English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a Markov process in continuous time with a finite number ofdiscrete states. The time-dependent probabilities of being in any state of theMarkov chain are governed by a set of ordinary differential equations, whosedimension might be large even for trivial systems. Here, we derive a reducedODE set that accurately approximates the probabilities of subspaces of interestwith a known error bound. Our methodology is based on model reduction bybalanced truncation and can be considerably more computationally efficient thanthe Finite State Projection Algorithm (FSP) when used for obtaining transientresponses. We show the applicability of our method by analysing stochasticchemical reactions. First, we obtain a reduced order model for theinfinitesimal generator of a Markov chain that models a reversible,monomolecular reaction. In such an example, we obtain an approximation of theoutput of a model with 301 states by a reduced model with 10 states. Later, weobtain a reduced order model for a catalytic conversion of substrate to aproduct; and compare its dynamics with a stochastic Michaelis-Mentenrepresentation. For this example, we highlight the savings on the computationalload obtained by means of the reduced-order model. Finally, we revisit thesubstrate catalytic conversion by obtaining a lower-order model thatapproximates the probability of having predefined ranges of product molecules.

Order Reduction of the Chemical Master Equation via Balanced Realisation