25 citations · 103 across the 19 of their papers we have counts for
19 papers
Optimal Risk-Sharing Rules in Network-based Decentralized Insurance
Heather N. Fogarty, Sooie-Hoe Loke, Nicholas F. Marshall +1
This paper studies decentralized risk-sharing on networks. In particular, we consider a model where agents are nodes in a given network structure. Agents directly connected by edge…
From the binomial reshuffling model to Poisson distribution of money
Fei Cao, Nicholas F. Marshall
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth and are redis…
Fast Principal Component Analysis for Cryo-EM Images
Nicholas F. Marshall, Oscar Mickelin, Yunpeng Shi +1
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modelin…
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
Nicholas F. Marshall, Oscar Mickelin, Amit Singer
We present a fast and numerically accurate method for expanding digitized images representing functions on supported on the disk $\{x \in \mathbb{R}^2 : |x|…
On a linearization of quadratic Wasserstein distance
Philip Greengard, Jeremy G. Hoskins, Nicholas F. Marshall +1
This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance . In particular, we compute an approximation of the negative homogeneous w…
An optimal scheduled learning rate for a randomized Kaczmarz algorithm
Nicholas F. Marshall, Oscar Mickelin
We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving , where is a consistent linear s…
A common variable minimax theorem for graphs
Ronald R. Coifman, Nicholas F. Marshall, Stefan Steinerberger
Let be a collection of graphs defined on a common set of vertices but with different edge sets .…
Multi-target detection with rotations
Tamir Bendory, Ti-Yen Lan, Nicholas F. Marshall +2
We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated…
Image recovery from rotational and translational invariants
Nicholas F. Marshall, Ti-Yen Lan, Tamir Bendory +1
We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the mul…
Randomized mixed Hölder function approximation in higher-dimensions
Nicholas F. Marshall
The purpose of this paper is to extend the result of arXiv:1810.00823 to mixed Hölder functions on for all . In particular, we prove that by sampling an -mixe…
A fast simple algorithm for computing the potential of charges on a line
Zydrunas Gimbutas, Nicholas F. Marshall, Vladimir Rokhlin
We present a fast method for evaluating expressions of the form where are…
A Cheeger inequality for graphs based on a reflection principle
Edward Gelernt, Diana Halikias, Charles Kenney +1
Given a graph with a designated set of boundary vertices, we define a new notion of a Neumann Laplace operator on a graph using a reflection principle. We show that the first eigen…
Approximating mixed Hölder functions using random samples
Nicholas F. Marshall
Suppose is a -mixed Hölder function that we sample at points chosen uniformly at random from the unit square. Let t…
Manifold learning with bi-stochastic kernels
Nicholas F. Marshall, Ronald R. Coifman
In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic wi…
Stretching convex domains to capture many lattice points
Nicholas F. Marshall
We consider an optimal stretching problem for strictly convex domains in that are symmetric with respect to each coordinate hyperplane, where stretching refers to tr…
Triangles capturing many lattice points
Nicholas F. Marshall, Stefan Steinerberger
We study a combinatorial problem that recently arose in the context of shape optimization: among all triangles with vertices , , and and fixed area, which one…
The Stability of the First Neumann Laplacian Eigenfunction Under Domain Deformations and Applications
Nicholas F. Marshall
The robustness of manifold learning methods is often predicated on the stability of the Neumann Laplacian eigenfunctions under deformations of the assumed underlying domain. Indeed…
Time Coupled Diffusion Maps
Nicholas F. Marshall, Matthew J. Hirn
We consider a collection of points in measured at times, which are encoded in an data tensor. Our objective is to define a single embed…
Extracting Geography from Trade Data
Yuke Li, Tianhao Wu, Nicholas Marshall +1
Understanding international trade is a fundamental problem in economics -- one standard approach is via what is commonly called the "gravity equation", which predicts the total amo…