Criticality and the Onset of Ordering in the Standard Vicsek Model

Experimental observations of animal collective behavior have shown stunning evidence for the emergence of large-scale cooperative phenomena resembling phase transitions in physical systems. Indeed, quantitative studies have found scale-free correlations and critical behavior consistent with the occurrence of continuous, second-order phase transitions. The Standard Vicsek Model (SVM), a minimal model of self-propelled particles in which their tendency to align with each other competes with perturbations controlled by a noise term, appears to capture the essential ingredients of critical flocking phenomena. In this paper, we review recent finite-size scaling and dynamical studies of the SVM, which present a full characterization of the continuous phase transition through dynamical and critical exponents. We also present a complex network analysis of SVM flocks and discuss the onset of ordering in connection with XY-like spin models.Comment: 15 pages, 4 figures. To appear in Interface Focu

Critical brain networks

Highly correlated brain dynamics produces synchronized states with no behavioral value, while weakly correlated dynamics prevents information flow. We discuss the idea put forward by Per Bak that the working brain stays at an intermediate (critical) regime characterized by power-law correlations.Comment: Contribution to the Niels Bohr Summer Institute on Complexity and Criticality (2003); to appear in a Per Bak Memorial Issue of PHYSICA

Genetic algorithms with self-organizing behaviour in dynamic environments

Copyright @ 2007 Springer-VerlagIn recent years, researchers from the genetic algorithm (GA) community have developed several approaches to enhance the performance of traditional GAs for dynamic optimization problems (DOPs). Among these approaches, one technique is to maintain the diversity of the population by inserting random immigrants into the population. This chapter investigates a self-organizing random immigrants scheme for GAs to address DOPs, where the worst individual and its next neighbours are replaced by random immigrants. In order to protect the newly introduced immigrants from being replaced by fitter individuals, they are placed in a subpopulation. In this way, individuals start to interact between themselves and, when the fitness of the individuals are close, one single replacement of an individual can affect a large number of individuals of the population in a chain reaction. The individuals in a subpopulation are not allowed to be replaced by individuals of the main population during the current chain reaction. The number of individuals in the subpopulation is given by the number of individuals created in the current chain reaction. It is important to observe that this simple approach can take the system to a self-organization behaviour, which can be useful for GAs in dynamic environments.Financial support was obtained from FAPESP (Proc. 04/04289-6)

Finite-size scaling as a way to probe near-criticality in natural swarms

Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behaviour of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes.Comment: Selected for Viewpoint in Physics; PRL Editor's Suggestio

Towards a Smart World: Hazard Levels for Monitoring of Autonomous Vehicles’ Swarms

This work explores the creation of quantifiable indices to monitor the safe operations and movement of families of autonomous vehicles (AV) in restricted highway-like environments. Specifically, this work will explore the creation of ad-hoc rules for monitoring lateral and longitudinal movement of multiple AVs based on behavior that mimics swarm and flock movement (or particle swarm motion). This exploratory work is sponsored by the Emerging Leader Seed grant program of the Mineta Transportation Institute and aims at investigating feasibility of adaptation of particle swarm motion to control families of autonomous vehicles. Specifically, it explores how particle swarm approaches can be augmented by setting safety thresholds and fail-safe mechanisms to avoid collisions in off-nominal situations. This concept leverages the integration of the notion of hazard and danger levels (i.e., measures of the “closeness” to a given accident scenario, typically used in robotics) with the concept of safety distance and separation/collision avoidance for ground vehicles. A draft of implementation of four hazard level functions indicates that safety thresholds can be set up to autonomously trigger lateral and longitudinal motion control based on three main rules respectively based on speed, heading, and braking distance to steer the vehicle and maintain separation/avoid collisions in families of autonomous vehicles. The concepts here presented can be used to set up a high-level framework for developing artificial intelligence algorithms that can serve as back-up to standard machine learning approaches for control and steering of autonomous vehicles. Although there are no constraints on the concept’s implementation, it is expected that this work would be most relevant for highly-automated Level 4 and Level 5 vehicles, capable of communicating with each other and in the presence of a monitoring ground control center for the operations of the swarm

Time-delayed autosynchronous swarm control

In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function which can be set to induce a stationary swarm, a rotating swarm with uniform translation and a rotating swarm with a stationary center-of-mass. An analysis of the mean field equations shows that without a spring potential the motion of the center-of-mass is determined explicitly by a multi-valued function. For a non-zero spring potential the swarm converges to a vortex formation about a stationary center-of-mass, except at discrete bifurcation points where the center-of-mass will periodically trace an ellipse. The analytical results defining the behavior of the center-of-mass are shown to correspond with the numerical swarm simulations