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Introduction A prominent policy, which has been proposed in many European municipalities over the last years is the promotion of cycling to decrease pollution and to increase public health. One important part of the assessment of this policy is the estimation of the induced change in bicycle crash numbers. Several recent works supported the ideas by reporting that cycling becomes safer if the number of cyclists increases, i.e., there seems to be a safety-in-numbers effect (SiN). Methods The problems related to the interpretation of bicycle crash and volume data are discussed and an approach aiming at a better understanding of the SiN-phenomenon is presented. In particular it is proposed to adopt models with memory to pursue causal relations and to study SiN at different time scales. To estimate daily cyclist volumes from irregular counts, a weather based model for bicycle volumes is developed. Results We provide a proof of concept for the proposed memory model by testing it on synthesized data and apply the proposed techniques on data provided by Berlin authorities. The application on synthetic data shows that improved fits with memory models can indicate temporal correlations within data and, thus, can give hints for causal relations. Although such a temporal correlation could not be substantiated in the real data, a surprising ambiguity was found to exist on different time scales. Over the long term, individual risks decline with increased bicycle volumes, while on shorter terms the opposite seems to be present: The more bicyclists are on the roads, the more unsafe cycling becomes. Conclusions The paper concludes by considering possible interpretations for the observed ambiguity. Further, a discussion of the developed methodology and some thoughts for a role that the SiN effect can play for transportation planning are included.

Spike time-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons.