Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

Delete all

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:
  • ST1_13:
  • ST3_17:

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 (55)
  • Articles in post-conference publications (2)
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  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. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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: 45667), Wydawca: Nature Publishing Group
    Status:
    Published
    DOI:
    10.1038/s41598-017-05911-y - link to the publication
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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: 45667), Wydawca: Public Library of Science
    Status:
    Published
    DOI:
    10.1371/journal.pone.0117722 - link to the publication
  31. 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: 45667), Wydawca: Nature Publishing Group
    Status:
    Published
    DOI:
    10.1038/s41598-017-05911-y - link to the publication
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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
  55. 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
  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
  2. 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

O Narodowym Centrum Nauki

Finansowanie nauki

Współpraca zagraniczna

Centrum prasowe

Deklaracja dostępności
Przetwarzanie danych osobowych
Polityka cookies

Partnerzy