The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
DYNAMIC PROGRAMMING AND A NEW FORMALISM IN THE CALCULUS OF VARIATIONS
Open accessAbstract
Mutations are important because they provide raw material for evolution. Some types of mutations occur more often than others, and the strength of such mutational bias varies across species. It is not clear how this variation arises. We ...Biased mutation spectra are pervasive, with wide variation in the magnitude of mutational biases that influence genome evolution and adaptation. How do such diverse biases evolve? Our experiments show that changing the mutation spectrum allows populations ...
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The dynamical system can be written in the form of Bellman equation and solved backwards using gradient descent or its variants.
“However, since the desired wealth distribution is known at the initial timestep, the dynamical system can be written in the form of Bellman equation and solved backwards (Bellman, 1954) . For this, gradient descent or its variants such as stochastic gradient descent can be used, but we will leave the evaluation of the performance of these techniques with respect to our framework for future”
From Decentralized token economy theory (DeTEcT): token pricing, stability and governance for token economies (2023) · cites this paper as Bellman, 1954
Citations
Cites
On the theory of dynamic programming
Bellman, R. (1952) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.38.8.716 · Cited by 998
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Sadykhov, R., Goodell, G., De Montigny, D., Schoernig, M., & Treleaven, P. (2023) · Frontiers in Blockchain · doi:10.3389/fbloc.2023.1298330 · Cited by 7
“However, since the desired wealth distribution is known at the initial timestep, the dynamical system can be written in the form of Bellman equation and solved backwards (Bellman, 1954) .”
Method
Metadata
- Authors
- Bellman, R.
- Corresponding author
- Bellman, Richard
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 1954-04
- Volume
- 40
- Issue
- 4
- Pages
- 231-235
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC527981
- OpenAlex
- W2116556878
- Cited by
- 123
- References
- 1
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 8 · 2023: 10 · 2022: 16 · 2021: 9 · 2020: 9 · 2019: 8 · 2018: 6 · 2017: 5 · 2016: 8 · 2015: 4 · 2014: 4 · 2013: 1 · 2012: 1
- FWCI
- 15.81
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimization and Mathematical Programming
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Keywords
- dynamic programming, calculus of variations, variational formulation, optimal control
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