Adaptation and Optimization of Biological Transport Networks

Abstract

It has been hypothesized that topological structures of biological transport networks are consequences of energy optimization. Motivated by experimental observation, we propose that adaptation dynamics may underlie this optimization. In contrast to the global nature of optimization, our adaptation dynamics responds only to local information and can naturally incorporate fluctuations in flow distributions. The adaptation dynamics minimizes the global energy consumption to produce optimal networks, which may possess hierarchical loop structures in the presence of strong fluctuations in flow distribution. We further show that there may exist a new phase transition as there is a critical open probability of sinks, above which there are only trees for network structures whereas below which loops begin to emerge.

Structural self-assembly and avalanchelike dynamics in locally adaptive networks

“…[3,[5][6][7][8]. In striving for generality this work may be seen as existing in parallel with a recent study by D. Hu and D. Cai [9], however where their work is primarily concerned with steady-state structure and the existence of 'optimal' solutions, we are more interested in the progression and character of the dynamics and the network topology over a much broader range of initial conditions. Like the specific Physarum model, our model uses an undirected, weighted graph representation of the transport network, where the graph's edges represent the tubes and its nodes their junctions.…”

“…The importance of γ as a control parameter has been widely discussed previously (see [9,15,16] and references therein), and γ = 1 has been identified as a transition point where the nature of the network (adaptive [9] or optimized [15,16]) qualitatively changes. A constant feedback function (γ = 0) uncouples the system of equations, leading to the same solution form C ij (t) for every edge in the network, independent of the flows:…”

Laser-assisted XUV double ionization of helium: Energy-sharing dependence of joint angular distributions

“…The role of an assisting IR-laser pulse was studied by Hu in 2013 as a step toward the coherent control of chemical reactions [29]. The author's ab initio calculations for the DI of helium by an attosecond XUV pulse showed that the delay of the assisting few-cycle IR laser very sensitively influences the photoelectron energy distribution and can be tuned to significantly enhance the emission of fast photoelectrons.…”

Laser-assisted XUV few-photon double ionization of helium: Joint angular distributions

“…In such experiments, the momenta of two particles in the final, fully fragmented state, consisting of the helium nucleus and the two released electrons, need to be detected in coincidence. On the theoretical side, the quantitative description of the three-body breakup process has made significant progress over the past two decades [7][8][9][10][11][12][13][14][15][16][17][18], most noticeably due to the development of improved analytical models for the correlated final three-body Coulomb state after the three-particle breakup [19,20] and extensive ab initio calculations made possible by efficient numerical algorithms [21,22] and much improved computational resources.…”