Inferring pattern generators on networks

Abstract Given a pattern on a network, i.e. a subset of nodes, can we assess, whether they are randomly distributed on the network or have been generated in a systematic fashion following the network architecture? This question is at the core of network-based data analyses across a range of disciplines – from incidents of infection in social networks to sets of differentially expressed genes in biological networks. Here we introduce generic ‘pattern generators’ based on an Eden growth model. We assess the capacity of different pattern measures like connectivity, edge density or various average distances, to infer the parameters of the generator from the observed patterns. Some measures perform consistently better than others in inferring the underlying pattern generator, while the best performing measures depend on the global topology of the underlying network. Moreover, we show that pattern generator inference remains possible in case of limited visibility of the patterns.

[1]  Marc-Thorsten Hütt,et al.  Toward a theory of coactivation patterns in excitable neural networks , 2018, PLoS Comput. Biol..

[2]  M. Hütt,et al.  Generative network model of transcriptome patterns in disease cohorts with tunable signal strength , 2020, Physical Review Research.

[3]  Marc-Thorsten Hütt,et al.  Connectivity and complex systems: learning from a multi-disciplinary perspective , 2018, Applied Network Science.

[4]  Dietrich Stauffer,et al.  Surface structure and anisotropy of Eden clusters , 1985 .

[5]  Benjamin J. Raphael,et al.  Network propagation: a universal amplifier of genetic associations , 2017, Nature Reviews Genetics.

[6]  D. Stauffer.  COMMENT: Monte Carlo study of biased diffusion at the percolation threshold , 1985 .

[7]  D. Stauffer.  Monte Carlo Study of Density Profile, Radius, and Perimeter for Percolation Clusters and Lattice Animals , 1978 .

[8]  Damian Szklarczyk,et al.  STRING v11: protein–protein association networks with increased coverage, supporting functional discovery in genome-wide experimental datasets , 2018, Nucleic Acids Res..

[9]  Livia Perfetto,et al.  SIGNOR 2.0, the SIGnaling Network Open Resource 2.0: 2019 update , 2019, Nucleic Acids Res..

[10]  Dietrich Stauffer,et al.  Self-similarity and covered neighborhoods of fractals: A random walk test , 1993 .

[11]  Marc-Thorsten Hütt,et al.  A network perspective on metabolic inconsistency , 2012, BMC Systems Biology.

[12]  Marc-Thorsten Hütt,et al.  A closer look at the apparent correlation of structural and functional connectivity in excitable neural networks , 2015, Scientific Reports.

[13]  B. Bollobás.  The evolution of random graphs , 1984 .

[14]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[15]  Wei Zhang,et al.  Systematic Evaluation of Molecular Networks for Discovery of Disease Genes. , 2018, Cell systems.

[16]  Dietrich Stauffer,et al.  Diffusion on random systems above, below, and at their percolation threshold in two and three dimensions , 1984 .

[17]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[18]  Martin Rosvall,et al.  Ranking and clustering of nodes in networks with smart teleportation , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Marc-Thorsten Hütt,et al.  Understanding genetic variation - the value of systems biology. , 2014, British journal of clinical pharmacology.

[20]  Kara Dolinski,et al.  The BioGRID interaction database: 2019 update , 2018, Nucleic Acids Res..

[21]  Yamir Moreno,et al.  Topological effects of data incompleteness of gene regulatory networks , 2012, BMC Systems Biology.

[22]  D. Heermann,et al.  Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment , 2007, Journal of biological physics.

[23]  A. Barabasi,et al.  Uncovering disease-disease relationships through the incomplete interactome , 2015, Science.

[24]  Ronan M. T. Fleming,et al.  A community-driven global reconstruction of human metabolism , 2013, Nature Biotechnology.

[25]  D. Helbing,et al.  The Hidden Geometry of Complex, Network-Driven Contagion Phenomena , 2013, Science.

[26]  Marc-Thorsten Hütt,et al.  Distinct metabolic network states manifest in the gene expression profiles of pediatric inflammatory bowel disease patients and controls , 2016, Scientific Reports.

[27]  Avlant Nilsson,et al.  Recon3D: A Resource Enabling A Three-Dimensional View of Gene Variation in Human Metabolism , 2018, Nature Biotechnology.

[28]  Marc-Thorsten Hütt,et al.  Analog regulation of metabolic demand , 2011, BMC Systems Biology.

[29]  Muhammad Sahimi,et al.  Diffusion in scale-free networks with annealed disorder. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[31]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[33]  K. Kułakowski,et al.  Errata: "Competing contact processes on homogeneous networks with tunable clusterization" , 2012, 1209.4034.