Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …

Neural circuits construct distributed representations of key variables—external stimuli or
internal constructs of quantities relevant for survival, such as an estimate of one's location in …

Detecting meaningful structure in neural activity and connectivity data is challenging in the
presence of hidden nonlinearities, where traditional eigenvalue-based methods may be …

Data analysis techniques from network science have fundamentally improved our
understanding of neural systems and the complex behaviors that they support. Yet the …

Measuring neuronal tuning curves has been instrumental for many discoveries in
neuroscience but requires a priori assumptions regarding the identity of the encoded …

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a
spatial coordinate system. However, irregularities in the grid pattern as well as responses of …

An animal's ability to navigate through space rests on its ability to create a mental map of its
environment. The hippocampus is the brain region centrally responsible for such maps, and …

We use topological data analysis to study “functional networks” that we construct from time-
series data from both experimental and synthetic sources. We use persistent homology with …

Neuroscience is undergoing a period of rapid experimental progress and expansion. New
mathematical tools, previously unknown in the neuroscience community, are now being …