Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Anomalous dynamics of complex physical and biological systems - stochastic modeling and statistical identification

2012/06/A/ST1/00258

Keywords:

anomalous dynamics subdiffusion superdiffusion random walk time series stochastic modeling statistical identification prediction

Descriptors:

  • ST1_18: Control theory and optimisation
  • ST1_13: Probability and statistics
  • ST3_17: Other related subjects

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Politechnika Wrocławska, Wydział Matematyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Aleksander Weron 

Number of co-investigators in the project: 6

Call: MAESTRO 3 - announced on 2012-06-15

Amount awarded: 1 759 000 PLN

Project start date (Y-m-d): 2013-04-18

Project end date (Y-m-d): 2018-04-17

Project duration:: 60 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. komputer stacjonarny z monitorem.
  2. laptop (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (45)
  • Articles in post-conference publications (1)
  1. Statistical analysis of superstatistical fractional Brownian motion and applications
    Authors:
    A. Mackala, M. Magdziarz
    Academic press:
    PHYSICAL REVIEW E (rok: 2019, tom: 99, strony: 12143), Wydawca: AMER PHYSICAL SOC
    Status:
    Published
    DOI:
    10.1103/PhysRevE.99.012143 - link to the publication
  2. An efficient algorithm for extracting the magnitude of the measurement error for fractional dynamics
    Authors:
    G.Sikora, E.Kepten, A.Weron, M.Balcerek, K.Burnecki
    Academic press:
    Physical Chemistry Chemical Physics (rok: 2017, tom: 19, strony: 26566-26581), Wydawca: Royal Society of Chemistry
    Status:
    Published
    DOI:
    10.1039/c7cp04464j - link to the publication
  3. Anomalous diffusion approach to non-exponential relaxation in complex physical systems
    Authors:
    Aleksander Stanislavsky, Karina Weron, Aleksander Weron
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2015, tom: 24, strony: 117-126), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2015.01.001 - link to the publication
  4. Comment on fractional Fokker-Planck equation with space and time dependent drift and diffusion
    Authors:
    Marcin Magdziarz, Janusz Gajda, Tomasz Żórawik
    Academic press:
    Journal of Statistical Physics (rok: 2014, tom: 154, strony: 1241-1250), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10955-014-0919-9 - link to the publication
  5. Discriminating between light- and heavy-tailed distributions with limit theorem
    Authors:
    Krzysztof Burnecki, Agnieszka Wylomanska, Aleksei Chechkin
    Academic press:
    PLoS ONE (rok: 2015, tom: 10(12), strony: e0145604), Wydawca: PUBLIC LIBRARY SCIENCE
    Status:
    Published
    DOI:
    10.1371/journal. - link to the publication
  6. Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion
    Authors:
    A. Wyłomańska, A. Kumar, R. Połoczański, P. Vellaisamy
    Academic press:
    Physical Review E (rok: 2016, tom: 94, strony: 42128), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1103/PhysRevE.94.042128 - link to the publication
  7. Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time series models
    Authors:
    Krzysztof Burnecki, Grzegorz Sikora, Aleksander Weron, Michael Tamkun, Diego Krapf
    Academic press:
    Physical Review E (rok: 2019, tom: 99, strony: 12101), Wydawca: AMER PHYSICAL SOC
    Status:
    Published
    DOI:
    10.1103/PhysRevE.99.012101 - link to the publication
  8. Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
    Authors:
    Krzysztof Burnecki, Aleksander Weron
    Academic press:
    Journal of Statistical Mechanics: Theory and Experiment (rok: 2014, tom: 10, strony: P10036(1)-P10036(26)), Wydawca: International School for Advanced Studies and IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1742-5468/2014/10/P10036 - link to the publication
  9. Anomalous diffusion with transient subordinators: A link to compound relaxation laws
    Authors:
    Aleksander Stanislavsky, Karina Weron, Aleksander Weron
    Academic press:
    THE JOURNAL OF CHEMICAL PHYSICS (rok: 2014, tom: 140, strony: 054113 1-7), Wydawca: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/1.4863995 - link to the publication
  10. Asymptotic behaviour of time averages for non-ergodic Gaussian processes
    Authors:
    Jakub Ślęzak
    Academic press:
    Annals of Physics (rok: 2017, tom: 383, strony: 285-311), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aop.2017.05.015 - link to the publication
  11. Ergodicity testing for anomalous diffusion: Small sample statistics
    Authors:
    Joanna Janczura, Aleksander Weron
    Academic press:
    The Journal of Chemical Physics (rok: 2015, tom: 142, strony: 144103), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1063/1.4916912 - link to the publication
  12. Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
    Authors:
    M.Magdziarz, M.Teuerle
    Academic press:
    Journal of Physics A: Mathematical and Theoretical (rok: 2017, tom: 50, strony: 184005), Wydawca: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1751-8121/aa651e - link to the publication
  13. Lamperti transformation - cure for ergodicity breaking
    Authors:
    M. Magdziarz, T. Zorawik
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2019, tom: 71, strony: 202–211), Wydawca: ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2018.11.020 - link to the publication
  14. Method of calculating densities for isotropic ballistic Lévy walks
    Authors:
    Marcin Magdziarz, Tomasz Zorawik
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2017, tom: 48, strony: 462-473), Wydawca: ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2016.11.026 - link to the publication
  15. Stable Levy process delayed by tempered stable subordinator
    Authors:
    J. Gajda, A. Kumar, A. Wyłomańska
    Academic press:
    Statistics and Probability Letters (rok: 2019, tom: 145, strony: 284–292), Wydawca: ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.spl.2018.09.008 - link to the publication
  16. Aging ballistic Levy walks
    Authors:
    M. Magdziarz, T. Zorawik
    Academic press:
    Physical Review E (rok: 2017, tom: 95, strony: 22126), Wydawca: AMER PHYSICAL SOC
    Status:
    Published
    DOI:
    10.1103/PhysRevE.95.022126 - link to the publication
  17. Asymptotic properties and numerical simulation of multidimensional Levy walks
    Authors:
    Marcin Magdziarz, Marek Teuerle
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2015, tom: 20, strony: 489-505), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2014.05.029 - link to the publication
  18. Densities of scaling limits of coupled continuous time random walks
    Authors:
    Marcin Magdziarz, Tomasz Zorawik
    Academic press:
    Fractional Calculus and Applied Analysis (rok: 2016, tom: 19, strony: 1488-1506), Wydawca: degruyter
    Status:
    Published
    DOI:
    10.1515/fca-2016-0077 - link to the publication
  19. Identifying ergodicity breaking for fractional anomalous diffusion: Criteria for minimal trajectory length
    Authors:
    Hanna Loch-Olszewska, Grzegorz Sikora, Joanna Janczura, Aleksander Weron
    Academic press:
    PHYSICAL REVIEW E (rok: 2016, tom: 94, strony: 52136), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1103/PhysRevE.94.052136 - link to the publication
  20. Large deviations for subordinated Brownian motion and applications
    Authors:
    Janusz Gajda, Marcin Magdziarz
    Academic press:
    Statistics & Probability Letters (rok: 2014, tom: 88, strony: 149–156), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2014.02.003 - link to the publication
  21. Stochastic representation of fractional subdiffusion equation. The case of infinitely divisible waiting times and space-time-dependent coefficients
    Authors:
    Marcin Magdziarz, Tomasz Żórawik
    Academic press:
    Proceedings of the American Mathematical Society (rok: 2016, tom: 144, strony: 1767-1778), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/12856 - link to the publication
  22. Scaling limits for Levy walks with rests
    Authors:
    M. Teuerle
    Academic press:
    Journal of Applied Probability , Wydawca: CAMBRIDGE UNIV PRESS
    Status:
    Submitted
    DOI:
    brak - link to the publication
  23. A fractional Fokker-Planck control framework for subdiffusion processes
    Authors:
    M. Annunziato, A. Borzi, M. Magdziarz, A. Weron
    Academic press:
    OPTIMAL CONTROL APPLICATIONS AND METHODS (rok: 2016, tom: 37, strony: 290–304), Wydawca: John Wiley & Sons, Ltd.
    Status:
    Published
    DOI:
    10.1002/oca.2168 - link to the publication
  24. Codifference as a practical tool to measure interdependence
    Authors:
    Agnieszka Wyłomańska, Aleksei Chechkin, Janusz Gajda, Igor M. Sokolov
    Academic press:
    Physica A (rok: 2015, tom: 421, strony: 412-429), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physa.2014.11.049 - link to the publication
  25. Detection of epsilon-ergodicity breaking in experimental data - a study of the dynamical functional sensibility
    Authors:
    Hanna Loch-Olszewska, Janusz Szwabiński
    Academic press:
    Journal of Chemical Physics (rok: 2018, tom: 148, strony: 204105), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1063/1.5025941 - link to the publication
  26. Ergodicity breaking on the neuronal surface emerges from random switching between diffusive states
    Authors:
    A.Weron, K.Burnecki, E.J.Akin, L.Sole, M.Balcerek, M.M.Tamkun, D.Krapf
    Academic press:
    Scientific Reports (rok: 2017, tom: 7, strony: 45301), Wydawca: Nature Publishing Group
    Status:
    Published
    DOI:
    10.1038/s41598-017-05911-y - link to the publication
  27. Explicit densities of multidimensional ballistic Levy walks
    Authors:
    Marcin Magdziarz, Tomasz Zorawik
    Academic press:
    Physical Review E (rok: 2016, tom: 94, strony: 22130), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1103/PhysRevE.94.022130 - link to the publication
  28. From physical linear systems to discrete-time series. A guide for analysis of the sampled experimental data
    Authors:
    Jakub Ślęzak, Aleksander Weron
    Academic press:
    Physical Review E (rok: 2015, tom: 91, strony: 53302), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.91.053302 - link to the publication
  29. Guidelines for the fitting of anomalous diffusion mean square displacement graphs from single particle tracking experiments
    Authors:
    Eldad Kepten, Aleksander Weron, Grzegorz Sikora, Krzysztof Burnecki, Yuval Garini
    Academic press:
    PLOS ONE (rok: 2015, tom: 2, strony: 45301), Wydawca: Public Library of Science
    Status:
    Published
    DOI:
    10.1371/journal.pone.0117722 - link to the publication
  30. Modelling of water usage by means of ARFIMA-GARCH processes
    Authors:
    Janusz Gajda, Grzegorz Bartnicki, Krzysztof Burnecki
    Academic press:
    Physica A (rok: 2018, tom: 512, strony: 644–657), Wydawca: ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.physa.2018.08.134 - link to the publication
  31. Moving average process underlying the holographic-optical-tweezers experiments
    Authors:
    Jakub Ślęzak, Sławomir Drobczyński, Karina Weron, Jan Masajada
    Academic press:
    Applied Optics (rok: 2014, tom: 53, strony: B254-B258), Wydawca: Optical Society of America
    Status:
    Published
    DOI:
    10.1364/AO.53.00B254 - link to the publication
  32. Rotational invariance of stochastic processes with application to fractional dynamics
    Authors:
    J. Ślęzak, M. Magdziarz
    Academic press:
    Journal of Statistical Mechanics-Theory and Experiment (rok: 2014, tom: 10, strony: P10028(1)-P10028(24)), Wydawca: IOP Publishing LTD
    Status:
    Published
    DOI:
    10.1088/1742-5468/2014/10/P10028 - link to the publication
  33. Solar X-ray variability in terms of a fractional heteroskedastic time series model
    Authors:
    A.A.Stanislavsky, K.Burnecki, J.Janczura, K.Niczyj, A.Weron
    Academic press:
    MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY (rok: 2019, tom: 485, strony: 3970–3980), Wydawca: OXFORD UNIV PRESS
    Status:
    Published
    DOI:
    10.1093/mnras/stz656 - link to the publication
  34. Time-changed Ornstein-Uhlenbeck process
    Authors:
    Janusz Gajda, Agnieszka Wyłomańska
    Academic press:
    Journal of Physics A: Mathematical and Theoretical (rok: 2015, tom: 48, strony: 135004), Wydawca: IOP SCIENCE
    Status:
    Published
    DOI:
    10.1088/1751-8113/48/13/135004 - link to the publication
  35. Ergodicity testing using an analytical formula for a dynamical functional of alpha-stable autoregressive fractionally integrated moving average processes
    Authors:
    Hanna Loch, Joanna Janczura, Aleksander Weron
    Academic press:
    PHYSICAL REVIEW E (rok: 2016, tom: 93, strony: 43317), Wydawca: APS
    Status:
    Published
    DOI:
    10.1103/PhysRevE.93.043317 - link to the publication
  36. Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach
    Authors:
    Krzysztof Burnecki, Eldad Kepten, Yuval Garini, Grzegorz Sikora, Aleksander Weron
    Academic press:
    Scientific Reports (rok: 2015, tom: 5, strony: 11306), Wydawca: NATURE PUBLISHING GROUP
    Status:
    Published
    DOI:
    10.1038/srep11306 - link to the publication
  37. Fractional Brownian motion time-changed by gamma and inverse gamma process
    Authors:
    A. Kumar, A. Wyłomańska, R. Połoczański, S. Sundar
    Academic press:
    Physica A (rok: 2017, tom: 468, strony: 648-667), Wydawca: ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.060 - link to the publication
  38. Fractional Brownian motions: memory, diffusion velocity, and correlation functions
    Authors:
    Andrzej Fuliński
    Academic press:
    J. Phys. A: Math. Theor. (rok: 2017, tom: 50, strony: 54002), Wydawca: IOP PUBLISHING LTD
    Status:
    Published
    DOI:
    10.1088/1751-8121/50/5/054002 - link to the publication
  39. Identification and validation of stable ARFIMA processes with application to UMTS data
    Authors:
    Krzysztof Burnecki, Grzegorz Sikora
    Academic press:
    Chaos, Solitons and Fractals (rok: 2017, tom: 102, strony: 456-466), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.chaos.2017.03.059 - link to the publication
  40. Mean-squared-displacement statistical test for fractional Brownian motion
    Authors:
    Grzegorz Sikora, Krzysztof Burnecki, Agnieszka Wyłomanska
    Academic press:
    Physical Review E (rok: 2017, tom: 95, strony: 32110), Wydawca: AIP
    Status:
    Published
    DOI:
    10.1103/PhysRevE.95.032110 - link to the publication
  41. Single-molecule imaging reveals receptor–G protein interactions at cell surface hot spots
    Authors:
    Titiwat Sungkaworn, Marie-Lise Jobin, Krzysztof Burnecki, Aleksander Weron, Martin J. Lohse, Davide Calebiro
    Academic press:
    Nature (rok: 2017, tom: 550, strony: 543-547), Wydawca: Nature Publishing Group
    Status:
    Published
    DOI:
    10.1038/nature24264 - link to the publication
  42. Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement
    Authors:
    G.Sikora, M. Teuerle, A. Wyłomańska, D. Grebenkov
    Academic press:
    Physical Review E (rok: 2017, tom: 96, strony: 22132), Wydawca: American Physical Society
    Status:
    Published
    DOI:
    10.1103/PhysRevE.96.022132 - link to the publication
  43. Statistical test for fractional Brownian motion based on detrending moving average algorithm
    Authors:
    G. Sikora
    Academic press:
    Chaos Solitons & Fractals (rok: 2018, tom: 116, strony: 54–62), Wydawca: PERGAMON-ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.chaos.2018.08.031 - link to the publication
  44. Time-series methods in analysis of the optical tweezers recordings
    Authors:
    Sławomir Drobczynski, Jakub Ślęzak
    Academic press:
    Applied Optics (rok: 2015, tom: 54, strony: 7106-7114), Wydawca: OSA Publishing
    Status:
    Published
    DOI:
    10.1364/AO.54.007106 - link to the publication
  45. Uniform Contraction-Expansion Description of Relative Centromere and Telomere Motion
    Authors:
    Eldad Kepten, Aleksander Weron, Irena Bronstein, Krzysztof Burnecki, Yuval Garini
    Academic press:
    Biophysical Journal (rok: 2015, tom: 109, strony: 1454-1462), Wydawca: CELL PRESS
    Status:
    Published
    DOI:
    10.1016/j.bpj.2015.07.031 - link to the publication
  1. Stochastic dynamics of G-Protein-Coupled Cell-Surface receptors
    Authors:
    M. Balcerek, A. Weron
    Conference:
    12th Workshop on Stochastic Models, Statistics and Their Applications (rok: 2015, ), Wydawca: Springer Proceedings in Mathematics & Statistics
    Data:
    konferencja 16-20.02
    Status:
    Published

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