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1.
Nano Lett ; 24(20): 5958-5967, 2024 May 22.
Artículo en Inglés | MEDLINE | ID: mdl-38738749

RESUMEN

Micro/nanorobots hold the potential to revolutionize biomedicine by executing diverse tasks in hard-to-reach biological environments. Nevertheless, achieving precise drug delivery to unknown disease sites using swarming micro/nanorobots remains a significant challenge. Here we develop a heterogeneous swarm comprising sensing microrobots (sensor-bots) and drug-carrying microrobots (carrier-bots) with collaborative tasking capabilities for precise drug delivery toward unknown sites. Leveraging robust interspecific hydrodynamic interactions, the sensor-bots and carrier-bots spontaneously synchronize and self-organize into stable heterogeneous microswarms. Given that the sensor-bots can create real-time pH maps employing pH-responsive structural-color changes and the doxorubicin-loaded carrier-bots exhibit selective adhesion to acidic targets via pH-responsive charge reversal, the sensor-carrier microswarm, when exploring unknown environments, can detect and localize uncharted acidic targets, guide itself to cover the area, and finally deploy therapeutic carrier-bots precisely there. This versatile platform holds promise for treating diseases with localized acidosis and inspires future theranostic microsystems with expandability, task flexibility, and high efficiency.


Asunto(s)
Doxorrubicina , Sistemas de Liberación de Medicamentos , Doxorrubicina/química , Doxorrubicina/farmacología , Concentración de Iones de Hidrógeno , Acidosis , Humanos , Portadores de Fármacos/química , Robótica
2.
Sensors (Basel) ; 24(2)2024 Jan 22.
Artículo en Inglés | MEDLINE | ID: mdl-38276398

RESUMEN

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms.

3.
Phys Biol ; 20(5)2023 08 22.
Artículo en Inglés | MEDLINE | ID: mdl-37557188

RESUMEN

In contrast with laboratory insect swarms, wild insect swarms display significant coordinated behaviour. It has been hypothesised that the presence of a fluctuating environment drives the formation of transient, local order (synchronized subgroups), and that this local order pushes the swarm into a new state that is robust to environmental perturbations. The hypothesis is supported by observations of swarming mosquitoes. Here I provide numerical evidence that the formation of transient, local order is an accidental by-product of the strengthening of short-range repulsion which is expected in the presence of environmental fluctuations. The results of the numerical simulations reveal that this strengthening of the short-range can drive swarms into a crystalline phase containing subgroups that participate in cooperative ring exchanges-a new putative form of collective animal movement lacking velocity correlation. I thereby demonstrate that the swarm state and structure may be tuneable with environmental noise as a control parameter. Predicted properties of the collective modes are consistent with observations of transient synchronized subgroups in wild mosquito swarms that contend with environmental disturbances. When mutual repulsion becomes sufficiently strong, swarms are, in accordance with observations, predicted to form near stationary crystalline states. The analysis suggests that the many different forms of swarming motions observed across insect species are not distinctly different phenomena but are instead different phases of a single phenomenon.


Asunto(s)
Conducta Animal , Insectos , Animales , Movimiento (Física) , Movimiento
4.
Artif Life ; 29(1): 21-36, 2023 01 02.
Artículo en Inglés | MEDLINE | ID: mdl-36222754

RESUMEN

There has been growing interest in the use of multi-robot systems in various tasks and scenarios. The main attractiveness of such systems is their flexibility, robustness, and scalability. An often overlooked yet promising feature is system modularity, which offers the possibility of harnessing agent specialization, while also enabling system-level upgrades. However, altering the agents' capacities can change the exploration-exploitation balance required to maximize the system's performance. Here, we study the effect of a swarm's heterogeneity on its exploration-exploitation balance while tracking multiple fast-moving evasive targets under the cooperative multi-robot observation of multiple moving targets framework. To this end, we use a decentralized search and tracking strategy with adjustable levels of exploration and exploitation. By indirectly tuning the balance, we first confirm the presence of an optimal balance between these two key competing actions. Next, by substituting slower moving agents with faster ones, we show that the system exhibits a performance improvement without any modifications to the original strategy. In addition, owing to the additional amount of exploitation carried out by the faster agents, we demonstrate that a heterogeneous system's performance can be further improved by reducing an agent's level of connectivity, to favor the conduct of exploratory actions. Furthermore, in studying the influence of the density of swarming agents, we show that the addition of faster agents can counterbalance a reduction in the overall number of agents while maintaining the level of tracking performance. Finally, we explore the challenges of using differentiated strategies to take advantage of the heterogeneous nature of the swarm.

5.
Proc Natl Acad Sci U S A ; 117(19): 10188-10194, 2020 05 12.
Artículo en Inglés | MEDLINE | ID: mdl-32345716

RESUMEN

Oceanic transform faults display a unique combination of seismic and aseismic slip behavior, including a large globally averaged seismic deficit, and the local occurrence of repeating magnitude (M) [Formula: see text] earthquakes with abundant foreshocks and seismic swarms, as on the Gofar transform of the East Pacific Rise and the Blanco Ridge in the northeast Pacific Ocean. However, the underlying mechanisms that govern the partitioning between seismic and aseismic slip and their interaction remain unclear. Here we present a numerical modeling study of earthquake sequences and aseismic transient slip on oceanic transform faults. In the model, strong dilatancy strengthening, supported by seismic imaging that indicates enhanced fluid-filled porosity and possible hydrothermal circulation down to the brittle-ductile transition, effectively stabilizes along-strike seismic rupture propagation and results in rupture barriers where aseismic transients arise episodically. The modeled slow slip migrates along the barrier zones at speeds ∼10 to 600 m/h, spatiotemporally correlated with the observed migration of seismic swarms on the Gofar transform. Our model thus suggests the possible prevalence of episodic aseismic transients in M [Formula: see text] rupture barrier zones that host active swarms on oceanic transform faults and provides candidates for future seafloor geodesy experiments to verify the relation between aseismic fault slip, earthquake swarms, and fault zone hydromechanical properties.

6.
IEEE Sens J ; 23(2): 955-968, 2023 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-36913217

RESUMEN

Recently, unmanned aerial vehicles (UAVs) are deployed in Novel Coronavirus Disease-2019 (COVID-19) vaccine distribution process. To address issues of fake vaccine distribution, real-time massive UAV monitoring and control at nodal centers (NCs), the authors propose SanJeeVni, a blockchain (BC)-assisted UAV vaccine distribution at the backdrop of sixth-generation (6G) enhanced ultra-reliable low latency communication (6G-eRLLC) communication. The scheme considers user registration, vaccine request, and distribution through a public Solana BC setup, which assures a scalable transaction rate. Based on vaccine requests at production setups, UAV swarms are triggered with vaccine delivery to NCs. An intelligent edge offloading scheme is proposed to support UAV coordinates and routing path setups. The scheme is compared against fifth-generation (5G) uRLLC communication. In the simulation, we achieve and 86% improvement in service latency, 12.2% energy reduction of UAV with 76.25% more UAV coverage in 6G-eRLLC, and a significant improvement of [Formula: see text]% in storage cost against the Ethereum network, which indicates the scheme efficacy in practical setups.

7.
Sensors (Basel) ; 23(23)2023 Nov 30.
Artículo en Inglés | MEDLINE | ID: mdl-38067897

RESUMEN

UAVs need to communicate along three dimensions (3D) with other aerial vehicles, ranging from above to below, and often need to connect to ground stations. However, wireless transmission in 3D space significantly dissipates power, often hindering the range required for these types of links. Directional transmission is one way to efficiently use available wireless channels to achieve the desired range. While multiple-input multiple-output (MIMO) systems can digitally steer the beam through channel matrix manipulation without needing directional awareness, the power resources required for operating multiple radios on a UAV are often logistically challenging. An alternative approach to streamline resources is the use of phased arrays to achieve directionality in the analog domain, but this requires beam sweeping and results in search-time delay. The complexity and search time can increase with the dynamic mobility pattern of the UAVs in aerial networks. However, if the direction of the receiver is known at the transmitter, the search time can be significantly reduced. In this work, multi-antenna channels between two UAVs in A2A links are analyzed, and based on these findings, an efficient machine learning-based method for estimating the direction of a transmitting node using channel estimates of 4 antennas (2 × 2 MIMO) is proposed. The performance of the proposed method is validated and verified through in-field drone-to-drone measurements. Findings indicate that the proposed method can estimate the direction of the transmitter in the A2A link with 86% accuracy. Further, the proposed direction estimation method is deployable for UAV-based massive MIMO systems to select the directional beam without the need to sweep or search for optimal communication performance.

8.
Sensors (Basel) ; 23(23)2023 Nov 30.
Artículo en Inglés | MEDLINE | ID: mdl-38067913

RESUMEN

This study presents the Drone Swarms Routing Problem (DSRP), which consists of identifying the maximum number of victims in post-disaster areas. The post-disaster area is modeled in a complete graph, where each search location is represented by a vertex, and the edges are the shortest paths between destinations, with an associated weight, corresponding to the battery consumption to fly to a location. In addition, in the DSRP addressed here, a set of drones are deployed in a cooperative drone swarms approach to boost the search. In this context, a V-shaped formation is applied with leader replacements, which allows energy saving. We propose a computation model for the DSRP that considers each drone as an agent that selects the next search location to visit through a simple and efficient method, the Drone Swarm Heuristic. In order to evaluate the proposed model, scenarios based on the Beirut port explosion in 2020 are used. Numerical experiments are presented in the offline and online versions of the proposed method. The results from such scenarios showed the efficiency of the proposed approach, attesting not only the coverage capacity of the computational model but also the advantage of adopting the V-shaped formation flight with leader replacements.

9.
Entropy (Basel) ; 25(4)2023 Apr 16.
Artículo en Inglés | MEDLINE | ID: mdl-37190455

RESUMEN

Greece exhibits the highest seismic activity in Europe, manifested in intense seismicity with large magnitude events and frequent earthquake swarms. In the present work, we analyzed the spatiotemporal properties of recent earthquake swarms that occurred in the broader area of Greece using the Non-Extensive Statistical Physics (NESP) framework, which appears suitable for studying complex systems. The behavior of complex systems, where multifractality and strong correlations among the elements of the system exist, as in tectonic and volcanic environments, can adequately be described by Tsallis entropy (Sq), introducing the Q-exponential function and the entropic parameter q that expresses the degree of non-additivity of the system. Herein, we focus the analysis on the 2007 Trichonis Lake, the 2016 Western Crete, the 2021-2022 Nisyros, the 2021-2022 Thiva and the 2022 Pagasetic Gulf earthquake swarms. Using the seismicity catalogs for each swarm, we investigate the inter-event time (T) and distance (D) distributions with the Q-exponential function, providing the qT and qD entropic parameters. The results show that qT varies from 1.44 to 1.58, whereas qD ranges from 0.46 to 0.75 for the inter-event time and distance distributions, respectively. Furthermore, we describe the frequency-magnitude distributions with the Gutenberg-Richter scaling relation and the fragment-asperity model of earthquake interactions derived within the NESP framework. The results of the analysis indicate that the statistical properties of earthquake swarms can be successfully reproduced by means of NESP and confirm the complexity and non-additivity of the spatiotemporal evolution of seismicity. Finally, the superstatistics approach, which is closely connected to NESP and is based on a superposition of ordinary local equilibrium statistical mechanics, is further used to discuss the temporal patterns of the earthquake evolution during the swarms.

10.
Entropy (Basel) ; 25(12)2023 Dec 11.
Artículo en Inglés | MEDLINE | ID: mdl-38136524

RESUMEN

Animal motion and flocking are ubiquitous nonequilibrium phenomena that are often studied within active matter. In examples such as insect swarms, macroscopic quantities exhibit power laws with measurable critical exponents and ideas from phase transitions and statistical mechanics have been explored to explain them. The widely used Vicsek model with periodic boundary conditions has an ordering phase transition but the corresponding homogeneous ordered or disordered phases are different from observations of natural swarms. If a harmonic potential (instead of a periodic box) is used to confine particles, then the numerical simulations of the Vicsek model display periodic, quasiperiodic, and chaotic attractors. The latter are scale-free on critical curves that produce power laws and critical exponents. Here, we investigate the scale-free chaos phase transition in two space dimensions. We show that the shape of the chaotic swarm on the critical curve reflects the split between the core and the vapor of insects observed in midge swarms and that the dynamic correlation function collapses only for a finite interval of small scaled times. We explain the algorithms used to calculate the largest Lyapunov exponents, the static and dynamic critical exponents, and compare them to those of the three-dimensional model.

11.
Sensors (Basel) ; 22(12)2022 Jun 11.
Artículo en Inglés | MEDLINE | ID: mdl-35746206

RESUMEN

For robot swarm applications, accurate positioning is one of the most important requirements for avoiding collisions and keeping formations and cooperation between individuals. However, in some worst cases, the GNSS (Global Navigation Satellite System) signals are weak due to the crowd being in a swarm or blocked by a forest, mountains, and high buildings in the environment. Thus, relative localization is an indispensable way to provide position information for the swarm. In this paper, we review the status and development of relative localization. It is first assessed that relative localization to obtain spatio-temporal relationships between individuals is necessary to achieve the stable operation of the group. After analyzing typical relative localization systems and algorithms from the perspective of functionality and practicality, this paper concludes that the UWB-based (ultra wideband) system is suitable for the relative localization of robots in large-scale applications. Finally, after analyzing the current challenges in the field of fully distributed localization for robotic swarms, a complete mechanism encompassing the relative localization process and the relationship between local and global localization that can be a possible direction for future research is proposed.


Asunto(s)
Robótica , Algoritmos , Humanos , Robótica/métodos
12.
Entropy (Basel) ; 24(7)2022 Jun 30.
Artículo en Inglés | MEDLINE | ID: mdl-35885140

RESUMEN

We study the collective motion of autonomous mobile agents in a ringlike environment. The agents' dynamics are inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary locations and initial orientations on a ring-shaped arena are observed to eventually all march in the same direction. In this work we ask whether, and how fast, a similar phenomenon occurs in a stochastic swarm of simple locust-inspired agents. The agents are randomly initiated as marching either clockwise or counterclockwise on a discretized, wide ring-shaped region, which we subdivide into k concentric tracks of length n. Collisions cause agents to change their direction of motion. To avoid this, agents may decide to switch tracks to merge with platoons of agents marching in their direction. We prove that such agents must eventually converge to a local consensus about their direction of motion, meaning that all agents on each narrow track must eventually march in the same direction. We give asymptotic bounds for the expected time it takes for such convergence or "stabilization" to occur, which depends on the number of agents, the length of the tracks, and the number of tracks. We show that when agents also have a small probability of "erratic", random track-jumping behavior, a global consensus on the direction of motion across all tracks will eventually be reached. Finally, we verify our theoretical findings in numerical simulations.

13.
Entropy (Basel) ; 24(10)2022 Sep 27.
Artículo en Inglés | MEDLINE | ID: mdl-37420384

RESUMEN

Despite the increasing applications, demands, and capabilities of drones, in practice they have only limited autonomy for accomplishing complex missions, resulting in slow and vulnerable operations and difficulty adapting to dynamic environments. To lessen these weaknesses, we present a computational framework for deducing the original intent of drone swarms by monitoring their movements. We focus on interference, a phenomenon that is not initially anticipated by drones but results in complicated operations due to its significant impact on performance and its challenging nature. We infer interference from predictability by first applying various machine learning methods, including deep learning, and then computing entropy to compare against interference. Our computational framework begins by building a set of computational models called double transition models from the drone movements and revealing reward distributions using inverse reinforcement learning. These reward distributions are then used to compute the entropy and interference across a variety of drone scenarios specified by combining multiple combat strategies and command styles. Our analysis confirmed that drone scenarios experienced more interference, higher performance, and higher entropy as they became more heterogeneous. However, the direction of interference (positive vs. negative) was more dependent on combinations of combat strategies and command styles than homogeneity.

14.
J Insect Sci ; 21(2)2021 Mar 01.
Artículo en Inglés | MEDLINE | ID: mdl-33908604

RESUMEN

The 2020 Student Debates of the Entomological Society of America (ESA) were live-streamed during the Virtual Annual Meeting to debate current, prominent entomological issues of interest to members. The Student Debates Subcommittee of the National ESA Student Affairs Committee coordinated the student efforts throughout the year and hosted the live event. This year, four unbiased introductory speakers provided background for each debate topic while four multi-university teams were each assigned a debate topic under the theme 'Technological Advances to Address Current Issues in Entomology'. The two debate topics selected were as follows: 1) What is the best taxonomic approach to identify and classify insects? and 2) What is the best current technology to address the locust swarms worldwide? Unbiased introduction speakers and debate teams began preparing approximately six months before the live event. During the live event, teams shared their critical thinking and practiced communication skills by defending their positions on either taxonomical identification and classification of insects or managing the damaging outbreaks of locusts in crops.


Asunto(s)
Entomología , Animales , Clasificación/métodos , Saltamontes , Control Biológico de Vectores , Plantas Modificadas Genéticamente
15.
Sensors (Basel) ; 21(12)2021 Jun 17.
Artículo en Inglés | MEDLINE | ID: mdl-34204272

RESUMEN

This article presents a framework for planning a drone swarm mission in a hostile environment. Elements of the planning framework are discussed in detail, including methods of planning routes for drone swarms using mixed integer linear programming (MILP) and methods of detecting potentially dangerous objects using EO/IR camera images and synthetic aperture radar (SAR). Methods of detecting objects in the field are used in the mission planning process to re-plan the swarm's flight paths. The route planning model is discussed using the example of drone formations managed by one UAV that communicates through another UAV with the ground control station (GCS). This article presents practical examples of using algorithms for detecting dangerous objects for re-planning of swarm routes. A novelty in the work is the development of these algorithms in such a way that they can be implemented on mobile computers used by UAVs and integrated with MILP tasks. The methods of detection and classification of objects in real time by UAVs equipped with SAR and EO/IR are presented. Different sensors require different methods to detect objects. In the case of infrared or optoelectronic sensors, a convolutional neural network is used. For SAR images, a rule-based system is applied. The experimental results confirm that the stream of images can be analyzed in real-time.


Asunto(s)
Robótica , Algoritmos , Redes Neurales de la Computación
16.
Sensors (Basel) ; 21(8)2021 Apr 09.
Artículo en Inglés | MEDLINE | ID: mdl-33918696

RESUMEN

The study of multi-agent systems such as drone swarms has been intensified due to their cooperative behavior. Nonetheless, automating the control of a swarm is challenging as each drone operates under fluctuating wireless, networking and environment constraints. To tackle these challenges, we consider drone swarms as Networked Control Systems (NCS), where the control of the overall system is done enclosed within a wireless communication network. This is based on a tight interconnection between the networking and computational systems, aiming to efficiently support the basic control functionality, namely data collection and exchanging, decision-making, and the distribution of actuation commands. Based on a literature analysis, we do not find revision papers about design of drone swarms as NCS. In this review, we introduce an overview of how to develop self-organized drone swarms as NCS via the integration of a networking system and a computational system. In this sense, we describe the properties of the proposed components of a drone swarm as an NCS in terms of networking and computational systems. We also analyze their integration to increase the performance of a drone swarm. Finally, we identify a potential design choice, and a set of open research challenges for the integration of network and computing in a drone swarm as an NCS.

17.
Entropy (Basel) ; 23(4)2021 Apr 12.
Artículo en Inglés | MEDLINE | ID: mdl-33921251

RESUMEN

In this paper, we propose a graph-transformational approach to swarm computation that is flexible enough to cover various existing notions of swarms and swarm computation, and it provides a mathematical basis for the analysis of swarms with respect to their correct behavior and efficiency. A graph transformational swarm consists of members of some kinds. They are modeled by graph transformation units providing rules and control conditions to specify the capability of members and kinds. The swarm members act on an environment-represented by a graph-by applying their rules in parallel. Moreover, a swarm has a cooperation condition to coordinate the simultaneous actions of the swarm members and two graph class expressions to specify the initial environments on one hand and to fix the goal on the other hand. Semantically, a swarm runs from an initial environment to one that fulfills the goal by a sequence of simultaneous actions of all its members. As main results, we show that cellular automata and particle swarms can be simulated by graph-transformational swarms. Moreover, we give an illustrative example of a simple ant colony the ants of which forage for food choosing their tracks randomly based on pheromone trails.

18.
J Comput Chem ; 41(5): 387-401, 2020 02 15.
Artículo en Inglés | MEDLINE | ID: mdl-31743478

RESUMEN

Atomic-level studies of protein activity represent a significant challenge as a result of the complexity of conformational changes occurring on wide-ranging timescales, often greatly exceeding that of even the longest simulations. A prime example is the elucidation of protein allosteric mechanisms, where localized perturbations transmit throughout a large macromolecule to generate a response signal. For example, the conversion of chemical to electrical signals during synaptic neurotransmission in the brain is achieved by specialized membrane proteins called pentameric ligand-gated ion channels. Here, the binding of a neurotransmitter results in a global conformational change to open an ion-conducting pore across the nerve cell membrane. X-ray crystallography has produced static structures of the open and closed states of the proton-gated GLIC pentameric ligand-gated ion channel protein, allowing for atomistic simulations that can uncover changes related to activation. We discuss a range of enhanced sampling approaches that could be used to explore activation mechanisms. In particular, we describe recent application of an atomistic string method, based on Roux's "swarms of trajectories" approach, to elucidate the sequence and interdependence of conformational changes during activation. We illustrate how this can be combined with transition analysis and Brownian dynamics to extract thermodynamic and kinetic information, leading to understanding of what controls ion channel function. © 2019 Wiley Periodicals, Inc.


Asunto(s)
Canales Iónicos Activados por Ligandos/química , Membrana Celular/química , Membrana Celular/metabolismo , Cristalografía por Rayos X , Cinética , Canales Iónicos Activados por Ligandos/metabolismo , Simulación de Dinámica Molecular , Termodinámica
19.
Entropy (Basel) ; 22(6)2020 May 27.
Artículo en Inglés | MEDLINE | ID: mdl-33286369

RESUMEN

Due to their growing number and increasing autonomy, drones and drone swarms are equipped with sophisticated algorithms that help them achieve mission objectives. Such algorithms vary in their quality such that their comparison requires a metric that would allow for their correct assessment. The novelty of this paper lies in analysing, defining and applying the construct of cross-entropy, known from thermodynamics and information theory, to swarms. It can be used as a synthetic measure of the robustness of algorithms that can control swarms in the case of obstacles and unforeseen problems. Based on this, robustness may be an important aspect of the overall quality. This paper presents the necessary formalisation and applies it to a few examples, based on generalised unexpected behaviour and the results of collision avoidance algorithms used to react to obstacles.

20.
Entropy (Basel) ; 22(10)2020 Oct 19.
Artículo en Inglés | MEDLINE | ID: mdl-33286944

RESUMEN

Many animal species, including many species of bats, exhibit collective behavior where groups of individuals coordinate their motion. Bats are unique among these animals in that they use the active sensing mechanism of echolocation as their primary means of navigation. Due to their use of echolocation in large groups, bats run the risk of signal interference from sonar jamming. However, several species of bats have developed strategies to prevent interference, which may lead to different behavior when flying with conspecifics than when flying alone. This study seeks to explore the role of this acoustic sensing on the behavior of bat pairs flying together. Field data from a maternity colony of gray bats (Myotis grisescens) were collected using an array of cameras and microphones. These data were analyzed using the information theoretic measure of transfer entropy in order to quantify the interaction between pairs of bats and to determine the effect echolocation calls have on this interaction. This study expands on previous work that only computed information theoretic measures on the 3D position of bats without echolocation calls or that looked at the echolocation calls without using information theoretic analyses. Results show that there is evidence of information transfer between bats flying in pairs when time series for the speed of the bats and their turning behavior are used in the analysis. Unidirectional information transfer was found in some subsets of the data which could be evidence of a leader-follower interaction.

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