viol, A., Viswanathan, G. M., & Santos, F. A. N. (2026). An exploratory persistent-homology analysis of resting-state fMRI functional connectivity under Ayahuasca. Chaos, Solitons and Fractals, 209, Article 118554. https://doi.org/10.1016/j.chaos.2026.118554 [details]

    2025

    • Barros de Souza, D., Teodomiro, J., Santos, F. A. N., Jost, J., & Rodrigues, S. (2025). Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481(2309), Article 20240364. https://doi.org/10.1098/rspa.2024.0364 [details]
    • Castro, D. M., Raposo, E. P., Copelli, M., & Santos, F. A. N. (2025). Interdependent Scaling Exponents in the Human Brain. Physical Review Letters, 135(19), Article 198401. https://doi.org/10.1103/lvwj-hjr3 [details]
    • Di Gaetano, L., Santos, F. A. N., Battiston, F., Bianconi, G., Defenu, N., Nissen, I. A., Van Straaten, E. C. W., Hillebrand, A., & Millán, A. P. (2025). Neighbourhood topology unveils pathological hubs in the brain networks of epilepsy-surgery patients. Brain Communications, 7(6), Article fcaf431. https://doi.org/10.1093/braincomms/fcaf431
    • Sardellitti, S., Bispo, B. C., Santos, F. A. N., & Lima, J. B. (2025). Cross-Laplacians Based Topological Signal Processing over Cell MultiComplexes. In 2025 33rd European Signal Processing Conference, EUSIPCO 2025 - Proceedings (pp. 2647-2651). IEEE. https://doi.org/10.23919/EUSIPCO63237.2025.11226604

    2024

    2023

    • Breedt, L. C., Santos, F. A. N., Hillebrand, A., Reneman, L., Rootselaar, A. F. V., Schoonheim, M. M., Stam, C. J., Ticheler, A., Tijms, B. M., Veltman, D. J., Vriend, C., Wagenmakers, M. J., van Wingen, G. A., Geurts, J. J. G., Schrantee, A., & Douw, L. (2023). Multimodal multilayer network centrality relates to executive functioning. Network Neuroscience, 7(1), 299-321. https://doi.org/10.1162/netn_a_00284
    • van Lingen, M. R., Breedt, L. C., Geurts, J. J. G., Hillebrand, A., Klein, M., Kouwenhoven, M. C. M., Kulik, S. D., Reijneveld, J. C., Stam, C. J., De Witt Hamer, P. C., Zimmermann, M. L. M., Santos, F. A. N., & Douw, L. (2023). The longitudinal relation between executive functioning and multilayer network topology in glioma patients. Brain imaging and behavior, 17(4), 425-435. https://doi.org/10.1007/s11682-023-00770-w

    2022

    • Barros de Souza, D., Figueirôa dos Santos, E., & Santos, F. A. N. (2022). The Euler characteristic as a topological marker for outbreaks in vector-borne disease. Journal of Statistical Mechanics: Theory and Experiment, 2022(12), Article 123501. https://doi.org/10.1088/1742-5468/aca0e5
    • Centeno, E. G. Z., Moreni, G., Vriend, C., Douw, L., & Nóbrega Santos, F. A. (2022). A hands-on tutorial on network and topological neuroscience. Brain Structure and Function, 227(3), 741-762. https://doi.org/10.1007/s00429-021-02435-0
    • De Souza, D. B., Araújo, H. A., Duarte-Filho, G. C., Gaffney, E. A., Santos, F. A. N., & Raposo, E. P. (2022). Fock-space approach to stochastic susceptible-infected-recovered models. Physical Review E, 106(1), Article 014136. https://doi.org/10.1103/PhysRevE.106.014136
    • de Amorim Filho, E. C., Moreira, R. A., & Santos, F. A. N. (2022). The Euler characteristic and topological phase transitions in complex systems. Journal of Physics: Complexity, 3(2), Article 025003. https://doi.org/10.1088/2632-072X/ac664c

    2021

    • Araújo, R., Miranda Filho, L. H., Santos, F. A. N., & Coutinho-Filho, M. D. (2021). Geometry and molecular dynamics of the Hamiltonian mean-field model in a magnetic field. Physical Review E, 103(1), Article 012203. https://doi.org/10.1103/PhysRevE.103.012203
    • Barros de Souza, D., Da Cunha, J. T. S., Figueirôa dos Santos, E., Correia, J. B., da Silva, H. P., de Lima Filho, J. L., Albuquerque, J., & Santos, F. A. N. (2021). Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk. Journal of Statistical Mechanics: Theory and Experiment, 2021(5), Article 053501. https://doi.org/10.1088/1742-5468/abed4e
    • Serafim, F., Santos, F. A. N., Lima, J. R. F., Fumeron, S., Berche, B., & Moraes, F. (2021). Magnetic and geometric effects on the electronic transport of metallic nanotubes. Journal of Applied Physics, 129(4), Article 044301. https://doi.org/10.1063/5.0031667

    2020

    • Araújo, H. A., Lukin, M. O., Da Luz, M. G. E., Viswanathan, G. M., Santos, F. A. N., & Raposo, E. P. (2020). Revisiting Lévy flights on bounded domains: a Fock space approach. Journal of Statistical Mechanics: Theory and Experiment, 2020(8), Article 083202. https://doi.org/10.1088/1742-5468/aba593
    • Duarte-Filho, G. C., Santos, F. A. N., & Gaffney, E. A. (2020). Fock-space methods for diffusion: Capturing volume exclusion via fermionic statistics. Physical Review E, 102(5), Article 052101. https://doi.org/10.1103/PhysRevE.102.052101
    • Fülöp, T., Desroches, M., A Cohen, A., Santos, F. A. N., & Rodrigues, S. (2020). Why we should use topological data analysis in ageing: Towards defining the “topological shape of ageing”. Mechanisms of Ageing and Development, 192, Article 111390. https://doi.org/10.1016/j.mad.2020.111390
    • Pirôpo, M., Moraes, F., & Santos, F. A. N. (2020). Surfing on curved surfaces—The Maple Package Surf. Computer Physics Communications, 249, Article 107002. https://doi.org/10.1016/j.cpc.2019.107002
    • Tewarie, P., Prasse, B., Meier, J. M., Santos, F. A. N., Douw, L., Schoonheim, M. M., Stam, C. J., Van Mieghem, P., & Hillebrand, A. (2020). Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches. NeuroImage, 216, Article 116805. https://doi.org/10.1016/j.neuroimage.2020.116805

    2019

    • Santos, F. A. N., Raposo, E. P., Coutinho-Filho, M. D., Copelli, M., Stam, C. J., & Douw, L. (2019). Topological phase transitions in functional brain networks. Physical Review E, 100(3), Article 032414. https://doi.org/10.1103/PhysRevE.100.032414
    • Serafim, F., Santos, F. A. N., Lima, J. R. F., Filgueiras, C., & Moraes, F. (2019). Position-dependent mass effects in the electronic transport of two-dimensional quantum systems: Applications to nanotubes. Physica E: Low-Dimensional Systems and Nanostructures, 108, 139-146. https://doi.org/10.1016/j.physe.2018.12.022

    2017

    • Fumeron, S., Berche, B., Medina, E., Santos, F. A. N., & Moraes, F. (2017). Using torsion to manipulate spin currents. EPL, 117(4), Article 47007. https://doi.org/10.1209/0295-5075/117/47007
    • Santos, F. A. N., Da Silva, L. C. B., & Coutinho-Filho, M. D. (2017). Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins. Journal of Statistical Mechanics: Theory and Experiment, 2017(1), Article 013202. https://doi.org/10.1088/1742-5468/2017/1/013202

    2016

    2015

    • Fumeron, S., Berche, B., Santos, F., Pereira, E., & Moraes, F. (2015). Optics near a hyperbolic defect. Physical Review A - Atomic, Molecular, and Optical Physics, 92(6), Article 063806. https://doi.org/10.1103/PhysRevA.92.063806
    • Santos, F. A. N., Gadêlha, H., & Gaffney, E. A. (2015). Fock space, symbolic algebra, and analytical solutions for small stochastic systems. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92(6), Article 062714. https://doi.org/10.1103/PhysRevE.92.062714

    2014

    • Santos, F. A. N., Rehn, J. A., & Coutinho-Filho, M. D. (2014). Topological and geometrical aspects of phase transitions. In Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade (pp. 153-180). World Scientific Publishing Co.. https://doi.org/10.1142/9789814590143_0009

    2012

    • Rehn, J. A., Santos, F. A. N., & Coutinho-Filho, M. D. (2012). Combinatorial and Topological Analysis of the Ising Chain in a Field. Brazilian journal of physics, 42(5-6), 410-421. https://doi.org/10.1007/s13538-012-0108-8

    2009

    • Santos, F. A. N., & Coutinho-Filho, M. D. (2009). Topology, symmetry, phase transitions, and noncollinear spin structures. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 80(3), Article 031123. https://doi.org/10.1103/PhysRevE.80.031123

    2025

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