2017/04/28 by Tom Bertalan, Yan Wu, Bertalan, Tom +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Neuroscience · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Complex Network Analysis Techniques #Complex network #Computer science #Context (archaeology) #FOS: Physical sciences #Functional Brain Connectivity Studies #Gene Regulatory Network Analysis #Heterogeneous network #Node (physics) #Physics #Premise #Statistical physics #Theoretical computer science #nlin.CD
paper · pdf · doi:10.48550/arxiv.1705.00104
openalex publication_date 2017/04/28 · arxiv created 2017/04/29 · arxiv updated 2017/05/02 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Finding accurate reduced descriptions for large, complex, dynamically\nevolving networks is a crucial enabler to their simulation, analysis, and,\nultimately, design. Here we propose and illustrate a systematic and powerful\napproach to obtaining good collective coarse-grained observables-- variables\nsuccessfully summarizing the detailed state of such networks. Finding such\nvariables can naturally lead to successful reduced dynamic models for the\nnetworks. The main premise enabling our approach is the assumption that the\nbehavior of a node in the network depends (after a short initial transient) on\nthe node identity: a set of descriptors that quantify the node properties,\nwhether intrinsic (e.g. parameters in the node evolution equations) or\nstructural (imparted to the node by its connectivity in the particular network\nstructure). The approach creates a natural link with modeling and\n"computational enabling technology" developed in the context of Uncertainty\nQuantification. In our case, however, we will not focus on ensembles of\ndifferent realizations of a problem, each with parameters randomly selected\nfrom a distribution. We will instead study many coupled heterogeneous units,\neach characterized by randomly assigned (heterogeneous) parameter value(s). One\ncould then coin the term Heterogeneity Quantification for this approach, which\nwe illustrate through a model dynamic network consisting of coupled oscillators\nwith one intrinsic heterogeneity (oscillator individual frequency) and one\nstructural heterogeneity (oscillator degree in the undirected network). The\ncomputational implementation of the approach, its shortcomings and possible\nextensions are also discussed.\n