Demongeot Jacques, Jelassi Mariem, Hazgui Hana, Ben Miled Slimane, Bellamine Ben Saoud Narjes, Taramasco Carla
Team AGIM (Autonomy, Gerontechnology, Imaging, Modelling & Tools for e-Gnosis Medical), Laboratory AGEIS, University Grenoble Alpes, Faculty of Medicine, La Tronche 38700, France.
Escuela de Ingeniería Civil en Informática, Universidad de Valparaíso, General Cruz 222, Valparaíso 2340000, Chile.
Entropy (Basel). 2018 Jan 13;20(1):36. doi: 10.3390/e20010036.
Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction graph associated to its Jacobian matrix , and also the concepts of frustrated nodes, positive or negative circuits of , kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.
用于不同尺度（分子、细胞和群体）生物应用的网络有不同类型：神经元网络、遗传网络和社会网络，但它们在连续微分形式（例如非线性威尔逊 - 考恩系统）以及离散布尔形式（例如非线性霍普菲尔德系统）中共享相同的动力学概念；在这两种情况下，与雅可比矩阵相关联的相互作用图的概念，以及受挫节点、 的正或负回路、动能、熵、吸引子、结构稳定性等概念，对于研究这些系统的动力学和鲁棒性都是相关且有用的。我们将给出一些适用于连续和离散生物网络的一般结果，然后研究三种新熵概念的一些具体应用：（i）吸引子熵，（ii）等时熵和（iii）熵中心性；在三个领域：涉及记忆唤起的神经网络、负责铁控制的遗传网络以及解释高中环境中肥胖传播的社会网络。
