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Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

Overview of attention for article published in Bulletin of Mathematical Biology, March 2010
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  • In the top 25% of all research outputs scored by Altmetric
  • Good Attention Score compared to outputs of the same age (79th percentile)
  • High Attention Score compared to outputs of the same age and source (90th percentile)

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1 policy source
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1 X user
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1 Wikipedia page

Citations

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188 Dimensions

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88 Mendeley
Title
Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks
Published in
Bulletin of Mathematical Biology, March 2010
DOI 10.1007/s11538-010-9517-4
Pubmed ID
Authors

David F. Anderson, Gheorghe Craciun, Thomas G. Kurtz

Abstract

We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists so long as the corresponding chemical network is weakly reversible and has a deficiency of zero. The main parameter of the stationary distribution for the stochastically modeled system is a complex balanced equilibrium value for the corresponding deterministically modeled system. We also generalize our main result to some non-mass-action kinetics.

X Demographics

X Demographics

The data shown below were collected from the profile of 1 X user who shared this research output. Click here to find out more about how the information was compiled.
Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 88 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 5 6%
United Kingdom 1 1%
Germany 1 1%
Australia 1 1%
Unknown 80 91%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 25 28%
Researcher 16 18%
Professor 12 14%
Student > Doctoral Student 7 8%
Student > Master 6 7%
Other 12 14%
Unknown 10 11%
Readers by discipline Count As %
Mathematics 24 27%
Physics and Astronomy 16 18%
Agricultural and Biological Sciences 10 11%
Computer Science 8 9%
Engineering 7 8%
Other 11 13%
Unknown 12 14%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 7. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 20 December 2021.
All research outputs
#4,662,554
of 24,717,692 outputs
Outputs from Bulletin of Mathematical Biology
#141
of 1,169 outputs
Outputs of similar age
#19,083
of 99,200 outputs
Outputs of similar age from Bulletin of Mathematical Biology
#1
of 11 outputs
Altmetric has tracked 24,717,692 research outputs across all sources so far. Compared to these this one has done well and is in the 80th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 1,169 research outputs from this source. They receive a mean Attention Score of 5.0. This one has done well, scoring higher than 87% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 99,200 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 79% of its contemporaries.
We're also able to compare this research output to 11 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 90% of its contemporaries.