Session GG04: V: Collective Dynamics and Network Theory in Complex Systems

When Swarms Collide: Using one swarm to capture another

Swarming patterns that emerge from the interaction of many mobile agents are a subject of great interest in fields ranging from biology to physics and robotics. In some application areas, multiple swarms effectively interact and collide, producing complex and chaotic spatio-temporal patterns. Recent studies of swarm-on-swarm dynamics deal with predicting the scattering of two large, colliding swarms with nonlinear interactions. By using a  combination of mean-field and time-series analysis techniques, we are able to predict physical parameters under which colliding swarms are  expected to form a combined milling state. That is, we predict when one swarm can capture another. Our semi-analytical methods rely on the  assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other. Using this approach we are  able to predict the critical swarm-on-swarm interaction coupling, below which two colliding swarms merely scatter, for near head-on collisions as a  function of control parameters. In general, we show that the critical coupling corresponds to a saddle-node bifurcation of a stable limit cycle.

    

Modeling firefly swarms as coupled oscillators

The study of mass synchronous behavior has primarily focused on the analysis of abstract and greatly simplified mathematical models. Many applications of these models to living systems have been proposed, but incorporation of real-world data is unfortunately rare. Here we present new data and analysis regarding synchronization phenomena observed in one species of firefly, Pteroptyx malaccae. Due to its relative immobility during synchronous flashing displays, this species offers a unique opportunity for reliable tracking and direct application of candidate models. In late 2022, we used stereo videography to document the three-dimensional behavior of multiple swarms over multiple nights. Our preliminary results show that swarms exhibit “meta oscillations” characterized by order parameters that rise and fall on an intermediate time scale (~40 times longer relative to the typical flashing period of a firefly), consistent with models suggesting a “breathing” chimera state.    

Conserved Quantities, Quasi-Periodicity and Liouville-Arnold Integrability of Ecological Networks

Complete odd tournaments are frequently used as abstract models of ecological systems via replicator dynamics. In these models, the payoff matrix is a skew-symmetric +1/-1 matrix and all species interactions result in a non-zero interaction payoff. These matrices correspond to directed graphs with species as vertices and edge direction giving the sign of the corresponding matrix entries. A circulant tournament is defined by a graph in which every vertex has the same in/out degree. It is known that the replicator dynamics derived from these tournaments admit polynomial conserved quantities. In this talk we extend this result to show that these circulant tournaments produce quasi-periodic dynamics and are Liouville-Arnold integrable by showing they commute under the action of a non-linear Poisson bracket (the quadratic bracket). Furthermore, we show that all tournaments constructed by embeddings are Liouville-Arnold integrable. By an embedding we mean a tournament constructed by recursively replacing vertices in an outer circulant tournament with other circulant tournaments and adding appropriate edges. We numerically illustrate that tournaments not constructed in this manner produce chaotic dynamics and classify all dynamics generated by any tournament with up to seven species.   

Scattering theory of active particles with social distancing: non-local closure and network noise

We consider self-propelled particles with velocity-dependent interactions where particles try to avoid each other. The particles undergo apparent Brownian motion, even though the particle's equations are fully deterministic and no explicit noise terms are included in the model. We show that the interactions lead to internal, dynamical noise which can be interpreted as the noise of a network with time-dependent topology. Starting from the exact N-particle Liouville equation, a kinetic equation for the one-particle distribution function is obtained. We show that the usual mean-field assumption of Molceular Chaos  which involves a simple factorization of the N-particle probability leads to unphysical predictions. Going beyond mean-field by explicitly taking into account two-particle-correlations during interactions and using a first-principle, non-local closure of the BBGKY-hierarchy, we analytically calculate the scattering of particles. As a result we obtain explicit expressions for the colored network noise of an effective one-particle Langevin-equation and the corresponding self-diffusion. The predicted theoretical expressions for the relaxation of hydrodynamic modes and the self-diffusion coefficient are in excellent, quantitative agreement with agent-based simulations, even far away from the stationary state.

    

collective behavior in human crowds

We conducted collective behavior experiments with a human crowd of 30 members moving within the area of a basketball court. This collective motion was recorded using a dron. To generate a possible emergent phenomenon, simple rules were given to the crowd, namely, 1) To move within the basketball court, and 2) To try to stay together at all times, and the crowd was disturbed by a simulated attack. The emergent collective behavior was characterized by extracting individual paths and velocity vectors, and by introducing global and local order parameters. With the latter order parameters we identify that dynamic emergence –defined as an entanglement of rotational (levo and dextro), translational phases in time– is present in our experiment. A numerical model is also proposed, and several interaction rules are tested to see which is the most efficient at mimicking the human collective behavior.   

Coherent Laser Networks as Energy-Based Neural Networks

In recent years, there has been a growing interest in developing new platforms for general-purpose or application-specific computing that offer an advantage over classical processors in terms of computational time, energy efficiency, and scalability. Here, we propose the use of coherently coupled laser networks for neural computing. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of phase patterns as stable fixed points of the governing dynamical equations and retrieving such patterns through proper excitation conditions, thus exhibiting an associative memory property. We further show that limitations on the number of images can be overcome by using nonreciprocal coupling between lasers, thus allowing for utilizing the large storage capacity inherent to the laser network. This work opens new possibilities for neural computation with coherent laser networks as a novel physical analog processor. In addition, the underlying dynamical model discussed here suggests a novel energy-based recurrent neural network that can directly handle continuous data as opposed to Hopfield networks and Boltzmann machines which are intrinsically binary systems.

    

Maximum Entropy Model for Genotype-Phenotype Map Organization Reveals Maximally Robust Neutral Networks

Genotype-phenotype (GP) maps, including protein/RNA primary sequences mapping to folded structures, gene regulatory network interactions mapping to expression cycles, and even non-biological examples like spin glass bond configurations mapping to ground states, tend to universally display similar scaling laws for mutational robustness and other neutral network properties. We propose a maximum entropy model for GP map organization in which only global robustness is constrained, generating a mapping onto a Potts model on a Hamming graph with conserved phenotype frequencies. Our mean field theory and simulations show existence of two phases, robust and fragile. In the robust phase, the neutral networks organize into maximally robust "bricklayer's graphs" whose robustness is related to the sums-of-digits function. We argue that mutational robustness, base information error, and population neutrality cannot be simultaneously optimized in general. We find that bricklayer's graphs naturally occur as component networks in RNA/HP protein folding GP maps.   

Driving stochastic many-particle systems using deep reinforcement learning

Ensembles of artificially intelligent agents have in recent years been successfully employed on tasks as diverse as autonomous navigation or drug delivery. Experiments have shown that such agents may develop collective behavior such as the emergence of hierarchies. We argue that such ensembles of intelligent agents constitute a novel and interesting form of active matter that can be understood using the tools of statistical physics. Here, we study stochastic many-particle systems where the transition rates of each particle are determined by a deep neural network specific to the particle. The networks are in turn trained using reinforcement learning on each particle's past trajectory. Using a one-dimensional lattice gas as an example we demonstrate how the interplay between neural network remodelling and collective, mesoscopic processes leads to the emergence of effective interactions between particles. These effective interactions lead to symmetry-breaking above a threshold density and to rich spatio-temporal structures. Our work shows that ensembles of artificial intelligent agents exhibit intriguing collective behavior and provide a testing ground for new non-equilibrium physics.   

Theoretical analysis of physical reservoir computing using spin waves

Reservoir computing (RC) is a variant of recurrent neural networks (RNNs), which has a single reservoir layer to transform an input signal into an output. In contrast with the conventional RNNs, RC does not update the weights in the reservoir. Therefore, by replacing the reservoir with a physical system, for example, magnetization dynamics, we may realize a neural network device to perform various tasks. A key issue to improve its performance is how to increase a reservoir dimension to memorize a lot of information. Wave-based computational systems have attractive features in this direction because the dynamics in the continuum media have inherently large degrees of freedom. Among the wave phenomena, spin waves are promising for high-speed nanoscale devices. However, the realization of high-performance computation has not yet been achieved.

 

Here we show, using reservoir computing with micromagnetic simulations, that spin-wave physical reservoir computing can achieve high computational power comparable with other state-of-art systems. We demonstrate the performance by memory capacity, information processing capacity, which is a nonlinear version of the memory capacity, NARMA10 task, and forecasting chaotic time series. We analyze the response function perturbatively, and clarify the mechanism of high computational performance in terms of the geometry and the number of input nodes and physical parameters.   

Low-Frequency Charge Noise of Bacteria as Indicator of Ion Concentration Regulation

Bacteria rely on the free energy provided by ionic concentration gradients across the bacterial

membrane to power various cellular processes. These concentration gradients are regulated by

ion channels and ion pumps within the membrane. Due to the stochasticity of the transport and

the physical dimensions of a bacterium, intracellular ion concentrations are bound to fluctuate.

Thus, bacterial ion homeostasis is expected to be highly dynamic and dominated by strong charge

noise. By employing sensitive electrical measurement techniques in a microfluidic system, we

investigate the charge noise of several hundred nonmotile bacteria. The power spectral density

of these fluctuations displays 1/f² behavior for frequencies 0.05 ≤ f ≤ 1 Hz. By fitting our

data to a simple noise model, we estimate the charge fluctuations of a single bacterium to be

±1.30 × 10⁶e (e ≈ 1.60 × 10⁻¹⁹ C). The charge noise is directly related to the fluctuations in the

membrane potential. However, the limited understanding of intracellular concentration gradients

makes current predictions unreliable.