78 research outputs found
Physarum Can Compute Shortest Paths
Physarum Polycephalum is a slime mold that is apparently able to solve
shortest path problems.
A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s0 and s1. We prove that, under this model, the mass of the
mold will eventually converge to the shortest s0 - s1 path of the network that
the mold lies on, independently of the structure of the network or of the
initial mass distribution.
This matches the experimental observations by the biologists and can be seen
as an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.Comment: Accepted in SODA 201
A revised model of fluid transport optimization in Physarum polycephalum
Optimization of fluid transport in the slime mold Physarum polycephalum has
been the subject of several modeling efforts in recent literature. Existing
models assume that the tube adaptation mechanism in P. polycephalum's tubular
network is controlled by the sheer amount of fluid flow through the tubes. We
put forward the hypothesis that the controlling variable may instead be the
flow's pressure gradient along the tube. We carry out the stability analysis of
such a revised mathematical model for a parallel-edge network, proving that the
revised model supports the global flow-optimizing behavior of the slime mold
for a substantially wider class of response functions compared to previous
models. Simulations also suggest that the same conclusion may be valid for
arbitrary network topologies.Comment: To appear in Journal of Mathematical Biolog
The simplicity of planar networks
Shortest paths are not always simple. In planar networks, they can be very
different from those with the smallest number of turns - the simplest paths.
The statistical comparison of the lengths of the shortest and simplest paths
provides a non trivial and non local information about the spatial organization
of these graphs. We define the simplicity index as the average ratio of these
lengths and the simplicity profile characterizes the simplicity at different
scales. We measure these metrics on artificial (roads, highways, railways) and
natural networks (leaves, slime mould, insect wings) and show that there are
fundamental differences in the organization of urban and biological systems,
related to their function, navigation or distribution: straight lines are
organized hierarchically in biological cases, and have random lengths and
locations in urban systems. In the case of time evolving networks, the
simplicity is able to reveal important structural changes during their
evolution.Comment: 8 pages, 4 figure
Maze solvers demystified and some other thoughts
There is a growing interest towards implementation of maze solving in
spatially-extended physical, chemical and living systems. Several reports of
prototypes attracted great publicity, e.g. maze solving with slime mould and
epithelial cells, maze navigating droplets. We show that most prototypes
utilise one of two phenomena: a shortest path in a maze is a path of the least
resistance for fluid and current flow, and a shortest path is a path of the
steepest gradient of chemoattractants. We discuss that substrates with
so-called maze-solving capabilities simply trace flow currents or chemical
diffusion gradients. We illustrate our thoughts with a model of flow and
experiments with slime mould. The chapter ends with a discussion of experiments
on maze solving with plant roots and leeches which show limitations of the
chemical diffusion maze-solving approach.Comment: This is a preliminary version of the chapter to be published in
Adamatzky A. (Ed.) Shortest path solvers. From software to wetware. Springer,
201
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