Mathematical and Physical modeling of Single Particle Tracking - Big Data approach (sptBIGDATA)

Grant no.: DFG-NCN 2016/23/G/ST1/04083
Funding agencies: German Research Foundation (DFG), Germany & National Science Centre (NCN), Poland
Funding scheme: BEETHOVEN
Funding period: 27.04.2018-26.04.2023 (60 months)
Budget: 818 900 PLN + 344 900 EUR (ca 529 420 EURO in total)
Title in Polish: Matematyczne i fizyczne modelowanie danych typu Big data dla eksperymentów Single Particle Tracking

Research team
Principal Investigators (Kierownicy)
  • Ralf Metzler (Potsdam, D)
  • Aleksander Weron (Wrocław, PL)
Investigators (Wykonawcy)
  • Krzysztof Burnecki (vice-coordinator; Wroclaw, PL)
  • Aleksei Chechkin (Potsdam, D)
  • Andrei Cherstvy (Potsdam, D)
  • Lyudmila Kirichenko (Kharkiv, UA)
  • Patrycja Kowalek (Wroclaw, PL), PhD
  • Marcin Magdziarz (Wroclaw, PL)
  • Weronika Nitka (Wroclaw, PL), PhD
  • Janusz Szwabiński (Wrocław, PL)
  • Jakub Ślęzak (Wroclaw, PL)
  • Katarzyna Hubicka (Wroclaw, PL), PhD
  • Hanna Loch-Olszewska (Wroclaw, PL), PhD
  • ...... (Potsdam, D), PhD
  • ...... (Potsdam, D), PhD
Collaborators (Współpracownicy)
  • Davide Calebiro (Birmingham, GB)
  • Maria F. Garcia-Parajo (Barcelona, E)
  • Carlo Manzo (Vic, E)
  • Diego Krapf (Fort Collins, USA)
  • Aleksander Stanislavsky (Kharkiv, UA)

Aims and scope

In the last decades, advances in fluorescence-based techniques such as single-particle-tracking (SPT) have allowed to characterize the diffusion of molecules in biological systems with nanometre precision in living cells. Moreover, the new imaging techniques allow acquisition of high-density SPT data in living cells, with up to millions of localizations in a few minutes leading to a big data problem. The concept of fractional anomalous diffusion has deeply penetrated the statistical and chemical physics communities. The subject has become also a major field in mathematics. However, this concept is by now most recognized in applied domains of life sciences such as biological physics, molecular biology or medicine. The European Molecular Biology Laboratory (EMBL) organized first Conference on ``Big Data in Biology & Health'' in Heidelberg, September 2016. Moreover, this timely interdisciplinary meeting aimed to enable the European research community to participate in and help drive the future development of big data research, as well as raise further awareness for this new and relevant research direction in the life sciences. In view of the above challenges we propose the following research tasks:

  • T1. Advancement of mathematical theory of transient fractional diffusion.
  • T2. Development of rigorous statistical inference methods tailored for single particle tracking (SPT) data.
  • T3. Identification, validation and prediction of transient fractional dynamics in living cells in big data era.
We believe that accomplishing these interdysciplinary tasks will result in many interesting discoveries not only in mathematics, but also in physics and biology. It wil lallow us to find proper models and to understand anomalous processes in living cells in the era of big data.


Peer-reviewed articles in JCR-listed journals

  • M. Balcerek, K. Burnecki, S. Thapa, A. Wyłomańska, A. Chechkin (2022) "Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions", Chaos 32, 093114 (2022).
  • A. Stanislavsky, A. Weron (2022) Subdiffusive search with home returns via stochastic resetting: A subordination scheme approach, Journal of Physics A: Mathematical and Theoretical, 55(7), 074004.
  • F. Sabzikar, J. Kabala and K. Burnecki (2022) Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model, Journal of Physics A: Mathematical and Theoretical, 55, 174002.
  • J. Janczura, K. Burnecki, M. Muszkieta, A. Stanislavsky, A. Weron (2022) "Classification of random trajectories based on the fractional Lévy stable motion", Chaos, Solitons & Fractals Available, 154, January 2022, 111606.

  • 2021
  • J. Janczura, M. Balcerek, K. Burnecki, A. Sabri, M. Weiss, D. Krapf (2021) "Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model", New Journal of Physics 23 053018.
  • M. Balcerek, K. Burnecki, G. Sikora, A. Wyłomańska (2021) "Discriminating Gaussian processes via quadratic form statistics", Chaos 31, 063101 (2021).
  • A. Stanislavsky, A. Weron (2021) "Optimal non-Gaussian search with stochastic resetting", Physical Review E 104, 014125.
  • A. Stanislavsky, A. Weron (2021) "Duality of fractional systems", Communications in Nonlinear Science and Numerical Simulation 101, 105861.

  • 2020
  • M. Balcerek, K. Burnecki (2020) "Testing of multifractional Brownian motion", Entropy 2020, 22(12), 1403;
  • M. Balcerek, K. Burnecki (2020) "Testing of fractional Brownian motion in a noisy environment", Chaos, Solitons & Fractals Volume 140, November 2020, 110097.
  • K. Hubicka, J. Janczura (2020) "Time-dependent classification of protein diffusion types: A statistical detection of mean-squared-displacement exponent transitions", Physical Review E 101, 022107 - Published 7 February 2020.
  • J. Janczura, P. Kowalek, H. Loch-Olszewska, J. Szwabiński, A. Weron (2020) "Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion", Physical Review E 102, 032402.
  • A. Stanislavsky, W. Nitka, M. Małek, K. Burnecki, J. Janczura (2020) "Prediction performance of Hidden Markov modelling for solar flares", Journal of Atmospheric and Solar-Terrestrial Physics Volume 208, 15 October 2020, 105407.
  • A. Stanislawsky, A. Weron (2020) "Accelerating and retarding anomalous diffusion: A Bernstein function approach", Physical Review E 101, 052119.
  • A. Stanislavsky, A.Weron (2020), Look at tempered subdiffusion in a conjugate map: Desire for the confinement, Entropy 2020, 22, 1317; doi:10.3390/e22111317.
  • A. Wyłomańska, D. R. Iskander, K. Burnecki (2020) "Omnibus test for normality based on the Edgeworth expansion", PLoS ONE 15(6): e0233901.

  • 2019
  • M. Balcerek, H. Loch-Olszewska, J.A. Torreno-Pina, M.F. Garcia-Parajo, A. Weron, C. Manzo, and K. Burnecki (2019), "Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model", Physical Chemistry Chemical Physics 21, 3114-3121 (doi: 10.1039/c8cp06781c).
  • K. Burnecki, G. Sikora, A. Weron, M.M. Tamkun, and D. Krapf (2019), "Identifying diffusive motions in single-particle trajectorieson the plasma membrane via fractional time series models", Physical Review E 99, 012101 (doi: 10.1103/PhysRevE.99.012101).
  • K. Hubicka, G. Marcjasz, R. Weron (2019), "A note on averaging day-ahead electricity price forecasts across calibration windows", IEEE Transactions on Sustainable Energy 10(1), 321-323 (doi: 10.1109/TSTE.2018.2869557).
  • P. Kowalek, H. Loch-Olszewska , J. Szwabiński (2019), "Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach", Physical Review E 100, 032410.
  • H. Loch-Olszewska, "Properties and distribution of the dynamical functional for the fractional Gaussian noise". Applied Mathematics and Computation 356, 252, doi: 10.1016/J.AMC.2019.03.038.
  • A.A. Stanislavsky, K. Burnecki, J. Janczura, K. Niczyj, A. Weron (2019), "Solar X-ray variability in terms of a fractional heteroskedastic time series model", Monthly Notices of the Royal Astronomical Society, Volume 485, Issue 3, May 2019, Pages 3970-3980, (doi:10.1093/mnras/stz656).
  • A.A. Stanislavsky, A. Weron (2019), "Control of the transient subdiffusion exponent at short and long times". Physical Review Research. 2019, vol. 1, nr 2, art. 023006, s. 1-6. ISSN: 2643-1564
  • J. Ślęzak, K. Burnecki, R.Metzler (2019) "Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems", New Journal of Physics, 2019, 21, 073056.
  • A. Weron, J. Janczura, E. Boryczka, T. Sungkaworn, D. Calebiro (2019), "Statistical testing approach for fractional anomalous diffusion classification", Physical Review E 99, 042149.

  • 2018
  • A.A.Stanislavsky and A.Weron (2018), "Transient anomalous diffusion with Prabhakar-type memory", Journal of Chemical Physics 149, 044107 ; (doi: 10.1063/1.5042075).
  • A.Weron (2018), "Mathematical models for dynamics of molecular processes in living biological cells. A single particle tracking approach". Annales Math. Silesianae 32 , 5-41 (doi: 10.1515/amsil-2017-0019).