Tracking the topology of neural manifolds across populations.

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships.

The importance of the whole: Topological data analysis for the network neuroscientist.

Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices.

Two's company, three (or more) is a simplex : Algebraic-topological tools for understanding higher-order structure in neural data.

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 critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad - two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model.

Euler integration over definable functions.

We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks.

Multiply loaded magneto-optical trap.

We report a two-chambered, differentially pumped system that permits rapid collection of trapped atoms with a vapor cell magneto-optical trap (MOT) and efficient transfer of these atoms to a second MOT in a lowerpressure chamber. During the transfer the atoms are guided down a long, thin tube by a magnetic potential, with 90(15%) transfer efficiency. By multiply loading, we accumulate and hold as many as 30 times the number collected by the vapor cell MOT.