Mathematical models for dynamics of molecular processes in living biological cells. A single particle tracking approach
Journal Title: Annales Mathematicae Silesianae - Year 2018, Vol 32, Issue
Abstract
In this survey paper we present a systematic methodology of how to identify origins of fractional dynamics. We consider three models leading to it, namely fractional Brownian motion (FBM), fractional Lévy stable motion (FLSM) and autoregressive fractionally integrated moving average (ARFIMA) process. The discrete-time ARFIMA process is stationary, and when aggregated, in the limit, it converges to either FBM or FLSM. In this sense it generalizes both models. We discuss three experimental data sets related to some molecular biology problems described by single particle tracking. They are successfully resolved by means of the universal ARFIMA time series model with various noises. Even if the finer details of the estimation procedures are case specific, we hope that the suggested checklist will still have been of great use as a practical guide. In Appendices A–F we describe useful fractional dynamics identification and validation methods.
Authors and Affiliations
Aleksander Weron
Keywords
Related Articles
- EP ID EP524574
- DOI 10.1515/amsil-2017-0019
- Views 139
- Downloads 0
Communication complexity and linearly ordered sets
The paper is devoted to the communication complexity of lattice operations in linearly ordered finite sets. All well known techniques ([4, Chapter 1]) to determine the communication complexity of the infimum function in...
A unique common fixed point for an infinity of set-valued maps
The main purpose of this paper is to establish some common fixed point theorems for single and set-valued maps in complete metric spaces, under contractive conditions by using minimal type commutativity and without conti...
Generalizations of some integral inequalities for fractional integrals
In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.
A general fixed point theorem for implicit cyclic multi-valued contraction mappings
In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15],...
A note on the square subgroups of decomposable torsion-free abelian groups of rank three
A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian...