Minimum-risk path finding by an adaptive amoebal network

Hydrophobic Barriers for Directing Physarum polycephalum Propulsion and Navigation

Physarum polycephalum (P. polycephalum) is a unicellular protist with unique properties, such as learning and remembering in its cultured environment without a brain or central nervous system. The organism has been extensively used in morphology, taxis, and positive feedback dynamics studies. However, the lack of standardization of materials and substrate designs used in P. polycephalum studies has significantly limited conducting such studies, increasing the cost and time. In this study, we introduce a method to control the direction and migration of P. polycephalum by drawing hydrophobic lines and patterns. Our study succeeded in controlling the movement of P. polycephalum by setting a variety of hydrophobic designs such as complete barrier, single-slit barrier, taper barrier, dumbbell barrier, and one-side-opened rectangular barrier, suggesting the effectiveness of the hydrophobic barrier in regulating the propulsion and navigation of the organisms. Moreover, we demonstrated that utilizing such geometric constraints can reduce the experimental time required for toxicity testing based on P. polycephalum by more than 300%. Our techniques open new possibilities for studying the biophysical properties and behaviors of P. polycephalum, while also facilitating toxicity testing.

Thoughts from the forest floor: a review of cognition in the slime mould Physarum polycephalum

Sensing, communication, navigation, decision-making, memory and learning are key components in a standard cognitive tool-kit that enhance an animal's ability to successfully survive and reproduce. However, these tools are not only useful for, or accessible to, animals-they evolved long ago in simpler organisms using mechanisms which may be either unique or widely conserved across diverse taxa. In this article, I review the recent research that demonstrates these key cognitive abilities in the plasmodial slime mould Physarum polycephalum, which has emerged as a model for non-animal cognition. I discuss the benefits and limitations of comparisons drawn between neural and non-neural systems, and the implications of common mechanisms across wide taxonomic divisions. I conclude by discussing future avenues of research that will draw the most benefit from a closer integration of Physarum and animal cognition research.

Network topology enables efficient response to environment inPhysarum polycephalum

The network-shaped body plan distinguishes the unicellular slime mouldPhysarum polycephalumin body architecture from other unicellular organisms. Yet, network-shaped body plans dominate branches of multi-cellular life such as in fungi. What survival advantage does a network structure provide when facing a dynamic environment with adverse conditions? Here, we probe how network topology impactsP. polycephalum's avoidance response to an adverse blue light. We stimulate either an elongated, I-shaped amoeboid or a Y-shaped networked specimen and subsequently quantify the evacuation process of the light-exposed body part. The result shows that Y-shaped specimen complete the avoidance retraction in a comparable time frame, even slightly faster than I-shaped organisms, yet, at a lower almost negligible increase in migration velocity. Contraction amplitude driving mass motion is further only locally increased in Y-shaped specimen compared to I-shaped-providing further evidence that Y-shaped's avoidance reaction is energetically more efficient than in I-shaped amoeboid organisms. The difference in the retraction behaviour suggests that the complexity of network topology provides a key advantage when encountering adverse environments. Our findings could lead to a better understanding of the transition from unicellular to multicellularity.

A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem

The ant colony optimization (ACO) is one efficient approach for solving the travelling salesman problem (TSP). Here, we propose a hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system (SSMFAS) to address the TSP. The state-adaptive slime mold (SM) model with two targeted auxiliary strategies emphasizes some critical connections and balances the exploration and exploitation ability of SSMFAS. The consideration of fractional-order calculus in the ant system (AS) takes full advantage of the neighboring information. The pheromone update rule of AS is modified to dynamically integrate the flux information of SM. To understand the search behavior of the proposed algorithm, some mathematical proofs of convergence analysis are given. The experimental results validate the efficiency of the hybridization and demonstrate that the proposed algorithm has the competitive ability of finding the better solutions on TSP instances compared with some state-of-the-art algorithms.

Stepwise slime mould growth as a template for urban design

The true slime mould, Physarum polycephalum, develops as a vascular network of protoplasm, connecting node-like sources of food in an effort to solve multi-objective transport problems. The organism first establishes a dense and continuous mesh, reinforcing optimal pathways over time through constructive feedbacks of protoplasmic streaming. Resolved vascular morphologies are the result of an evolutionarily-refined mechanism of computation, which can serve as a versatile biological model for network design at the urban scale. Existing digital Physarum models typically use positive reinforcement mechanisms to capture meshing and refinement behaviours simultaneously. While these automations generate accurate descriptions of sensory and constructive feedback, they limit stepwise design control, reducing flexibility and applicability. A model that decouples the two “phases” of Physarum behaviour would enable multistage control over network growth. Here we introduce such a system, first by producing a site-responsive mesh from a population of nutrient-attracted agents, and then by independently calculating from it a flexible, proximity-defined shortest-walk to produce a final network. We develop and map networks within existing urban environments that perform similarly to those biologically grown, establishing a versatile tool for bio-inspired urban network design.

Fungi anaesthesia

Electrical activity of fungus Pleurotus ostreatus is characterised by slow (h) irregular waves of baseline potential drift and fast (min) action potential likes spikes of the electrical potential. An exposure of the myceliated substrate to a chloroform vapour lead to several fold decrease of the baseline potential waves and increase of their duration. The chloroform vapour also causes either complete cessation of spiking activity or substantial reduction of the spiking frequency. Removal of the chloroform vapour from the growth containers leads to a gradual restoration of the mycelium electrical activity.

Complex population dynamics in a spatial microbial ecosystem with Physarum polycephalum

This research addresses the interactions between the unicellular slime mold Physarum polycephalum and a red yeast in a spatial ecosystem over week-long imaging experiments. An inverse relationship between the growth rates of both species is shown, where P. polycephalum has positive growth when the red yeast has a negative growth rate and vice versa. The data also captures successional and oscillatory dynamics between both species. An advanced image analysis methodology for semantic segmentation is used to quantify population density over time, for all components of the ecosystem. We suggest that P. polycephalum is capable of exhibiting a sustainable feeding strategy by depositing a nutritive slime trail, allowing yeast to serve as a periodic food source. This opens a new direction of P. polycephalum research, where the population dynamics of spatial ecosystems can be readily quantified and complex ecological dynamics can be studied.

Substrate and cell fusion influence on slime mold network dynamics

The acellular slime mold Physarum polycephalum provides an excellent model to study network formation, as its network is remodelled constantly in response to mass gain/loss and environmental conditions. How slime molds networks are built and fuse to allow for efficient exploration and adaptation to environmental conditions is still not fully understood. Here, we characterize the network organization of slime molds exploring homogeneous neutral, nutritive and adverse environments. We developed a fully automated image analysis method to extract the network topology and followed the slime molds before and after fusion. Our results show that: (1) slime molds build sparse networks with thin veins in a neutral environment and more compact networks with thicker veins in a nutritive or adverse environment; (2) slime molds construct long, efficient and resilient networks in neutral and adverse environments, whereas in nutritive environments, they build shorter and more centralized networks; and (3) slime molds fuse rapidly and establish multiple connections with their clone-mates in a neutral environment, whereas they display a late fusion with fewer connections in an adverse environment. Our study demonstrates that slime mold networks evolve continuously via pruning and reinforcement, adapting to different environmental conditions.

Slime Mold Inspired Distribution Network Initial Solution

Electricity distribution network optimisation has attracted attention in recent years due to the widespread penetration of distributed generation. A considerable portion of network optimisation algorithms rely on an initial solution that is supposed to bypass the time-consuming steps of optimisation routines. The aim of this paper is to present a nature inspired algorithm for initial network generation. Based on slime mold behaviour, the algorithm can generate a large-scale network in a reasonable computation time. A mathematical formulation and parameter exploration of the slime mold algorithm are presented. Slime mold networks resemble a relaxed minimum spanning tree with better balance between the investment and loss costs of a distribution network. Results indicate lower total costs for suburban and urban networks.

Application of Biomimetics to Architectural and Urban Design: A Review across Scales

Application of biomimetics has expanded progressively to other fields in recent years, including urban and architectural design, scaling up from materials to a larger scale. Besides its contribution to design and functionality through a long evolutionary process, the philosophy of biomimetics contributes to a sustainable society at the conceptual level. The aim of this review is to shed light on trends in the application of biomimetics to architectural and urban design, in order to identify potential issues and successes resulting from implementation. In the application of biomimetics to architectural design, parts of individual “organisms”, including their form and surface structure, are frequently mimicked, whereas in urban design, on a larger scale, biomimetics is applied to mimic whole ecosystems. The overall trends of the reviewed research indicate future research necessity in the field of on biomimetic application in architectural and urban design, including Biophilia and Material. As for the scale of the applications, the urban-scale research is limited and it is a promising research which can facilitate the social implementation of biomimetics. As for facilitating methods of applications, it is instrumental to utilize different types of knowledge, such as traditional knowledge, and providing scientific clarification of functions and systems based on reviews. Thus, interdisciplinary research is required additionally to reach such goals.

A Two-Way Parallel Slime Mold Algorithm by Flow and Distance for the Travelling Salesman Problem

In order to solve the problem of poor local optimization of the Slime Mold Algorithm (SMA) in the Travelling Salesman Problem (TSP), a Two-way Parallel Slime Mold Algorithm by Flow and Distance (TPSMA) is proposed in this paper. Firstly, the flow between each path point is calculated by the “critical pipeline and critical culture” model of SMA; then, according to the two indexes of flow and distance, the set of path points to be selected is obtained; finally, the optimization principle with a flow index is improved with two indexes of flow and distance and added random strategy. Hence, a two-way parallel optimization method is realized and the local optimal problem is solved effectively. Through the simulation of Traveling Salesman Problem Library (TSPLIB) on ulysses16, city31, eil51, gr96, and bier127, the results of TPSMA were improved by 24.56, 36.10, 41.88, 49.83, and 52.93%, respectively, compared to SMA. Furthermore, the number of path points is more and the optimization ability of TPSMA is better. At the same time, TPSMA is closer to the current optimal result than other algorithms by multiple sets of tests, and its time complexity is obviously better than others. Therefore, the superiority of TPSMA is adequately proven.

The brain: a concept in flux

One of the most important aspects of the scientific endeavour is the definition of specific concepts as precisely as possible. However, it is also important not to lose sight of two facts: (i) we divide the study of nature into manageable parts in order to better understand it owing to our limited cognitive capacities and (ii) definitions are inherently arbitrary and heavily influenced by cultural norms, language, the current political climate, and even personal preferences, among many other factors. As a consequence of these facts, clear-cut definitions, despite their evident importance, are oftentimes quite difficult to formulate. One of the most illustrative examples about the difficulty of articulating precise scientific definitions is trying to define the concept of a brain. Even though the current thinking about the brain is beginning to take into account a variety of organisms, a vertebrocentric bias still tends to dominate the scientific discourse about this concept. Here I will briefly explore the evolution of our 'thoughts about the brain', highlighting the difficulty of constructing a universally (or even a generally) accepted formal definition of it and using planarians as one of the earliest examples of organisms proposed to possess a 'traditional', vertebrate-style brain. I also suggest that the time is right to attempt to expand our view of what a brain is, going beyond exclusively structural and taxa-specific criteria. Thus, I propose a classification that could represent a starting point in an effort to expand our current definitions of the brain, hopefully to help initiate conversations leading to changes of perspective on how we think about this concept. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

An Accelerated Physarum Solver for Network Optimization

As a novel computational paradigm, Physarum solver has received increasing attention from the researchers in tackling a plethora of network optimization problems. However, the convergence of Physarum solver is grounded by solving a system of linear equations iteratively, which often leads to low computational performance. Two factors have been highlighted along the process: 1) high time complexity in solving the system of linear equations and 2) extensive iterations required for convergence. Thus, Physarum solver has been largely restricted by its unsatisfactory computational performance. In this paper, we aim to address these two issues by developing two enhancement strategies: 1) pruning inactive nodes and 2) terminating Physarum solver in advance. First, extensive nodes and edges become and stay inactive after a few iterations in identifying the shortest path. Removing these inactive nodes and edges significantly decreases the graph size, thereby reducing computational complexity. Second, we define a transition phase for edges. All of the paths experiencing such a transition phase are dynamically aggregated to form a set of near-optimal paths among which the optimal path is included. Depth-first search is then leveraged to identify the optimal path from the near-optimal paths set. Earlier termination of Physarum solver saves considerable iterations while guaranteeing the optimality of the found solution. Empirically, 20 randomly generated sparse and complete graphs with network sizes ranging from 50 to 2000 as well as two real-world traffic networks are used to compare the performance of accelerated Physarum solver to the other two state-of-the-art algorithms.

Optimizing biologically inspired transport networks by control

Transportation networks with intrinsic flow dynamics governed by the Kirchhoff's current law are ubiquitous in natural and engineering systems. There has been recent work on designing optimal transportation networks based on biological principles with the goal to minimize the total dissipation associated with the flow. Despite being biologically inspired, e.g., adaptive network design based on slime mold Physarum polycephalum, such methods generally lead to suboptimal networks due to the difficulty in finding a global or nearly global optimum of the nonconvex optimization function. Here we articulate a design paradigm that combines engineering control and biological principles to realize optimal transportation networks. In particular, we show how small control signals applied only to a fraction of edges in an adaptive network can lead to solutions that are far more optimal than those based solely on biological principles. We also demonstrate that control signals, if not properly designed, can lead to networks that are less optimal. Incorporating control principle into biology-based optimal network design has broad applications not only in biomedical science and engineering but also in other disciplines such as civil engineering for designing resilient infrastructure systems.

A Physarum Centrality Measure of the Human Brain Network

The most important goals of brain network analyses are to (a) detect pivotal regions and connections that contribute to disproportionate communication flow, (b) integrate global information, and (c) increase the brain network efficiency. Most centrality measures assume that information propagates in networks with the shortest connection paths, but this assumption is not true for most real networks given that information in the brain propagates through all possible paths. This study presents a methodological pipeline for identifying influential nodes and edges in human brain networks based on the self-regulating biological concept adopted from the Physarum model, thereby allowing the identification of optimal paths that are independent of the stated assumption. Network hubs and bridges were investigated in structural brain networks using the Physarum model. The optimal paths and fluid flow were used to formulate the Physarum centrality measure. Most network hubs and bridges are overlapped to some extent, but those based on Physarum centrality contain local and global information in the superior frontal, anterior cingulate, middle temporal gyrus, and precuneus regions. This approach also reduced individual variation. Our results suggest that the Physarum centrality presents a trade-off between the degree and betweenness centrality measures.

Towards fungal computer

We propose that fungi Basidiomycetes can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In a series of scoping experiments, we demonstrate that electrical activity recorded on fruits might act as a reliable indicator of the fungi's response to thermal and chemical stimulation. A stimulation of a fruit is reflected in changes of electrical activity of other fruits of a cluster, i.e. there is distant information transfer between fungal fruit bodies. In an automaton model of a fungal computer, we show how to implement computation with fungi and demonstrate that a structure of logical functions computed is determined by mycelium geometry.

Remarkable problem-solving ability of unicellular amoeboid organism and its mechanism

Choosing a better move correctly and quickly is a fundamental skill of living organisms that corresponds to solving a computationally demanding problem. A unicellular plasmodium of Physarum polycephalum searches for a solution to the travelling salesman problem (TSP) by changing its shape to minimize the risk of being exposed to aversive light stimuli. In our previous studies, we reported the results on the eight-city TSP solution. In this study, we show that the time taken by plasmodium to find a reasonably high-quality TSP solution grows linearly as the problem size increases from four to eight. Interestingly, the quality of the solution does not degrade despite the explosive expansion of the search space. Formulating a computational model, we show that the linear-time solution can be achieved if the intrinsic dynamics could allocate intracellular resources to grow the plasmodium terminals with a constant rate, even while responding to the stimuli. These results may lead to the development of novel analogue computers enabling approximate solutions of complex optimization problems in linear time.

A Bio-Inspired Approach to Traffic Network Equilibrium Assignment Problem

Finding an equilibrium state of the traffic assignment plays a significant role in the design of transportation networks. We adapt the path finding mathematical model of slime mold Physarum polycephalum to solve the traffic equilibrium assignment problem. We make three contributions in this paper. First, we propose a generalized Physarum model to solve the shortest path problem in directed and asymmetric graphs. Second, we extend it further to resolve the network design problem with multiple source nodes and sink nodes. At last, we demonstrate that the Physarum solver converges to the user-optimized (Wardrop) equilibrium by dynamically updating the costs of links in the network. In addition, convergence of the developed algorithm is proved. Numerical examples are used to demonstrate the efficiency of the proposed algorithm. The superiority of the proposed algorithm is demonstrated in comparison with several other algorithms, including the Frank-Wolfe algorithm, conjugate Frank-Wolfe algorithm, biconjugate Frank-Wolfe algorithm, and gradient projection algorithm.

Collective behaviour and swarm intelligence in slime moulds

The study of collective behaviour aims to understand how individual-level behaviours can lead to complex group-level patterns. Collective behaviour has primarily been studied in animal groups such as colonies of insects, flocks of birds and schools of fish. Although less studied, collective behaviour also occurs in microorganisms. Here, we argue that slime moulds are powerful model systems for solving several outstanding questions in collective behaviour. In particular, slime mould may hold the key to linking individual-level mechanisms to colony-level behaviours. Using well-established principles of collective animal behaviour as a framework, we discuss the extent to which slime mould collectives are comparable to animal groups, and we highlight some potentially fruitful areas for future research.

Physarum machines imitating a Roman road network: the 3D approach

Physarum Polycephalum is a single cell visible by unaided eye. This is a plasmodial, vegetative stage of acellular slime mould. This single cell has myriad of nuclei which contribute to a network of bio-chemical oscillators responsible for the slime mould’s distributed sensing, concurrent information processing and decision making, and parallel actuation. When presented with a spatial configuration of sources of nutrients, the slime mould spans the sources with networks of its protoplasmic tube. These networks belong to a family of planar proximity graphs. The protoplasmic networks also show a degree of similarity to vehicular transport networks. Previously, we have shown that the foraging behaviour of the slime mould can be applied in archaeological research to complement and enhance conventional geographic information system tools. The results produced suffered from limitation of a flat substrate: transport routes imitated by the slime mould did not reflect patterns of elevations. To overcome the limitation of the ‘flat world’ we constructed a three-dimensional model of Balkans. In laboratory experiments and computer modelling we uncovered patterns of the foraging behaviour that might shed a light onto development of Roman roads in the Balkans during the imperial period (1st century BC – 4th century AD).

Current reinforcement model reproduces center-in-center vein trajectory of Physarum polycephalum

Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio-temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the 'current reinforcement rule', was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze-solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center-in-center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width. In this report, we confirm that the mathematical model reproduces the center-in-center trajectory of veins around corners observed in the maze-solving experiment.

The foundations of plant intelligence

Intelligence is defined for wild plants and its role in fitness identified. Intelligent behaviour exhibited by single cells and systems similarity between the interactome and connectome indicates neural systems are not necessary for intelligent capabilities. Plants sense and respond to many environmental signals that are assessed to competitively optimize acquisition of patchily distributed resources. Situations of choice engender motivational states in goal-directed plant behaviour; consequent intelligent decisions enable efficient gain of energy over expenditure. Comparison of swarm intelligence and plant behaviour indicates the origins of plant intelligence lie in complex communication and is exemplified by cambial control of branch function. Error correction in behaviours indicates both awareness and intention as does the ability to count to five. Volatile organic compounds are used as signals in numerous plant interactions. Being complex in composition and often species and individual specific, they may represent the plant language and account for self and alien recognition between individual plants. Game theory has been used to understand competitive and cooperative interactions between plants and microbes. Some unexpected cooperative behaviour between individuals and potential aliens has emerged. Behaviour profiting from experience, another simple definition of intelligence, requires both learning and memory and is indicated in the priming of herbivory, disease and abiotic stresses.

The foundations of plant intelligence

Intelligence is defined for wild plants and its role in fitness identified. Intelligent behaviour exhibited by single cells and systems similarity between the interactome and connectome indicates neural systems are not necessary for intelligent capabilities. Plants sense and respond to many environmental signals that are assessed to competitively optimize acquisition of patchily distributed resources. Situations of choice engender motivational states in goal-directed plant behaviour; consequent intelligent decisions enable efficient gain of energy over expenditure. Comparison of swarm intelligence and plant behaviour indicates the origins of plant intelligence lie in complex communication and is exemplified by cambial control of branch function. Error correction in behaviours indicates both awareness and intention as does the ability to count to five. Volatile organic compounds are used as signals in numerous plant interactions. Being complex in composition and often species and individual specific, they may represent the plant language and account for self and alien recognition between individual plants. Game theory has been used to understand competitive and cooperative interactions between plants and microbes. Some unexpected cooperative behaviour between individuals and potential aliens has emerged. Behaviour profiting from experience, another simple definition of intelligence, requires both learning and memory and is indicated in the priming of herbivory, disease and abiotic stresses.

The role of noise in self-organized decision making by the true slime mold Physarum polycephalum

Self-organized mechanisms are frequently encountered in nature and known to achieve flexible, adaptive control and decision-making. Noise plays a crucial role in such systems: It can enable a self-organized system to reliably adapt to short-term changes in the environment while maintaining a generally stable behavior. This is fundamental in biological systems because they must strike a delicate balance between stable and flexible behavior. In the present paper we analyse the role of noise in the decision-making of the true slime mold Physarum polycephalum, an important model species for the investigation of computational abilities in simple organisms. We propose a simple biological experiment to investigate the reaction of P. polycephalum to time-variant risk factors and present a stochastic extension of an established mathematical model for P. polycephalum to analyze this experiment. It predicts that-due to the mechanism of stochastic resonance-noise can enable P. polycephalum to correctly assess time-variant risk factors, while the corresponding noise-free system fails to do so. Beyond the study of P. polycephalum we demonstrate that the influence of noise on self-organized decision-making is not tied to a specific organism. Rather it is a general property of the underlying process dynamics, which appears to be universal across a wide range of systems. Our study thus provides further evidence that stochastic resonance is a fundamental component of the decision-making in self-organized macroscopic and microscopic groups and organisms.

Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology-pruning in the foraging state-causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.

Pea Plants Show Risk Sensitivity

Sensitivity to variability in resources has been documented in humans, primates, birds, and social insects, but the fit between empirical results and the predictions of risk sensitivity theory (RST), which aims to explain this sensitivity in adaptive terms, is weak [1]. RST predicts that agents should switch between risk proneness and risk aversion depending on state and circumstances, especially according to the richness of the least variable option [2]. Unrealistic assumptions about agents' information processing mechanisms and poor knowledge of the extent to which variability imposes specific selection in nature are strong candidates to explain the gap between theory and data. RST's rationale also applies to plants, where it has not hitherto been tested. Given the differences between animals' and plants' information processing mechanisms, such tests should help unravel the conflicts between theory and data. Measuring root growth allocation by split-root pea plants, we show that they favor variability when mean nutrient levels are low and the opposite when they are high, supporting the most widespread RST prediction. However, the combination of non-linear effects of nitrogen availability at local and systemic levels may explain some of these effects as a consequence of mechanisms not necessarily evolved to cope with variance [3, 4]. This resembles animal examples in which properties of perception and learning cause risk sensitivity even though they are not risk adaptations [5].

PhysarumSpreader: A New Bio-Inspired Methodology for Identifying Influential Spreaders in Complex Networks

Identifying influential spreaders in networks, which contributes to optimizing the use of available resources and efficient spreading of information, is of great theoretical significance and practical value. A random-walk-based algorithm LeaderRank has been shown as an effective and efficient method in recognizing leaders in social network, which even outperforms the well-known PageRank method. As LeaderRank is initially developed for binary directed networks, further extensions should be studied in weighted networks. In this paper, a generalized algorithm PhysarumSpreader is proposed by combining LeaderRank with a positive feedback mechanism inspired from an amoeboid organism called Physarum Polycephalum. By taking edge weights into consideration and adding the positive feedback mechanism, PhysarumSpreader is applicable in both directed and undirected networks with weights. By taking two real networks for examples, the effectiveness of the proposed method is demonstrated by comparing with other standard centrality measures.

Slime mould processors, logic gates and sensors

A heterotic, or hybrid, computation implies that two or more substrates of different physical nature are merged into a single device with indistinguishable parts. These hybrid devices then undertake coherent acts on programmable and sensible processing of information. We study the potential of heterotic computers using slime mould acting under the guidance of chemical, mechanical and optical stimuli. Plasmodium of acellular slime mould Physarum polycephalum is a gigantic single cell visible to the unaided eye. The cell shows a rich spectrum of behavioural morphological patterns in response to changing environmental conditions. Given data represented by chemical or physical stimuli, we can employ and modify the behaviour of the slime mould to make it solve a range of computing and sensing tasks. We overview results of laboratory experimental studies on prototyping of the slime mould morphological processors for approximation of Voronoi diagrams, planar shapes and solving mazes, and discuss logic gates implemented via collision of active growing zones and tactile responses of P. polycephalum. We also overview a range of electronic components--memristor, chemical, tactile and colour sensors-made of the slime mould.

A would-be nervous system made from a slime mold

The slime mold Physarum polycephalum is a huge single cell that has proved to be a fruitful material for designing novel computing architectures. The slime mold is capable of sensing tactile, chemical, and optical stimuli and converting them to characteristic patterns of its electrical potential oscillations. The electrical responses to stimuli may propagate along protoplasmic tubes for distances exceeding tens of centimeters, as impulses in neural pathways do. A slime mold makes decisions about its propagation direction based on information fusion from thousands of spatially extended protoplasmic loci, similarly to a neuron collecting information from its dendritic tree. The analogy is distant yet inspiring. We speculate on whether alternative-would-be-nervous systems can be developed and practically implemented from the slime mold. We uncover analogies between the slime mold and neurons, and demonstrate that the slime mold can play the roles of primitive mechanoreceptors, photoreceptors, and chemoreceptors; we also show how the Physarum neural pathways develop. The results constituted the first step towards experimental laboratory studies of nervous system implementation in slime molds.

An improved bio-inspired algorithm for the directed shortest path problem

Because most networks are intrinsically directed, the directed shortest path problem has been one of the fundamental issues in network optimization. In this paper, a novel algorithm for finding the shortest path in directed networks is proposed. It extends a bio-inspired path finding model of Physarum polycephalum, which is designed only for undirected networks, by adopting analog circuit analysis. Illustrative examples are given to show the effectiveness of the proposed algorithm in finding the directed shortest path.

An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.

An improved Physarum polycephalum algorithm for the shortest path problem

Shortest path is among classical problems of computer science. The problems are solved by hundreds of algorithms, silicon computing architectures and novel substrate, unconventional, computing devices. Acellular slime mould P. polycephalum is originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients. Several algorithms were designed based on properties of the slime mould. Many of the Physarum-inspired algorithms suffer from a low converge speed. To accelerate the search of a solution and reduce a number of iterations we combined an original model of Physarum-inspired path solver with a new a parameter, called energy. We undertook a series of computational experiments on approximating shortest paths in networks with different topologies, and number of nodes varying from 15 to 2000. We found that the improved Physarum algorithm matches well with existing Physarum-inspired approaches yet outperforms them in number of iterations executed and a total running time. We also compare our algorithm with other existing algorithms, including the ant colony optimization algorithm and Dijkstra algorithm.

Route 20, Autobahn 7, and Slime Mold: Approximating the Longest Roads in USA and Germany With Slime Mold on 3-D Terrains

A cellular slime mould Physarum polycephalum is a monstrously large single cell visible by an unaided eye. The slime mold explores space in parallel, is guided by gradients of chemoattractants, and propagates toward sources of nutrients along nearly shortest paths. The slime mold is a living prototype of amorphous biological computers and robotic devices capable of solving a range of tasks of graph optimization and computational geometry. When presented with a distribution of nutrients, the slime mold spans the sources of nutrients with a network of protoplasmic tubes. This protoplasmic network matches a network of major transport routes of a country when configuration of major urban areas is represented by nutrients. A transport route connecting two cities should ideally be a shortest path, and this is usually the case in computer simulations and laboratory experiments with flat substrates. What searching strategies does the slime mold adopt when exploring 3-D terrains? How are optimal and transport routes approximated by protoplasmic tubes? Do the routes built by the slime mold on 3-D terrain match real-world transport routes? To answer these questions, we conducted pioneer laboratory experiments with Nylon terrains of USA and Germany. We used the slime mold to approximate route 20, the longest road in USA, and autobahn 7, the longest national motorway in Europe. We found that slime mold builds longer transport routes on 3-D terrains, compared to flat substrates yet sufficiently approximates man-made transport routes studied. We demonstrate that nutrients placed in destination sites affect performance of slime mold, and show how the mold navigates around elevations. In cellular automaton models of the slime mold, we have shown variability of the protoplasmic routes might depends on physiological states of the slime mold. Results presented will contribute toward development of novel algorithms for sensorial fusion, information processing, and decision making, and will provide inspirations in design of bioinspired amorphous robotic devices.

Memory models of adaptive behavior

Adaptive response to varying environment is a common feature of biological organisms. Reproducing such features in electronic systems and circuits is of great importance for a variety of applications. We consider memory models inspired by an intriguing ability of slime molds to both memorize the period of temperature and humidity variations and anticipate the next variations to come, when appropriately trained. Effective circuit models of such behavior are designed using: 1) a set of LC contours with memristive damping and 2) a single memcapacitive system-based adaptive contour with memristive damping. We consider these two approaches in detail by comparing their results and predictions. Finally, possible biological experiments that would discriminate between the models are discussed. In this paper, we also introduce an effective description of certain memory circuit elements.

True-slime-mould-inspired hydrostatically coupled oscillator system exhibiting versatile behaviours

Behavioural diversity is an indispensable attribute of living systems, which makes them intrinsically adaptive and responsive to the demands of a dynamically changing environment. In contrast, conventional engineering approaches struggle to suppress behavioural diversity in artificial systems to reach optimal performance in given environments for desired tasks. The goals of this research include understanding the essential mechanism that endows living systems with behavioural diversity and implementing the mechanism in robots to exhibit adaptive behaviours. For this purpose, we have focused on an amoeba-like unicellular organism: the plasmodium of true slime mould. Despite the absence of a central nervous system, the plasmodium exhibits versatile spatiotemporal oscillatory patterns and switches spontaneously among these patterns. By exploiting this behavioural diversity, it is able to exhibit adaptive behaviour according to the situation encountered. Inspired by this organism, we built a real physical robot using hydrostatically coupled oscillators that produce versatile oscillatory patterns and spontaneous transitions among the patterns. The experimental results show that exploiting physical hydrostatic interplay—the physical dynamics of the robot—allows simple phase oscillators to promote versatile behaviours. The results can contribute to an understanding of how a living system generates versatile and adaptive behaviours with physical interplays among body parts.

Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.