  Topological data analyses are rapidly turning into key tools for quantifying
large volumes of neurobiological data, e.g., for organizing the spiking outputs
of large neuronal ensembles and thus gaining insights into the information
produced by various networks. Below we discuss a case in which several
convergent topological analyses not only provide a description of the data
structure, but also produce insights into how these data may be processed in
the hippocampus---a brain part that plays a key role in learning and memory.
The resulting functional model provides a unifying framework for integrating
spiking information at different timescales and understanding the course of
spatial learning at different levels of spatiotemporal granularity. In
particular, the model allows quantifying contributions of various physiological
phenomena---brain waves, synaptic strengths, synaptic architectures, etc., into
spatial cognition.
