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Balancing building and maintenance costs in growing transport networks
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
UCL, Ctr Adv Spatial Anal, 90 Tottenham Court Rd, London W1T 4TJ, England.
UPMC Univ Paris 06, Sorbonne Univ, UMR 7238, Computat & Quantitat Biol, 15 Rue Ecole Med, Paris, France.; Univ Milan, Dipartimento Fis, Via Celoria 16, I-20133 Milan, Italy..
2017 (English)In: Physical revview E, ISSN 2470-0045, Vol. 96, no 3, article id 032316Article in journal (Refereed) Published
Abstract [en]

The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost. By varying the coefficient of the combination, the model interpolates between global and local length minimization, i.e., between minimum spanning trees and a local version known as dynamical minimum spanning trees. We show that cost balance within this ensemble of dynamical networks is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport efficiency, and of optimal strategies of construction. At the transition between two qualitatively different regimes, the dynamics builds up power-law distributed waiting times between global rearrangements, indicating a point of nonoptimality. Finally, we use our model as a framework to analyze empirical ant trail networks, showing its relevance as a null model for cost-constrained network formation.

Place, publisher, year, edition, pages
2017. Vol. 96, no 3, article id 032316
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-303938DOI: 10.1103/PhysRevE.96.032316ISI: 000411991200004OAI: oai:DiVA.org:uu-303938DiVA, id: diva2:974648
Available from: 2016-09-27 Created: 2016-09-27 Last updated: 2017-12-20Bibliographically approved
In thesis
1. Modelling collective movement and transport network formation in living systems
Open this publication in new window or tab >>Modelling collective movement and transport network formation in living systems
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The emergence of collective patterns from repeated local interactions between individuals is a common feature to most living systems, spanning a variety of scales from cells to animals and humans. Subjects of this thesis are two aspects of emergent complexity in living systems: collective movement and transport network formation. For collective movement, this thesis studies the role of movement-mediated information transfer in fish decision-making. The second project on collective movement takes inspiration from granular media and soft mode analysis and develops a new approach to describe the emergence of collective phenomena from physical interactions in extremely dense crowds. As regards transport networks, this thesis proposes a model of network growth to extract simple, biologically plausible rules that reproduce topological properties of empirical ant trail networks.  In the second project on transport networks, this thesis starts from the simple rule of “connecting each new node to the closest one”, that describes ants building behavior, to study how balancing local building costs and global maintenance costs influences the growth and topological properties of transport networks. These projects are addressed through a modeling approach and with the aim of identifying minimal sets of basic mechanisms that are most likely responsible of large-scale complex patterns. Mathematical models are always based on empirical observations and are, when possible, compared to experimental data.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2016. p. 56
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 96
Keywords
animal collective behaviour, transport networks, crowd dynamics, complex systems, ants, fish
National Category
Mathematics
Research subject
Applied Mathematics and Statistics
Identifiers
urn:nbn:se:uu:diva-303943 (URN)978-91-506-2599-8 (ISBN)
Public defence
2016-11-25, Häggsalen, Ångströmslaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2016-11-03 Created: 2016-09-27 Last updated: 2016-11-15

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