Inference on the Macroscopic Dynamics of Spiking Neurons.

The process of inference on networks of spiking neurons is essential to decipher the underlying mechanisms of brain computation and function. In this study, we conduct inference on parameters and dynamics of a mean-field approximation, simplifying the interactions of neurons. Estimating parameters of this class of generative model allows one to predict the system's dynamics and responses under changing inputs and, indeed, changing parameters. We first assume a set of known state-space equations and address the problem of inferring the lumped parameters from observed time series. Crucially, we consider this problem in the setting of bistability, random fluctuations in system dynamics, and partial observations, in which some states are hidden. To identify the most efficient estimation or inversion scheme in this particular system identification, we benchmark against state-of-the-art optimization and Bayesian estimation algorithms, highlighting their strengths and weaknesses. Additionally, we explore how well the statistical relationships between parameters are maintained across different scales. We found that deep neural density estimators outperform other algorithms in the inversion scheme, despite potentially resulting in overestimated uncertainty and correlation between parameters. Nevertheless, this issue can be improved by incorporating time-delay embedding. We then eschew the mean-field approximation and employ deep neural ODEs on spiking neurons, illustrating prediction of system dynamics and vector fields from microscopic states. Overall, this study affords an opportunity to predict brain dynamics and responses to various perturbations or pharmacological interventions using deep neural networks.

Geometrical multiscale tortuosity of desert ant walking trajectories.

Desert ants stand out as some of the most intriguing insect navigators, having captured the attention of scientists for decades. This includes the structure of walking trajectories during goal approach and search behaviour for the nest and familiar feeding sites. In the present study, we analysed such trajectories with regard to changes in walking direction. The directional change of the ants was quantified, i.e. an angle θ between trajectory increments of a given arclength λ was computed. This was done for different length scales λ, according to our goal of analysing desert ant path characteristics with respect to length scale. First, varying λ through more than two orders of magnitude demonstrated Brownian motion characteristics typical of the random walk component of search behaviour. Unexpectedly, this random walk component was also present in - supposedly rather linear - approach trajectories. Second, there were small but notable deviations from a uniform angle distribution that is characteristic of random walks. This was true for specific search situations, mostly close to the (virtual) goal position. And third, experience with a feeder position resulted in straighter approaches and more focused searches, which was also true for nest searches, albeit to a lesser extent. Taken together, these results both verify and extend previous studies on desert ant path characteristics. Of particular interest are the ubiquitous Brownian motion signatures and specific deviations thereof close to the goal position, indicative of unexpectedly structured search behaviour.

Geometrical multiscale tortuosity of desert ant walking trajectories.

Desert ants stand out as some of the most intriguing insect navigators, having captured the attention of scientists for decades. This includes the structure of walking trajectories during goal approach and search behaviour for the nest and familiar feeding sites. In the present study, we analysed such trajectories with regard to changes in walking direction. The directional change of the ants was quantified, i.e. an angle θ between trajectory increments of a given arclength λ was computed. This was done for different length scales λ, according to our goal of analysing desert ant path characteristics with respect to length scale. First, varying λ through more than two orders of magnitude demonstrated Brownian motion characteristics typical of the random walk component of search behaviour. Unexpectedly, this random walk component was also present in - supposedly rather linear - approach trajectories. Second, there were small but notable deviations from a uniform angle distribution that is characteristic of random walks. This was true for specific search situations, mostly close to the (virtual) goal position. And third, experience with a feeder position resulted in straighter approaches and more focused searches, which was also true for nest searches, albeit to a lesser extent. Taken together, these results both verify and extend previous studies on desert ant path characteristics. Of particular interest are the ubiquitous Brownian motion signatures and specific deviations thereof close to the goal position, indicative of unexpectedly structured search behaviour.