arXiv subjects

Agnieszka Wyłomańska

Publications and source records attributed to Agnieszka Wyłomańska.

43 records · Page 3Linked to original sources

arXiv2017

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

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 cultured neurons. However, the interactions of these molecules with surface nanodomains display a considerable degree of heterogeneity. Here, we investigate this heterogeneity and develop statistical tools based on the recurrence of individual trajectories to identify subpopulations within ion channels in the neuronal surface. We specifically study the dynamics of the K$^+$ channel Kv1.4 and the Na$^+$ channel Nav1.6 on the surface of cultured hippocampal neurons at the single-molecule level. We find that both these molecules are expressed in two different forms with distinct kinetics with regards to surface interactions, emphasizing the complex proteomic landscape of the neuronal surface. Further, the tools presented in this work provide new methods for the analysis of membrane nanodomains, transient confinement, and identification of populations within single-particle trajectories.

physics.bio-ph↗

arXiv2016

Modified cumulative distribution function in application to waiting time analysis in CTRW scenario

The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random walk approach they are realizations of the sequence called waiting times. The main attention of the paper is paid on the analysis of waiting times distribution. We introduce here novel methods of estimation and statistical investigation of such distribution. The methods are based on the modified cumulative distribution function. In this paper we consider three special cases of waiting time distributions, namely $α$-stable, tempered stable and gamma. However the proposed methodology can be applied to broad set of distributions - in general it may serve as a method of fitting any distribution function if the observations are rounded. The new statistical techniques we apply to the simulated data as well as to the real data describing $CO_2$ concentration in indoor air.

physics.data-an↗

arXiv2014

Codifference as a practical tool to measure interdependence

Correlation and spectral analysis represent the standard tools to study interdependence in statistical data. However, for the stochastic processes with heavy-tailed distributions such that the variance diverges, these tools are inadequate. The heavy-tailed processes are ubiquitous in nature and finance. We here discuss codifference as a convenient measure to study statistical interdependence, and we aim to give a short introductory review of its properties. By taking different known stochastic processes as generic examples, we present explicit formulas for their codifferences. We show that for the Gaussian processes codifference is equivalent to covariance. For processes with finite variance these two measures behave similarly with time. For the processes with infinite variance the covariance does not exist, however, the codifference is relevant. We demonstrate the practical importance of the codifference by extracting this function from simulated as well as from real experimental data. We conclude that the codifference serves as a convenient practical tool to study interdependence for stochastic processes with both infinite and finite variances as well.

cond-mat.stat-mech↗

arXiv2012

Recognition of stable distribution with Levy index alpha close to 2

We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data. Furthermore, we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator type fusion device and demonstrate that the phenomenon of L-H transition occurring in this device is accompanied by the transition from Levy to Gaussian fluctuation statistics.

physics.data-an↗

arXiv2012

Regime variance testing - a quantile approach

This paper is devoted to testing time series that exhibit behavior related to two or more regimes with different statistical properties. Motivation of our study are two real data sets from plasma physics with observable two-regimes structure. In this paper we develop estimation procedure for critical point of division the structure change of a time series. Moreover we propose three tests for recognition such specific behavior. The presented methodology is based on the empirical second moment and its main advantage is lack of the distribution assumption. Moreover, the examined statistical properties we express in the language of empirical quantiles of the squared data therefore the methodology is an extension of the approach known from the literature. The theoretical results we confirm by simulations and analysis of real data of turbulent laboratory plasma.

math-ph↗

arXiv2012

Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one - to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters' estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.

math-ph↗

arXiv2011

Anomalous diffusion models: different types of subordinator distribution

Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time series, it is possible to conclude on the main properties of the subordinator. In this paper we analyze the anomalous diffusion models with three types of subordinator distribution: α-stable, tempered stable and gamma. We present similarities and differences between the analyzed processes and point at their main properties (like the behavior of moments or the mean squared displacement).

math-ph↗