2020
DOI: 10.3390/e22030312
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A Maximum Entropy Method for the Prediction of Size Distributions

Abstract: We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of constant size, which contains exit of balls and urns (or nodes and edges for the network case). Knowing mean size (degree) and turnover rate, the power law exponent and exponential cutoff can be derived. Our results are confirmed by simulations and by computation of exact p… Show more

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Cited by 5 publications
(7 citation statements)
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“…(2) MEP mixes hyperchaotic system with improved AES algorithm. First, the MEP function reads the data set after slicing and reads it in the way of key value pair [31]. <zej W in , value W in > represents the input key value…”
Section: Algorithm Designmentioning
confidence: 99%
“…(2) MEP mixes hyperchaotic system with improved AES algorithm. First, the MEP function reads the data set after slicing and reads it in the way of key value pair [31]. <zej W in , value W in > represents the input key value…”
Section: Algorithm Designmentioning
confidence: 99%
“…remembering that β i ≡ β i (λ i ) is defined by (46). To show that function ( 54) is a SPM we show that…”
Section: B the Expected Value Of The Replica Field Network Partition ...mentioning
confidence: 99%
“…For instance, using the heat bath analogy, where the energy states are related to the eigenvalues of a matrix representation of network structure, particles, which are in thermal equilibrium with the heat bath, begin to populate these energy states. Within this thermalization process, the energy states can be described by Maxwell-Boltzmann [40,46], Bose-Einstein [27,40], and Fermi-Dirac [40,[47][48][49][50] occupation statistics. On the other hand, in [35] the authors show that the partition function can be computed from the matrix characteristic polynomial.…”
Section: Introductionmentioning
confidence: 99%
“…Trees contain both branch lengths and information in the form of the tree topology or shape. Phylogenetic trees have been used in infectious disease to estimate the basic reproduction number [3], parameters of transmission models [4], aspects of underlying contact networks [5][6][7][8] and in densely sampled datasets even person-to-person transmission events and timing [9][10][11][12]. It is therefore natural to hypothesize that phylogenetic tree structures and branching patterns contain information about short-term growth and fitness.…”
Section: Introductionmentioning
confidence: 99%
“…Tree information is central in some predictive models for short-term influenza virus evolution and models of fitness [1,2]. However, the mapping between the phylogenetic tree structure and interpretable biological information can be subtle, [7,8,13,14] and trees do not directly reveal the short-term evolutionary trajectories of groups of taxa.…”
Section: Introductionmentioning
confidence: 99%