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Basak US, Sattari S, Hossain M, Horikawa K, Komatsuzaki T. Transfer entropy dependent on distance among agents in quantifying leader-follower relationships. Biophys Physicobiol 2021; 18:131-144. [PMID: 34178564 PMCID: PMC8214925 DOI: 10.2142/biophysico.bppb-v18.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 05/13/2021] [Indexed: 12/01/2022] Open
Abstract
Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.
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Affiliation(s)
- Udoy S. Basak
- Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Sapporo, Hokkaido 060-0812, Japan
- Pabna University of Science and Technology, Pabna 6600, Bangladesh
| | - Sulimon Sattari
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020, Japan
| | - Motaleb Hossain
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020, Japan
- University of Dhaka, Dhaka 1000, Bangladesh
| | - Kazuki Horikawa
- Department of Optical Imaging, The Institute of Biomedical Sciences, Tokushima University Graduate School, Tokushima 770-8503, Japan
| | - Tamiki Komatsuzaki
- Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Sapporo, Hokkaido 060-0812, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido 001-0020, Japan
- Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo, Hokkaido 001-0021, Japan
- Graduate School of Chemical Sciences and Engineering Materials Chemistry and Engineering Course, Hokkaido University, Sapporo, Hokkaido 060-0812, Japan
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Clusella P, Pastor-Satorras R. Phase transitions on a class of generalized Vicsek-like models of collective motion. CHAOS (WOODBURY, N.Y.) 2021; 31:043116. [PMID: 34251260 DOI: 10.1063/5.0046926] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 03/18/2021] [Indexed: 06/13/2023]
Abstract
Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper, we propose a generalization of the Vicsek model characterized by an angular noise term following an arbitrary probability density function, which might depend on the state of the system and thus have a multiplicative character. We show that the well established vectorial Vicsek model can be expressed in this general formalism by deriving the corresponding angular probability density function, as well as we propose two new multiplicative models consisting of bivariate Gaussian and wrapped Gaussian distributions. With the proposed formalism, the mean-field system can be solved using the mean resultant length of the angular stochastic term. Accordingly, when the SPPs interact globally, the character of the phase transition depends on the choice of the noise distribution, being first order with a hybrid scaling for the vectorial and wrapped Gaussian distributions, and second order for the bivariate Gaussian distribution. Numerical simulations reveal that this scenario also holds when the interactions among SPPs are given by a static complex network. On the other hand, using spatial short-range interactions displays, in all the considered instances, a discontinuous transition with a coexistence region, consistent with the original formulation of the Vicsek model.
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Affiliation(s)
- Pau Clusella
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
| | - Romualdo Pastor-Satorras
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
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3
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Basak US, Sattari S, Horikawa K, Komatsuzaki T. Inferring domain of interactions among particles from ensemble of trajectories. Phys Rev E 2020; 102:012404. [PMID: 32795064 DOI: 10.1103/physreve.102.012404] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 06/24/2020] [Indexed: 11/07/2022]
Abstract
An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.
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Affiliation(s)
- Udoy S Basak
- Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan and Pabna University of Science and Technology, Pabna 6600, Bangladesh
| | - Sulimon Sattari
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Kazuki Horikawa
- Department of Optical Imaging, Institute of Biomedical Sciences, Tokushima University Graduate School, 3-18-15 Kuramoto-cho, Tokushima City, Tokushima 770-8503, Japan
| | - Tamiki Komatsuzaki
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan; Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21, Nishi 10, Kita-ku, Sapporo 001-0021, Japan; Graduate School of Life Science, Transdisciplinary Life Science Course, Hokkaido University, Kita 12, Nishi 6, Kita-ku, Sapporo 060-0812, Japan; and Graduate School of Chemical Sciences and Engineering Materials, Chemistry and Engineering Course, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
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Dadhichi LP, Kethapelli J, Chajwa R, Ramaswamy S, Maitra A. Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks. Phys Rev E 2020; 101:052601. [PMID: 32575192 DOI: 10.1103/physreve.101.052601] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
As the constituent particles of a flock are polar and in a driven state, their interactions must, in general, be fore-aft asymmetric and nonreciprocal. Within a model that explicitly retains the classical spin angular momentum field of the particles we show that the resulting asymmetric contribution to interparticle torques, if large enough, leads to a buckling instability of the flock. More precisely, this asymmetry also yields a natural mechanism for a difference between the speed of advection of polarization information along the flock and the speed of the flock itself, concretely establishing that the absence of detailed balance, and not merely the breaking of Galilean invariance, is crucial for this distinction. To highlight this we construct a model of asymmetrically interacting spins fixed to lattice points and demonstrate that the speed of advection of polarization remains nonzero. We delineate the conditions on parameters and wave number for the existence of the buckling instability. Our theory should be consequential for interpreting the behavior of real animal groups as well as experimental studies of artificial flocks composed of polar motile rods on substrates.
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Affiliation(s)
- Lokrshi Prawar Dadhichi
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500 107, India
| | - Jitendra Kethapelli
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560 089, India
| | - Rahul Chajwa
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560 089, India
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Ananyo Maitra
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005, Paris, France
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Brown J, Bossomaier T, Barnett L. Information flow in finite flocks. Sci Rep 2020; 10:3837. [PMID: 32123185 PMCID: PMC7052242 DOI: 10.1038/s41598-020-59080-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2019] [Accepted: 12/27/2019] [Indexed: 11/09/2022] Open
Abstract
We explore information flow in finite active matter flocks by simulating the canonical Vicsek model and estimating the flow of information as a function of noise (the variability in the extent to which each animal aligns with its neighbours). We show that the global transfer entropy for finite flocks not only fails to peak near the phase transition, as demonstrated for the canonical 2D Ising model, but remains constant from the transition throughout the entire ordered regime to very low noise values. This provides a foundation for future study regarding information flow in more complex models and real-world flocking data.
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Affiliation(s)
- J Brown
- School of Computing & Mathematics, Charles Sturt University, Bathurst, NSW, Australia.
| | - T Bossomaier
- Centre for Research in Complex Systems, Charles Sturt University, Bathurst, NSW, Australia
| | - L Barnett
- Sackler Centre for Consciousness Science, Department of Informatics, University of Sussex, Brighton, UK
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Roy S, Shirazi MJ, Jantzen B, Abaid N. Effect of visual and auditory sensing cues on collective behavior in Vicsek models. Phys Rev E 2020; 100:062415. [PMID: 31962433 DOI: 10.1103/physreve.100.062415] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Indexed: 11/07/2022]
Abstract
In the present study, we consider two independent sensing modes (auditory and visual) in Vicsek-like models and compare the emergent group-level behaviors in terms of polarization, cohesion, and cluster size. The auditory and visual modes differ in the determination of particle neighbors, which at the level of groups results in higher polarization, lower cohesion, and larger cluster size for the auditory mode relative to the visual. With the increase in average density of the particles, these differences are more pronounced. These differences are due to the fact that these sense modalities robustly generate distinct spatial distributions of the particles. We demonstrate the use of a data-driven approach, called transfer entropy, to distinguish the sensing modalities by considering only a pair of particle trajectories. Such an approach could be applicable to real-world systems, where it may be a challenge to measure the position and velocity of every particle within a swarm.
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Affiliation(s)
- Subhradeep Roy
- Department of Mechanical Engineering, California State University, Northridge, California 91330, USA
| | | | - Benjamin Jantzen
- Department of Philosophy, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Nicole Abaid
- Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061, USA
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Li B, Wu ZX, Guan JY. Collective motion patterns of self-propelled agents with both velocity alignment and aggregation interactions. Phys Rev E 2019; 99:022609. [PMID: 30934226 DOI: 10.1103/physreve.99.022609] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 11/07/2022]
Abstract
We combine the velocity alignment and aggregation mechanisms to study the collective motion of active agents in noisy circumstances. The agents are located on a two-dimensional square plane, and the proportion of velocity alignment and aggregation interactions are, respectively, set to be k and 1-k. In the case of k=1 our model is similar to the classical Vicsek model, while it degenerates to the view angle model for k=0. By tuning the intensity of the external noise η and the proportional coefficient k, and carrying out extensive numerical simulations, we find that the system can exhibit diverse dynamic patterns widely observed in real biological systems. By means of finite-size scaling analysis, we confirm that the presence of the aggregation interaction affects not only the position of the critical noise η_{c} (beyond which the agents display disordered motion) but also the type of the phase transition of the collective motion. In particular, under a weak external noise environment, the transition from disordered to ordered state by increasing k (i.e., by decreasing the proportion of aggregation interaction) is found to be of first order. Besides, for moderate external noise, we also find the existence of the optimal proportion of the aggregation interaction for the system to achieve the highest degree of order. Our results highlights the important role of the aggregation interaction in the collective motion and may have promising potential applications in natural self-propelled particles and artificial multiagent systems.
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Affiliation(s)
- Bo Li
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Zhi-Xi Wu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jian-Yue Guan
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China
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Durve M, Saha A, Sayeed A. Active particle condensation by non-reciprocal and time-delayed interactions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:49. [PMID: 29626264 DOI: 10.1140/epje/i2018-11653-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Accepted: 03/15/2018] [Indexed: 06/08/2023]
Abstract
We consider the flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision-cone. Also, the communication occurs with some time-delay. The communication among the agents are modeled by Vicsek rules. In this study we explore the combined effect of non-reciprocal interaction (induced by limited vision-cone) among the agents and the presence of delay in the interactions on the dynamical pattern formation within the flock. We find that under these two influences, without any position-based attractive interactions or confining boundaries, the agents can spontaneously condense into "drops". Though the agents are in motion within the drop, the drop as a whole is pinned in space. We find that this novel state of the flock has a well-defined order and it is stabilized by the noise present in the system.
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Affiliation(s)
- Mihir Durve
- Department of Physics, Università degli studi di Trieste, 34127, Trieste, Italy
- The Abdus Salam International Centre for Theoretical Physics, 34151, Trieste, Italy
| | - Arnab Saha
- Department of Physics, Savitribai Phule Pune University, 411007, Pune, India.
| | - Ahmed Sayeed
- Department of Physics, Savitribai Phule Pune University, 411007, Pune, India
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Abstract
This paper investigates the effect of the form of an obstacle on the time that a crowd takes to evacuate a room, using a toy model. Pedestrians are modeled as active soft matter moving toward a point with intended velocities. An obstacle is placed in front of the exit, and it has one of four shapes: a cylindrical column, a triangular prism, a quadratic prism, or a diamond prism. Numerical results indicate that the evacuation-completion time depends on the shape of the obstacle. Obstacles with a circular cylinder (C.C.) shape yield the shortest evacuation-completion time in the proposed model.
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Affiliation(s)
- Ryosuke Yano
- Tokio, Marine and Nichido Risk Consulting Co. Ltd., 1-5-1 Otemachi, Chiyoda-ku, Tokyo, Japan
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Chen QS, Patelli A, Chaté H, Ma YQ, Shi XQ. Fore-aft asymmetric flocking. Phys Rev E 2017; 96:020601. [PMID: 28950612 DOI: 10.1103/physreve.96.020601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Indexed: 06/07/2023]
Abstract
We show that fore-aft asymmetry, a generic feature of living organisms and some active matter systems, can have a strong influence on the collective properties of even the simplest flocking models. Specifically, an arbitrarily weak asymmetry favoring front neighbors changes qualitatively the phase diagram of the Vicsek model. A region where many sharp traveling band solutions coexist is present at low noise strength, below the Toner-Tu liquid, at odds with the phase-separation scenario well describing the usual isotropic model. Inside this region, a "banded-liquid" phase with algebraic density distribution coexists with band solutions. Linear stability analysis at the hydrodynamic level suggests that these results are generic and not specific to the Vicsek model.
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Affiliation(s)
- Qiu-Shi Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Aurelio Patelli
- ISC-CNR, UoS Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, Beijing 100094, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
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Barberis L, Peruani F. Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates. PHYSICAL REVIEW LETTERS 2016; 117:248001. [PMID: 28009185 DOI: 10.1103/physrevlett.117.248001] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2016] [Indexed: 05/27/2023]
Abstract
We study a minimal cognitive flocking model, which assumes that the moving entities navigate using the available instantaneous visual information exclusively. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force, which acts inside a vision cone (VC), and lack velocity-velocity alignment. We show that this active system can exhibit-due to the VC that breaks Newton's third law-various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or millinglike patterns, the formation of moving-locally polar-files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and nonlinear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and nonliving active systems.
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Affiliation(s)
- Lucas Barberis
- Université Côte d'Azur, Laboratoire J.A. Dieudonné, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France
- IFEG, FaMAF, CONICET, UNC, X5000HUA Córdoba, Argentina
| | - Fernando Peruani
- Université Côte d'Azur, Laboratoire J.A. Dieudonné, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France
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