A Comparison of the Maximum Entropy Principle Across Biological Spatial Scales

Abstract

Despite their differences, biological systems at different spatial scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are often hard to grasp due to the highly specialized nature of modern science and the parcelled terminology employed by various scientific sub-disciplines. To explore these common organizational features, this paper provides a comparative study of diverse applications of the maximum entropy principle, which has found many uses at different biological spatial scales ranging from amino acids up to societies. By presenting these studies under a common approach and language, this paper aims to establish a unified view over these seemingly highly heterogeneous scenarios.

Inferring excitation-inhibition dynamics using a maximum entropy model unifying brain structure and function

“…In this work, we first convert our BOLD time series to z-scores, ensuring that our BOLD date is represented as zero-mean with unitary variance, without altering the correlations between brain regions. As maximum entropy models of neural activity are developed based on Ising dynamics, studies investigating pairwise interactions using BOLD time course data are binarized to define activation states (either +1 for active, or −1 for inactive) in both simulated and empirical fMRI-based studies ( Ashourvan et al, 2021 ; Cofré et al, 2019 ; Ezaki et al, 2020 ; Ezaki et al, 2017 ; Gu et al, 2018 ; Nghiem et al, 2018 ; Niu et al, 2019 ; Watanabe et al, 2013 ). We will show how the binarization strategy may be validated using Monte Carlo simulations, whereby we use the inferred interaction networks to reconstruct functional correlations.…”

Effects of intraspecific cooperative interactions in large ecosystems

“…Our outcomes can therefore lead to wide-ranging applications in population dynamics, genetics, epidemiology up to cancer evolution thanks also to recent advances in modern engineering and synthetic biology. Maximum entropy principle [50] can be for instance employed for inferring model parameters -as the Allee threshold, which allows one to select one minimum or the other depending on the initial conditions -from large-scale biological data-set and for reconstructing the optimal probability distribution compatible with external constraints, i.e. limitation of resources, multi-level bottom-up structures.…”

To Be or to Have Been Lucky, That Is the Question

“…Using the prevalence and the twin concordance rate of the disease D, we have access to, and only to, the mean Φ and dispersion Σ 2 of f (p). The principle of maximum entropy then provides us with the least arbitrary distribution [16,17]. Dowson and Wragg proved [18] that in the class P of absolutely continuous probability distributions on [0, 1] with given first and second moments (i.e., given mean and variance), there exists a distribution in P which maximizes the entropy…”