Unravelling the kinetics of time-resolved spectra by Matrix-Factorization without separability assumption and by Markov State Modeling with PCCA+ projection

Sechi, Renata

doi:10.17169/refubium-32500

Cited by 1 publication

(4 citation statements)

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“…Regarding the requirements of the SepFree NMF method, the non-negativity condition of the matrix W holds or not, depending on the kind of analyzed spectrum. For example, in transition absorption spectra, the intensities in W can be also negative [18].…”

Section: Sepfree Nmfmentioning

confidence: 99%

“…The MSM is underlying SepFree, thus the relation to EDMD and SepFree NMF gives the foundation to introduce how to compute the minimal memory effect by SepFree NMF. The relation between the two representations of the transition matrix with EDMD and SepFree NMF are analyzed in [18]. The concept of the minimal memory effect is based on the theory of the rebinding effect of [5].…”

Section: Relation Between Edmd and Sepfree Nmfmentioning

confidence: 99%

“…Furthermore, in the supplementary material section, a tutorial explains how to use the hereby presented method for the analysis of a dataset. This version of the SepFree NMF algorithm was developed in [18].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The SepFree NMF yields also a transition matrix K(τ) for the process [6]. Examining the transition matrix allows to understand the kinetic model underlying the reaction mechanism [18]. The crystallization process of this dataset is a sequential process.…”

Section: Raman Experiment-crystallization Of Paracetamol In Methanolmentioning

confidence: 99%

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SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data

2022

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This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.

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Section: Sepfree Nmfmentioning

confidence: 99%

Section: Relation Between Edmd and Sepfree Nmfmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Raman Experiment-crystallization Of Paracetamol In Methanolmentioning

confidence: 99%

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