相关论文: A Single--Index Theory of Optimal Branching: Murra…
The branching geometry of biological transport networks is characterized by a diameter scaling exponent $\alpha$. Two structural attractors compete: impedance matching ($\alpha \sim 2$) for pulsatile flow and viscous-metabolic minimization…
Murray's cubic branching law ($\alpha=3$) predicts a universal diameter scaling exponent for all hierarchical transport networks, yet arterial trees yield $\alpha \sim 2.7-2.9$. We show that this discrepancy has a structural origin:…
Consider designing a transportation network on $n$ vertices in the plane, with traffic demand uniform over all source-destination pairs. Suppose the cost of a link of length $\ell$ and capacity $c$ scales as $\ell c^\beta$ for fixed…
The Gilbert-Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain power of the "flow". In this paper, we introduce a new…
We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metabolic) cost terms, constrained by a local mass conservation…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that…
We study hierarchical properties of optimal transportation networks with biological background. The networks are obtained as minimizers of an energy functional which involves a metabolic cost term of a power-law form with exponent…
In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of…
The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transport plan. A specific feature of the problem is that the cost…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
Transport networks must balance viscous pumping losses with the energetic cost of maintaining an operative architecture. This paper formulates that trade-off as an entropy-per-information-cost (EPIC) extremum that prices structural upkeep…
The branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria. Our synthetic tree model does not incorporate…
Despite its importance for practical applications, not much is known about the optimal shape of a network that connects in an efficient way a set of points. This problem can be formulated in terms of a multiplex network with a fast layer…
Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected…
We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with…