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Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach

• Krzysztof Burnecki, Eldad Kepten, Yuval Garini, Grzegorz Sikora, Aleksander Weron
• Scientific reports
• 2015

Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single… (More)

Mean-squared-displacement statistical test for fractional Brownian motion.

• Grzegorz Sikora, Krzysztof Burnecki, Agnieszka Wyłomańska
• Physical review. E
• 2017

Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the… (More)

Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments

• Eldad Kepten, Aleksander Weron, Grzegorz Sikora, Krzysztof Burnecki, Yuval Garini
• PloS one
• 2015

Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive… (More)

Estimation of FARIMA Parameters in the Case of Negative Memory and Stable Noise

• Krzysztof Burnecki, Grzegorz Sikora
• IEEE Transactions on Signal Processing
• 2013

In this paper, we extend a method of estimation of parameters of the fractional autoregressive integrated moving average (FARIMA) process with stable noise to the case of negative memory parameter… (More)

Identification and validation of stable ARFIMA processes with application to UMTS data

• Krzysztof Burnecki, Grzegorz Sikora
• 2017

In this paper we present an identification and validation scheme for stable autoregressive fractionally integrated moving average (ARFIMA) time series. The identification part relies on a recently… (More)

Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis.

• Grzegorz Sikora, Agnieszka Wyłomańska, +4 authors Diego Krapf
• Physical review. E
• 2017

Protein and lipid nanodomains are prevalent on the surface of mammalian cells. In particular, it has been recently recognized that ion channels assemble into surface nanoclusters in the soma of… (More)

Identifying ergodicity breaking for fractional anomalous diffusion: Criteria for minimal trajectory length.

• Hanna Loch-Olszewska, Grzegorz Sikora, Joanna Janczura, Aleksander Weron
• Physical review. E
• 2016

In this paper, we study ergodic properties of α-stable autoregressive fractionally integrated moving average (ARFIMA) processes which form a large class of anomalous diffusions. A crucial practical… (More)

OIL AGING INFLUENCE ON THE SLIDE JOURNAL BEARING LUBRICATION

• Andrzej Miszczak, Grzegorz Sikora
• 2011

In this study authors solve the fundamental set of equations of the hydrodynamic theory of lubrication, namely are: the continuity equation, conservation of momentum and conservation of energy for… (More)

Krzysztof Dębicki and Grzegorz Sikora (Wrocław) FINITE TIME ASYMPTOTICS OF FLUID AND RUIN MODELS: MULTIPLEXED FRACTIONAL BROWNIAN

• Grzegorz Sikora
• 2011

Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of P ( sup t∈[0,T ] ( n ∑ i=1 λiBHi(t)− ct ) > u ) , where {BHi(t) : t ≥ 0}, i = 1, . . . , n, are… (More)

Modeling anomalous diffusion by a subordinated fractional Lévy-stable process

• Agnieszka Wy lomańska, Grzegorz Sikora
• 2013

Two phenomena that can be discovered in systems with anomalous diffusion are long-range dependence and trapping events. The first effect concerns events that are arbitrarily distant but still… (More)

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