Phase transitions in Pareto optimal complex networks.

@article{Seoane2015PhaseTI,
  title={Phase transitions in Pareto optimal complex networks.},
  author={Lu{\'i}s F. Seoane and Ricard V. Sol{\'e}},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={92 3},
  pages={
          032807
        }
}
  • L. F. Seoane, R. Solé
  • Published 26 May 2015
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring… 
View on PubMed
arxiv.org
28 Citations
Background Citations
10
Methods Citations
1

Figures from this paper

28 Citations

Evolving complexity: how tinkering shapes cells, software and ecological networks
TLDR
This analysis suggests a serious consideration of the role played by selection as the origin of network topology and suggests that the amplification processes associated with reuse might shape these graphs at the topological level.
Multiobjective Optimization and Phase Transitions
TLDR
A robust framework is summarized that accounts for phase transitions located through SOO techniques and indicates what MOO features resolutely lead to phase transitions, suggesting that the similarities between transitions in MOO-SOO and Statistical Mechanics go beyond mere coincidence.
The Phenotypes of Fluctuating Flow: Development of Distribution Networks in Biology and the Trade-off between Efficiency, Cost, and Resilience
TLDR
It is shown how hierarchically organized reticulation can be generated and maintained through spatially collective load fluctuations on a particular length scale and identified the Pareto-efficient front that evolution is expected to favor and select for.
Fate of Duplicated Neural Structures
TLDR
This work focuses on the fate of duplicated neural circuits, and derives phase diagrams and (phase-like) transitions between single and duplicated circuits, which constrain evolutionary paths to complex cognition.
The morphospace of language networks
TLDR
A detailed analysis of network properties on a generic model of a communication code reveals a rather complex and heterogeneous morphospace of language graphs and indicates a surprisingly simple structure in human language unless particles with the ability of naming any other concept are introduced in the vocabulary.
Phase Transitions in Wireless MESH Networks and Their Application in Early Detection of Network Coherence Loss
TLDR
The paper presents the use of phase transition analysis for early detection of network coherence loss at the physical layer level and a new mechanism for assessing the level of network communication and an active method of preventing its failure using the arbiter and a set of limited diagnostic information are described.
Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis
TLDR
A comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: the automatic design of synthetic oscillators from a library of biological parts and the inference of design principles based on Pareto optimality concepts.
Pareto Optimality in Multilayer Network Growth.
TLDR
The results shed light on the fundamental role played by multiobjective optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes.
Optimization of spatial complex networks
Aging, computation, and the evolution of neural regeneration processes
TLDR
The organism’s lifespan and the external damage rates are found to act as an evolutionary pressure that improve the exploration of the space of solutions and poses tighter optimality conditions.
...
...

References

SHOWING 1-10 OF 58 REFERENCES
Optimization in Complex Networks
TLDR
Here it is shown that a simple optimization process can also account for the observed regularities displayed by most complex nets, and constraints provide a new explanation for scaling of exponent about -3.3.
Exploring the Morphospace of Communication Efficiency in Complex Networks
TLDR
This work defines analytic measures directed at characterizing network communication when signals flow in a random walk process and identifies specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes.
Emergence of hierarchy in cost-driven growth of spatial networks
TLDR
A generic model for the growth of spatial networks based on the general concept of cost–benefit analysis is introduced and it is shown that spatial hierarchy emerges naturally, with structures composed of various hubs controlling geographically separated service areas, and appears as a large-scale consequence of local cost– benefit considerations.
Collective dynamics of ‘small-world’ networks
TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
The Evolutionary Origins of Hierarchy
TLDR
The results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability.
Spatial Networks
  • M. Barthelemy
  • Computer Science
    Encyclopedia of Social Network Analysis and Mining
  • 2014
Network morphospace
TLDR
Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.
Network structures from selection principles.
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the…
Small worlds: how and why.
  • N. Mathias, V. Gopal
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
This work uses simulated annealing to study the properties of a randomly rewired network as the relative tradeoff between wiring and connectivity is varied, and finds an alternate route to small-world behavior through the formation of hubs, small clusters where one vertex is connected to a large number of neighbors.
Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits
TLDR
It is shown that human brain structural networks, and the nervous system of the nematode C. elegans, also obey Rent's rule, and exhibit some degree of hierarchical modularity, suggesting that these principles of nervous system design are highly conserved.
...
...