arXiv subjects

Vishwesha Guttal

Publications and source records attributed to Vishwesha Guttal.

13 recordsLinked to original sources

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↗

arXiv2021

Randomness in the choice of neighbours promotes cohesion in mobile animal groups

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarised. Here, we ask -- how do organisms maintain group cohesion? Using a spatially-explicit model, inspired from empirical investigations, we show that group cohesion can be achieved even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in collective motion.

nlin.AO↗

arXiv2021

Demographic noise can promote abrupt transitions in ecological systems

Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes in finite systems -- makes the transitions gradual or continuous. In this paper, we show that demographic noise may, in fact, promote abrupt transitions in systems that would otherwise show continuous transitions. We present our methods and results in a tutorial-like format. We begin with a simple spatially-explicit individual-based model with local births and deaths influenced by positive feedback processes. We then derive a stochastic differential equation that describes how local probabilistic rules scale to stochastic population dynamics. The infinite-size well-mixed limit of this SDE for our model is consistent with mean-field models of abrupt regime-shifts. Finally, we analytically show that as a consequence of demographic noise, finite-size systems can undergo abrupt shifts even with weak positive interactions. Numerical simulations of our spatially-explicit model confirm this prediction. Thus, we predict that small-sized populations and ecosystems may undergo abrupt collapse even when larger systems - with the same microscopic interactions - show a smooth response to environmental stress.

q-bio.PE↗

arXiv2020

Noise-induced Effects in Collective Dynamics and Inferring Local Interactions from Data

In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise. Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects due to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterise the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives with the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature.

q-bio.PE↗

arXiv2019

Noise-Induced Schooling of Fish

We report on the dynamics of collective alignment in groups of the cichlid fish, Etroplus suratensis. Focusing on small-to-intermediate sized groups ($10<N<100$), we demonstrate that schooling (highly polarised and coherent motion) is noise-induced, arising from the intrinsic stochasticity associated with finite numbers of interacting fish. The fewer the fish, the greater the (multiplicative) noise and therefore the likelihood of alignment. Such empirical evidence is rare, and tightly constrains the possible underlying interactions between fish: computer simulations indicate that E. suratensis align with each other one at a time, which is at odds with the canonical mechanism of collective alignment, local direction-averaging. More broadly, our results confirm that, rather than simply obscuring otherwise deterministic dynamics, noise is fundamental to the characterisation of emergent collective behaviours, suggesting a need to re-appraise aspects of both collective motion and behavioural inference.

cond-mat.stat-mech↗

arXiv2019

Fission-fusion dynamics and group-size dependent composition in heterogeneous populations

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyse a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type/species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte-Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems.

nlin.AO↗

arXiv2019

Deriving mesoscopic models of collective behaviour for finite populations

Animal groups exhibit emergent properties that are a consequence of local interactions. Linking individual-level behaviour to coarse-grained descriptions of animal groups has been a question of fundamental interest. Here, we present two complementary approaches to deriving coarse-grained descriptions of collective behaviour at so-called mesoscopic scales, which account for the stochasticity arising from the finite sizes of animal groups. We construct stochastic differential equations (SDEs) for a coarse-grained variable that describes the order/consensus within a group. The first method of construction is based on van Kampen's system-size expansion of transition rates. The second method employs Gillespie's chemical Langevin equations. We apply these two methods to two microscopic models from the literature, in which organisms stochastically interact and choose between two directions/choices of foraging. These `binary-choice' models differ only in the types of interactions between individuals, with one assuming simple pair-wise interactions, and the other incorporating higher-order effects. In both cases, the derived mesoscopic SDEs have multiplicative, or state-dependent, noise. However, the different models demonstrate the contrasting effects of noise: increasing order in the pair-wise interaction model, whilst reducing order in the higher-order interaction model. Although both methods yield identical SDEs for such binary-choice, or one-dimensional, systems, the relative tractability of the chemical Langevin approach is beneficial in generalizations to higher-dimensions. In summary, this book chapter provides a pedagogical review of two complementary methods to construct mesoscopic descriptions from microscopic rules and demonstrates how resultant multiplicative noise can have counter-intuitive effects on shaping collective behaviour.

q-bio.PE↗

arXiv2006

Model for Folding and Aggregation in RNA Secondary Structures

We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the secondary structure and the energy gained by pairing drives the RNA to undergo a `temperature independent' second order phase transition from a molten to an aggregated phase'. The aggregated phase thus obtained has a macroscopically large number of contacts between different RNAs. The partition function scaling exponent for this phase is θ~ 1/2 and the crossover exponent of the phase transition is ν~ 5/3. The relevance of these calculations to the aggregation of biological molecules is discussed.

physics.bio-ph↗

arXiv2005

Model for a Macroscopically Disordered Conductor with an Exactly Linear High-Field Magnetoresistance

We calculate the effective resistivity of a macroscopically disordered two dimensional conductor consisting of two components in a perpendicular magnetic field. When two components have equal area fractions, we use a duality theorem to show that the magnetoresistance is non-saturating and at high fields varies exactly linearly with magnetic field. At other compositions, an effective medium calculation leads to a saturating magnetoresistance. We briefly discuss possible connections between these results and magnetoresistance measurements on heavily disordered chalconide semiconductors.

cond-mat.mtrl-sci↗

arXiv2003

A cellular-automata model of flow in ant-trails: non-monotonic variation of speed with density

Generically, in models of driven interacting particles the average speed of the particles decreases monotonically with increasing density. We propose a counter-example, motivated by the motion of ants in a trail, where the average speed of the particles varies {\it non-monotonically} with their density because of the coupling of their dynamics with another dynamical variable. These results, in principle, can be tested experimentally.

cond-mat.stat-mech↗