Atsushi Tero

Rules for Biologically Inspired Adaptive Network Design

Miniature Transport Engineers In its vegetative phase, the slime mold Physarum polycephalum “slimes” its way through the world seeking food. As it explores, it links previously found food sources with tubular structures. Tero et al. (p. 439) report that if food sources are deposited on a plate in a pattern corresponding in miniature to the positions of the cities that surround Tokyo, the resulting network of Physarum tubules that develops is rather similar in structure to the railroad network that connects the Japanese cities. A model was produced that describes the adaptive network development displayed by the slime mold. This biologically inspired model might provide insight into how to implement properties like resistance of transport systems to local failures into similar human-designed systems. Human municipal transportation engineers might learn design strategies from the lowly slime mold. Transport networks are ubiquitous in both social and biological systems. Robust network performance involves a complex trade-off involving cost, transport efficiency, and fault tolerance. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. Furthermore, they develop without centralized control and may represent a readily scalable solution for growing networks in general. We show that the slime mold Physarum polycephalum forms networks with comparable efficiency, fault tolerance, and cost to those of real-world infrastructure networks—in this case, the Tokyo rail system. The core mechanisms needed for adaptive network formation can be captured in a biologically inspired mathematical model that may be useful to guide network construction in other domains.

Flow-network adaptation in Physarum amoebae.

Understanding how biological systems solve problems could aid the design of novel computational methods. Information processing in unicellular eukaryotes is of particular interest, as these organisms have survived for more than a billion years using a simple system. The large amoeboid plasmodium of Physarum is able to solve a maze and to connect multiple food locations via a smart network. This study examined how Physarum amoebae compute these solutions. The mechanism involves the adaptation of the tubular body, which appears to be similar to a network, based on cell dynamics. Our model describes how the network of tubes expands and contracts depending on the flux of protoplasmic streaming, and reproduces experimental observations of the behavior of the organism. The proposed algorithm based on Physarum is simple and powerful.

Simple robot suggests physical interlimb communication is essential for quadruped walking

Quadrupeds have versatile gait patterns, depending on the locomotion speed, environmental conditions and animal species. These locomotor patterns are generated via the coordination between limbs and are partly controlled by an intraspinal neural network called the central pattern generator (CPG). Although this forms the basis for current control paradigms of interlimb coordination, the mechanism responsible for interlimb coordination remains elusive. By using a minimalistic approach, we have developed a simple-structured quadruped robot, with the help of which we propose an unconventional CPG model that consists of four decoupled oscillators with only local force feedback in each leg. Our robot exhibits good adaptability to changes in weight distribution and walking speed simply by responding to local feedback, and it can mimic the walking patterns of actual quadrupeds. Our proposed CPG-based control method suggests that physical interaction between legs during movements is essential for interlimb coordination in quadruped walking.

Traffic optimization in railroad networks using an algorithm mimicking an amoeba-like organism, Physarum plasmodium

Traffic optimization of railroad networks was considered using an algorithm that was biologically inspired by an amoeba-like organism, plasmodium of the true slime mold, Physarum polycephalum. The organism developed a transportation network consisting of a tubular structure to transport protoplasm. It was reported that plasmodium can find the shortest path interconnecting multiple food sites during an adaptation process (Nakagaki et al., 2001. Biophys. Chem. 92, 47-52). By mimicking the adaptation process a path finding algorithm was developed by Tero et al. (2007). In this paper, the algorithm is newly modified for applications of traffic distribution optimization in transportation networks of infrastructure such as railroads under the constraint that the network topology is given. Application of the algorithm to a railroad in metropolitan Tokyo, Japan is demonstrated. The results are evaluated using three performance functions related to cost, traveling efficiency, and network weakness. The traffic distribution suggests that the modified Physarum algorithm balances the performances under a certain parameter range, indicating a biological process.

Computational Ability of Cells based on Cell Dynamics and Adaptability

Learning how biological systems solve problems could help to design new methods of computation. Information processing in simple cellular organisms is interesting, as they have survived for almost 1 billion years using a simple system of information processing. Here we discuss a well-studied model system: the large amoeboid Physarum plasmodium. This amoeba can find approximate solutions for combinatorial optimization problems, such as solving a maze or a shortest network problem. In this report, we describe problem solving by the amoeba, and the computational methods that can be extracted from biological behaviors. The algorithm designed based on Physarum is both simple and useful.

Current-reinforced random walks for constructing transport networks

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by ‘walking’ particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

A mathematical model of cleavage.

In the present paper, we propose a mathematical model of cleavage. Cleavage is a process during the early stages of development in which the fertile egg undergoes repeated division keeping the cluster size almost constant. During the cleavage process individual cells repeat cell division in an orderly manner to form a blastula, however, the mechanism which achieves such a coordination is still not very clear. In the present research, we took sea urchin as an example and focused on the diffusion of chemical substances from the animal and vegetal pole. By considering chemotactic motion of the centrosomes, we constructed a mathematical model that describes the processes in the early stages of cleavage.

Effects of amount of food on path selection in the transport network of an amoeboid organsim

We studied the effect of the size of food sources (FSs) presented to the true slime mould Physarum polycephalum on the tubular networks formed by the organism to absorb nutrient. The amount of plasmodium gathering at an FS was shown to be proportional to both the concentration of nutrient and the surface area of the FS. We presented two FSs to test which connection the organism selected in response to varying amounts of food and derived a simple rule for connection persistence: the longer connection collapses earlier. A mathematical model for tube selection in response to amount of food was derived and predicted our experimental findings regarding the choice of connection. When three FSs were presented to the organism, the longer tubes were also the first to collapse, explained by the relative probability of disconnection. The size of the FS is thus a key parameter determining network formation.

A CPG-based decentralized control of a quadruped robot inspired by true slime mold

Despite its appeal, a systematic design of an autonomous decentralized control system is yet to be realized. To bridge this gap, we have so far employed a “back-to-basics” approach inspired by true slime mold, a primitive living creature whose behavior is purely controlled by coupled biochemical oscillators similar to central pattern generators (CPGs). Based on this natural phenomenon, we have successfully developed a design scheme for local sensory feedback control leading to system-wide adaptive behavior. This design scheme is based on a “discrepancy function” that extracts the discrepancies among the mechanical system (i:e:, body), control system (i:e:, brain-nervous system) and the environment. The aim of this study is to intensively investigate the validity of this design scheme by applying it to the control of a quadruped locomotion. Simulation results show that the quadruped robot exhibits remarkably adaptive behavior in response to environmental changes and changes in body properties. Our results shed a new light on design methodologies for CPG-based decentralized control of various types of locomotion.

Theta-alpha EEG phase distributions in the frontal area for dissociation of visual and auditory working memory

Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations separately synchronize with task-relevant sensory brain areas remains an open question. Here, we focused on theta-alpha phase relationships in frontal areas using EEG, and then verified their functional roles with mathematical models. EEG data showed that the relationship between theta (6 Hz) and alpha (12 Hz) phases in the frontal areas was about 1:2 during both auditory and visual WM, and that the phase distributions between auditory and visual WM were different. Next, we used the differences in phase distributions to construct FitzHugh-Nagumo type mathematical models. The results replicated the modality-specific branching by orthogonally of the trigonometric functions for theta and alpha oscillations. Furthermore, mathematical and experimental results were consistent with regards to the phase relationships and amplitudes observed in frontal and sensory areas. These results indicate the important role that different phase distributions of theta and alpha oscillations have in modality-specific dissociation in the brain.