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Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Published on: December 15, 2023

Complex network view of evolving manifolds.

Diamantino C da Silva¹, Ginestra Bianconi², Rui A da Costa¹

¹Departamento de Física da Universidade de Aveiro & I3N, Campus Universitário de Santiago, Aveiro 3810-193, Portugal.

Physical Review. E

|May 20, 2018

Summary

This summary is machine-generated.

This study explores complex networks from evolving manifolds, revealing diverse architectures like small-world networks. Simulations characterize geometries, dimensions, and distributions of these random networks.

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Area of Science:

Complex Systems
Network Science
Computational Geometry

Background:

Complex networks are fundamental in various scientific domains.
Understanding the geometry and topology of evolving networks is crucial.

Purpose of the Study:

To investigate the architectures and geometries of complex networks generated from triangulations and simplicial complexes.
To characterize the local structural properties of these evolving networks.

Main Methods:

Stochastic application of network transformations on triangulations and simplicial complexes.
Extensive numerical simulations to explore network growth and equilibrium states.
Characterization of Hausdorff and spectral dimensions, degree distributions, and structural correlations.

Main Results:

Discovered a diverse range of network architectures, including small-world networks.
Identified networks with finite dimensions, some exceeding the original manifold dimensionality.
Observed spectral dimensions ranging from approximately 1.4 to infinity for evolving triangulations.
Modeled evolving simplicial complexes, such as an h-holed torus, exhibiting small-world properties and heavy-tailed degree distributions.

Conclusions:

The study reveals a rich variety of network architectures and geometries arising from manifold-based transformations.
Evolving complex networks can exhibit complex topological and dimensional properties, including small-world characteristics and heavy-tailed distributions.