Density-functional fluctuation theory of crowds

Small-area population forecasting in a segregated city using density-functional fluctuation theory

Policy decisions concerning housing, transportation, and resource allocation would all benefit from accurate small-area population forecasts. However, despite the success of regional-scale migration models, developing neighborhood-scale forecasts remains a challenge due to the complex nature of residential choice. Here, we introduce an innovative approach to this challenge by extending density-functional fluctuation theory (DFFT), a proven approach for modeling group spatial behavior in biological systems, to predict small-area population shifts over time. The DFFT method uses observed fluctuations in small-area populations to disentangle and extract effective social and spatial drivers of segregation, and then uses this information to forecast intra-regional migration. To demonstrate the efficacy of our approach in a controlled setting, we consider a simulated city constructed from a Schelling-type model. Our findings indicate that even without direct access to the underlying agent preferences, DFFT accurately predicts how broader demographic changes at the city scale percolate to small-area populations. In particular, our results demonstrate the ability of DFFT to incorporate the impacts of segregation into small-area population forecasting using interactions inferred solely from steady-state population count data.

Synchronized locomotion can improve spatial accessibility inside ant colonies

Synchronization is a conspicuous form of collective behaviour that is of crucial importance in numerous biological systems. Ant colonies from the genera Leptothorax and Temnothorax form small colonies, typically made up of only a few hundred workers, and exhibit a form of synchronized behaviour where workers inside colonies' nests become active together in rhythmic cycles that have a period of approximately 20-200 min. However, it is not currently known if these synchronized rhythms of locomotion confer any functional benefit to colonies. By using a combination of multiple image analysis techniques, we show that inactive Leptothorax ants can act as immobile obstacles to moving ants, and that synchronized activity has the potential to reduce the likelihood that individual ants will encounter regions of immobile obstacles that impede access to portions of the nest. We demonstrate qualitatively similar findings using a computational model of confined active particles with oscillating activity.

A density functional theory for ecology across scales

Ecology lacks a holistic approach that can model phenomena across temporal and spatial scales, largely because of the challenges in modelling systems with a large number of interacting constituents. This hampers our understanding of complex ecosystems and the impact that human interventions (e.g., deforestation, wildlife harvesting and climate change) have on them. Here we use density functional theory, a computational method for many-body problems in physics, to develop a computational framework for ecosystem modelling. Our methods accurately fit experimental and synthetic data of interacting multi-species communities across spatial scales and can project to unseen data. As the key concept we establish and validate a cost function that encodes the trade-offs between the various ecosystem components. We show how this single general modelling framework delivers predictions on par with established, but specialised, approaches for systems from predatory microbes to territorial flies to tropical tree communities. Our density functional framework thus provides a promising avenue for advancing our understanding of ecological systems.

Evolving symbolic density functionals

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite emerging applications of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain more than tens of thousands of parameters, leading to a huge gap in the formulation with the conventional human-designed symbolic functionals. We propose a new framework, Symbolic Functional Evolutionary Search (SyFES), that automatically constructs accurate functionals in the symbolic form, which is more explainable to humans, cheaper to evaluate, and easier to integrate to existing codes than other ML functionals. We first show that, without prior knowledge, SyFES reconstructed a known functional from scratch. We then demonstrate that evolving from an existing functional ωB97M-V, SyFES found a new functional, GAS22 (Google Accelerated Science 22), that performs better for most of the molecular types in the test set of Main Group Chemistry Database (MGCDB84). Our framework opens a new direction in leveraging computing power for the systematic development of symbolic density functionals.

Dominating lengthscales of zebrafish collective behaviour

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the collective dynamics of fifty zebrafish. We observed the emergence of collective behaviour changing between ordered to randomised, upon adaptation to new environmental conditions. We quantify the spatial and temporal correlation functions of the fish and identify two length scales, the persistence length and the nearest neighbour distance, that capture the essence of the behavioural changes. The ratio of the two length scales correlates robustly with the polarisation of collective motion that we explain with a reductionist model of self-propelled particles with alignment interactions.

Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory

For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. In this work, we present an extended model for disease spread based on combining a susceptible-infected-recovered model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. We show that the model exhibits interesting transient phase separation associated with a reduction of the number of infections, and allows for new insights into the control of pandemics.

Synchronization of complex human networks

The synchronization of human networks is essential for our civilization and understanding its dynamics is important to many aspects of our lives. Human ensembles were investigated, but in noisy environments and with limited control over the network parameters which govern the network dynamics. Specifically, research has focused predominantly on all-to-all coupling, whereas current social networks and human interactions are often based on complex coupling configurations. Here, we study the synchronization between violin players in complex networks with full and accurate control over the network connectivity, coupling strength, and delay. We show that the players can tune their playing period and delete connections by ignoring frustrating signals, to find a stable solution. These additional degrees of freedom enable new strategies and yield better solutions than are possible within current models such as the Kuramoto model. Our results may influence numerous fields, including traffic management, epidemic control, and stock market dynamics.

Local interactions and their group-level consequences in flocking jackdaws

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula) in flocks containing 2-338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

Correcting locomotion dependent observation biases in thermal preference of Drosophila

Sensing environmental temperatures is essential for the survival of ectothermic organisms. In Drosophila, two of the most used methodologies to study temperature preferences (T_P) and the genes involved in thermosensation are two-choice assays and temperature gradients. Whereas two-choice assays reveal a relative T_P, temperature gradients can identify the absolute T_p. One drawback of gradients is that small ectothermic animals are susceptible to cold-trapping: a physiological inability to move at the cold area of the gradient. Often cold-trapping cannot be avoided, biasing the resulting T_P to lower temperatures. Two mathematical models were previously developed to correct for cold-trapping. These models, however, focus on group behaviour which can lead to overestimation of cold-trapping due to group aggregation. Here we present a mathematical model that simulates the behaviour of individual Drosophila in temperature gradients. The model takes the spatial dimension and temperature difference of the gradient into account, as well as the rearing temperature of the flies. Furthermore, it allows the quantification of cold-trapping and reveals unbiased T_P. Additionally, our model reveals that flies have a range of tolerable temperatures, and this measure is more informative about the behaviour than commonly used T_P. Online simulation is hosted at http://igloo.uni-goettingen.de. The code can be accessed at https://github.com/zerotonin/igloo.