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Embeddable Markov Matrices
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TL;DR: In this article, it was shown that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.
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Abstract: We give an account of some results, both old and new, about any $n\times n$ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.
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Non-Hermitian Physics
TL;DR: In this article, a review of non-Hermitian classical and quantum physics can be found, with an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-hermitian wave physics.
806
Is the General Time-Reversible Model Bad for Molecular Phylogenetics?
Jeremy G. Sumner,Peter D. Jarvis,Jesús Fernández-Sánchez,Bodie T. Kaine,Michael D. Woodhams,Barbara R. Holland +5 more
TL;DR: Examples are given that demonstrate why the general time-reversible GTR model may pose a problem for phylogenetic analysis and add GTR to the growing list of factors that are known to cause model misspecification in phylogenetics.
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Efficient maximum likelihood parameterization of continuous-time Markov processes
TL;DR: A maximum likelihood estimator is introduced for constructing continuous-time Markov processes over finite state-spaces from data observed at a finite time interval that is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models.
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Lie Markov models with purine/pyrimidine symmetry
TL;DR: This paper derives the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines—that is, models with purine/pyrimidine symmetry.
Gender and the business cycle: An analysis of labour markets in the US and UK
Giovanni Razzu,Carl Singleton +1 more
TL;DR: This article analyzed the contributing role of flows in the US and UK in the post-2008 recession period and found that the subsequent greater rise in male unemployment can mostly be explained by a less cyclical response of flows between employment and unemployment for women, especially the entry into unemployment.
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References
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The Representation of Social Processes by Markov Models
TL;DR: In this article, the authors consider a class of issues which are central to modeling social phenomena by continuous-time Markov structures and discuss how to select the specific structure from the list of alternatives which should be associated with the empirical process.