We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.

Since the presentation of the radiation model, much work has been done to compare its findings with those obtained from gravitational models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin–destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However, the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyse the impact of the introduction of a new transportation network, a bus rapid transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able to not only better assess the goodness of fit and the impact of this intervention, but also understand reasons for the systematic similarities and differences in their predictions.

Characterising road networks has been the focus of a large body of research due to it being the main driver of activities in an urban ecosystem and the structuring factor in the dynamics of the city. One of these activities, and one with the largest economical impact in a city, is retail dynamics and its evolution. Therefore, the mathematical modeling of the location of retail activities and of the emergence of clustering in retail centers has as well generated a large number of works. Despite these two interwoven components strongly depending on one another and their fundamental importance in understanding cities, little work has been done in order to compare their local and global properties. Here we compare the road network’s hierarchical structure, unveiled through a percolation analysis of the network, with the retail location distribution defined by exploiting a gravity-based retail model. We interpret the great agreement in the city’s organizations as it emerges from both methodologies as new evidence of the interdependence of these two crucial dimensions of a city’s life.

We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean field equations. Numerical analysis of the high dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation is found to be a good early-warning of the transitions occurring intermittently.Introduction -Many complex high dimensional systems are characterised by intermittent dynamics, where relatively long quiescent periods are interrupted by sudden and quick bursts of activity during which the system suffers hectic rearrangements. [6] can exhibit sudden changes both overall or in one of its subsystems, like when a bloom of harmful algae suddenly forms in the sea [7]. Due to their widespread occurrence, these transitions have gathered a huge interest in the last decade, with research mainly focused on developing statistical methods to forecast them from the observed time series [8][9][10] and on the development of a general mathematical framework to describe them [11]. In the present paper we contribute to both efforts by developing a mathematical analysis by use of a paradigmatic model exhibiting intermittent stochastic evolution and by identifying systemic observables that can deliver early-warning of impending transitions. We focus on the Tangled Nature (TaNa) model [12][13][14] of evolutionary ecology. The initial aim of the model was to establish a sound and simple mathematically framework for "punctuated equilibrium", i.e. the observed intermittent mode of macro-evolution.

Abstract. We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation we are able to construct a good early-warning indicator of the transitions occurring intermittently.