TopoStats - A program for automated tracing of biomolecules from AFM images.

We present TopoStats, a Python toolkit for automated editing and analysis of Atomic Force Microscopy images. The program automates identification and tracing of individual molecules in circular and linear conformations without user input. TopoStats was able to identify and trace a range of molecules within AFM images, finding, on average, ~90% of all individual molecules and molecular assemblies within a wide field of view, and without the need for prior processing. DNA minicircles of varying size, DNA origami rings and pore forming proteins were identified and accurately traced with contour lengths of traces typically within 10 nm of the predicted contour length. TopoStats was also able to reliably identify and trace linear and enclosed circular molecules within a mixed population. The program is freely available via GitHub (https://github.com/afm-spm/TopoStats) and is intended to be modified and adapted for use if required.

Partial mean-field model for neurotransmission dynamics.

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

Modelling opinion dynamics under the impact of influencer and media strategies.

Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel framework for opinion dynamics that can accommodate various versions of opinion dynamics as well as account for different roles, namely that of individuals, media and influencers, who change their own opinion positions on different time scales. Numerical simulations of instances of this framework show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. The framework allows for mean-field approximations by partial differential equations, which reproduce those dynamics and allow for efficient large-scale simulations when the number of individuals is large. Based on the mean-field approximations, we can study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, our framework allows us to demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to a more flexible modelling approach in opinion dynamics and a better understanding of the different roles and strategies in the increasingly complex information ecosystem.

The furnace and the goat-A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century ce.

Scholars frequently cite fuel scarcity after deforestation as a reason for the abandonment of most of the Roman iron smelting sites on Elba Island (Tuscan Archipelago, Italy) in the 1st century bce. Whereas the archaeological record clearly indicates the decrease in smelting activities, evidence confirming the 'deforestation narrative' is ambiguous. Therefore, we employed a stochastic, spatio-temporal model of the wood required and consumed for iron smelting on Elba Island in order to assess the availability of fuelwood on the island. We used Monte Carlo simulations to cope with the limited knowledge available on the past conditions on Elba Island and the related uncertainties in the input parameters. The model includes both, wood required for the furnaces and to supply the workforce employed in smelting. Although subject to high uncertainties, the outcomes of our model clearly indicate that it is unlikely that all woodlands on the island were cleared in the 1st century bce. A lack of fuel seems only likely if a relatively ineffective production process is assumed. Therefore, we propose taking a closer look at other reasons for the abandonment of smelting sites, e.g. the occupation of new Roman provinces with important iron ore deposits; or a resource-saving strategy in Italia. Additionally, we propose to read the development of the 'deforestation narrative' originating from the 18th/19th century in its historical context.