Gerber, S. and Olsson, S. and Noé, F. and Horenko, I. (2018) A scalable approach to the computation of invariant measures for highdimensional Markovian systems. Sci. Rep., 8 (1796). ISSN 20452322

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Official URL: http://dx.doi.org/10.1038/s41598018198634
Abstract
The Markovian invariant measure is a central concept in many disciplines. Conventional numerical techniques for datadriven computation of invariant measures rely on estimation and further numerical processing of a transition matrix. Here we show how the quality of datadriven estimation of a transition matrix crucially depends on the validity of the statistical independence assumption for transition probabilities. Moreover, the cost of the invariant measure computation in general scales cubically with the dimension  and is usually unfeasible for realistic highdimensional systems. We introduce a method relaxing the independence assumption of transition probabilities that scales quadratically in situations with latent variables. Applications of the method are illustrated on the Lorenz63 system and for the molecular dynamics (MD) simulation data of the alphasynuclein protein. We demonstrate how the conventional methodologies do not provide good estimates of the invariant measure based upon the available alphasynuklein MD data. Applying the introduced approach to these MD data we detect two robust metastable states of alphasynuclein and a linear transition between them, involving transient formation of secondary structure, qualitatively consistent with previous purely experimental reports.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint 09/2017 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  2114 
Deposited By:  Silvia Hoemke 
Deposited On:  29 Sep 2017 11:41 
Last Modified:  20 Feb 2018 13:56 
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