From Lévy to Brownian: a computational model based on biological fluctuation

An Embodied Intelligence-Based Biologically Inspired Strategy for Searching a Moving Target

Bacterial chemotaxis in unicellular Escherichia coli, the simplest biological creature, enables it to perform effective searching behaviour even with a single sensor, achieved via a sequence of "tumbling" and "swimming" behaviours guided by gradient information. Recent studies show that suitable random walk strategies may guide the behaviour in the absence of gradient information. This article presents a novel and minimalistic biologically inspired search strategy inspired by bacterial chemotaxis and embodied intelligence concept: a concept stating that intelligent behaviour is a result of the interaction among the "brain," body morphology including the sensory sensitivity tuned by the morphology, and the environment. Specifically, we present bacterial chemotaxis inspired searching behaviour with and without gradient information based on biological fluctuation framework: a mathematical framework that explains how biological creatures utilize noises in their behaviour. Via extensive simulation of a single sensor mobile robot that searches for a moving target, we will demonstrate how the effectiveness of the search depends on the sensory sensitivity and the inherent random walk strategies produced by the brain of the robot, comprising Ballistic, Levy, Brownian, and Stationary search. The result demonstrates the importance of embodied intelligence even in a behaviour inspired by the simplest creature.

The evolutionary maintenance of Lévy flight foraging

Lévy flight is a type of random walk that characterizes the behaviour of many natural phenomena studied across a multiplicity of academic disciplines; within biology specifically, the behaviour of fish, birds, insects, mollusks, bacteria, plants, slime molds, t-cells, and human populations. The Lévy flight foraging hypothesis states that because Lévy flights can maximize an organism's search efficiency, natural selection should result in Lévy-like behaviour. Empirical and theoretical research has provided ample evidence of Lévy walks in both extinct and extant species, and its efficiency across models with a diversity of resource distributions. However, no model has addressed the maintenance of Lévy flight foraging through evolutionary processes, and existing models lack ecological breadth. We use numerical simulations, including lineage-based models of evolution with a distribution of move lengths as a variable and heritable trait, to test the Lévy flight foraging hypothesis. We include biological and ecological contexts such as population size, searching costs, lifespan, resource distribution, speed, and consider both energy accumulated at the end of a lifespan and averaged over a lifespan. We demonstrate that selection often results in Lévy-like behaviour, although conditional; smaller populations, longer searches, and low searching costs increase the fitness of Lévy-like behaviour relative to Brownian behaviour. Interestingly, our results also evidence a bet-hedging strategy; Lévy-like behaviour reduces fitness variance, thus maximizing geometric mean fitness over multiple generations.

Intrinsic and environmental factors modulating autonomous robotic search under high uncertainty

Autonomous robotic search problems deal with different levels of uncertainty. When uncertainty is low, deterministic strategies employing available knowledge result in most effective searches. However, there are domains where uncertainty is always high since information about robot location, environment boundaries or precise reference points is unattainable, e.g., in cave, deep ocean, planetary exploration, or upon sensor or communications impairment. Furthermore, latency regarding when search targets move, appear or disappear add to uncertainty sources. Here we study intrinsic and environmental factors that affect low-informed robotic search based on diffusive Brownian, naive ballistic, and superdiffusive strategies (Lévy walks), and in particular, the effectiveness of their random exploration. Representative strategies were evaluated considering both intrinsic (motion drift, energy or memory limitations) and extrinsic factors (obstacles and search boundaries). Our results point towards minimum-knowledge based modulation approaches that can adjust distinct spatial and temporal aspects of random exploration to lead to effective autonomous search under uncertainty.

Excitable dynamics of Physarum polycephalum plasmodial nodes under chemotaxis

Recent results show that the chemotactic response of uni-cellular decentralized systems such as amoeboid and mammalian cells, is excitable. The same observation has not yet been reported for multi-nucleated decentralized biological systems. Here we present experimental results that shows the Physarum polycephalum plasmodial nodes spatio-temporal chemotactic dynamics as an excitable response. We found a highly optimized signal synthesis method wherein the Physarum nodes employ two intensity thresholds to properly navigate the chemoattractant field and generate corresponding spike dynamics in the node count. The node spike dynamics was found to correspond to the polarized-depolarized transition in the Physarum polycephalum morphology. Validation of our experimental observations via Brownian lattice simulations yields the same quantitative results with our experiments.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

Path Meander of Male Codling Moths (Cydia pomonella) Foraging for Sex Pheromone Plumes: Field Validation of a Novel Method for Quantifying Path Meander of Random Movers Developed Using Computer Simulations

Simple Summary

Measures of insect movement patterns are key to understanding how insects forage for resources and mating opportunities in their environment. Directly observing large numbers of these small organisms can be extremely challenging, especially for flying insects in low light conditions such as codling moth (Cydia pomonella), a key pest of apple. Here we provide a novel approach to indirectly measure the path meander of randomly moving organisms. Computer simulations were used to simulate insect movement across a wide range of possible movement patterns, measured in circular standard deviation (c.s.d.) of turn angles between track segments. For each c.s.d., the pattern of catch across a rectangular grid of traps was plotted and the resulting exponential decay constant (k) of the fitted lines were used to generate a standard curve describing this linear relationship. Using this standard curve, field data from target organisms caught in the described trapping grid can reveal the pattern of movement employed by these movers. Here we have demonstrated methodology for indirect measure of the movement patterns employed by random walkers such as C. pomonella. While we employed codling moth as our model system, we suggest this approach could prove useful in a wide range of other systems.

Abstract

Measures of path meander are highly relevant to studies of optimal foraging by animals. However, directly recording paths of small animals such as insects can be difficult because of small size or crepuscular activity. Computer simulations of correlated random walkers demonstrated that the rates of decay in captures across a rectangular grid of traps when movers were released at its corner can be used to produce calibration curves for quantifying path meander indirectly. Simulations using spatial parameters matching those previously documented for male codling moths (Cydia pomonella (L.)) foraging for female pheromone plumes in the field predicted that meander, as measured in circular standard deviation (c.s.d.) of turn angles between track segments, should be ca. 50° and 30° when the target population density is high vs. low, respectively. Thus, if optimized, the mean value measured for C. pomonella populations encountering an unknown target density should fall between these limits. We recorded decay in C. pomonella catch across a 5 × 5 grid of pheromone-baited traps each separated by 15 m on 39 occasions where batches of ca. 800 males were released 10 m outside the corner of trapping grids arranged in five large Michigan apple orchards. This decay constant was translated into mean c.s.d value for path meander using the standard curve generated by the computer simulations. The measured decay constant for C. pomonella males was negative 0.99 ± 0.02 (S.E.M.), which translates to a path meander of 37 ± 2° c.s.d. Thus, the measured path meander of 37° fell between the 50° and 30° values optimal for dense and sparse populations, respectively. In addition to providing a rare documented example of optimal foraging for odor plumes, this research offers proof-of-concept for a novel approach to quantifying path meander of movers that could prove useful across diverse taxa.

Muscle Coordination Control for an Asymmetrically Antagonistic-Driven Musculoskeletal Robot Using Attractor Selection

Recently, numerous musculoskeletal robots have been developed to realize the flexibility and dexterity analogous to human beings and animals. However, because the arrangement of many actuators is complex, the design of the control system for the robot is difficult and challenging. We believe that control methods inspired by living things are important in the development of the control systems for musculoskeletal robots. In this study, we propose a muscle coordination control method using attractor selection, a biologically inspired search method, for an antagonistic-driven musculoskeletal robot in which various muscles (monoarticular muscles and a polyarticular muscle) are arranged asymmetrically. First, muscle coordination control models for the musculoskeletal robot are built using virtual antagonistic muscle structures with a virtually symmetric muscle arrangement. Next, the attractor selection is applied to the control model and subsequently applied to the previous control model without muscle coordination to compare the control model's performance. Finally, position control experiments are conducted, and the effectiveness of the proposed muscle coordination control and the virtual antagonistic muscle structure is evaluated.

Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion

We investigate the logical information transmission of a synthetic gene network under Lévy flight superdiffusion by an information-based methodology. We first present the stochastic synthetic gene network model driven by a square wave signal under Lévy noise caused by Lévy flight superdiffusion. Then, to quantify the potential of logical information transmission and logical stochastic resonance, we theoretically obtain an information-based methodology of the symbol error rate, the noise entropy, and the mutual information of the logical information transmission. Consequently, based on the complementary "on" and "off" states shown in the logical information transmission for the repressive proteins, we numerically calculate the symbol error rate for logic gates, which demonstrate that the synthetic gene network under Lévy noise can achieve some logic gates as well as logical stochastic resonance. Furthermore, we calculate the noise entropy and the mutual information between the square wave signal and the logical information transmission, which reveal and quantify the potential of logical information transmission and logical stochastic resonance. In addition, we analyze the synchronization degree of the mutual information for the accomplished logical stochastic resonance of two repressive proteins of the synthetic gene network by synchronization variances, which shows that those mutual information changes almost synchronously.

Lévy noise improves the electrical activity in a neuron under electromagnetic radiation

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Lévy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Lévy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Lévy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Lévy noise intensity are depicted. The increasing of Lévy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Lévy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Lévy noise distribution are detected.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed.

Immune-inspired search strategies for robot swarms

Detection of targets distributed randomly in space is a task common to both robotic and biological systems. Lévy search has previously been used to characterize T cell search in the immune system. We use a robot swarm to evaluate the effectiveness of a Lévy search strategy and map the relationship between search parameters and target configurations. We show that the fractal dimension of the Lévy search which optimizes search efficiency depends strongly on the distribution of targets but only weakly on the number of agents involved in search. Lévy search can therefore be tuned to the target configuration while also being scalable. Implementing search behaviors observed in T cells in a robot swarm provides an effective, adaptable, and scalable swarm robotic search strategy. Additionally, the adaptability and scalability of Lévy search may explain why Lévy-like movement has been observed in T cells in multiple immunological contexts.

Ringed Seal Search for Global Optimization via a Sensitive Search Model

The efficiency of a metaheuristic algorithm for global optimization is based on its ability to search and find the global optimum. However, a good search often requires to be balanced between exploration and exploitation of the search space. In this paper, a new metaheuristic algorithm called Ringed Seal Search (RSS) is introduced. It is inspired by the natural behavior of the seal pup. This algorithm mimics the seal pup movement behavior and its ability to search and choose the best lair to escape predators. The scenario starts once the seal mother gives birth to a new pup in a birthing lair that is constructed for this purpose. The seal pup strategy consists of searching and selecting the best lair by performing a random walk to find a new lair. Affected by the sensitive nature of seals against external noise emitted by predators, the random walk of the seal pup takes two different search states, normal state and urgent state. In the normal state, the pup performs an intensive search between closely adjacent lairs; this movement is modeled via a Brownian walk. In an urgent state, the pup leaves the proximity area and performs an extensive search to find a new lair from sparse targets; this movement is modeled via a Levy walk. The switch between these two states is realized by the random noise emitted by predators. The algorithm keeps switching between normal and urgent states until the global optimum is reached. Tests and validations were performed using fifteen benchmark test functions to compare the performance of RSS with other baseline algorithms. The results show that RSS is more efficient than Genetic Algorithm, Particles Swarm Optimization and Cuckoo Search in terms of convergence rate to the global optimum. The RSS shows an improvement in terms of balance between exploration (extensive) and exploitation (intensive) of the search space. The RSS can efficiently mimic seal pups behavior to find best lair and provide a new algorithm to be used in global optimization problems.

Goal-directed multimodal locomotion through coupling between mechanical and attractor selection dynamics

One of the most significant challenges in bio-inspired robotics is how to realize and take advantage of multimodal locomotion, which may help robots perform a variety of tasks adaptively in different environments. In order to address the challenge properly, it is important to notice that locomotion dynamics are the result of interactions between a particular internal control structure, the mechanical dynamics and the environment. From this perspective, this paper presents an approach to enable a robot to take advantage of its multiple locomotion modes by coupling the mechanical dynamics of the robot with an internal control structure known as an attractor selection model. The robot used is a curved-beam hopping robot; this robot, despite its simple actuation method, possesses rich and complex mechanical dynamics that are dependent on its interactions with the environment. Through dynamical coupling, we will show how this robot performs goal-directed locomotion by gracefully shifting between different locomotion modes regulated by sensory input, the robot's mechanical dynamics and an internally generated perturbation. The efficacy of the approach is validated and discussed based on the simulation and on real-world experiments.

Scavengers on the move: behavioural changes in foraging search patterns during the annual cycle

BACKGROUND

Optimal foraging theory predicts that animals will tend to maximize foraging success by optimizing search strategies. However, how organisms detect sparsely distributed food resources remains an open question. When targets are sparse and unpredictably distributed, a Lévy strategy should maximize foraging success. By contrast, when resources are abundant and regularly distributed, simple brownian random movement should be sufficient. Although very different groups of organisms exhibit Lévy motion, the shift from a Lévy to a brownian search strategy has been suggested to depend on internal and external factors such as sex, prey density, or environmental context. However, animal response at the individual level has received little attention.

METHODOLOGY/PRINCIPAL FINDINGS

We used GPS satellite-telemetry data of Egyptian vultures Neophron percnopterus to examine movement patterns at the individual level during consecutive years, with particular interest in the variations in foraging search patterns during the different periods of the annual cycle (i.e. breeding vs. non-breeding). Our results show that vultures followed a brownian search strategy in their wintering sojourn in Africa, whereas they exhibited a more complex foraging search pattern at breeding grounds in Europe, including Lévy motion. Interestingly, our results showed that individuals shifted between search strategies within the same period of the annual cycle in successive years.

CONCLUSIONS/SIGNIFICANCE

Results could be primarily explained by the different environmental conditions in which foraging activities occur. However, the high degree of behavioural flexibility exhibited during the breeding period in contrast to the non-breeding period is challenging, suggesting that not only environmental conditions explain individuals' behaviour but also individuals' cognitive abilities (e.g., memory effects) could play an important role. Our results support the growing awareness about the role of behavioural flexibility at the individual level, adding new empirical evidence about how animals in general, and particularly scavengers, solve the problem of efficiently finding food resources.