Damage and fluctuations induce loops in optimal transport networks
arXiv:0906.0006 · doi:10.1103/PhysRevLett.104.048704
Abstract
Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.
References in corpus (5)
- Fluctuations and redundancy in optimal transport networks
- Structure, Scaling and Phase Transition in the Optimal Transport Network
- Architecture of optimal transport networks
- Structure of Optimal Transport Networks Subject to a Global Constraint
- The role of elastic stresses on leaf venation morphogenesis
Cited by in corpus (107)
- Spatial Networks
- Fluctuations and redundancy in optimal transport networks
- Network Analysis of Particles and Grains
- Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks
- Limited Urban Growth: London's Street Network Dynamics since the 18th Century
- Learning without neurons in physical systems
- Critical links and nonlocal rerouting in complex supply networks
- Self-healing networks: redundancy and structure
- Quantifying loopy network architectures
- Soliton solutions of nonlinear Schroedinger equation on simple networks
- Weighted simplicial complexes and their representation power of higher-order network data and topology
- Rockfall susceptibility and network-ranked susceptibility along the Italian railway
- The limits of multifunctionality in tunable networks
- A Dual Method for Computing Power Transfer Distribution Factors
- Cycle flows and multistabilty in oscillatory networks: an overview
- Phenotypes of vascular flow networks
- Inhibiting failure spreading in complex networks
- Nonlocal failures in complex supply networks by single link additions
- Hierarchical ordering of reticular networks
- Topological phenotypes constitute a new dimension in the phenotypic space of leaf venation networks
- Quieting a noisy antenna reproduces photosynthetic light harvesting spectra
- Topological data analysis of continuum percolation with disks
- Optimal noise-canceling networks
- Interplay of river and tidal forcings promotes loops in coastal channel networks
- Non-Local Impact of Link Failures in Linear Flow Networks
- Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks
- Turing patterns on discrete topologies: from networks to higher-order structures
- Stochastic cycle selection in active flow networks
- Scaling of phloem structure and optimality of photoassimilate transport in conifer needles
- Dirac synchronization is rhythmic and explosive
- Towards the Generation of Synthetic Images of Palm Vein Patterns: A Review
- Diffusion-driven instability of topological signals coupled by the Dirac operator
- Flow rate of transport network controls uniform metabolite supply to tissue
- Resilience in Hierarchical Fluid Flow Networks
- Enhancing synchronization by optimal correlated noise
- Discontinuous transition to loop formation in optimal supply networks
- Optimal transport in multilayer networks for traffic flow optimization
- Transitions from trees to cycles in adaptive flow networks
- Revealing structure-function relationships in functional flow networks via persistent homology
- Urban transportation networks and optimal transport-based infrastructures: similarity and economy of scale
- Resiliently evolving supply-demand networks
- Transport in simple networks described by integrable discrete nonlinear SchrÄodinger equation
- Branching principles of animal and plant networks identified by combining extensive data, machine learning, and modeling
- Distributed flow optimization and cascading effects in weighted complex networks
- Optimal elasticity of biological networks
- Resilience of three-dimensional sinusoidal networks in liver tissue
- Optimal Transport Flows for Distributed Production Networks
- Asymmetries arising from the space-filling nature of vascular networks
- Network extraction by routing optimization
- Topological theory of resilience and failure spreading in flow networks
- Designing optimal networks for multi-commodity transport problem
- Central loops in random planar graphs
- Hysteretic percolation from locally optimal individual decisions
- Extracting Hidden Hierarchies in 3D Distribution Networks
- Finding the Resistance Distance and Eigenvector Centrality from the Network's Eigenvalues
- From State Estimation to Network Reconstruction
- Global topological synchronization of weighted simplicial complexes
- A growth model for water distribution networks with loops
- Multicommodity routing optimization for engineering networks
- Fair sharing of resources in a supply network with constraints
- Collective effects of link failures in linear flow networks
- Quantitative analyses of the plant cytoskeleton reveal underlying organizational principles
- Temporal Evolution of Flow in Pore-Networks: From Homogenization to Instability
- Cohesive urban bicycle infrastructure design through optimal transport routing in multilayer networks
- Emergence of biological transportation networks as a self-regulated process
- Intermittent air invasion in pervaporating compliant microchannels
- Transitions in spatial networks
- Infrastructure adaptation and emergence of loops in network routing with time-dependent loads
- Emergent properties and the multiscale characterization challenge in condensed matter, from crystals to complex materials: a Review
- Bilevel Optimization for Traffic Mitigation in Optimal Transport Networks
- Comparing spatial networks: A 'one size fits all' efficiency-driven approach
- Dual communities in spatial networks
- System Size Identification from Sinusoidal Probing in Diffusive Complex Networks
- Dynamic cost allocation allows network-forming forager to switch between search strategies
- How to Pare a Pair: Topology Control and Pruning in Intertwined Complex Networks
- Comparison of two aspects of a PDE model for biological network formation
- Breakthrough-Induced Loop Formation in Evolving Transport Networks
- Antifragility of stochastic transport on networks with damage
- Convergence properties of optimal transport-based temporal networks
- Ultrametricity of optimal transport substates for multiple interacting paths over a square lattice network
- Antifragility and response to damage in the synchronization of oscillators on networks
- Memory capacity of adaptive flow networks
- Optimal transport with constraints: from mirror descent to classical mechanics
- Immiscible Color Flows in Optimal Transport Networks for Image Classification
- Bacterial cartels at steady supply
- Maximum entropy modeling of Optimal Transport: the sub-optimality regime and the transition from dense to sparse networks
- Network structure and dynamics of effective models of non-equilibrium quantum transport
- Stochastic Modeling of Filtration with Sieving in Graded Pore Networks
- Crowding controls the scaling of bus frequency with demand
- Belief propagation for supply networks: Efficient clustering of their factor graphs
- Minimal transport networks with general boundary conditions
- A Gradient Descent Method for Optimization of Model Microvascular Networks
- The impact of clogging on the transfer dynamics of hydraulic networks
- Flow network controlled shape transformation of a thin membrane through differential fluid storage and surface expansion
- Optimal counter-current exchange networks
- Formation of trade networks by economies of scale and product differentiation
- Adaptive Node Positioning in Biological Transport Networks
- Decision-making in light-trapped slime molds involves active mechanical processes
- General analytical solutions for DC/AC circuit network analysis
- Fluid flows shaping organism morphology
- Ageing related states of complex network formation in areca nuts
- Synaptic plasticity and neuronal refractory time cause scaling behaviour of neuronal avalanches
- Metabolic scaling from Fibonacci dynamics
- Les Houches Lectures on Flow Networks in Biology
- Opportunities and challenges in partitioning the graph measure space of real-world networks
- Diffusive search and trajectories on spatial networks: a propagator approach
- Resistance distance distribution in large sparse random graphs