Fokker–Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker–Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker–Planck equations in low and moderate dimensions. The proposed gradient–log–density estimator is also of independent interest, for example, in the context of optimal control.
Brainhack is an innovative meeting format that promotes scientific collaboration and education in an open, inclusive environment. This NeuroView describes the myriad benefits for participants and the research community and how Brainhacks complement conventional formats to augment scientific progress.
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution, although these are often experimentally inaccessible. Here we propose a theory for revealing physical connectivity of networked systems only from the event time series their intrinsic collective dynamics generate. Representing the patterns of event timings in an event space spanned by interevent and cross-event intervals, we reveal which other units directly influence the interevent times of any given unit. For illustration, we linearize an event-space mapping constructed from the spiking patterns in model neural circuits to reveal the presence or absence of synapses between any pair of neurons, as well as whether the coupling acts in an inhibiting or activating (excitatory) manner. The proposed model-independent reconstruction theory is scalable to larger networks and may thus play an important role in the reconstruction of networks from biology to social science and engineering.
Brainhack is an innovative meeting format that promotes scientific collaboration and education in an open and inclusive environment. Departing from the formats of typical scientific workshops, these events are based on grassroots projects and training, and foster open and reproducible scientific practices. We describe here the multifaceted, lasting benefits of Brainhacks for individual participants, particularly early career researchers. We further highlight the unique contributions that Brainhacks can make to the research community, contributing to scientific progress by complementing opportunities available in conventional formats.
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