English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Using an information theoretic point of view, we investigate how a dynamicsacting on a network can be coarse grained through the use of graph partitions.Specifically, we are interested in how aggregating the state space of a Markovprocess according to a partition impacts on the thus obtained lower-dimensionaldynamics. We highlight that for a dynamics on a particular graph there may bemultiple coarse grained descriptions that capture different, incomparablefeatures of the original process. For instance, a coarse graining induced byone partition may be commensurate with a time-scale separation in the dynamics,while another coarse graining may correspond to a different lower-dimensionaldynamics that preserves the Markov property of the original process. Takinginspiration from the literature of Computational Mechanics, we find that aconvenient tool to summarise and visualise such dynamical properties of acoarse grained model (partition) is the entrogram. The entrogram gatherscertain information-theoretic measures, which quantify how information flowsacross time steps. These information theoretic quantities include the entropyrate, as well as a measure for the memory contained in the process, i.e., howwell the dynamics can be approximated by a first order Markov process. We usethe entrogram to investigate how specific macro-scale connection patterns inthe state-space transition graph of the original dynamics result in desirableproperties of coarse grained descriptions. We thereby provide a freshperspective on the interplay between structure and dynamics in networks, andthe process of partitioning from an information theoretic perspective. We focuson networks that may be approximated by both a core-periphery or a clusteredorganization, and highlight that each of these coarse grained descriptions cancapture different aspects of a Markov process acting on the network.

Entrograms and coarse graining of dynamics on complex networks