Collective Motion Patterns Research Articles

Abstract PR005: The dynamic tumor microenvironment: Oncostreams are self-organizing structures that modulate glioma progression and treatment

Abstract Intratumoral heterogeneity is a hallmark of high grade gliomas. However, whether heterogeneity is static or dynamic remains unknown. Here we demonstrate that gliomas’ core and border regions display areas of self-organized collective motion, which we have termed oncostreams. Histologically oncostreams appear as multicellular fascicles of elongated and aligned glioma cells with mesenchymal-like morphology, and their density correlates positively with tumor malignant behavior. Using time lapse confocal imaging of organotypic brain slices of experimental glioma we discovered oncostream dynamics, namely, as two self-organizing patterns of collective motion: streams (bidirectional motion) and flocks (unidirectional motion). Oncostreams were also present in human glioblastoma multiforme, and could also be detected using objective artificial indigent approaches. They were present in 47% of TCGA-GBM grade IV tumor tissues, in 8.6 % of TCGA-LGG grade III, and were absent in TCGA-LGG grade II. Oncostreams are heterogeneous, contain GFAP+ cells, Iba1+ microglia/macrophages cells, and ACTA2+ mesenchymal cells aligned along Sox2+ tumor cells. We propose that oncostreams function as highways possibly stimulating the spread of slower-moving glioma cells and/or non-tumor cells throughout the tumor mass, reinforcing a potential role of oncostreams in determining spatial heterogeneity and remodeling of the tumor microenvironment. To analyze the molecular landscape of oncostreams we used laser capture microdissection coupled to RNA-Seq and bioinformatics analysis: we detected the existence of genetic networks specific to oncostreams. Oncostreams were aligned along highly expressed extracellular matrix proteins, among them Col1a1 was the most differentially expressed. Genetic inhibition of Col1a1 dissembled oncostreams, decreased glioma heterogeneity and improved animal survival. We propose that oncostreams dynamics will be a promising avenue to understand glioma behavior, and treat these malignant tumors. Citation Format: Andrea Comba, Sebastien Motsch, Patrick Dunn, Todd Hollon, Daniel Zamler, Anna Argento, Alon Kahana, Phillip Kish, Maria Castro, Pedro Lowenstein. The dynamic tumor microenvironment: Oncostreams are self-organizing structures that modulate glioma progression and treatment [abstract]. In: Proceedings of the AACR Virtual Special Conference on the Evolving Tumor Microenvironment in Cancer Progression: Mechanisms and Emerging Therapeutic Opportunities; in association with the Tumor Microenvironment (TME) Working Group; 2021 Jan 11-12. Philadelphia (PA): AACR; Cancer Res 2021;81(5 Suppl):Abstract nr PR005.

Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling.

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell-cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell-cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell-cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta-Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.

Development of Basketball Tactics Basic Cooperation Teaching System Based on CNN and BP Neural Network.

The traditional basketball teaching mode cannot meet the needs of students for the basic cooperation of basketball tactics. Therefore, a basic cooperation teaching system of basketball tactics based on artificial neural network is studied and designed. The system has a professional basketball game video tactical learning module. The events in the basketball game video are classified through a convolutional neural network and combined with the explanation of teachers to make the students have an intuitive understanding of the basic cooperation of basketball tactics and then design the basketball game module based on a BP neural network to provide students with an online basketball tactics training platform. Finally, the teacher scores the performance of the actual on-site training students in the basic cooperation of basketball tactics through the tactical scoring module on the system. The results show that after the introduction of global and collective motion patterns, the classification accuracy of the convolutional neural network is improved by 22.48%, which has significant optimization. The average accuracy of basketball game video event classification is 62.35%, and the accuracy of snatch event classification is improved to 95.28%. The recognition rate of the BP neural network combined with momentum gradient descent method is 75%, the number of weight adjustment is less, and the memory is small while ensuring fast running speed. Students who accept the basic basketball tactics cooperation teaching system based on the artificial neural network for basketball teaching have an overall score of 27.99 ± 2.11 points The overall score of exchange defense cooperation was 24.12 ± 2.03, which was higher than that of the control group. The above results show that the basketball tactical basic cooperation teaching system based on the artificial neural network has a good teaching effect in improving students' basketball tactical basic cooperation ability.

Multi-scale alignment of respiratory cilia and its relation to mucociliary function

The tracheobronchial tree is lined by a mucociliary epithelium containing millions of multiciliated cells. Their integrated oscillatory activity continuously propels an overlying pollution-protecting mucus layer in cranial direction, leading to mucociliary clearance – the primary defence mechanism of the airways. Mucociliary transport is commonly thought to co-emerge with the collective ciliary motion pattern under appropriate geometrical and rheological conditions. Proper ciliary alignment is therefore considered essential to establish mucociliary clearance in the respiratory system. Here, we used volume electron microscopy in combination with high-speed reflection contrast microscopy in order to examine ciliary orientation and its spatial organization, as well as to measure the propagation direction of metachronal waves and the direction of mucociliary transport on bovine tracheal epithelia with reference to the tracheal long axis (TLA). Ciliary orientation is measured in terms of the basal body orientation (BBO) and the axonemal orientation (AO), which are commonly considered to coincide, both equivalently indicating the effective stroke as well as the mucociliary transport direction. Our results, however, reveal that only the AO is in line with the mucociliary transport, which was found to run along a left-handed helical trajectory, whereas the BBO was found to be aligned with the TLA. Furthermore, we show that even if ciliary orientation remains consistent between adjacent cells, ciliary orientation exhibits a gradual shift within individual cells. Together with the symplectic beating geometry, this intracellular orientational pattern could provide for the propulsion of highly viscous mucus and likely constitutes a compromise between efficiency and robustness.

Emergent pattern formation of active magnetic suspensions in an external field

We study collective self-organization of weakly magnetic active suspensions in a uniform external field by analyzing a mesoscopic continuum model that we have recently developed. Our model is based on a Smoluchowski equation for a particle probability density function in an alignment field coupled to a mean-field description of the flow arising from the activity and the alignment torque. Performing linear stability analysis of the Smoluchowski equation and the resulting orientational moment equations combined with non-linear 3D simulations, we provide a comprehensive picture of instability patterns as a function of strengths of activity and magnetic field. For sufficiently high activity and moderate magnetic field strengths, the competition between the activity-induced flow and external magnetic torque renders a homogeneous polar steady state unstable. As a result, four distinct dynamical patterns of collective motion emerge. The instability patterns for pushers include traveling sheets governed by bend-twist instabilities and dynamical aggregates. For pullers, finite-sized and system spanning pillar-like concentrated regions predominated by splay deformations emerge which migrate in the field direction. Notably, at very strong magnetic fields, we observe a reentrant hydrodynamic stability of the polar steady state.

Abstract 3950: Spatiotemporal analysis of gliomas: Dynamics of mesenchymal multicellular structures as novel target for tumor treatment

Abstract Glioblastoma multiforme (GBM) is the most frequent and lethal tumor of the central nervous system. GBM are characterized by diffuse invasion and cellular heterogeneity which challenges treatment efficacy. Tumors with mesenchymal properties display the most aggressive phenotype. However, the biological function and molecular mechanisms underlying GBM mesenchymal transformation remain unknown. Analysis of mouse and human malignant gliomas revealed the presence of organized multicellular structures formed by elongated and aligned cells. These structures resemble areas of GBM mesenchymal transformation that we named Oncostreams. We determined the molecular signature underlying oncostreams function by performing laser capture microdissection followed by transcriptomic analysis. We found that oncostreams overexpressed Col1a1, ACTA2, MMP9, MMP10 and ADAMTS2 genes, all of them associated with regulation of extracellular matrix organization, collagen catabolic process and cellular migration pathways. Functional network analysis indicated that Col1a1 was a primary regulator gene. To analyze whether these structures display migratory properties we used time lapse imagining in a 3D organotypic glioma model. Morphological and statistical analysis revealed that oncostreams displayed a collective motion pattern, organized as streams or flocks. This dynamic patterns participate in local invasion and function as tumoral highways to facilitate the spread of several cells as intra-. Further analysis showed that oncostreams presence correlates with increased collagen expression and decreased animal survival. Patient's glioma biopsies also evidenced that these areas of Col1a1 overexpression were present in high grade but no in low-grade gliomas. We corroborated by immune-hystochemistry that Col1a1 were overexpressed and co-localized within GFP positive tumoral cells. Further, to analyze the origin and role of Col1a1 in glioma malignancy we generated genetically engineered mouse glioma models (GEMM) with Col1a1 downregulation. Interestingly, Col1a1 was retained only surrounding the blood vessel but was completed absent within the tumor parenchyma. We demonstrated that Col1a1 downregulation ablates oncostreams structures, reversed the malignant phenotype resembling low grade glioma histopathology and prolonged animal survival. This study reveals that oncostreams are organized dynamic structures that regulate glioma growth and invasion. They are areas of mesenchymal transformation defined by a molecular signature associated to extracellular matrix proteins expressed as Col1a1. Oncostreams with high expression of Col1a1 within glioma cells represent a novel potential targets for future translational development. Disruption of oncostreams will provide a new avenue to treat GBM. Citation Format: Andrea Comba, Patrick Dunn, Anna E. Argento, Padma Kadiyala, Sebastien Motsch, Daniel Zamler, Alon Kahana, Phillips E. Kish, Maria G. Castro, Pedro R. Lowenstein. Spatiotemporal analysis of gliomas: Dynamics of mesenchymal multicellular structures as novel target for tumor treatment [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 3950.

Collective movement analysis reveals coordination tactics of team players in football matches

Abstract Collective behavior is a hallmark of every living system and utilizing methods from statistical physics (such as correlation functions) could aid in our understanding of their underlying rules. We analyzed five football (soccer) matches as this game provides a unique but yet mostly unexplored example to study a system of collective cooperation and competition. The aim of our study was to analyze the collective motion patterns exhibited by football players to unfold the underlying coordination among them in order to understand collective strategies associated with team performance. By analyzing pairwise relationships among all the players using spatio-temporal correlation functions we reveal that there exist identifiable collective dynamics that characterize winning and losing teams. Using our metric we find clear and robust differences between the players, indicating a difference in their behavior and their interactions. And this enables us to assign a unique behavioral pattern - a ‘fingerprint’ - for each individual and for each team. Furthermore, we reveal there exists a relationship between the market value of the players and the metrics introduced here, suggesting that these metrics could potentially serve as valuable performance indicators in the future, with applications ranging from talent identification to player scouting. In a broader context team sports could open up new directions for quantitative analyses of human collective behavior.

The role of visual angle in pattern phase transition of collective motions

Abundant collective motion patterns of animal groups have different kinds of functions like migration, predator avoidance and foraging. To explore the phase transition mechanism behind such charming collective behaviors, some self-propelled particle models have been proposed, most of which however have isotropic inter-particle interactions and hence could not reproduce sophisticated natural collective patterns. As a remedy, this letter develops an anisotropic self-propelled particle model. By slightly tweaking the vision range and inter-particle attraction, the proposed model demonstrate transitions between four distinct collective motion patterns, i.e., torus, dumbbell, twist, and worm. To investigate more insightfully into the phase transition nature, quantitative analysis is carried out, revealing the relationship of visual angle-based inter-agent interactions and abundant pattern transitions existing in large numbers of natural, social and artificial grouping behaviors. From the industrial application point of view, the present study can help adjust the formation of multiple unmanned systems by simply tweaking a couple of vision-related parameters in their models.

Detecting anomalous crowd scenes by oriented Tracklets’ approach in active contour region

Video imagery based crowd analysis has become a topic of great interest for public safety at the venues of mass gathering events. This paper presents a novel approach to detect anomalous scene in high density crowded places. We propose an oriented tracklets approach in active contour region and measure the entropy and temporal occupancy deviation of oriented tracklets over the frames. To this end, an oriented trajectory algorithm is designed to extract tracklets of moving crowd. For trajectory extraction, spatio-temporal interest points are detected by adopting Harris corner features. The detected interest points are tracked over the frames within the optimized region. An active contour segmentation approach is applied to optimize the tracking region as a moving crowd is not distributed in entire frame region. The flow direction of each oriented tracklet is distributed into histogram bins at a specified interval, which defines the flow of collective motion pattern. A real-time scene updating procedure is also followed to adapt the changes of crowd scenes. Further, an entropy of histogram of oriented tracklets is computed based on the probability of occurrence of the tracklets. It has been shown that entropy of flow direction changes markedly in the unusual state of affairs. A simulation on a large number of the anomalous scene has been exercised to see the characteristics of an entropy. Also, temporal occupancy deviation is computed which measures the area occupied by the extracted tracklets of the crowd during a certain interval of time. If entropy and temporal occupancy deviation increase beyond a certain threshold, an alert is issued to detect anomaly to prevent potentially dangerous crowd-related disasters. Experiments conducted on three publicly available benchmark crowd datasets such as UMN, UCF Web, and Violent Flows, obtained interesting and promising results. We also evaluated some manually collected challenging real-world crowd video sequences. We compared the proposed approach with various state-of-the-art methods, and achieve remarkable accuracy while maintaining the lower computational complexity.

3131 ONCOSTREAMS: NOVEL DYNAMICS PATHOLOGICAL MULTICELLULAR STRUCTURES INVOLVED IN GLIOBLATOMA GROWTH AND INVASION

OBJECTIVES/SPECIFIC AIMS: Oncostreams represent a novel growth pattern of GBM. In this study we uncovered the cellular and molecular mechanism that regulates the oncostreams function in GBM growth and invasion. METHODS/STUDY POPULATION: We studied oncostreams organization and function using genetically engineered mouse gliomas models (GEMM), mouse primary patient derived GBM model and human glioma biopsies. We evaluated the molecular landscape of oncostreams by laser capture microdissection (LCM) followed by RNA-Sequencing and bioinformatics analysis. RESULTS/ANTICIPATED RESULTS: Oncostreams are multicellular structures of 10-20 cells wide and 2-400 μm long. They are distributed throughout the tumors in mouse and human GBM. Oncostreams are heterogeneous structures positive for GFAP, Nestin, Olig2 and Iba1 cells and negative for Neurofilament. Using GEMM we found a negative correlation between oncostream density and animal survival. Moreover, examination of patient’s glioma biopsies evidenced that oncostreams are present in high grade but no in low grade gliomas. This suggests that oncostreams may play a role in tumor malignancy. Our data also indicated that oncostreams aid local invasion of normal brain. Transcriptome analysis of oncostreams revealed 43 differentially expressed (DE) genes. Functional enrichment analysis of DE genes showed that “collagen catabolic processes”, “positive regulation of cell migration”, and “extracellular matrix organization” were the most over-represented GO biological process. Network analysis indicated that Col1a1, ACTA2, MMP9 and MMP10 are primary target genes. These genes were also overexpressed in more malignant tumors (WT-IDH) compared to the less malignant (IDH1- R132H) tumors. Confocal time lapse imagining of 3D tumor slices demonstrated that oncostreams display a collective motion pattern within gliomas that has not been seen before. DISCUSSION/SIGNIFICANCE OF IMPACT: In summary, oncostreams are anatomically and molecularly distinctive, regulate glioma growth and invasion, display collective motion and are regulated by the extracellular matrix. We propose oncostreams as novel pathological markers valuable for diagnosis, prognosis and designing therapeutics for GBM patients.

Collective motion patterns of self-propelled agents with both velocity alignment and aggregation interactions.

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.

Ontology Based Global and Collective Motion Patterns for Event Classification in Basketball Videos

In multi-person videos, especially team sport videos, a semantic event is usually represented as a confrontation between two teams of players, which can be represented as collective motion. In broadcast basketball videos, specific camera motions are used to present specific events. Therefore, a semantic event in broadcast basketball videos is closely related to both the global motion (camera motion) and the collective motion. A semantic event in basketball videos can be generally divided into three stages: pre-event, event occurrence (event-occ), and post-event. In this paper, we propose an ontology-based global and collective motion pattern (On_GCMP) algorithm for basketball event classification. First, a two-stage GCMP based event classification scheme is proposed. The GCMP is extracted using optical flow. The two-stage scheme progressively combines a five-class event classification algorithm on event-occs and a two-class event classification algorithm on pre-events. Both algorithms utilize sequential convolutional neural networks (CNNs) and long short-term memory (LSTM) networks to extract the spatial and temporal features of GCMP for event classification. Second, we utilize post-event segments to predict success/failure using deep features of images in the video frames (RGB_DF_VF) based algorithms. Finally the event classification results and success/failure classification results are integrated to obtain the final results. To evaluate the proposed scheme, we collected a new dataset called NCAA+, which is automatically obtained from the NCAA dataset by extending the fixed length of video clips forward and backward of the corresponding semantic events. The experimental results demonstrate that the proposed scheme achieves the mean average precision of 58.10% on NCAA+. It is higher by 6.50% than state-of-the-art on NCAA.

Controlling stability and transport of magnetic microswimmers by an external field

The interplay between external field and fluid-mediated interactions in active suspensions leads to patterns of collective motion that are poorly understood. Here, we study the hydrodynamic stability and transport of microswimmers with weak magnetic dipole moments in an external field using a kinetic theory framework. Combining linear stability analysis and non-linear 3D continuum simulations, we show that for sufficiently high activity and moderate magnetic field strengths, a homogeneous polar steady state is unstable and distinct types of splay and bend instabilities for puller and pusher swimmers emerge. The instabilities arise from the amplification of anisotropic hydrodynamic interactions due to the external alignment and lead to a partial depolarisation and a reduction of the average transport speed of the swimmers in the field direction. Interestingly, at higher field strengths the homogeneous polar state becomes stable and a transport efficiency identical to that of active particles without hydrodynamic interactions is restored.

Molecular dynamics simulations on the dynamics of two-dimensional rounded squares**Project supported by the National Natural Science Foundation of China (Grant Nos. 21573159 and 21621004).

The collective motion of rounded squares with different corner-roundness ζ is studied by molecular dynamics (MD) simulation in this work. Three types of translational collective motion pattern are observed, including gliding, hopping and a mixture of gliding and hopping. Quantitatively, the dynamics of each observed ordered phase is characterized by both mean square displacement and van Hove functions for both translation and rotation. The effect of corner-roundness on the dynamics is further studied by comparing the dynamics of the rhombic crystal phases formed by different corner-rounded particles at a same surface fraction. The results show that as ζ increases from 0.286 to 0.667, the translational collective motion of particles changes from a gliding-dominant pattern to a hopping-dominant pattern, whereas the rotational motion pattern is hopping-like and does not change in its type, but the rotational hopping becomes much more frequent as ζ increases (i.e., as particles become more rounded). A simple geometrical model is proposed to explain the trend of gliding motion observed in MD simulations.

Experiments and open-loop control of multiple catalytic microrobots

The ability to direct microrobots in the low Reynolds number regime has broad applications in engineering, biology and medicine. In contrast to externally driven robots, catalytically driven microrobots utilize chemical reactions to hyphenate all instances in solution. Controlling multiple self propelled microrobots in the same workspace has been an ongoing challenge for the field. In this paper we present a novel method for open loop control of multiple microrobots in the same workspace by combining their catalytic actuation with magnetic actuation. By using a catalytic cap to regulate the directions of motion and leveraging the inherent variations in model parameters in a collection of paramagnetic microrobots, we show how collective motion patterns can be achieved. We validate our proposed strategy in simulations using a simple kinematic model of each robot, and in experiments. Our results suggest that simultaneous steering of multiple microrobots to arbitrary locations might be controllable using sophisticated control techniques such as ensemble control.

Spontaneous emergence of milling (vortex state) in a Vicsek-like model

Collective motion is of interest to laymen and scientists in different fields. In groups of animals, many patterns of collective motion arise such as polarized schools and mills (i.e. circular motion). Collective motion can be generated in computational models of different degrees of complexity. In these models, moving individuals coordinate with others nearby. In the more complex models, individuals attract each other, aligning their headings, and avoiding collisions. Simpler models may include only one or two of these types of interactions. The collective pattern that interests us here is milling, which is observed in many animal species. It has been reproduced in the more complex models, but not in simpler models that are based only on alignment, such as the well-known Vicsek model. Our aim is to provide insight in the minimal conditions required for milling by making minimal modifications to the Vicsek model. Our results show that milling occurs when both the field of view and the maximal angular velocity are decreased. Remarkably, apart from milling, our minimal model also exhibits many of the other patterns of collective motion observed in animal groups.

How to: Using Mode Analysis to Quantify, Analyze, and Interpret the Mechanisms of High-Density Collective Motion

While methods from statistical mechanics were some of the earliest analytical tools used to understand collective motion, the field has expanded in scope beyond phase transitions and fluctuating order parameters. In part, this expansion is driven by the increasing variety of systems being studied, which in turn, has increased the need for innovative approaches to quantify, analyze, and interpret a growing zoology of collective behaviors. For example, concepts from material science become particularly relevant when considering the collective motion that emerges at high densities. Here, we describe methods originally developed to study inert jammed granular materials that have been borrowed and adapted to study dense aggregates of active particles. This analysis is particularly useful because it projects difficult-to-analyze patterns of collective motion onto an easier-to-interpret set of eigenmodes. Carefully viewed in the context of non-equilibrium systems, mode analysis identifies hidden long-range motions and localized particle rearrangements based solely on the knowledge of particle trajectories. In this work, we take a ``how-to'' approach and outline essential steps, methods, diagnostics, and know-how used to apply this analysis to study densely-packed active systems.

Hydrodynamic Equations for Flocking Models without Velocity Alignment

The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previously reported results. In particular, we show that three distinct macroscopic collective behaviors can be observed: i) the coarsening of aggregates with no orientational order, ii) the emergence of static, elongated nematic bands, and iii) the formation of moving, locally polar structures, which we call worms. The derived hydrodynamic equations indicate that active particles interacting via position-based interactions belong to a distinct class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems.

Curvature-controlled defect dynamics in active systems.

We have studied the collective motion of polar active particles confined to ellipsoidal surfaces. The geometric constraints lead to the formation of vortices that encircle surface points of constant curvature (umbilics). We have found that collective motion patterns are particularly rich on ellipsoids with four umbilics where vortices tend to be located near pairs of umbilical points to minimize their interaction energy. Our results provide a perspective on the migration of living cells, which most likely use the information provided from the curved substrate geometry to guide their collective motion.

Crowd Behavior Analysis via Curl and Divergence of Motion Trajectories

In the field of crowd behavior analysis, existing methods mainly focus on using local representations inspired by models found in other disciplines (e.g., fluid dynamics and social dynamics) to describe motion patterns. However, less attention is paid to exploiting motion structures (e.g., visual information contained in trajectories) for behavior analysis. In this paper, we consider both local characteristics and global structures of a motion vector field, and propose the Curl and Divergence of motion Trajectories (CDT) descriptors to describe collective motion patterns. To this end, a trajectory-based motion coding algorithm is designed to extract the CDT descriptors. For each motion vector field we construct its conjugate field, in which each vector is perpendicular to the counterpart in the original vector field. The trajectories in the motion and corresponding conjugate fields indicate the tangential and radial motion structures, respectively. By integrating curl (and divergence, respectively) along the tangential paths (and the radial paths, respectively), the CDT descriptors are extracted. We show that the proposed motion descriptors are scale- and rotation-invariant for effective crowd behavior analysis. For concreteness, we apply the CDT descriptors to identify five typical crowd behaviors (lane, clockwise arch, counterclockwise arch, bottleneck and fountainhead) with a pipeline including motion decomposition. Extensive experimental results on two benchmark datasets demonstrate the effectiveness of the CDT descriptors for describing and classifying crowd behaviors.