PMID: 11607293May 15, 1992Paper

Approximating Markov chains

Proceedings of the National Academy of Sciences of the United States of America
S Pincus

Abstract

A common framework of finite state approximating Markov chains is developed for discrete time deterministic and stochastic processes. Two types of approximating chains are introduced: (i) those based on stationary conditional probabilities (time averaging) and (ii) transient, based on the percentage of the Lebesgue measure of the image of cells intersecting any given cell. For general dynamical systems, stationary measures for both approximating chains converge weakly to stationary measures for the true process as partition width converges to 0. From governing equations, transient chains and resultant approximations of all n-time unit probabilities can be computed analytically, despite typically singular true-process stationary measures (no density function). Transition probabilities between cells account explicitly for correlation between successive time increments. For dynamical systems defined by uniformly convergent maps on a compact set (e.g., logistic, Henon maps), there also is weak continuity with a control parameter. Thus all moments are continuous with parameter change, across bifurcations and chaotic regimes. Approximate entropy is seen as the information-theoretic rate of entropy for approximating Markov chains and ...Continue Reading

References

Apr 1, 1991·Biophysical Journal·D T KaplanA L Goldberger
Jan 21, 1985·Journal of Theoretical Biology·W M Schaffer, M Kot
Mar 15, 1991·Proceedings of the National Academy of Sciences of the United States of America·S M Pincus

❮ Previous
Next ❯

Citations

Sep 9, 2006·Medical & Biological Engineering & Computing·James McNames, Mateo Aboy
Aug 1, 1994·Mathematical Biosciences·S M Pincus
Mar 9, 1999·Clinical Physiology·M K YumY S Yun
Nov 26, 1996·Proceedings of the National Academy of Sciences of the United States of America·S M PincusJ D Veldhuis
Jul 13, 2006·IEEE Transactions on Bio-medical Engineering·Pablo Casaseca-de-la-HigueraCarlos Alberola-López
Oct 21, 2005·IEEE Transactions on Bio-medical Engineering·Roberto HorneroBrahm Goldstein
Jan 3, 2006·Artificial Intelligence in Medicine·Félix del CampoDaniel Alvarez
Oct 16, 2004·American Journal of Physiology. Regulatory, Integrative and Comparative Physiology·Peter Y LiuJohannes D Veldhuis
Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E RaccaL Ridolfi
Feb 1, 1997·The American Journal of Physiology·O SchmitzS M Pincus
Jul 28, 2017·Journal of the Royal Society, Interface·Ankit GuptaMustafa Khammash
Jan 19, 2002·Annals of the New York Academy of Sciences·S M Pincus
Mar 5, 1998·The American Journal of Physiology·E GeversJ D Veldhuis
May 28, 2019·Entropy·Alfonso Delgado-Bonal, Alexander Marshak
Jan 1, 1996·The American Journal of Physiology·S M PincusJ D Veldhuis

❮ Previous
Next ❯

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Proceedings of the National Academy of Sciences of the United States of America
Steve Pincus, B H Singer
Proceedings of the National Academy of Sciences of the United States of America
S Pincus, R E Kalman
Annals of Noninvasive Electrocardiology : the Official Journal of the International Society for Holter and Noninvasive Electrocardiology, Inc
Sudhir Ken MehtaElizabeth S Kaufman
Proceedings of the National Academy of Sciences of the United States of America
Steve Pincus, B H Singer
© 2021 Meta ULC. All rights reserved