Swarming bacteria migrate by Lévy Walk

Harnessing Disparities in Magnetic Microswarms: From Construction to Collaborative Tasks

Individual differences in size, experience, and task specialization in natural swarms often result in heterogeneity and hierarchy, facilitating efficient and coordinated task accomplishment. Drawing inspiration from this phenomenon, a general strategy is proposed for organizing magnetic micro/nanorobots (MNRs) with apparent differences in size, shape, and properties into cohesive microswarms with tunable heterogeneity, controlled spatial hierarchy, and collaborative tasking capability. In this strategy, disparate magnetic MNRs can be manipulated to show reversible transitions between synchronization and desynchronization by elaborately regulating parameter sets of the rotating magnetic field. Utilizing these transitions, alongside local robust hydrodynamic interactions, diverse heterospecific pairings of disparate magnetic MNRs can be organized into heterogeneous microswarms, and their spatial organization can be dynamically adjusted from egalitarian to leader-follower-like hierarchies on the fly, both in open space and complex microchannels. Furthermore, when specializing the disparate MNRs with distinct functions ("division of labor") such as sensing and drug carrying, they can execute precise drug delivery targeting unknown sites in a collaborative sensing-navigating-cargo dropping sequence, demonstrating significant potential for precise tumor treatment. These findings highlight the critical roles of attribute differences and hierarchical organization in designing efficient swarming micro/nanorobots for biomedical applications.

Complex behavior from intrinsic motivation to occupy future action-state path space

Most theories of behavior posit that agents tend to maximize some form of reward or utility. However, animals very often move with curiosity and seem to be motivated in a reward-free manner. Here we abandon the idea of reward maximization and propose that the goal of behavior is maximizing occupancy of future paths of actions and states. According to this maximum occupancy principle, rewards are the means to occupy path space, not the goal per se; goal-directedness simply emerges as rational ways of searching for resources so that movement, understood amply, never ends. We find that action-state path entropy is the only measure consistent with additivity and other intuitive properties of expected future action-state path occupancy. We provide analytical expressions that relate the optimal policy and state-value function and prove convergence of our value iteration algorithm. Using discrete and continuous state tasks, including a high-dimensional controller, we show that complex behaviors such as "dancing", hide-and-seek, and a basic form of altruistic behavior naturally result from the intrinsic motivation to occupy path space. All in all, we present a theory of behavior that generates both variability and goal-directedness in the absence of reward maximization.

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Nonequilibrium hyperuniform states in active turbulence

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to nonhyperuniformity and antihyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and nonuniversal diffusion in these systems, this allows for a biological interpretation and the speculation of nonequilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

Emerging Mesoscale Flows and Chaotic Advection in Dense Active Matter

We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Both models support active mesoscale flows, leading to chaotic advection and transport over large length scales in their homogeneous dense fluid states, away from dynamical arrest. They form streams and vortices reminiscent of multiscale flow patterns in turbulence. We show that the characteristics of these flows do not depend on the specific details of the active fluids, and result from the competition between crowding effects and persistent propulsions. This observation suggests that dense active suspensions of self-propelled particles present a type of "active turbulence" distinct from collective flows reported in other types of active systems.

Anomalous dynamics of a passive droplet in active turbulence

Motion of a passive deformable object in an active environment serves as a representative of both in-vivo systems such as intracellular particle motion in Acanthamoeba castellanii, or in-vitro systems such as suspension of beads inside dense swarms of Escherichia coli. Theoretical modeling of such systems is challenging due to the requirement of well resolved hydrodynamics which can explore the spatiotemporal correlations around the suspended passive object in the active fluid. We address this critical lack of understanding using coupled hydrodynamic equations for nematic liquid crystals with finite active stress to model the active bath, and a suspended nematic droplet with zero activity. The droplet undergoes deformation fluctuations and its movement shows periods of "runs" and "stays". At relatively low interfacial tension, the droplet begins to break and mix with the outer active bath. We establish that the motion of the droplet is influenced by the interplay of spatial correlations of the flow and the size of the droplet. The mean square displacement shows a transition from ballistic to normal diffusion which depends on the droplet size. We discuss this transition in relation to spatiotemporal scales associated with velocity correlations of the active bath and the droplet.

Lévy Flight Model of Gaze Trajectories to Assist in ADHD Diagnoses

The precise mathematical description of gaze patterns remains a topic of ongoing debate, impacting the practical analysis of eye-tracking data. In this context, we present evidence supporting the appropriateness of a Lévy flight description for eye-gaze trajectories, emphasizing its beneficial scale-invariant properties. Our study focuses on utilizing these properties to aid in diagnosing Attention-Deficit and Hyperactivity Disorder (ADHD) in children, in conjunction with standard cognitive tests. Using this method, we found that the distribution of the characteristic exponent of Lévy flights statistically is different in children with ADHD. Furthermore, we observed that these children deviate from a strategy that is considered optimal for searching processes, in contrast to non-ADHD children. We focused on the case where both eye-tracking data and data from a cognitive test are present and show that the study of gaze patterns in children with ADHD can help in identifying this condition. Since eye-tracking data can be gathered during cognitive tests without needing extra time-consuming specific tasks, we argue that it is in a prime position to provide assistance in the arduous task of diagnosing ADHD.

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.

Transition from active motion to anomalous diffusion for Bacillus subtilis confined in hydrogel matrices

We investigate the motility of B. subtilis under different degrees of confinement induced by transparent porous hydrogels. The dynamical behavior of the bacteria at short times is linked to characteristic parameters describing the hydrogel porosity. Mean squared displacements (MSDs) reveal that the run-and-tumble dynamics of unconfined B. subtilis progressively turns into sub-diffusive motion with increasing confinement. Correspondingly, the median instantaneous velocity of bacteria decreases and becomes more narrowly distributed, while the reorientation rate increases and reaches a plateau value. Analyzing single-trajectories, we show that the average dynamical behavior is the result of complex displacements, in which active, diffusive and sub-diffusive segments coexist. For small and moderate confinements, the number of active segments reduces, while the diffusive and sub-diffusive segments increase. The alternation of sub-diffusion, diffusion and active motion along the same trajectory can be described as a hopping ad trapping motion, in which hopping events correspond to displacements with an instantaneous velocity exceeding the corresponding mean value along a trajectory. Different from previous observations, escape from local trapping occurs for B. subtilis through active runs but also diffusion. Interestingly, the contribution of diffusion is maximum at intermediate confinements. At sufficiently long times transport coefficients estimated from the experimental MSDs under different degrees of confinement can be reproduced using a recently proposed hopping and trapping model. Finally, we propose a quantitative relationship linking the median velocity of confined and unconfined bacteria through the characteristic confinement length of the hydrogel matrix. Our work provides new insights for the bacterial motility in complex media that mimic natural environments and are relevant to important problems like sterilization, water purification, biofilm formation, membrane permeation and bacteria separation.

Order, chaos, and dimensionality transition in a system of swarmalators

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.

Size-dependent self-avoidance enables superdiffusive migration in macroscopic unicellulars

Many cells face search problems, such as finding food, mates, or shelter, where their success depends on their search strategy. In contrast to other unicellular organisms, the slime mold Physarum polycephalum forms a giant network-shaped plasmodium while foraging for food. What is the advantage of the giant cell on the verge of multicellularity? We experimentally study and quantify the migration behavior of P. polycephalum plasmodia on the time scale of days in the absence and presence of food. We develop a model which successfully describes its migration in terms of ten data-derived parameters. Using the mechanistic insights provided by our data-driven model, we find that regardless of the absence or presence of food, P. polycephalum achieves superdiffusive migration by performing a self-avoiding run-and-tumble movement. In the presence of food, the run duration statistics change, only controlling the short-term migration dynamics. However, varying organism size, we find that the long-term superdiffusion arises from self-avoidance determined by cell size, highlighting the potential evolutionary advantage that this macroscopically large cell may have.

In vivo imaging in transgenic songbirds reveals superdiffusive neuron migration in the adult brain

Neuron migration is a key phase of neurogenesis, critical for the assembly and function of neuronal circuits. In songbirds, this process continues throughout life, but how these newborn neurons disperse through the adult brain is unclear. We address this question using in vivo two-photon imaging in transgenic zebra finches that express GFP in young neurons and other cell types. In juvenile and adult birds, migratory cells are present at a high density, travel in all directions, and make frequent course changes. Notably, these dynamic migration patterns are well fit by a superdiffusive model. Simulations reveal that these superdiffusive dynamics are sufficient to disperse new neurons throughout the song nucleus HVC. These results suggest that superdiffusive migration may underlie the formation and maintenance of nuclear brain structures in the postnatal brain and indicate that transgenic songbirds are a useful resource for future studies into the mechanisms of adult neurogenesis.

Time-dependent properties of run-and-tumble particles: Density relaxation

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equation with anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross section and D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

Self-organization of active colloids mediated by chemical interactions

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

Anisotropic Diffusion of Elongated Particles in Active Coherent Flows

The study of particle diffusion, a classical conundrum in scientific inquiry, holds manifold implications for various real-world applications. Particularly within the domain of active flows, where the motion of self-propelled particles instigates fluid movement, extensive research has been dedicated to unraveling the dynamics of passive spherical particles. This scrutiny has unearthed intriguing phenomena, such as superdiffusion at brief temporal scales and conventional diffusion at longer intervals. In contrast to the spherical counterparts, anisotropic particles, which manifest directional variations, are prevalent in nature. Although anisotropic behavior in passive fluids has been subject to exploration, enigmatic aspects persist in comprehending the interplay of anisotropic particles within active flows. This research delves into the intricacies of anisotropic passive particle diffusion, exposing a notable escalation in translational and rotational diffusion coefficients, as well as the superdiffusion index, contingent upon bacterial concentration. Through a detailed examination of particle coordinates, the directional preference of particle diffusion is not solely dependent on the particle length, but rather determined by the ratio of the particle length to the associated length scale of the background flow field. These revelations accentuate the paramount importance of unraveling the nuances of anisotropic particle diffusion within the context of active flows. Such insights not only contribute to the fundamental understanding of particle dynamics, but also have potential implications for a spectrum of applications.

Anomalous diffusion, non-Gaussianity, nonergodicity, and confinement in stochastic-scaled Brownian motion with diffusing diffusivity dynamics

Scaled Brownian motions (SBMs) with power-law time-dependent diffusivity have been used to describe various types of anomalous diffusion yet Gaussian observed in granular gases kinetics, turbulent diffusion, and molecules mobility in cells, to name a few. However, some of these systems may exhibit non-Gaussian behavior which can be described by SBM with diffusing diffusivity (DD-SBM). Here, we numerically investigate both free and confined DD-SBM models characterized by fixed or stochastic scaling exponent of time-dependent diffusivity. The effects of distributed scaling exponent, random diffusivity, and confinement are considered. Different regimes of ultraslow diffusion, subdiffusion, normal diffusion, and superdiffusion are observed. In addition, weak ergodic and non-Gaussian behaviors are also detected. These results provide insights into diffusion in time-fluctuating diffusivity landscapes with potential applications to time-dependent temperature systems spreading in heterogeneous environments.

Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling

We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system described by the reaction-diffusion (RD) equation of Turing, focusing on anisotropic diffusion using the Finsler geometry (FG) modeling technique. In FG modeling, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor. Because of this dynamical diffusion coefficient, FG modeling of the RD equation sharply contrasts with the standard numerical technique in which direction-dependent coefficients are manually assumed. To find the solution of the RD equations in FG modeling, we use a hybrid numerical technique combining the Metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of the activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are a possible origin of spontaneously emergent anisotropic patterns of living organisms, such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with the direction of cell diffusion accompanied by thermal fluctuations.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Grazing livestock move by Lévy walks: Implications for soil health and environment

Grazing livestock plays an important role in the context of food security, agricultural sustainability and climate change. Understanding how livestock move and interact with their environment may offer new insights on how grazing practices impact soil and ecosystem functions at spatial and temporal scales where knowledge is currently limited. We characterized daily and seasonal grazing patterns using Global Positioning System (GPS) data from two grazing strategies: conventionally- and rotationally-grazed pastures. Livestock movement was consistent with the so-called Lévy walks, and could thus be simulated with Lévy-walk based probability density functions. Our newly introduced "Moovement model" links grazing patterns with soil structure and related functions by coupling animal movement and soil structure dynamics models, allowing to predict spatially-explicit changes in key soil properties. Predicted post-grazing management-specific bulk densities were consistent with field measurements and confirmed that rotational grazing produced similar disturbance as conventional grazing despite hosting higher stock densities. Harnessing information on livestock movement and its impacts in soil structure within a modelling framework can help testing and optimizing grazing strategies for ameliorating their impact on soil health and environment.

Random walk and cell morphology dynamics in Naegleria gruberi

Amoeboid cell movement and migration are wide-spread across various cell types and species. Microscopy-based analysis of the model systems Dictyostelium and neutrophils over the years have uncovered generality in their overall cell movement pattern. Under no directional cues, the centroid movement can be quantitatively characterized by their persistence to move in a straight line and the frequency of re-orientation. Mathematically, the cells essentially behave as a persistent random walker with memory of two characteristic time-scale. Such quantitative characterization is important from a cellular-level ethology point of view as it has direct connotation to their exploratory and foraging strategies. Interestingly, outside the amoebozoa and metazoa, there are largely uncharacterized species in the excavate taxon Heterolobosea including amoeboflagellate Naegleria. While classical works have shown that these cells indeed show typical amoeboid locomotion on an attached surface, their quantitative features are so far unexplored. Here, we analyzed the cell movement of Naegleria gruberi by employing long-time phase contrast imaging that automatically tracks individual cells. We show that the cells move as a persistent random walker with two time-scales that are close to those known in Dictyostelium and neutrophils. Similarities were also found in the shape dynamics which are characterized by the appearance, splitting and annihilation of the curvature waves along the cell edge. Our analysis based on the Fourier descriptor and a neural network classifier point to importance of morphology features unique to Naegleria including complex protrusions and the transient bipolar dumbbell morphologies.

Hexanic extract of Achyrocline satureioides: antimicrobial activity and in vitro inhibitory effect on mechanisms related to the pathogenicity of Paenibacillus larvae

INTRODUCTION

Paenibacillus larvae is a spore-forming bacillus, the most important bacterial pathogen of honeybee larvae and the causative agent of American foulbrood (AFB). Control measures are limited and represent a challenge for both beekeepers and researchers. For this reason, many studies focus on the search for alternative treatments based on natural products.

AIM

The objective of this study was to determine the antimicrobial activity of the hexanic extract (HE) of Achyrocline satureioides on P. larvae and the inhibitory activity on some mechanisms related to pathogenicity.

MATERIAL AND METHODS

The Minimum Inhibitory Concentration (MIC) of the HE was determined by the broth microdilution technique and the Minimum Bactericidal Concentration (MBC) by the microdrop technique. Swimming and swarming motility was evaluated in plates with 0.3 and 0.5% agar, respectively. Biofilm formation was evaluated and quantified by the Congo red and crystal violet method. The protease activity was evaluated by the qualitative technique on skim milk agar plates.

RESULTS

It was determined that the MIC of the HE on four strains of P. larvae ranged between 0.3 and 9.37 µg/ml and the MBC between 1.17 and 150 µg/ml. On the other hand, sub-inhibitory concentrations of the HE were able to decrease swimming motility, biofilm formation and the proteases production of P. larvae.

Cells collectively migrate during ammonium chemotaxis in Chlamydomonas reinhardtii

The mechanisms governing chemotaxis in Chlamydomonas reinhardtii are largely unknown compared to those regulating phototaxis despite equal importance on the migratory response in the ciliated microalga. To study chemotaxis, we made a simple modification to a conventional Petri dish assay. Using the assay, a novel mechanism governing Chlamydomonas ammonium chemotaxis was revealed. First, we found that light exposure enhances the chemotactic response of wild-type Chlamydomonas strains, yet phototaxis-incompetent mutant strains, eye3-2 and ptx1, exhibit normal chemotaxis. This suggests that Chlamydomonas transduces the light signal pathway in chemotaxis differently from that in phototaxis. Second, we found that Chlamydomonas collectively migrate during chemotaxis but not phototaxis. Collective migration during chemotaxis is not clearly observed when the assay is conducted in the dark. Third, the Chlamydomonas strain CC-124 carrying agg1^-, the AGGREGATE1 gene (AGG1) null mutation, exhibited a more robust collective migratory response than strains carrying the wild-type AGG1 gene. The expression of a recombinant AGG1 protein in the CC-124 strain suppressed this collective migration during chemotaxis. Altogether, these findings suggest a unique mechanism; ammonium chemotaxis in Chlamydomonas is mainly driven by collective cell migration. Furthermore, it is proposed that collective migration is enhanced by light and suppressed by the AGG1 protein.

Optimal foraging strategies for mutually avoiding competitors

Many animals are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Lévy distribution. Previous studies have shown that, under sparse and random resource conditions, solitary non-destructive (with regenerating resources) foragers perform a maximally efficient search with Lévy exponent μ equal to 2, while for destructive foragers, efficiency decreases with μ monotonically and there is no optimal μ. However, in nature, there also exist situations where multiple foragers, displaying avoidance behavior, interact with each other competitively. To understand the effects of such competition, we develop a stochastic agent-based simulation that models competitive foraging among mutually avoiding individuals by incorporating an avoidance zone, or territory, of a certain size around each forager which is not accessible for foraging by other competitors. For non-destructive foraging, our results show that with increasing size of the territory and number of agents the optimal Lévy exponent is still approximately 2 while the overall efficiency of the search decreases. At low values of the Lévy exponent, however, increasing territory size actually increases efficiency. For destructive foraging, we show that certain kinds of avoidance can lead to qualitatively different behavior from solitary foraging, such as the existence of an optimal search with 1<μ<2. Finally, we show that the variance among the efficiencies of the agents increases with increasing Lévy exponent for both solitary and competing foragers, suggesting that reducing variance might be a selective pressure for foragers adopting lower values of μ. Taken together, our results suggest that, for multiple foragers, mutual avoidance and efficiency variance among individuals can lead to optimal Lévy searches with exponents different from those for solitary foragers.

A machine learning approach to discover migration modes and transition dynamics of heterogeneous dendritic cells

Dendritic cell (DC) migration is crucial for mounting immune responses. Immature DCs (imDCs) reportedly sense infections, while mature DCs (mDCs) move quickly to lymph nodes to deliver antigens to T cells. However, their highly heterogeneous and complex innate motility remains elusive. Here, we used an unsupervised machine learning (ML) approach to analyze long-term, two-dimensional migration trajectories of Granulocyte-macrophage colony-stimulating factor (GMCSF)-derived bone marrow-derived DCs (BMDCs). We discovered three migratory modes independent of the cell state: slow-diffusive (SD), slow-persistent (SP), and fast-persistent (FP). Remarkably, imDCs more frequently changed their modes, predominantly following a unicyclic SD→FP→SP→SD transition, whereas mDCs showed no transition directionality. We report that DC migration exhibits a history-dependent mode transition and maturation-dependent motility changes are emergent properties of the dynamic switching of the three migratory modes. Our ML-based investigation provides new insights into studying complex cellular migratory behavior.

Inhibitory Potential of Thymus vulgaris Essential Oil against Growth, Biofilm Formation, Swarming, and Swimming in Pseudomonas syringae Isolates

As a follow-up to previous studies, the effects of Thymus vulgaris essential oil on selected virulence factors (growth, sessile cell survival, swimming, swarming, and exopolysaccharide production) were evaluated in phytopathogenic Pseudomonas syringae strains isolated from soybean fields in Argentina; reference strains Pseudomonas savastanoi pv. glycinea B076 and Pseudomonas aeruginosa PAO1. P. syringae are responsible for bacterial blight, a disease that affects crops worldwide. Plant bacterioses are usually treated with antibiotics and copper compounds, which may contribute to the development of resistance in pathogens and damage the environment. For these reasons, eco-friendly alternatives are necessary. Although aromatic plants are a natural source of antimicrobial substances, the effects of these substances on phytopathogenic bacteria remain largely unexplored. Subinhibitory concentrations of the oil significantly reduced the slope and rate of bacterial growth. In addition, biofilm and exopolysaccharide (EPS) production were inhibited, with swimming and swarming motility patterns being affected at all of the oil concentrations tested. Therefore, TEO could potentially be a highly efficient antipseudomonal agent for treating plant infections caused by P. syringae.

Population heterogeneity in the fractional master equation, ensemble self-reinforcement, and strong memory effects

We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population heterogeneity generates a random walk with conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). Through this, we establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We find the ensemble-averaged solution of the fractional master equation through subordination involving the fractional Poisson process counting the number of steps at a given time and the underlying discrete random walk with self-reinforcement. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1.

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.

Coexistence of ergodicity and nonergodicity in the aging two-state random walks

The two-state stochastic phenomenon is observed in various systems and is attracting more interest, and it can be described by the two-state random walk (TSRW) model. The TSRW model is a typical two-state renewal process alternating between the continuous-time random walk state and the Lévy walk state, in both of which the sojourn time distributions follow a power law. In this paper, by discussing the statistical properties and calculating the ensemble averaged and time averaged mean squared displacement, the ergodic property and the ultimate diffusive behavior of the aging TSRW is studied. Results reveal that because of the two-state intermittent feature, ergodicity and nonergodicity can coexist in the aging TSRW, which behave as the time scalings of the time averages and ensemble averages not being identically equal. In addition, we find that the unique state occupation mechanism caused by the diverging mean of the sojourn times of one state, determines the aging TSRW's ultimate diffusive behavior at extremely large timescales, i.e., instead of the term with the larger diffusion exponent, the diffusion is surprisingly characterized by the term with the smaller one, which is distinctly different from previous conclusions and known results. At last, we note that the Lévy walk with rests model which also displays aging and ergodicity breaking, can be generalized by the TSRW model.

Giant vortex dynamics in confined bacterial turbulence

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

Mixed-species bacterial swarms show an interplay of mixing and segregation across scales

Bacterial swarms are a highly-researched example of natural active matter. In particular, the interplay between biological interactions and the physics underlying the swarming dynamics is of both biological and physical interest. In this paper, we study mixed swarms of Bacillus subtilis and Pseudomonas aeruginosa. We find intricate interactions between the species, showing both cooperation and segregation across different spatial and temporal scales. On one hand, even though axenic colonies grow on disparate time scale, an order of magnitude apart, the two-species swarm together, forming a single, combined colony. However, the rapidly moving populations are locally segregated, with different characteristic speeds and lengths (or cluster sizes) that depend on the ratio between the species. Comparison with controlled mutant strains suggest that both the physical and known biological differences in species characteristics may not be enough to explain the segregation between the species in the mixed swarm. We hypothesize that the heterogeneous spatial distribution is due to some mechanism that enables bacteria to recognize their own kind, whose precise origin we could not identify.

Novel form of collective movement by soil bacteria

Although migrations are essential for soil microorganisms to exploit scarce and heterogeneously distributed resources, bacterial mobility in soil remains poorly studied due to experimental limitations. In this study, time-lapse images collected using live microscopy techniques captured collective and coordinated groups of B. subtilis cells exhibiting "crowd movement". Groups of B. subtilis cells moved through transparent soil (nafion polymer with particle size resembling sand) toward plant roots and re-arranged dynamically around root tips in the form of elongating and retracting "flocks" resembling collective behaviour usually associated with higher organisms (e.g., bird flocks or fish schools). Genetic analysis reveals B. subtilis flocks are likely driven by the diffusion of extracellular signalling molecules (e.g., chemotaxis, quorum sensing) and may be impacted by the physical obstacles and hydrodynamics encountered in the soil like environment. Our findings advance understanding of bacterial migration through soil matrices and expand known behaviours for coordinated bacterial movement.

Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells

Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D in vivo imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.

Discrepancy strategies of sediment abundant and rare microbial communities in response to floating microplastic disturbances: Study using a microcosmic experiment

Floating microplastics (FMPs) in surface water have been extensively studied, but their influence on sedimentary microbial ecosystems is poorly understood. Here, we investigated response patterns of abundant and rare sedimentary microbes to FMP disturbances by performing microcosmic experiments using fluvial sediment with polyethylene (PE), polylactic acid (PLA), polystyrene (PS) and polyvinyl chloride (PVC) MPs. The results indicated that FMPs altered sediment microbial community diversity and composition. Some organic-degrading, nitrifying and denitrifying bacteria significantly decreased in response to FMP disturbances, which may affect the sediment carbon and nitrogen cycles. Rare taxa persisted under FMP disturbances, whereas abundant taxa were more susceptible to FMP disturbances, suggesting a higher sensitivity of abundant taxa to FMP disturbances. Although stochastic processes governed the assembly of the overall microbial communities, the assembly mechanisms of abundant and rare populations have significantly different responses to FMP interference. The relative contribution of deterministic processes was reinforced by enhanced homogenous selection in abundant populations, while it markedly decreased in rare populations under FMP disturbances. Furthermore, FMPs substantially decreased the network complexity, loosened the coexistence relationships, and increased the negative correlations. Rare species play an important role in reshaping complex microbial interactions and coexistence networks in response to FMP disturbances. This research broadens our perspectives for comprehensively evaluating the ecological effects of FMPs in the aquatic environment to formulate further policy controls.

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.

Nanozyme-Triggered Cascade Reactions from Cup-Shaped Nanomotors Promote Active Cellular Targeting

Self-propelled nanomotors have shown enormous potential in biomedical applications. Herein, we report on a nanozyme-powered cup-shaped nanomotor for active cellular targeting and synergistic photodynamic/thermal therapy under near-infrared (NIR) laser irradiation. The nanomotor is constructed by the asymmetric decoration of platinum nanoparticles (PtNPs) at the bottom of gold nanocups (GNCs). PtNPs with robust peroxidase- (POD-) like activity are employed not only as propelling elements for nanomotors but also as continuous O₂ generators to promote photodynamic therapy via catalyzing endogenous H₂O₂ decomposition. Owing to the Janus structure, asymmetric propulsion force is generated to trigger the short-ranged directional diffusion, facilitating broader diffusion areas and more efficient cellular searching and uptake. This cascade strategy combines key capabilities, i.e., endogenous substrate-based self-propulsion, active cellular targeting, and enhanced dual-modal therapy, in one multifunctional nanomotor, which is crucial in advancing self-propelled nanomotors towards eventual therapeutic agents.

Biophysical aspects underlying the swarm to biofilm transition

Bacteria organize in a variety of collective states, from swarming-rapid surface exploration, to biofilms-highly dense immobile communities attributed to stress resistance. It has been suggested that biofilm and swarming are oppositely controlled, making this transition particularly interesting for understanding the ability of bacterial colonies to adapt to challenging environments. Here, the swarm to biofilm transition is studied in Bacillus subtilis by analyzing the bacterial dynamics both on the individual and collective scales. We show that both biological and physical processes facilitate the transition. A few individual cells that initiate the biofilm program cause nucleation of large, approximately scale-free, stationary aggregates of trapped swarm cells. Around aggregates, cells continue swarming almost unobstructed, while inside, trapped cells are added to the biofilm. While our experimental findings rule out previously suggested purely physical effects as a trigger for biofilm formation, they show how physical processes, such as clustering and jamming, accelerate biofilm formation.

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Physical characteristics of mixed-species swarming colonies

In nature, bacterial collectives typically consist of multiple species, which are interacting both biochemically and physically. Nonetheless, past studies on the physical properties of swarming bacteria were focused on axenic (single-species) populations. In bacterial swarming, intricate interactions between the individuals lead to clusters, rapid jets, and vortices that depend on cell characteristics such as speed and length. In this work, we show the first results of rapidly swarming mixed-species populations of Bacillus subtilis and Serratia marcescens, two model swarm species that are known to swarm well in axenic situations. In mixed liquid cultures, both species have higher reproduction rates. We show that the mixed population swarms together well and that the fraction between the species determines all dynamical scales-from the microscopic (e.g., speed distribution), mesoscopic (vortex size), and macroscopic (colony structure and size). Understanding mixed-species swarms is essential for a comprehensive understanding of the bacterial swarming phenomenon and its biological and evolutionary implications.

Infinite density and relaxation for Lévy walks in an external potential: Hermite polynomial approach

Lévy walks are continuous-time random-walk processes with a spatiotemporal coupling of jump lengths and waiting times. We here apply the Hermite polynomial method to study the behavior of LWs with power-law walking time density for four different cases. First we show that the known result for the infinite density of an unconfined, unbiased LW is consistently recovered. We then derive the asymptotic behavior of the probability density function (PDF) for LWs in a constant force field, and we obtain the corresponding qth-order moments. In a harmonic external potential we derive the relaxation dynamic of the LW. For the case of a Poissonian walking time an exponential relaxation behavior is shown to emerge. Conversely, a power-law decay is obtained when the mean walking time diverges. Finally, we consider the case of an unconfined, unbiased LW with decaying speed v(τ)=v_{0}/sqrt[τ]. When the mean walking time is finite, a universal Gaussian law for the position-PDF of the walker is obtained explicitly.

Strong anomalous diffusive behaviors of the two-state random walk process

The phenomenon of the two-state process is observed in various systems and is increasingly attracting attention, such that there is a need for a theoretical model of the process. In this paper, we present a prototypal two-state random walk (TSRW) model of a renewal process alternating between the continuous-time random walk (CTRW) state and Lévy walk (LW) state. The jump length distribution of the CTRW state is assumed to be Gaussian whereas the time distributions of the two states are both considered to follow a power law. The diffusive behavior is analyzed and discussed by calculating the mean squared displacement (MSD) analytically and numerically. The results reveal that it displays strong anomalous diffusive behaviors caused by random motions of both states, i.e., two anomalous diffusion terms coexist in the expression of the MSD, and the time distribution which has the heavier tail determines their forms. Moreover, because the two diffusion terms originate from different mechanisms, we find that the diffusion can be characterized by either the term with the largest diffusion exponent or the term with the largest diffusion coefficient at long timescales, which shows very different properties from the single-state process. In addition, the two-state nature of the process of the particle moving in a velocity field makes the TSRW model applicable to describe it. Results obtained from the two-state model reveal that the diffusion can even exhibit subdiffusive behavior, which is significantly different from known results obtained using the single-state model.

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.

Lévy walks with rests: Long-time analysis

In this paper we analyze the asymptotic behavior of Lévy walks with rests. Applying recent results in the field of functional convergence of continuous-time random walks we find the corresponding limiting processes. Depending on the parameters of the model, we show that in the limit we can obtain standard Lévy walk or the process describing competition between subdiffusion and Lévy flights. Some other more complicated limit forms are also possible to obtain. Finally we present some numerical results, which confirm our findings.

Orientational memory of active particles in multistate non-Markovian processes

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.

Surveying a Swarm: Experimental Techniques to Establish and Examine Bacterial Collective Motion

The survival and successful spread of many bacterial species hinges on their mode of motility. One of the most distinct of these is swarming, a collective form of motility where a dense consortium of bacteria employ flagella to propel themselves across a solid surface. Surface environments pose unique challenges, derived from higher surface friction/tension and insufficient hydration. Bacteria have adapted by deploying an array of mechanisms to overcome these challenges. Beyond allowing bacteria to colonize new terrain in the absence of bulk liquid, swarming also bestows faster speeds and enhanced antibiotic resistance to the collective. These crucial attributes contribute to the dissemination, and in some cases pathogenicity, of an array of bacteria. This mini-review highlights; 1) aspects of swarming motility that differentiates it from other methods of bacterial locomotion. 2) Facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges. 3) The (often difficult) approaches required to cultivate genuine swarmers. 4) The methods available to observe and assess the various facets of this collective motion, as well as the features exhibited by the population as a whole.

Single-cell tracking reveals super-spreading brain cancer cells with high persistence

Cell migration is a fundamental characteristic of vital processes such as tissue morphogenesis, wound healing and immune cell homing to lymph nodes and inflamed or infected sites. Therefore, various brain defect diseases, chronic inflammatory diseases as well as tumor formation and metastasis are associated with aberrant or absent cell migration. We embedded multicellular brain cancer spheroids in Matrigel™ and utilized single-particle tracking to extract the paths of cells migrating away from the spheroids. We found that - in contrast to local invasion - single cell migration is independent of Matrigel™ concentration and is characterized by high directionality and persistence. Furthermore, we identified a subpopulation of super-spreading cells with >200-fold longer persistence times than the majority of cells. These results highlight yet another aspect of cell heterogeneity in tumors.

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.

Correlated continuous-time random walk in the velocity field: the role of velocity and weak asymptotics

Within the framework of a space-time correlated continuous-time random walk model, anomalous diffusion of particles moving in the velocity field is studied in this paper. The weak asymptotic form ω(t) ∼ t^-(1+α), 1 < α < 2 for large t, is considered to be the waiting time distribution. The analytical results reveal that the diffusion in the velocity field, i.e., the mean squared displacement, can display a multi-fractional form caused by dispersive bias and space-time correlation. The numerical results indicate that the multi-fractional diffusion leads to a crossover phenomenon in-between the process at an intermediate timescale, followed by a steady state which is always determined by the largest diffusion exponent term. In addition, the role of velocity and weak asymptotics is discussed. The extremely small fluid velocity can characterize the diffusion by a diffusion coefficient instead of diffusion exponent, which is distinctly different from the former definition. In particular, for the waiting time displaying a weak asymptotic property, if the anomalous part is suppressed by the normal part, a second crossover phenomenon appears at an intermediate timescale, followed by a steady normal diffusion, which implies that the anomalies underlying the process are smoothed out at large timescales. Moreover, we discuss that the consideration of bias and correlation could help to avoid a possible not readily noticeable mistake in studying the topic concerned in this paper, which may be helpful in the relevant experimental research.

Objective comparison of methods to decode anomalous diffusion

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.