Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks
Henrik Ronellenfitsch, Eleni Katifori
(Submitted on 1 Jun 2016 (v1), last revised 22 Sep 2016 (this version, v4))
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that natural selection slowly guides the network towards an optimized state. However, general coarse grained models for flow networks with local positive feedback rules for the vessel conductivity typically get trapped in low efficiency, local minima. In this work we show how the growth of the underlying tissue, coupled to the dynamical equations for network development, can drive the system to a dramatically improved optimal state. This general model provides a surprisingly simple explanation for the appearance of highly optimized transport networks in biology such as leaf and animal vasculature.
Comments: 5 pages, 4 figures. Accepted at PRL
Subjects: Biological Physics (physics.bio-ph); Adaptation and Self-Organizing Systems (nlin.AO); Tissues and Organs (q-bio.TO)
Journal reference: Phys. Rev. Lett. 117, 138301 (2016)
Cite as: arXiv:1606.00331 [physics.bio-ph]
(or arXiv:1606.00331v4 [physics.bio-ph] for this version)
Submission history
From: Henrik Ronellenfitsch [view email]
[v1] Wed, 1 Jun 2016 15:47:47 GMT (1802kb,D)
[v2] Wed, 6 Jul 2016 19:13:26 GMT (2814kb,AD)
[v3] Wed, 24 Aug 2016 15:56:14 GMT (4625kb,AD)
[v4] Thu, 22 Sep 2016 19:58:19 GMT (4625kb,AD)
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