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We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the NOAA Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific Garbage Patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.

Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.

Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.

The interesting dynamical regimes in agent-based models (ABMs) of social dynamics are the transient dynamics leading to metastable or absorbing states, and the transition paths between metastable states possibly caused by external influences. In this thesis, we are particularly interested in the pathways of rare and critical transitions such as the tipping of the public opinion in a population or the forming of social movements. For a detailed quantitative analysis of these transition paths, we consider the agent-based models as Markov chains and employ Transition Path Theory. Since ABMs are usually not considered in stationarity and possibly even forced, we generalize Transition Path Theory to time-dependent dynamics, for example on finite-time intervals or with periodically varying transition probabilities. We also specifically consider the case of dynamics with absorbing states and show how the transitions prior to absorption can be studied. These generalizations can also be useful in other application domains such as for studying tipping in climate models or transitions in molecular models with external stimuli. Another obstacle when analysing the dynamics of agent-based models is the large number of agents resulting in a high-dimensional state space for the model. However, the emergent dynamics of the ABM usually has significantly fewer degrees of freedom and many symmetries enabling a model reduction. On the example of two stationary ABMs we demonstrate how a long model simulation can be employed to find a lower-dimensional parametrization of the state space using a manifold learning algorithm called Diffusion Maps. In the considered models, agents adapt their binary behaviour to the local neighbourhood. When the interaction network consists of several densely connected communities, the dynamics result in a largely coherent behaviour in each community. The low-dimensional structure of the state space is therefore a hypercube. The corners represent metastable states with coherent agent behaviour in each group and the edges correspond to transition paths where agents in a community change their behaviour through a chain reaction. Finally, we can apply Transition Path Theory to the effective dynamics in the reduced space to reveal, for example, the dominant transition paths or the agents that are most indicative of an impending tipping event.

Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.