22 citations · 52 across the 24 of their papers we have counts for
25 papers
On the Abundance of Critical Points of the t-SNE Energy
Nakul Haridas, Ryan Murray
This paper considers the energy landscape of the t-SNE algorithm. While this algorithm has enjoyed broad adoption, the non-convexity of the associated energy has made it difficult…
Stability of the -Plane Transform on Measures and Hölder-Type Comparisons of Wasserstein Metrics
Fatma Terzioglu, Ryan Murray
We establish stability estimates for the -plane transform on finite positive Radon measures, with emphasis on Fourier and Wasserstein metrics. We first introduce a metric on …
On the continuum limit of t-SNE for data visualization
Jeff Calder, Zhonggan Huang, Ryan Murray +1
This work is concerned with the continuum limit of a graph-based data visualization technique called the t-Distributed Stochastic Neighbor Embedding (t-SNE), which is widely used f…
Non-Linear Singularity Formation for Circular Vortex Sheets
Ryan Murray, Galen Wilcox
We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation i…
On the long-time behavior of scale-invariant solutions to the 2d Euler equation and applications
Tarek. M. Elgindi, Ryan. W. Murray, Ayman. R. Said
We study the long-time behavior of scale-invariant solutions of the 2d Euler equation satisfying a discrete symmetry. We show that all scale-invariant solutions with bounded variat…
The Influence of Vortex Sheet Geometry on the Kelvin-Helmholtz Instability
Ryan Murray, Galen Wilcox
This article revisits the instability of sharp shear interfaces, also called vortex sheets, in incompressible fluid flows. We study the Birkhoff-Rott equation, which describes the…