Characterising experimental time series using local intrinsic dimension

1995 ◽  
Vol 202 (2-3) ◽  
pp. 183-190 ◽  
Author(s):  
Thorsten M. Buzug ◽  
Jens von Stamm ◽  
Gerd Pfister
Author(s):  
Mikhail A. Mishchenko ◽  
Denis I. Bolshakov ◽  
Alexander S. Vasin ◽  
Valery V. Matrosov ◽  
Ilya V. Sysoev

2013 ◽  
Vol 10 (80) ◽  
pp. 20120935 ◽  
Author(s):  
Abdullah Hamadeh ◽  
Brian Ingalls ◽  
Eduardo Sontag

The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli . It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this property is known as fold-change detection (FCD). In the light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behaviour. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behaviour where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.


Author(s):  
Krzysztof Podlaski ◽  
Michał Durka ◽  
Tomasz Gwizdałła ◽  
Alicja Miniak-Górecka ◽  
Krzysztof Fortuniak ◽  
...  

Author(s):  
Takaaki Maehara ◽  
Mikio Nakai

This study employs topological methods to extract unstable fixed points in phase space from both numerical and experimental time series data. Conley index of an isolated invariant subset and the R-B method can determine unstable fixed points contained in strange attractor from numerical time series data. For experimental time series data, the theorem for the relationship between index pairs and Conley index enables one to predict them with acceptable accuracy. As a corollary, some results for Duffing oscillator and piecewise linear system are shown.


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