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Optimal growth trajectories with finite carrying capacity

Overview of attention for article published in arXiv, August 2016
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About this Attention Score

  • Above-average Attention Score compared to outputs of the same age (63rd percentile)
  • High Attention Score compared to outputs of the same age and source (82nd percentile)

Mentioned by

twitter
6 tweeters

Citations

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2 Dimensions

Readers on

mendeley
9 Mendeley
Title
Optimal growth trajectories with finite carrying capacity
Published in
arXiv, August 2016
DOI 10.1103/physreve.94.022315
Pubmed ID
Authors

F. Caravelli, L. Sindoni, F. Caccioli, C. Ududec

Abstract

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Twitter Demographics

The data shown below were collected from the profiles of 6 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 9 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
France 1 11%
Unknown 8 89%

Demographic breakdown

Readers by professional status Count As %
Researcher 3 33%
Student > Ph. D. Student 2 22%
Student > Doctoral Student 1 11%
Student > Master 1 11%
Unknown 2 22%
Readers by discipline Count As %
Physics and Astronomy 3 33%
Mathematics 2 22%
Agricultural and Biological Sciences 1 11%
Unknown 3 33%

Attention Score in Context

This research output has an Altmetric Attention Score of 3. 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 24 August 2016.
All research outputs
#4,453,545
of 14,546,169 outputs
Outputs from arXiv
#97,840
of 557,380 outputs
Outputs of similar age
#89,237
of 262,269 outputs
Outputs of similar age from arXiv
#2,620
of 15,899 outputs
Altmetric has tracked 14,546,169 research outputs across all sources so far. This one is in the 49th percentile – i.e., 49% of other outputs scored the same or lower than it.
So far Altmetric has tracked 557,380 research outputs from this source. They receive a mean Attention Score of 3.9. This one has done well, scoring higher than 81% 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 262,269 tracked outputs that were published within six weeks on either side of this one in any source. This one has gotten more attention than average, scoring higher than 63% of its contemporaries.
We're also able to compare this research output to 15,899 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 82% of its contemporaries.