spBIGDATA_Mathematische und physikalische Modellierung von Einzelteilchentrajektorien - Big Data Ansatz

• Antragsteller: Professor Dr. Ralf Metzler
• Fachliche Zuordnung: Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik ; Mathematik
• Förderung: Förderung von 2017 bis 2023
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 380893586

• Erstellungsjahr: 2023

Zusammenfassung der Projektergebnisse

Moderne mikroskopische Techniken und Supercomputing-Studien enthüllen die detaillierte Bewegung von Tracerpartikeln in lebenden biologischen Zellen, die Bewegung von Lipiden und Proteine in Membranen oder die innere Dynamik von Biomolekülen. Oft weicht die dabei beobachtete Diffusionsbewegung von den Gesetzen der normalen Brownschen Bewegung (lineare mittlere quadratische Verschiebung, Gauß’sche Verschiebungswahrscheinlichkeitsdichtefunktion) ab. Dieses Phänomen wird als anomale Diffusion bezeichnet. Seit den 1960er Jahren wurden eine Reihe anomaler Diffusionsmodelle formuliert, einschließlich langreichweitig korrelierter Bewegung (typischerweise beobachtet in viskoelastischen Systemen) oder Bewegung, die durch skalenfreie Verteilungen von Immobilisationszeiten unterbrochen wird (beispielsweise in der internen Proteindynamik oder der Bewegung von Membranproteinen). Allerdings erfordert die immer weiter verbesserte Auflösung sowie die Länge der gemessenen Trajektorien immer ausgefeiltere stochastische Modelle, um die beobachtete Dynamik adäquat zu beschreiben. Gleichzeitig wollen wir aus den gesammelten Daten physikalische Informationen über das beobachtete System erhalten. Zu diesem Zweck müssen spezifische datenzentrierte Methoden entwickelt werden. Innerhalb dieses Projekts bündeln wir die Expertise der Angewandten Mathematikgruppe an der Wrocław University of Science & Technology und der Gruppe für Theoretische Physik an der Universität Potsdam, um neuartige stochastische Modelle zu entwerfen und zu studieren sowie neue Strategien zur Bestimmung physikalischer Prozesse und deren Parameter aus gemessenen Zeitreihen von Tracerpartikeln zu entwickeln. Für beide Richtungen lieferte unser polnisch-deutsches Konsortium eine breite Reihe verschiedener und komplementärer Ansätze, einschließlich neuer anomaler Diffusionsmodelle für ungeordnete Systeme, neue statistische Observablen sowie dedizierte computergestützte, datenzentrierte Ansätze auf Basis der Bayes’schen Statistik, Featurebasiertem maschinellem Lernen und Deep-Learning-Methoden.

Projektbezogene Publikationen (Auswahl)

• Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data. Physical Chemistry Chemical Physics, 20(46), 29018-29037.
  Thapa, Samudrajit; Lomholt, Michael A.; Krog, Jens; Cherstvy, Andrey G. & Metzler, Ralf
  
• Conservative random walks in confining potentials. Journal of Physics A: Mathematical and Theoretical, 52(1), 015001.
  Dybiec, Bartłomiej; Capała, Karol; Chechkin, Aleksei V. & Metzler, Ralf
  
• Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers. New Journal of Physics, 20(10), 103027.
  Molina-Garcia, Daniel; Sandev, Trifce; Safdari, Hadiseh; Pagnini, Gianni; Chechkin, Aleksei & Metzler, Ralf
  
• Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks. Physical Review E, 98(2).
  Akimoto, Takuma; Cherstvy, Andrey G. & Metzler, Ralf
  
• First passage statistics for diffusing diffusivity. Journal of Physics A: Mathematical and Theoretical, 52(4), 04LT01.
  Sposini, Vittoria; Chechkin, Aleksei & Metzler, Ralf
  
• Fluctuations of random walks in critical random environments. Physical Chemistry Chemical Physics, 20(31), 20427-20438.
  Mardoukhi, Yousof; Jeon, Jae-Hyung; Chechkin, Aleksei V. & Metzler, Ralf
  
• Mathematical Models for Dynamics of Molecular Processes in Living Biological Cells. A Single Particle Tracking Approach. Annales Mathematicae Silesianae, 32(1), 5-41.
  Weron, Aleksander
  
• Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells. Physical Chemistry Chemical Physics, 20(35), 23034-23054.
  Cherstvy, Andrey G.; Nagel, Oliver; Beta, Carsten & Metzler, Ralf
  
• Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity. Physical Review E, 98(2).
  Cherstvy, Andrey G.; Thapa, Samudrajit; Mardoukhi, Yousof; Chechkin, Aleksei V. & Metzler, Ralf
  
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells. Physical Chemistry Chemical Physics, 20(24), 16393-16401.
  Grebenkov, Denis S.; Metzler, Ralf & Oshanin, Gleb
  
• Transient anomalous diffusion with Prabhakar-type memory. The Journal of Chemical Physics, 149(4).
  Stanislavsky, Aleksander & Weron, Aleksander
  
• A Note on Averaging Day-Ahead Electricity Price Forecasts Across Calibration Windows. IEEE Transactions on Sustainable Energy, 10(1), 321-323.
  Hubicka, Katarzyna; Marcjasz, Grzegorz & Weron, Rafal
  
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion. Journal of Statistical Mechanics: Theory and Experiment, 2019(11), 114003.
  Metzler, Ralf
  
• Burst statistics in an early biofilm quorum sensing model: the role of spatial colony-growth heterogeneity. Scientific Reports, 9(1).
  Kindler, Oliver; Pulkkinen, Otto; Cherstvy, Andrey G. & Metzler, Ralf
  
• Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach. Physical Review E, 100(3).
  Kowalek, Patrycja; Loch-Olszewska, Hanna & Szwabiński, Janusz
  
• Codifference can detect ergodicity breaking and non-Gaussianity. New Journal of Physics, 21(5), 053008.
  Ślęzak, Jakub; Metzler, Ralf & Magdziarz, Marcin
  
• Control of the transient subdiffusion exponent at short and long times. Physical Review Research, 1(2).
  Stanislavsky, Aleksander & Weron, Aleksander
  
• First passage and first hitting times of Lévy flights and Lévy walks. New Journal of Physics, 21(10), 103028.
  Palyulin, Vladimir V.; Blackburn, George; Lomholt, Michael A.; Watkins, Nicholas W.; Metzler, Ralf; Klages, Rainer & Chechkin, Aleksei V.
  
• First-passage properties of asymmetric Lévy flights. Journal of Physics A: Mathematical and Theoretical, 52(45), 454004.
  Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartlomiej; Pavlyukevich, Ilya; Shokri, Babak & Metzler, Ralf
  
• Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries. New Journal of Physics, 21(2), 022002.
  Guggenberger, T.; Pagnini, G.; Vojta, T. & Metzler, R.
  
• Full distribution of first exit times in the narrow escape problem. New Journal of Physics, 21(12), 122001.
  Grebenkov, Denis S.; Metzler, Ralf & Oshanin, Gleb
  
• Gumbel central limit theorem for max-min and min-max. Physical Review E, 100(2).
  Eliazar, Iddo; Metzler, Ralf & Reuveni, Shlomi
  
• Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models. Physical Review E, 99(1).
  Burnecki, Krzysztof; Sikora, Grzegorz; Weron, Aleksander; Tamkun, Michael M. & Krapf, Diego
  
• Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model. Physical Chemistry Chemical Physics, 21(6), 3114-3121.
  Balcerek, Michał; Loch-Olszewska, Hanna; Torreno-Pina, Juan A.; Garcia-Parajo, Maria F.; Weron, Aleksander; Manzo, Carlo & Burnecki, Krzysztof
  
• Money distribution in agent-based models with position-exchange dynamics: the Pareto paradigm revisited. The European Physical Journal B, 92(5).
  Aydiner, Ekrem; Cherstvy, Andrey G. & Metzler, Ralf
  
• Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels. Soft Matter, 15(12), 2526-2551.
  Cherstvy, Andrey G.; Thapa, Samudrajit; Wagner, Caroline E. & Metzler, Ralf
  
• Poisson-process limit laws yield Gumbel max-min and min-max. Physical Review E, 100(2).
  Eliazar, Iddo; Metzler, Ralf & Reuveni, Shlomi
  
• Probability density of the fractional Langevin equation with reflecting walls. Physical Review E, 100(4).
  Vojta, Thomas; Skinner, Sarah & Metzler, Ralf
  
• Properties and distribution of the dynamical functional for the fractional Gaussian noise. Applied Mathematics and Computation, 356, 252-271.
  Loch-Olszewska, Hanna
  
• Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems. New Journal of Physics, 21(7), 073056.
  Ślęzak, Jakub; Burnecki, Krzysztof & Metzler, Ralf
  
• Solar X-ray variability in terms of a fractional heteroskedastic time series model. Monthly Notices of the Royal Astronomical Society, 485(3), 3970-3980.
  Stanislavsky, Aleksander A.; Burnecki, Krzysztof; Janczura, Joanna; Niczyj, Karol & Weron, Aleksander
  
• Spectral Content of a Single Non-Brownian Trajectory. Physical Review X, 9(1).
  Krapf, Diego; Lukat, Nils; Marinari, Enzo; Metzler, Ralf; Oshanin, Gleb; Selhuber-Unkel, Christine; Squarcini, Alessio; Stadler, Lorenz; Weiss, Matthias & Xu, Xinran
  
• Statistical testing approach for fractional anomalous diffusion classification. Physical Review E, 99(4).
  Weron, Aleksander; Janczura, Joanna; Boryczka, Ewa; Sungkaworn, Titiwat & Calebiro, Davide
  
• Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells. The Journal of Chemical Physics, 150(14).
  Thapa, Samudrajit; Lukat, Nils; Selhuber-Unkel, Christine; Cherstvy, Andrey G. & Metzler, Ralf
  
• Transport in exclusion processes with one-step memory: density dependence and optimal acceleration. Journal of Physics A: Mathematical and Theoretical, 52(38), 385001.
  Teomy, Eial & Metzler, Ralf
  
• Accelerating and retarding anomalous diffusion: A Bernstein function approach. Physical Review E, 101(5).
  Stanislavsky, Aleksander & Weron, Aleksander
  
• Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise. Physical Review E, 102(1).
  Wang, Wei; Cherstvy, Andrey G.; Liu, Xianbin & Metzler, Ralf
  
• Buckling transitions and soft-phase invasion of two-component icosahedral shells. Physical Review E, 102(6).
  Emanuel, Marc D.; Cherstvy, Andrey G.; Metzler, Ralf & Gompper, Gerhard
  
• Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion. Physical Review E, 102(3).
  Janczura, Joanna; Kowalek, Patrycja; Loch-Olszewska, Hanna; Szwabiński, Janusz & Weron, Aleksander
  
• Continuous time random walk in a velocity field: role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing. New Journal of Physics, 22(7), 073048.
  Le Vot, F.; Abad, E.; Metzler, R. & Yuste, S. B.
  
• Critical adsorption of multiple polyelectrolytes onto a nanosphere: splitting the adsorption–desorption transition boundary. Journal of The Royal Society Interface, 17(167), 20200199.
  Caetano, Daniel L. Z.; de Carvalho, Sidney J.; Metzler, Ralf & Cherstvy, Andrey G.
  
• Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers. Physical Review E, 102(3).
  Kosztołowicz, Tadeusz & Metzler, Ralf
  
• First passage time moments of asymmetric Lévy flights. Journal of Physics A: Mathematical and Theoretical, 53(27), 275002.
  Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartłomiej; Magdziarz, Marcin; Shokri, Babak & Metzler, Ralf
  
• Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. Journal of Physics A: Mathematical and Theoretical, 53(47), 474001.
  Wang, Wei; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thapa, Samudrajit; Seno, Flavio; Liu, Xianbin & Metzler, Ralf
  
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of N random walkers. New Journal of Physics, 22(10), 103004.
  Grebenkov, Denis S.; Metzler, Ralf & Oshanin, Gleb
  
• Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes. Physical Review E, 102(6).
  Xu, Yong; Liu, Xuemei; Li, Yongge & Metzler, Ralf
  
• Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion. Entropy, 22(12), 1436.
  Loch-Olszewska, Hanna & Szwabiński, Janusz
  
• Insight into the intestinal microbiome of farrowing sows following the administration of garlic (Allium sativum) extract and probiotic bacteria cultures under farming conditions. BMC Veterinary Research, 16(1).
  Satora, Marta; Magdziarz, Marcin; Rząsa, Anna; Rypuła, Krzysztof & Płoneczka-Janeczko, Katarzyna
  
• Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement. Entropy, 22(11), 1317.
  Stanislavsky, Aleksander & Weron, Aleksander
  
• Lévy noise-driven escape from arctangent potential wells. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12).
  Capała, Karol; Padash, Amin; Chechkin, Aleksei V.; Shokri, Babak; Metzler, Ralf & Dybiec, Bartłomiej
  
• Lévy walk dynamics in an external harmonic potential. Physical Review E, 101(6).
  Xu, Pengbo; Zhou, Tian; Metzler, Ralf & Deng, Weihua
  
• Omnibus test for normality based on the Edgeworth expansion. PLOS ONE, 15(6), e0233901.
  Wyłomańska, Agnieszka; Iskander, D. Robert & Burnecki, Krzysztof
  
• Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity. New Journal of Physics, 22(5), 053016.
  Li, Yongge; Mei, Ruoxing; Xu, Yong; Kurths, Jürgen; Duan, Jinqiao & Metzler, Ralf
  
• Prediction performance of Hidden Markov modelling for solar flares. Journal of Atmospheric and Solar-Terrestrial Physics, 208, 105407.
  Stanislavsky, A.; Nitka, W.; Małek, M.; Burnecki, K. & Janczura, J.
  
• Reflected fractional Brownian motion in one and higher dimensions. Physical Review E, 102(3).
  Vojta, Thomas; Halladay, Samuel; Skinner, Sarah; Janušonis, Skirmantas; Guggenberger, Tobias & Metzler, Ralf
  
• Resetting dynamics in a confining potential. Journal of Physics A: Mathematical and Theoretical, 53(50), 505003.
  Singh, R. K.; Metzler, R. & Sandev, T.
  
• Spurious ergodicity breaking in normal and fractional Ornstein–Uhlenbeck process. New Journal of Physics, 22(7), 073012.
  Mardoukhi, Yousof; Chechkin, Aleksei & Metzler, Ralf
  
• Stochastic dynamics driven by combined Lévy–Gaussian noise: fractional Fokker–Planck–Kolmogorov equation and solution. Journal of Physics A: Mathematical and Theoretical, 53(38), 385001.
  Zan, Wanrong; Xu, Yong; Kurths, Jürgen; Chechkin, Aleksei V. & Metzler, Ralf
  
• Superstatistics and non-Gaussian diffusion. The European Physical Journal Special Topics, 229(5), 711-728.
  Metzler, Ralf
  
• Testing of fractional Brownian motion in a noisy environment. Chaos, Solitons & Fractals, 140, 110097.
  Balcerek, Michał & Burnecki, Krzysztof
  
• Testing of Multifractional Brownian Motion. Entropy, 22(12), 1403.
  Balcerek, Michał & Burnecki, Krzysztof
  
• The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated. Physical Chemistry Chemical Physics, 22(48), 27955-27965.
  Díez, Fernández Amanda; Charchar, Patrick; Cherstvy, Andrey G.; Metzler, Ralf & Finnis, Michael W.
  
• Time-dependent classification of protein diffusion types: A statistical detection of mean-squared-displacement exponent transitions. Physical Review E, 101(2).
  Hubicka, Katarzyna & Janczura, Joanna
  
• Transition path dynamics across rough inverted parabolic potential barrier. The European Physical Journal Plus, 135(9).
  Li, Hua; Xu, Yong; Li, Yongge & Metzler, Ralf
  
• Transition path properties for one-dimensional systems driven by Poisson white noise. Chaos, Solitons & Fractals, 141, 110293.
  Li, Hua; Xu, Yong; Metzler, Ralf & Kurths, Jürgen
  
• Unexpected crossovers in correlated random-diffusivity processes. New Journal of Physics, 22(8), 083041.
  Wang, Wei; Seno, Flavio; Sokolov, Igor M.; Chechkin, Aleksei V. & Metzler, Ralf
  
• Universal spectral features of different classes of random-diffusivity processes. New Journal of Physics, 22(6), 063056.
  Sposini, Vittoria; Grebenkov, Denis S.; Metzler, Ralf; Oshanin, Gleb & Seno, Flavio
  
• Detection of Anomalous Diffusion with Deep Residual Networks. Entropy, 23(6), 649.
  Gajowczyk, Miłosz & Szwabiński, Janusz
  
• Discriminating Gaussian processes via quadratic form statistics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(6).
  Balcerek, Michał; Burnecki, Krzysztof; Sikora, Grzegorz & Wyłomańska, Agnieszka
  
• Duality of fractional systems. Communications in Nonlinear Science and Numerical Simulation, 101, 105861.
  Stanislavsky, Aleksander & Weron, Aleksander
  
• Exact distributions of the maximum and range of random diffusivity processes. New Journal of Physics, 23(2), 023014.
  Grebenkov, Denis S.; Sposini, Vittoria; Metzler, Ralf; Oshanin, Gleb & Seno, Flavio
  
• Exact first-passage time distributions for three random diffusivity models. Journal of Physics A: Mathematical and Theoretical, 54(4), 04LT01.
  Grebenkov, Denis S.; Sposini, Vittoria; Metzler, Ralf; Oshanin, Gleb & Seno, Flavio
  
• First-passage problem for stochastic differential equations with combined parametric Gaussian and Lévy white noises via path integral method. Journal of Computational Physics, 435, 110264.
  Zan, Wanrong; Xu, Yong; Metzler, Ralf & Kurths, Jürgen
  
• Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model. New Journal of Physics, 23(5), 053018.
  Janczura, Joanna; Balcerek, Michał; Burnecki, Krzysztof; Sabri, Adal; Weiss, Matthias & Krapf, Diego
  
• Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories. New Journal of Physics, 23(1), 013008.
  Thapa, Samudrajit; Wyłomańska, Agnieszka; Sikora, Grzegorz; Wagner, Caroline E.; Krapf, Diego; Kantz, Holger; Chechkin, Aleksei V. & Metzler, Ralf
  
• Objective comparison of methods to decode anomalous diffusion. Nature Communications, 12(1).
  Muñoz-Gil, Gorka; Volpe, Giovanni; Garcia-March, Miguel Angel; Aghion, Erez; Argun, Aykut; Hong, Chang Beom; Bland, Tom; Bo, Stefano; Conejero, J. Alberto; Firbas, Nicolás; Garibo, i. Orts Òscar; Gentili, Alessia; Huang, Zihan; Jeon, Jae-Hyung; Kabbech, Hélène; Kim, Yeongjin; Kowalek, Patrycja; Krapf, Diego; Loch-Olszewska, Hanna; ... & Manzo, Carlo
  
• Optimal non-Gaussian search with stochastic resetting. Physical Review E, 104(1).
  Stanislavsky, Aleksander & Weron, Aleksander
  
• Scaled geometric Brownian motion features sub- or superexponential ensemble-averaged, but linear time-averaged mean-squared displacements. Physical Review E, 103(6).
  Cherstvy, Andrey G.; Vinod, Deepak; Aghion, Erez; Sokolov, Igor M. & Metzler, Ralf
  
• Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach. Applied Mathematics and Computation, 396, 125902.
  Muszkieta, Monika; Janczura, Joanna & Weron, Aleksander
  
• Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes. Physical Review E, 104(2).
  Wang, Wei; Cherstvy, Andrey G.; Kantz, Holger; Metzler, Ralf & Sokolov, Igor M.
  
• Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution. Physical Review Letters, 126(12).
  Yamamoto, Eiji; Akimoto, Takuma; Mitsutake, Ayori & Metzler, Ralf
  
• Universality of delay-time averages for financial time series: analytical results, computer simulations, and analysis of historical stock-market prices. Journal of Physics: Complexity, 2(4), 045003.
  Ritschel, Stefan; Cherstvy, Andrey G. & Metzler, Ralf
  
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features. Journal of Physics A: Mathematical and Theoretical, 55(24), 244005.
  Kowalek, Patrycja; Loch-Olszewska, Hanna; Łaszczuk, Łukasz; Opała, Jarosław & Szwabiński, Janusz
  
• Classification of random trajectories based on the fractional Lévy stable motion. Chaos, Solitons & Fractals, 154, 111606.
  Janczura, Joanna; Burnecki, Krzysztof; Muszkieta, Monika; Stanislavsky, Aleksander & Weron, Aleksander
  
• Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(9).
  Balcerek, Michał; Burnecki, Krzysztof; Thapa, Samudrajit; Wyłomańska, Agnieszka & Chechkin, Aleksei
  
• Functional convergence of continuous-time random walks with continuous paths. Communications in Contemporary Mathematics, 25(05).
  Magdziarz, Marcin & Zebrowski, Piotr
  
• Subdiffusive search with home returns via stochastic resetting: a subordination scheme approach. Journal of Physics A: Mathematical and Theoretical, 55(7), 074004.
  Stanislavsky, Aleksander A. & Weron, Aleksander
  
• Temperature and friction fluctuations inside a harmonic potential. Physical Review E, 106(6).
  Lanoiselée, Yann; Stanislavsky, Aleksander; Calebiro, Davide & Weron, Aleksander
  
• Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model. Journal of Physics A: Mathematical and Theoretical, 55(17), 174002.
  Sabzikar, Farzad; Kabala, Jinu & Burnecki, Krzysztof
  
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories. The Journal of Physical Chemistry Letters, 14(35), 7910-7923.
  Seckler, Henrik; Szwabiński, Janusz & Metzler, Ralf
  
• Memory-multi-fractional Brownian motion with continuous correlations. Physical Review Research, 5(3).
  Wang, Wei; Balcerek, Michał; Burnecki, Krzysztof; Chechkin, Aleksei V.; Janušonis, Skirmantas; Ślęzak, Jakub; Vojta, Thomas; Wyłomańska, Agnieszka & Metzler, Ralf
  
• Minimal model of diffusion with time changing Hurst exponent. Journal of Physics A: Mathematical and Theoretical, 56(35), 35LT01.
  Ślęzak, Jakub & Metzler, Ralf