299 citations · 924 across the 25 of their papers we have counts for
6 papers · 1 filter
Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discovery
Gal Mishne, Ronen Talmon, Ron Meir +3
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of…
Provable approximation properties for deep neural networks
Uri Shaham, Alexander Cloninger, Ronald R. Coifman
We discuss approximation of functions using deep neural nets. Given a function on a -dimensional manifold , we construct a sparsely-connected depth-4…
Nonlinear phase unwinding of functions
Ronald R. Coifman, Stefan Steinerberger
We study a natural nonlinear analogue of Fourier series. Iterative Blaschke factorization allows one to formally write any holomorphic function as a series which successively u…
Bigeometric Organization of Deep Nets
Alexander Cloninger, Ronald R. Coifman, Nicholas Downing +1
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of th…
Parsimonious Representation of Nonlinear Dynamical Systems Through Manifold Learning: A Chemotaxis Case Study
Carmeline J. Dsilva, Ronen Talmon, Ronald R. Coifman +1
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithm…
Data-Driven Reduction for Multiscale Stochastic Dynamical Systems
Carmeline J. Dsilva, Ronen Talmon, C. William Gear +2
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is ofte…