arXiv subjects

Arshed Nabeel

Publications and source records attributed to Arshed Nabeel.

7 recordsLinked to original sources

arXiv2026

Hydrodynamic interactions mask the true heterogeneity of a microscopic collective

Coordinated movement and self-organisation of active self-driven agents is common in nature and is seen across different scales, from herds of animals to collective motion in bacteria. Often, these systems are heterogeneous in composition, with different agents having different intrinsic motilities. Inferring these intrinsic characteristics and quantifying the level of heterogeneity in a collective system is crucial to understanding the observed emergent phenomena. However, when interaction effects dominate, i.e. the observed movement of an agent is strongly influenced by its interacting neighbours, inferring the intrinsic characteristics of agents becomes a challenge. We consider a collective system of agents that undergo purely physical interactions like collisions and long-range hydrodynamic interactions, which resembles a system of microswimmers immersed in a fluid medium. We incorporate heterogeneity into the system through variations in agent motility and examine how the perceived heterogeneity, inferred from measured speeds, depends on the strength of hydrodynamic interactions and the true intrinsic variability. The interplay between short-range collisions, long-range hydrodynamic interactions, and intrinsic heterogeneity makes the inference problem non-trivial. When hydrodynamic effects dominate, true heterogeneity is effectively masked, making even a homogeneous collective appear heterogeneous. The competing effects of collisions, which slow agents down, and hydrodynamic interactions, which enhance their motion, further complicate reliable inference. Hydrodynamic interactions also modify collision angles, rendering them more isotropic. Overall, the findings show highlight experimentally measured properties of microscopic collectives may not accurately reflect their true characteristics.

nlin.AO↗

arXiv2026

Flocking by stopping: a novel mechanism of emergent order in collective movement

Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors, resulting in ordered movement. In small flocks, noise induced order can also emerge with individuals copying only a randomly chosen single neighbor at a time. We propose a new model of collective movement, inspired by how real animals move, where individuals can move in two directions or remain stationary. We demonstrate that when individuals interact with a single neighbor through a novel form of halting interaction -- where an individual may stop upon encountering an oppositely moving neighbor rather than instantly aligning -- persistent collective order can emerge even in large populations. This represents a fundamentally different mechanism from conventional averaging-based or noise-induced ordering. Using deterministic and stochastic mean-field approximations, we characterize the conditions under which such ``flocking by stopping'' behavior can occur, and confirm the mean-field predictions using individual-based simulations. Our results highlight how incorporating a stopped state and halting interactions can generate new routes to order in collective movement.

q-bio.QM↗

arXiv2024

Discovering stochastic dynamical equations from biological time series data

Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the role of stochasticity in real datasets. Therefore, the inverse problem of inferring the governing stochastic equations from datasets is important. Here, we present an equation discovery methodology that takes time series data of state variables as input and outputs a stochastic differential equation. We achieve this by combining traditional approaches from stochastic calculus with the equation-discovery techniques. We demonstrate the generality of the method via several applications. First, we deliberately choose various stochastic models with fundamentally different governing equations; yet they produce nearly identical steady-state distributions. We show that we can recover the correct underlying equations, and thus infer the structure of their stability, accurately from the analysis of time series data alone. We demonstrate our method on two real-world datasets -- fish schooling and single-cell migration -- which have vastly different spatiotemporal scales and dynamics. We illustrate various limitations and potential pitfalls of the method and how to overcome them via diagnostic measures. Finally, we provide our open-source codes via a package named PyDaDDy (Python library for Data Driven Dynamics).

q-bio.QM↗

arXiv2024

Discovering mesoscopic descriptions of collective movement with neural stochastic modelling

Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000 individuals, also called the `mesoscale'), can show nontrivial features due to stochasticity. Therefore, characterizing both the deterministic and stochastic aspects of the dynamics is crucial in the study of mesoscale collective phenomena. Here, we use a physics-inspired, neural-network based approach to characterize the stochastic group dynamics of interacting individuals, through a stochastic differential equation (SDE) that governs the collective dynamics of the group. We apply this technique on both synthetic and real-world datasets, and identify the deterministic and stochastic aspects of the dynamics using drift and diffusion fields, enabling us to make novel inferences about the nature of order in these systems.

cs.LG↗

arXiv2023

Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple self-propelled particle (SPP) model of collective motion. In our SPP model, a focal individual can interact with k randomly chosen neighbours within an interaction radius. We consider k = 1 (called stochastic pairwise interactions), k = 2 (stochastic ternary interactions), and k equalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). The data-driven mesoscopic equations reveal that the stochastic pairwise interaction model produces a novel form of collective motion driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, yield collective motion driven primarily by the deterministic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasizes the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

q-bio.QM↗

arXiv2022

Inferring the stability of concentrated emulsions from droplet configuration information

When droplets are tightly packed in a 2D microchannel, coalescence of a pair of droplets can trigger an avalanche of coalescence events that propagate through the entire emulsion. This propagation is found to be stochastic, i.e. every coalescence event does not necessarily trigger another. To study how the local probabilistic propagation affects the dynamics of the avalanche, as a whole, a stochastic agent based model is used. Taking as input, i) how the droplets are packed (configuration) and ii) a measure of local probabilistic propagation (experimentally derived; function of fluid and other system parameters), the model predicts the expected size distribution of avalanches. In this article, we investigate how droplet configuration affects the avalanche dynamics. We find the mean size of these avalanches to depend non-trivially on how droplets are packed together. Large variations in the avalanche dynamics are observed when droplet packing are different, even when the other system properties (number of droplets, fluid properties, channel geometry, etc.) are kept constant. Bidisperse emulsions show less variation in the dynamics and they are surprisingly more stable than monodisperse emulsions. To get a systems-level understanding of how a given droplet-configuration either facilitates or impedes the propagation of an avalanche, we employ a graph-theoretic analysis, where emulsions are expressed as graphs. We find that the properties of the underlying graph, namely the mean degree and the algebraic connectivity, are well correlated with the observed avalanche dynamics. We exploit this dependence to derive a data-based model that predicts the expected avalanche sizes from the properties of the graph.

cond-mat.soft↗

arXiv2022

Disentangling intrinsic motion from neighbourhood effects in heterogeneous collective motion

Most real world collectives, including active particles, living cells, and grains, are heterogeneous, where individuals with differing properties interact. The differences among individuals in their intrinsic properties have emergent effects at the group level. It is often of interest to infer how the intrinsic properties differ among the individuals, based on their observed movement patterns. However, the true individual properties may be masked by emergent effects in the collective. We investigate the inference problem in the context of a bidisperse collective with two types of agents, where the goal is to observe the motion of the collective and classify the agents according to their types. Since collective effects such as jamming and clustering affect individual motion, an agent's own movement does not have sufficient information to perform the classification well: a simple observer algorithm, based only on individual velocities cannot accurately estimate the level of heterogeneity of the system, and often misclassifies agents. We propose a novel approach to the classification problem, where collective effects on an agent's motion is explicitly accounted for. We use insights about the physics of collective motion to quantify the effect of the neighbourhood on an agent using a neighbourhood parameter. Such an approach can distinguish between agents of two types, even when their observed motion is identical. This approach estimates the level of heterogeneity much more accurately, and achieves significant improvements in classification. Our results demonstrate that explicitly accounting for neighbourhood effects is often necessary to correctly infer intrinsic properties of individuals.

cs.LG↗