Publications (4)
Endoscopic Fourier-transform infrared spectroscopy through a fiber microprobe
Jaehyeon Kim, Yue Tian, Guanhua Qiao +7
Fourier-transform infrared spectroscopy (FTIR) is a powerful analytical method for not only the chemical identification of solid, liquid, and gas species, but also the quantificati…
A Simple Proof of the Cayley Formula using Random Graphs
Scott Wu, Ray Li, Andrew He +1
We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous…
DeepMartNet -- A Martingale Based Deep Neural Network Learning Method for Dirichlet BVPs and Eigenvalue Problems of Elliptic PDEs in R^d
Wei Cai, Andrew He, Daniel Margolis
In this paper, we propose DeepMartNet - a Martingale based deep neural network learning method for solving Dirichlet boundary value problems (BVPs) and eigenvalue problems for elli…
An Elementary Proof of the Cayley Formula Using Random Maps
Steven Hao, Andrew He, Ray Li +1
Cayley's formula states that the number of labelled trees on vertices is , and many of the current proofs involve complex structures or rigorous computation. We presen…