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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Lagrangian Betweenness As A Measure Of Bottlenecks In Dynamical Systems With Oceanographic Examples, Enrico Ser-Giacomi, Alberto Baudena, Vincent Rossi, Mick Follows, Sophie Clayton, Ruggero Vasile, Cristóbal López, Emilio Hernández-García
Lagrangian Betweenness As A Measure Of Bottlenecks In Dynamical Systems With Oceanographic Examples, Enrico Ser-Giacomi, Alberto Baudena, Vincent Rossi, Mick Follows, Sophie Clayton, Ruggero Vasile, Cristóbal López, Emilio Hernández-García
OES Faculty Publications
The study of connectivity patterns in networks has brought novel insights across diverse fields ranging from neurosciences to epidemic spreading or climate. In this context, betweenness centrality has demonstrated to be a very effective measure to identify nodes that act as focus of congestion, or bottlenecks, in the network. However, there is not a way to define betweenness outside the network framework. By analytically linking dynamical systems and network theory, we provide a trajectory-based formulation of betweenness, called Lagrangian betweenness, as a function of Lyapunov exponents. This extends the concept of betweenness beyond the context of network theory relating hyperbolic …
Fibration Symmetries Uncover The Building Blocks Of Biological Networks, Flaviano Morone, Ian Leifer, Hernán A. Makse
Fibration Symmetries Uncover The Building Blocks Of Biological Networks, Flaviano Morone, Ian Leifer, Hernán A. Makse
Publications and Research
A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these networks as a set of input trees, one for each node, which contains all pathways along which information can be transmitted in the network. In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional building blocks called fibers. Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity. Each …
Entropy And The Complexity Of Graphs Revisited, Abbe Mowshowitz, Matthias Dehmer
Entropy And The Complexity Of Graphs Revisited, Abbe Mowshowitz, Matthias Dehmer
Publications and Research
This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures) and extrinsic (e.g., Körner entropy) variants of entropy-based models are discussed in some detail.