TY  - JOUR
A1  - Makarava, Natallia
A1  - Menz, Stephan
A1  - Theves, Matthias
A1  - Huisinga, Wilhelm
A1  - Beta, Carsten
A1  - Holschneider, Matthias
T1  - Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Amoebae explore their environment in a random way, unless external cues like, e. g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.
Y1  - 2014
U6  - https://doi.org/10.1103/PhysRevE.90.042703
SN  - 1539-3755
SN  - 1550-2376
VL  - 90
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Benmehdi, Sabah
A1  - Makarava, Natallia
A1  - Benhamidouche, N.
A1  - Holschneider, Matthias
T1  - Bayesian estimation of the self-similarity exponent of the Nile River fluctuation
JF  - Nonlinear processes in geophysics
N2  - The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.
Y1  - 2011
U6  - https://doi.org/10.5194/npg-18-441-2011
SN  - 1023-5809
VL  - 18
IS  - 3
SP  - 441
EP  - 446
PB  - Copernicus
CY  - Göttingen
ER  - 
TY  - JOUR
A1  - Makarava, Natallia
A1  - Benmehdi, Sabah
A1  - Holschneider, Matthias
T1  - Bayesian estimation of self-similarity exponent
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevE.84.021109
SN  - 1539-3755
VL  - 84
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Makarava, Natallia
A1  - Bettenbühl, Mario
A1  - Engbert, Ralf
A1  - Holschneider, Matthias
T1  - Bayesian estimation of the scaling parameter of fixational eye movements
JF  - epl : a letters journal exploring the frontiers of physics
N2  - In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably.
Y1  - 2012
U6  - https://doi.org/10.1209/0295-5075/100/40003
SN  - 0295-5075
VL  - 100
IS  - 4
PB  - EDP Sciences
CY  - Mulhouse
ER  -