When the path is never shortest: a reality check on shortest path biocomputation

Shortest path problems are a touchstone for evaluating the computing performance and functional range of novel computing substrates. Much has been published in recent years regarding the use of biocomputers to solve minimal path problems such as route optimisation and labyrinth navigation, but their outputs are typically difficult to reproduce and somewhat abstract in nature, suggesting that both experimental design and analysis in the field require standardising. This chapter details laboratory experimental data which probe the path finding process in two single-celled protistic model organisms, Physarum polycephalum and Paramecium caudatum, comprising a shortest path problem and labyrinth navigation, respectively. The results presented illustrate several of the key difficulties that are encountered in categorising biological behaviours in the language of computing, including biological variability, non-halting operations and adverse reactions to experimental stimuli. It is concluded that neither organism examined are able to efficiently or reproducibly solve shortest path problems in the specific experimental conditions that were tested. Data presented are contextualised with biological theory and design principles for maximising the usefulness of experimental biocomputer prototypes.Comment: To appear in: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 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

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201