Current status and future directions of Lévy walk research

Semi-autonomous touch method merging robot's autonomous touch and user-operated touch for improving user experience in robot touch

The demand for therapeutic robots to alleviate mental health problems is growing. Studies have shown that people's mental health improves when they are touched. Consequently, therapeutic robots are designed to alleviate stress through robot's autonomous touch. However, robot's autonomous touch can sometimes cause discomfort to recipients. This paper proposes a semi-autonomous touch method that merges robot's autonomous touch with user-operated touch to mitigate discomfort while maintaining the sensation of being touched by another person. We conducted an experiment involving 24 participants who were touched on the neck by robots under three conditions: robot's autonomous touch, user-operated touch, and the proposed semi-autonomous touch method condition. Additionally, the study investigated participants' impressions of the robot in each condition. The results showed that semi-autonomous touch condition mitigated discomfort more effectively compared with the robot's autonomous touch method condition. It also enhanced the feeling of being touched by another person entity and suppressed interaction boredom compared with the user-operated touch method condition. Participants reported higher trustworthiness and perceived friendliness in robots utilizing the semi-autonomous touch method compared to those with autonomous touch method condition. These findings indicate that robots featuring the proposed semi-autonomous touch method can provide a comforting experience, leveraging the therapeutic benefits of being touched by another person, and underscore their potential in mental health applications.

Random walks with spatial and temporal resets can explain individual and colony-level searching patterns in ants

Central place foragers, such as many ants, exploit the environment around their nest. The extent of their foraging range is a function of individual movement, but how the movement patterns of large numbers of foragers result in an emergent colony foraging range remains unclear. Here, we introduce a random walk model with stochastic resetting to depict the movements of searching ants. Stochastic resetting refers to spatially resetting at random times the position of agents to a given location, here the nest of searching ants. We investigate the effect of a range of resetting mechanisms and compare the macroscopic predictions of our model to laboratory and field data. We find that all returning mechanisms very robustly ensure that scouts exploring the surroundings of a nest will be exponentially distributed with distance from the nest. We also find that a decreasing probability for searching ants to return to their nest is compatible with empirical data, resulting in scouts going further away from the nest as the number of foraging trips increases. Our findings highlight the importance of resetting random walk models for depicting the movements of central place foragers and nurture novel questions regarding the searching behaviour of ants.

Physiography, foraging mobility, and the first peopling of Sahul

The route and speed of migration into Sahul by Homo sapiens remain a major research question in archaeology. Here, we introduce an approach which models the impact of the physical environment on human mobility by combining time-evolving landscapes with Lévy walk foraging patterns, this latter accounting for a combination of short-distance steps and occasional longer moves that hunter-gatherers likely utilised for efficient exploration of new environments. Our results suggest a wave of dispersal radiating across Sahul following riverine corridors and coastlines. Estimated migration speeds, based on archaeological sites and predicted travelled distances, fall within previously reported range from Sahul and other regions. From our mechanistic movement simulations, we then analyse the likelihood of archaeological sites and highlight areas in Australia that hold archaeological potential. Our approach complements existing methods and provides interesting perspectives on the Pleistocene archaeology of Sahul that could be applied to other regions around the world.

Smart active particles learn and transcend bacterial foraging strategies

Throughout evolution, bacteria and other microorganisms have learned efficient foraging strategies that exploit characteristic properties of their unknown environment. While much research has been devoted to the exploration of statistical models describing the dynamics of foraging bacteria and other (micro-) organisms, little is known, regarding the question of how good the learned strategies actually are. This knowledge gap is largely caused by the absence of methods allowing to systematically develop alternative foraging strategies to compare with. In the present work, we use deep reinforcement learning to show that a smart run-and-tumble agent, which strives to find nutrients for its survival, learns motion patterns that are remarkably similar to the trajectories of chemotactic bacteria. Strikingly, despite this similarity, we also find interesting differences between the learned tumble rate distribution and the one that is commonly assumed for the run and tumble model. We find that these differences equip the agent with significant advantages regarding its foraging and survival capabilities. Our results uncover a generic route to use deep reinforcement learning for discovering search and collection strategies that exploit characteristic but initially unknown features of the environment. These results can be used, e.g., to program future microswimmers, nanorobots, and smart active particles for tasks like searching for cancer cells, micro-waste collection, or environmental remediation.

Intermittent Search, Not Strict Lévy Flight, Evolves under Relaxed Foraging Distribution Constraints

AbstractThe survival of an animal depends on its success as a forager, and understanding the adaptations that result in successful foraging strategies is an enduring endeavour of behavioral ecology. Random walks are one of the primary mathematical descriptions of foraging behavior. Power law distributions are often used to model random walks, as they can characterize a wide range of behaviors, including Lévy walks. Empirical evidence indicates the prevalence and efficiency of Lévy walks as a foraging strategy, and theoretical work suggests an evolutionary origin. However, previous evolutionary models have assumed a priori that move lengths are drawn from a power law or other families of distributions. Here, we remove this restriction with a model that allows for the evolution of any distribution. Instead of Lévy walks, our model unfailingly results in the evolution of intermittent search, a random walk composed of two disjoint modes-frequent localized walks and infrequent extensive moves-that consistently outcompeted Lévy walks. We also demonstrate that foraging using intermittent search may resemble a Lévy walk because of interactions with the resources within an environment. These extrinsically generated Lévy-like walks belie an underlying behavior and may explain the prevalence of Lévy walks reported in the literature.

Exploring the interplay between small and large scales movements in a neotropical small mammal

We record and analyze the movement patterns of the marsupial Didelphis aurita at different temporal scales. Animals trajectories are collected at a daily scale by using spool-and-line techniques and, with the help of radio-tracking devices, animals traveled distances are estimated at intervals of weeks. Small-scale movements are well described by truncated Lévy flight, while large-scale movements produce a distribution of distances which is compatible with a Brownian motion. A model of the movement behavior of these animals, based on a truncated Lévy flight calibrated on the small scale data, converges towards a Brownian behavior after a short time interval of the order of 1 week. These results show that whether Lévy flight or Brownian motion behaviors apply, will depend on the scale of aggregation of the animals paths. In this specific case, as the effect of the rude truncation present in the daily data generates a fast convergence towards Brownian behaviors, Lévy flights become of scarce interest for describing the local dispersion properties of these animals, which result well approximated by a normal diffusion process and not a fast, anomalous one. Interestingly, we are able to describe two movement phases as the consequence of a statistical effect generated by aggregation, without the necessity of introducing ecological constraints or mechanisms operating at different spatio-temporal scales. This result is of general interest, as it can be a key element for describing movement phenomenology at distinct spatio-temporal scales across different taxa and in a variety of systems.

Catastrophic storms, forest disturbance, and the natural history of Swainson's warbler

The core breeding range of Swainson's warbler (Limnothlypis swainsonii) overlaps a zone of exceptionally high tornado frequency in southeastern North America. The importance of tornadoes in creating breeding habitat for this globally rare warbler and other disturbance-dependent species has been largely overlooked. This paper estimates tornado frequency (1950-2021) and forest disturbance in the 240 counties and parishes in which breeding was documented from 1988 to 2014. The frequency of destructive tornadoes (EF1-EF5) varied 6-fold across the breeding range with a peak in the Gulf Coast states. Counties from east Texas to Alabama experienced the lowest median return interval of 5.4 years per 1000 km2, resulting in approximately 2477 ha of forest damage per 1000 km2 per century, based on current forestland cover. Tornadoes were significantly less frequent north and east of the core breeding range, with return intervals increasing to 9.1 years per 1000 km2 for breeding counties on the Atlantic coastal plain, 10.2 years per 1000 km2 in the Ozark Mountains, and 32.3 years per 1000 km2 in the Appalachian Mountains. Breeding counties within 150 km of the coastline from east Texas to North Carolina are also subjected to the highest frequency of hurricanes in the Western Hemisphere. Hurricanes often cause massive forest damage but archived meteorological and forestry data are insufficient to estimate the aggregate extent of forest disturbance in breeding counties. Nevertheless, the combined impact of tornadoes and hurricanes in the pre-Anthropogenic era was likely sufficient to produce a dynamic mosaic of early-successional forest crucial for the breeding ecology of Swainson's warbler. To ensure the long-term survival of this rare warbler, it is advisable to develop habitat management plans that incorporate remote sensing data on early-successional forest generated by catastrophic storms as well as anthropogenic activities.

Statistical modeling of mRNP transport in dendrites: A comparative analysis of β-actin and Arc mRNP dynamics

Localization of messenger RNA (mRNA) in dendrites is crucial for regulating gene expression during long-term memory formation. mRNA binds to RNA-binding proteins (RBPs) to form messenger ribonucleoprotein (mRNP) complexes that are transported by motor proteins along microtubules to their target synapses. However, the dynamics by which mRNPs find their target locations in the dendrite have not been well understood. Here, we investigated the motion of endogenous β-actin and Arc mRNPs in dissociated mouse hippocampal neurons using the MS2 and PP7 stem-loop systems, respectively. By evaluating the statistical properties of mRNP movement, we found that the aging Lévy walk model effectively describes both β-actin and Arc mRNP transport in proximal dendrites. A critical difference between β-actin and Arc mRNPs was the aging time, the time lag between transport initiation and measurement initiation. The longer mean aging time of β-actin mRNP (~100 s) compared with that of Arc mRNP (~30 s) reflects the longer half-life of constitutively expressed β-actin mRNP. Furthermore, our model also permitted us to estimate the ratio of newly generated and pre-existing β-actin mRNPs in the dendrites. This study offers a robust theoretical framework for mRNP transport, which provides insight into how mRNPs locate their targets in neurons.

Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks

Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues. Whether or not such control is achieved by utilizing different movement strategies in different tissues remains poorly understood. Liver-localized CD8 T cells perform correlated random walks  --- a type of a Brownian walk -- in liver sinusoids but in some condition these T cells may also perform Levy flights -- rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-localized CD8 T cells, specific to Toxoplasma gondii, perform generalized Levy walks -- a walk type in which T cells alternate pausing and displacing long distances --- which may indicate that brain is a unique organ where T cells exhibit movement strategies different from other tissues. Methods.  We quantified movement patterns of brain-localized Plasmodium berghei-specific CD4 and CD8 T cells by using well-established statistical and computational methods. Results.  We found that T cells change their movement pattern with time since infection and that CD4 T cells move faster and turn less than CD8 T cells. Importantly, both CD4 and CD8 T cells move in the brain by correlated random walks without long displacements challenging previous observations. We have also re-analyzed the movement data of brain-localized CD8 T cells in T. gondii-infected mice and found no evidence of Levy walks. We hypothesize that the previous conclusion of Levy walks of T. gondii-specific CD8 T cells in the brain was reached due to missing time-frames in the data that create an impression of large movement lengths between assumed-to-be-sequential movements.  Conclusion. Our results suggests that movement strategies of CD8 T cells are largely similar between LNs, liver, and the brain and consistent with correlated random walks and not Levy walks.

Linking neural circuits to the mechanics of animal behavior in Drosophila larval locomotion

The motions that make up animal behavior arise from the interplay between neural circuits and the mechanical parts of the body. Therefore, in order to comprehend the operational mechanisms governing behavior, it is essential to examine not only the underlying neural network but also the mechanical characteristics of the animal's body. The locomotor system of fly larvae serves as an ideal model for pursuing this integrative approach. By virtue of diverse investigation methods encompassing connectomics analysis and quantification of locomotion kinematics, research on larval locomotion has shed light on the underlying mechanisms of animal behavior. These studies have elucidated the roles of interneurons in coordinating muscle activities within and between segments, as well as the neural circuits responsible for exploration. This review aims to provide an overview of recent research on the neuromechanics of animal locomotion in fly larvae. We also briefly review interspecific diversity in fly larval locomotion and explore the latest advancements in soft robots inspired by larval locomotion. The integrative analysis of animal behavior using fly larvae could establish a practical framework for scrutinizing the behavior of other animal species.

Scanning behaviour in ants: an interplay between random-rate processes and oscillators

At the start of a journey home or to a foraging site, ants often stop, interrupting their forward movement, turn on the spot a number of times, and fixate in different directions. These scanning bouts are thought to provide visual information for choosing a path to travel. The temporal organization of such scanning bouts has implications about the neural organisation of navigational behaviour. We examined (1) the temporal distribution of the start of such scanning bouts and (2) the dynamics of saccadic body turns and fixations that compose a scanning bout in Australian desert ants, Melophorus bagoti, as they came out of a walled channel onto open field at the start of their homeward journey. Ants were caught when they neared their nest and displaced to different locations to start their journey home again. The observed parameters were mostly similar across familiar and unfamiliar locations. The turning angles of saccadic body turning to the right or left showed some stereotypy, with a peak just under 45°. The direction of such saccades appears to be determined by a slow oscillatory process as described in other insect species. In timing, however, both the distribution of inter-scanning-bout intervals and individual fixation durations showed exponential characteristics, the signature for a random-rate or Poisson process. Neurobiologically, therefore, there must be some process that switches behaviour (starting a scanning bout or ending a fixation) with equal probability at every moment in time. We discuss how chance events in the ant brain that occasionally reach a threshold for triggering such behaviours can generate the results.

Functional duality in group criticality via ambiguous interactions

Critical phenomena are wildly observed in living systems. If the system is at criticality, it can quickly transfer information and achieve optimal response to external stimuli. Especially, animal collective behavior has numerous critical properties, which are related to other research regions, such as the brain system. Although the critical phenomena influencing collective behavior have been extensively studied, two important aspects require clarification. First, these critical phenomena never occur on a single scale but are instead nested from the micro- to macro-levels (e.g., from a Lévy walk to scale-free correlation). Second, the functional role of group criticality is unclear. To elucidate these aspects, the ambiguous interaction model is constructed in this study; this model has a common framework and is a natural extension of previous representative models (such as the Boids and Vicsek models). We demonstrate that our model can explain the nested criticality of collective behavior across several scales (considering scale-free correlation, super diffusion, Lévy walks, and 1/f fluctuation for relative velocities). Our model can also explain the relationship between scale-free correlation and group turns. To examine this relation, we propose a new method, applying partial information decomposition (PID) to two scale-free induced subgroups. Using PID, we construct information flows between two scale-free induced subgroups and find that coupling of the group morphology (i.e., the velocity distributions) and its fluctuation power (i.e., the fluctuation distributions) likely enable rapid group turning. Thus, the flock morphology may help its internal fluctuation convert to dynamic behavior. Our result sheds new light on the role of group morphology, which is relatively unheeded, retaining the importance of fluctuation dynamics in group criticality.

Ants combine systematic meandering and correlated random walks when searching for unknown resources

Animal search movements are typically assumed to be mostly random walks, although non-random elements may be widespread. We tracked ants (Temnothorax rugatulus) in a large empty arena, resulting in almost 5 km of trajectories. We tested for meandering by comparing the turn autocorrelations for empirical ant tracks and simulated, realistic Correlated Random Walks. We found that 78% of ants show significant negative autocorrelation around 10 mm (3 body lengths). This means that turns in one direction are likely followed by turns in the opposite direction after this distance. This meandering likely makes the search more efficient, as it allows ants to avoid crossing their own paths while staying close to the nest, avoiding return-travel time. Combining systematic search with stochastic elements may make the strategy less vulnerable to directional inaccuracies. This study is the first to find evidence for efficient search by regular meandering in a freely searching animal.

Shortcuts to adiabaticity for Lévy processes in harmonic traps

Lévy stochastic processes, with noise distributed according to a Lévy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding "shortcuts to adiabaticity": After the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually employed for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach allowing to find exact analytical solutions for the required protocol. We generalize the approach to the wider class of Lévy stochastic processes, both in the overdamped and (for pure translations) in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.

aRNAque: an evolutionary algorithm for inverse pseudoknotted RNA folding inspired by Lévy flights

BACKGROUND

We study in this work the inverse folding problem for RNA, which is the discovery of sequences that fold into given target secondary structures.

RESULTS

We implement a Lévy mutation scheme in an updated version of aRNAque an evolutionary inverse folding algorithm and apply it to the design of RNAs with and without pseudoknots. We find that the Lévy mutation scheme increases the diversity of designed RNA sequences and reduces the average number of evaluations of the evolutionary algorithm. Compared to antaRNA, aRNAque CPU time is higher but more successful in finding designed sequences that fold correctly into the target structures.

CONCLUSION

We propose that a Lévy flight offers a better standard mutation scheme for optimizing RNA design. Our new version of aRNAque is available on GitHub as a python script and the benchmark results show improved performance on both Pseudobase++ and the Eterna100 datasets, compared to existing inverse folding tools.

Living on fire: Deactivating fire coral polyps for larval settlement and symbiosis in the fire coral-associated barnacle Wanella milleporae (Thoracicalcarea: Wanellinae)

Symbiosis is increasingly recognized as being an important component in marine systems, and many such relationships are initiated when free-swimming larvae of one partner settle and become sedentary on a host partner. Therefore, several crucial questions emerge such as the larva's mechanism of locating a host, selection of substratum and finally settlement on the surface of its future partner. Here, we investigated these mechanisms by studying how larvae of the fire coral-associated barnacle Wanella milleporae move, settle and establish symbiosis with their host, Millepora tenera. Cyprids of W. milleporae possess a pair of specialized antennules with bell-shaped attachment discs that enable them to explore and settle superficially on the hostile surface of the fire coral. Intriguingly, the stinging polyps of the fire coral remain in their respective pores when the cyprids explore the fire coral surface. Even when cyprids come into contact with the nematocysts on the extended stinging polyps during the exploratory phase, no immobilization effects against the cyprids were observed. The exploratory phase of Wanella cyprids can be divided into a sequence of wide searching (large step length and high walking speed), close searching (small step length and low speed) and inspection behavior, eventually resulting in permanent settlement and metamorphosis. After settlement, xenogeneic interactions occur between the fire coral and the newly metamorphosed juvenile barnacle. This involved tissue necrosis and regeneration in the fire coral host, leading to a callus ring structure around the juvenile barnacle, enhancing survival rate after settlement. The complex exploratory and settlement patterns and interactions documented here represent a breakthrough in coral reef symbiosis studies to show how invertebrates start symbiosis with fire corals.

Challenges of a small world analysis for the continuous monitoring of behavior in mice

Documenting a mouse's "real world" behavior in the "small world" of a laboratory cage with continuous video recordings offers insights into phenotypical expression of mouse genotypes, development and aging, and neurological disease. Nevertheless, there are challenges in the design of a small world, the behavior selected for analysis, and the form of the analysis used. Here we offer insights into small world analyses by describing how acute behavioral procedures can guide continuous behavioral methodology. We show how algorithms can identify behavioral acts including walking and rearing, circadian patterns of action including sleep duration and waking activity, and the organization of patterns of movement into home base activity and excursions, and how they are altered with aging. We additionally describe how specific tests can be incorporated within a mouse's living arrangement. We emphasize how machine learning can condense and organize continuous activity that extends over extended periods of time.

Drivers of fine-scale diurnal space use by a coral-reef mesopredatory fish

The habitat preferences of many reef fishes are well established, but the use of space within these habitats by non-site-attached species is poorly studied. The authors examined the space use of a functionally important mesopredator, graysby (Cephalopholis cruentata), on six patch reefs in the Florida Keys. A 1 m² -scale grid was constructed on each reef and 16 individual C. cruentata were tracked diurnally in situ to identify space use. At the patch reef scale, larger C. cruentata were more active and had larger observed home ranges, although home ranges were also affected by fish density and the abundances of prey and predators. The total time in each 1 m² grid cell was regressed against a range of fine-scale biotic variables, including multiple variables derived from structure-from-motion three-dimensional digital reconstructions of each reef. Nonetheless, time in grid cells (preferred microhabitats) was only significantly positively correlated with the height of carbonate structures, likely because the cavities they enclose are particularly suitable for predator avoidance, resting and ambushing prey. The ongoing flattening of reefs in the region caused by negative carbonate budgets is thus likely to have significant effects on the abundance and space use of C. cruentata. In addition to examining spatial patterns, we analysed C. cruentata waiting times in each grid cell before moving. These times were best approximated by a truncated power-law (heavy-tailed) distribution, indicating a "bursty" pattern of relatively long periods of inactivity interspersed with multiple periods of activity. Such a pattern has previously been identified in a range of temperate ambush predators, and the authors extend this move-wait behaviour, which may optimize foraging success, to a reef fish for the first time. Understanding how C. cruentata uses space and time is critical to fully identify their functional role and better predict the implications of fishing and loss of reef structure.

Liver Environment-Imposed Constraints Diversify Movement Strategies of Liver-Localized CD8 T Cells

Pathogen-specific CD8 T cells face the problem of finding rare cells that present their cognate Ag either in the lymph node or in infected tissue. Although quantitative details of T cell movement strategies in some tissues such as lymph nodes or skin have been relatively well characterized, we still lack quantitative understanding of T cell movement in many other important tissues, such as the spleen, lung, liver, and gut. We developed a protocol to generate stable numbers of liver-located CD8 T cells, used intravital microscopy to record movement patterns of CD8 T cells in livers of live mice, and analyzed these and previously published data using well-established statistical and computational methods. We show that, in most of our experiments, Plasmodium-specific liver-localized CD8 T cells perform correlated random walks characterized by transiently superdiffusive displacement with persistence times of 10-15 min that exceed those observed for T cells in lymph nodes. Liver-localized CD8 T cells typically crawl on the luminal side of liver sinusoids (i.e., are in the blood); simulating T cell movement in digital structures derived from the liver sinusoids illustrates that liver structure alone is sufficient to explain the relatively long superdiffusive displacement of T cells. In experiments when CD8 T cells in the liver poorly attach to the sinusoids (e.g., 1 wk after immunization with radiation-attenuated Plasmodium sporozoites), T cells also undergo Lévy flights: large displacements occurring due to cells detaching from the endothelium, floating with the blood flow, and reattaching at another location. Our analysis thus provides quantitative details of movement patterns of liver-localized CD8 T cells and illustrates how structural and physiological details of the tissue may impact T cell movement patterns.

A stochastic model of word occurrences in hierarchically structured written texts

In previous studies, we have treated real written texts as time series data and have tried to investigate dynamic correlations of word occurrences by utilizing autocorrelation functions (ACFs) and also by simulation of pseudo-text synthesis. The results showed that words that appear in written texts can be classified into two groups: a group of words showing dynamic correlations (Type-I words), and a group of words showing no dynamic correlations (Type-II words). In this study, we investigate the characteristics of these two types of words in terms of their waiting time distributions (WTDs) of word occurrences. The results for Type-II words show that the stochastic processes that govern generating Type-II words are superpositions of Poisson point processes with various rate constants. We further propose a model of WTDs for Type-I words in which the hierarchical structure of written texts is considered. The WTDs of Type-I words in real written texts agree well with the predictions of the proposed model, indicating that the hierarchical structure of written texts is important for generating long-range dynamic correlations of words.

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.

Simulations of Lévy Walk

The simulation of stable distributions was performed to study an ideal movement pattern for the spread of a virus using an autonomous carrier. It has been observed that Lévy walks are the most ideal way to spread and further study was done on how the parameters in Lévy distribution affect the spread.

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.

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale

BACKGROUND

To mitigate the spread of the COVID-19 coronavirus, some countries have adopted more stringent non-pharmaceutical interventions in contrast to those widely used. In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies also have been implemented, such as the total lockdown of fragmented regions, which are composed of sparsely and highly populated areas.

METHODS

In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host is infected if in close spatial proximity of the infectious host with an assigned transmission probability. Our focus is on a short-time scale (∼ 3 days), which is the average time lag time before an infected individual becomes infectious.

RESULTS

We find that the level of infection remains approximately constant with an increase in population diffusion, and also in the case of faster population dispersal (super-diffusion). Moreover, we demonstrate how the efficacy of imposing a lockdown depends heavily on how susceptible and infectious individuals are distributed over space.

CONCLUSION

Our results indicate that on a short-time scale, the type of movement behaviour does not play an important role in rising infection levels. Also, lock-down restrictions are ineffective if the population distribution is homogeneous. However, in the case of a heterogeneous population, lockdowns are effective if a large proportion of infectious carriers are distributed in sparsely populated sub-regions.

Intravascular Crawling of Patrolling Monocytes: A Lèvy-Like Motility for Unique Search Functions?

Patrolling monocytes (PMo) are the organism’s preeminent intravascular guardians by their continuous search of damaged endothelial cells and harmful microparticles for their removal and to restore homeostasis. This surveillance is accomplished by PMo crawling on the apical side of the endothelium through regulated interactions of integrins and chemokine receptors with their endothelial ligands. We propose that the search mode governs the intravascular motility of PMo in vivo in a similar way to T cells looking for antigen in tissues. Signs of damage to the luminal side of the endothelium (local death, oxidized LDL, amyloid deposits, tumor cells, pathogens, abnormal red cells, etc.) will change the diffusive random towards a Lèvy-like crawling enhancing their recognition and clearance by PMo damage receptors as the integrin αMβ2 and CD36. This new perspective can help identify new actors to promote unique PMo intravascular actions aimed at maintaining endothelial fitness and combating harmful microparticles involved in diseases as lung metastasis, Alzheimer’s angiopathy, vaso-occlusive disorders, and sepsis.

Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence

Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behavior of microorganisms, our Letter underlines the essential differences between active and inertial turbulence.

Weierstrassian Lévy walks are a by-product of crawling

Weierstrassian Lévy walks are one of the simplest random walks which do not satisfy the central limit theorem and have come to epitomize scale invariance even though they were initially regarded as being a mathematical abstraction. Here, I show how these Lévy walks can be generated intrinsically as a by-product of crawling, a common but ancient form of locomotion. This may explain why Weierstrassian Lévy walks provide accurate representations of the movement patterns of a diverse group of molluscs-certain mussels, mud snails and limpets. I show that such movements are not specific to molluscs as they are also evident in Drosophila larvae. The findings add to the growing realization that there are many idiosyncratic, seemingly accidental pathways to Lévy walking. And that the occurrence of Lévy walks need not be attributed to the execution of an advantageous searching strategy.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

Optimal escape-and-feeding dynamics of random walkers: Rethinking the convenience of ballistic strategies

Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dynamics is adaptive, so at short times an area-restricted search is carried out, and a switch to extensive or ballistic motion occurs later if necessary. We derive for this case explicit analytical expressions of the mean escape time and the asymptotic growth of the depleted region in one dimension. These, together with numerical results in two dimensions, provide surprising evidence that ballistic searches are detrimental in such scenarios, a result which could explain why ballistic movement is barely observed in animal searches at microscopic and millimetric scales, therefore providing significant implications for biological foraging.

Hypothetical control of postural sway

Quiet standing exhibits strongly intermittent variability that has inspired at least two interpretations. First, variability can be intermittent through the alternating engagement and disengagement of complementary control processes at distinct scales. A second and perhaps deeper way to interpret this intermittency is through the possibility that postural control depends on cascade-like interactions across many timescales at once, suggesting specific non-Gaussian distributional properties at different timescales. Multiscale probability density function (PDF) analysis shows that quiet standing on a stable surface exhibits a crossover from low, increasing non-Gaussianity (consistent with exponential distributions) at shorter timescales, reflecting inertial control, towards higher non-Gaussianity. Feedback-based control at medium to longer timescales yields a linear decrease that is characteristic of cascade dynamics. Destabilizing quiet standing with an unstable surface or closed eyes serves to attenuate inertial control and to elicit more of the feedback-based control over progressively shorter timescales. The result was to strengthen the appearance of the linear decay indicating cascade dynamics. Finally, both linear and nonlinear indices of postural sway also govern the relative strength of crossover or of linear decay, suggesting that tempering of non-Gaussianity across log-timescale is a function of both extrinsic constraints and endogenous postural control. These results provide new evidence that cascading interactions across longer timescales supporting postural corrections can even recruit shorter timescale processes with novel task constraints that can destabilize posture.

Foraging behavior in visual search: A review of theoretical and mathematical models in humans and animals

Visual search (VS) is a fundamental task in daily life widely studied for over half a century. A variant of the classic paradigm-searching one target among distractors-requires the observer to look for several (undetermined) instances of a target (so-called foraging) or several targets that may appear an undefined number of times (recently named as hybrid foraging). In these searches, besides looking for targets, the observer must decide how much time is needed to exploit the area, and when to quit the search to eventually explore new search options. In fact, visual foraging is a very common search task in the real world, probably involving additional cognitive functions than typical VS. It has been widely studied in natural animal environments, for which several mathematical models have been proposed, and just recently applied to humans: Lévy processes, composite and area-restricted search models, marginal value theorem, and Bayesian learning (among others). We conducted a systematic search in the literature to understand those mathematical models and study its applicability in human visual foraging. The review suggests that these models might be the first step, but they seem to be limited to fully comprehend foraging in visual search. There are essential variables involving human visual foraging still to be established and understood. Indeed, a jointly theoretical interpretation based on the different models reviewed could better account for its understanding. In addition, some other relevant variables, such as certain individual differences or time perception might be crucial to understanding visual foraging in humans.

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)10.1038/nmat4239]. We derive the nonhomogeneous in space and time, hyperbolic partial differential equation for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.

Sediment availability provokes a shift from Brownian to Lévy-like clonal expansion in a dune building grass

In biogeomorphic landscapes, plant traits can steer landscape development through plant-mediated feedback interactions. Interspecific differences in clonal expansion strategy can therefore lead to the emergence of different landscape organisations. Yet, whether landscape-forming plants adopt different clonal expansion strategies depending on their physical environment remains to be tested. Here, we use a field survey and a complementary mesocosm approach to investigate whether sediment deposition affects the clonal expansion strategy employed by dune-building marram grass individuals. Our results reveal a consistent shift in expansion pattern from more clumped, Brownian-like, movement in sediment-poor conditions, to patchier, Lévy-like, movement under high sediment supply rates. Additional model simulations illustrate that the sediment-dependent shift in movement strategies induces a shift in optimisation of the cost-benefit relation between landscape engineering (i.e. dune formation) and expansion. Plasticity in expansion strategy may therefore allow landscape-forming plants to optimise their engineering ability depending on their physical landscape.

Mechanism of C60 rotation and translation on hexagonal boron-nitride monolayer

Newly synthesized nanocars have shown great potential to transport molecular payloads. Since wheels of nanocars dominate their motion, the study of the wheels helps us to design a suitable surface for them. We investigated C₆₀ thermal diffusion on the hexagonal boron-nitride (h-BN) monolayer as the wheel of nanocars. We calculated C₆₀ potential energy variation during the translational and rotational motions at different points on the substrate. The study of the energy barriers and diffusion coefficients of the molecule at different temperatures indicated three noticeable changes in the C₆₀ motion regime. C₆₀ starts to slide on the surface at 30 K-40 K, slides freely on the boron-nitride monolayer at 100 K-150 K, and shows rolling motions at temperatures higher than 500 K. The anomaly parameter of the motion reveals that C₆₀ has a diffusive motion on the boron-nitride substrate at low temperatures and experiences superdiffusion with Levy flight motions at higher temperatures. A comparison of the fullerene motion on the boron-nitride and graphene surfaces demonstrated that the analogous structure of the graphene and hexagonal boron-nitride led to similar characteristics such as anomaly parameters and the temperatures at which the motion regime changes. The results of this study empower us to predict that fullerene prefers to move on boron-nitride sections on a hybrid substrate composed of graphene and boron-nitride. This property can be utilized to design pathways or regions on a surface to steer or trap the C₆₀ or other molecular machines, which is a step toward directional transportation at the molecular scale.

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

Development of an automatic turntable-type multiple T-maze device and observation of pill bug behavior

In recent years, various animal observation instruments have been developed to support long-term measurement and analysis of animal behaviors. This study proposes an automatic observation instrument that specializes for turning behaviors of pill bugs and aims to obtain new knowledge in the field of ethology. Pill bugs strongly tend to turn in the opposite direction of a preceding turn. This alternation of turning is called turn alternation reaction. However, a repetition of turns in the same direction is called turn repetition reaction and has been considered a malfunction of turn alternation. In this research, the authors developed an automatic turntable-type multiple T-maze device and observed the turning behavior of 34 pill bugs for 6 h to investigate whether turn repetition is a malfunction. As a result, most of the pill bug movements were categorized into three groups: sub-diffusion, Brownian motion, and Lévy walk. This result suggests that pill bugs do not continue turn alternation mechanically but elicit turn repetition moderately, which results in various movement patterns. In organisms with relatively simple nervous systems such as pill bugs, stereotypical behaviors such as turn alternation have been considered mechanical reactions and variant behaviors such as turn repetition have been considered malfunctions. However, our results suggest that a moderate generation of turn repetition is involved in the generation of various movement patterns. This study is expected to provide a new perspective on the conventional view of the behaviors of simple organisms.

The growth and form of knowledge networks by kinesthetic curiosity

Throughout life, we might seek a calling, companions, skills, entertainment, truth, self-knowledge, beauty, and edification. The practice of curiosity can be viewed as an extended and open-ended search for valuable information with hidden identity and location in a complex space of interconnected information. Despite its importance, curiosity has been challenging to computationally model because the practice of curiosity often flourishes without specific goals, external reward, or immediate feedback. Here, we show how network science, statistical physics, and philosophy can be integrated into an approach that coheres with and expands the psychological taxonomies of specific-diversive and perceptual-epistemic curiosity. Using this interdisciplinary approach, we distill functional modes of curious information seeking as searching movements in information space. The kinesthetic model of curiosity offers a vibrant counterpart to the deliberative predictions of model-based reinforcement learning. In doing so, this model unearths new computational opportunities for identifying what makes curiosity curious.

Functional advantages of Lévy walks emerging near a critical point

A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might be enhanced by criticality. However, the functional advantages of Lévy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Lévy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed empirically that the Lévy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained on the basis of these functional advantages.

Intravital Imaging of Adoptive T-Cell Morphology, Mobility and Trafficking Following Immune Checkpoint Inhibition in a Mouse Melanoma Model

Efficient T-cell targeting, infiltration and activation within tumors is crucial for successful adoptive T-cell therapy. Intravital microscopy is a powerful tool for the visualization of T-cell behavior within tumors, as well as spatial and temporal heterogeneity in response to immunotherapy. Here we describe an experimental approach for intravital imaging of adoptive T-cell morphology, mobility and trafficking in a skin-flap tumor model, following immune modulation with immune checkpoint inhibitors (ICIs) targeting PD-L1 and CTLA-4. A syngeneic model of ovalbumin and mCherry-expressing amelanotic mouse melanoma was used in conjunction with adoptively transferred OT-1+ cytotoxic T-cells expressing GFP to image antigen-specific live T-cell behavior within the tumor microenvironment. Dynamic image analysis of T-cell motility showed distinct CD8+ T-cell migration patterns and morpho-dynamics within different tumor compartments in response to ICIs: this approach was used to cluster T-cell behavior into four groups based on velocity and meandering index. The results showed that most T-cells within the tumor periphery demonstrated Lévy-like trajectories, consistent with tumor cell searching strategies. T-cells adjacent to tumor cells had reduced velocity and appeared to probe the local environment, consistent with cell-cell interactions. An increased number of T-cells were detected following treatment, traveling at lower mean velocities than controls, and demonstrating reduced displacement consistent with target engagement. Histogram-based analysis of immunofluorescent images from harvested tumors showed that in the ICI-treated mice there was a higher density of CD31+ vessels compared to untreated controls and a greater infiltration of T-cells towards the tumor core, consistent with increased cellular trafficking post-treatment.

Jellyfish and Fish Solve the Challenges of Turning Dynamics Similarly to Achieve High Maneuverability

Turning maneuvers by aquatic animals are essential for fundamental life functions such as finding food or mates while avoiding predation. However, turning requires resolution of a fundamental dilemma based in rotational mechanics: the force powering a turn (torque) is favored by an expanded body configuration that maximizes lever arm length, yet minimizing the resistance to a turn (the moment of inertia) is favored by a contracted body configuration. How do animals balance these opposing demands? Here, we directly measure instantaneous forces along the bodies of two animal models—the radially symmetric Aurelia aurita jellyfish, and the bilaterally symmetric Danio rerio zebrafish—to evaluate their turning dynamics. Both began turns with a small, rapid shift in body kinematics that preceded major axial rotation. Although small in absolute magnitude, the high fluid accelerations achieved by these initial motions generated powerful pressure gradients that maximized torque at the start of a turn. This pattern allows these animals to initially maximize torque production before major body curvature changes. Both animals then subsequently minimized the moment of inertia, and hence resistance to axial rotation, by body bending. This sequential solution provides insight into the advantages of re-arranging mass by bending during routine swimming turns.

Universality in the Onset of Superdiffusion in Lévy Walks

Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic superdiffusive behavior is explored using the 1D Lévy walk of order 1<β<2. The approach towards superdiffusion, as captured by the leading correction to the asymptotic behavior, is shown to remarkably undergo a transition as β crosses the critical value β_{c}=3/2. Above β_{c}, this correction scales as |x|∼t^{1/2}, describing simple diffusion. However, below β_{c} it is instead found to remain superdiffusive, scaling as |x|∼t^{1/(2β-1)}. This transition is shown to be independent of the precise model details and is thus argued to be universal.

Mechanisms underlying attraction to odors in walking Drosophila

Mechanisms that control movements range from navigational mechanisms, in which the animal employs directional cues to reach a specific destination, to search movements during which there are little or no environmental cues. Even though most real-world movements result from an interplay between these mechanisms, an experimental system and theoretical framework for the study of interplay of these mechanisms is not available. Here, we rectify this deficit. We create a new method to stimulate the olfactory system in Drosophila or fruit flies. As flies explore a circular arena, their olfactory receptor neuron (ORNs) are optogenetically activated within a central region making this region attractive to the flies without emitting any clear directional signals outside this central region. In the absence of ORN activation, the fly’s locomotion can be described by a random walk model where a fly’s movement is described by its speed and turn-rate (or kinematics). Upon optogenetic stimulation, the fly’s behavior changes dramatically in two respects. First, there are large kinematic changes. Second, there are more turns at the border between light-zone and no-light-zone and these turns have an inward bias. Surprisingly, there is no increase in turn-rate, rather a large decrease in speed that makes it appear that the flies are turning at the border. Similarly, the inward bias of the turns is a result of the increase in turn angle. These two mechanisms entirely account for the change in a fly’s locomotion. No complex mechanisms such as path-integration or a careful evaluation of gradients are necessary.

The strategy an animal employs to explore the environment and to find and return to the location where it has previously found food or mates is an important part of its behavior. In nature, animals have incomplete information about their environment, and must use this incomplete information to navigate. In most laboratory experiments, there is usually clear directional information making it difficult to infer an animal’s real strategy from laboratory behavioral experiments. In this study, we devise a new behavioral task wherein we remotely activate olfactory neurons when fruit flies are in a given location. This activation makes a given location attractive to the flies without providing any directional information and allows us to assess how flies navigate under these conditions. We find that flies navigate towards the activated location using two simple mechanisms: First, its speed in the activated region and its turn rate is much lower than it is elsewhere. Second, at the boundary of the odor-zone, its speed decreases dramatically and its turns become much sharper. Essentially, these simple mechanisms appear to be extremely robust.

Rare events in generalized Lévy Walks and the Big Jump principle

The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare events. According to the principle, in heavy-tailed processes a rare huge fluctuation is caused by a single event and not by the usual coherent accumulation of small deviations. We consider generalized Lévy walks, a class of stochastic processes with power law distributed step durations and with complex microscopic dynamics in the single stretch. We derive the bulk of the probability distribution and using the big jump principle, the exact form of the tails that describes rare events. We show that the tails of the distribution present non-universal and non-analytic behaviors, which depend crucially on the dynamics of the single step. The big jump estimate also provides a physical explanation of the processes driving the rare events, opening new possibilities for their correct prediction.

Optimal searching behaviour generated intrinsically by the central pattern generator for locomotion

Efficient searching for resources such as food by animals is key to their survival. It has been proposed that diverse animals from insects to sharks and humans adopt searching patterns that resemble a simple Lévy random walk, which is theoretically optimal for 'blind foragers' to locate sparse, patchy resources. To test if such patterns are generated intrinsically, or arise via environmental interactions, we tracked free-moving Drosophila larvae with (and without) blocked synaptic activity in the brain, suboesophageal ganglion (SOG) and sensory neurons. In brain-blocked larvae, we found that extended substrate exploration emerges as multi-scale movement paths similar to truncated Lévy walks. Strikingly, power-law exponents of brain/SOG/sensory-blocked larvae averaged 1.96, close to a theoretical optimum (µ ≅ 2.0) for locating sparse resources. Thus, efficient spatial exploration can emerge from autonomous patterns in neural activity. Our results provide the strongest evidence so far for the intrinsic generation of Lévy-like movement patterns.