Nicholas F. Marshall
Assistant Professor
Department of Mathematics
Oregon State University
Email: [email protected]
Office: Kidder 292
Directory Link
Research interests
I am interested in problems that involve an interplay between analysis, geometry,
and probability (especially such problems motivated by data
science).
About
Research
-
arXiv:2406.05922
Fast expansion into harmonics on the ball
with
Joe Kileel,
Oscar Mickelin,
Amit Singer
-
arXiv:2406.01552
Learning equivariant tensor functions with applications to sparse vector recovery
with
Wilson G. Gregory,
Josué Tonelli-Cueto,
Andrew S. Lee,
Soledad Villar
-
arXiv:2404.10759
Laplace-HDC: Understanding the geometry of binary hyperdimensional computing
with
Saeid Pourmand,
Wyatt Whiting,
Alireza Aghasi
-
arXiv:2401.15183
Moment-based metrics for molecules computable from cryo-EM images
with
Andy Zhang,
Oscar Mickelin,
Joe Kileel,
Eric Verbeke,
Marc Gilles,
Amit Singer
Biological Imaging
doi.org/10.1017/S2633903X24000023
-
arXiv:2401.09415
Randomized Kaczmarz with geometrically smoothed momentum
with
Seth Alderman, Roan Luikart
SIAM Journal on Matrix Analysis and Applications (to appear)
-
arXiv:2212.14288
From the binomial reshuffling model to Poisson distribution of money
with
Fei Cao
Networks and Heterogeneous Media
doi.org/10.3934/nhm.2024002
-
arXiv:2210.17501
Fast Principal Component Analysis for Cryo-EM Images
with
Oscar Mickelin,
Yunpeng Shi,
Amit Singer
Biological Imaging
doi.org/10.1017/S2633903X23000028
-
arXiv:2207.13674
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
with
Oscar Mickelin, Amit Singer
SIAM Journal on Scientific Computing
doi.org/10.1137/22M1542775
-
arXiv:2202.12224
An optimal scheduled learning rate for a randomized Kaczmarz algorithm
with
Oscar Mickelin
SIAM Journal on Matrix Analysis and Applications doi.org/10.1137/22M148803X
-
arXiv:2201.13386
On a linearization of quadratic Wasserstein distance
with
Philip Greengard, Jeremy Hoskins, Amit Singer
-
arXiv:2107.14747
A common variable minimax theorem for graphs
with
Ronald Coifman,
Stefan Steinerberger
Foundations of Computational Mathematics
doi.org/10.1007/s10208-022-09558-8
-
arXiv:2101.07709
Multi-target detection with rotations
with
Tamir Bendory,
Ti-Yen Lan,
Iris Rukshin, Amit Singer
Inverse Problems and Imaging doi.org/10.3934/ipi.2022046
-
arXiv:1910.10006
Image recovery from rotational and translational invariants
with
Tamir Bendory,
Ti-Yen Lan,
Amit Singer
ICASSP
doi.org/10.1109/ICASSP40776.2020.9053932
-
arXiv:1910.04201
Randomized mixed Hölder function approximation in higher-dimensions
Technical Report
-
arXiv:1907.03873
A fast simple algorithm for computing the potential of charges on a line
with
Zydrunas Gimbutas, Vladimir Rokhlin
Applied and Computational Harmonic Analysis
doi.org/10.1016/j.acha.2020.06.002
-
arXiv:1902.06633
A Cheeger inequality for graphs based on a reflection
principle
with
Edward Gelernt, Diana Halikias, Charles Kenney
Involve
doi.org/10.2140/involve.2020.13.475
-
arXiv:1810.00823
Approximating mixed Hölder functions using random samples
Annals of Applied Probability
doi.org/10.1214/19-AAP1471
-
arXiv:1711.06711
Manifold learning with bi-stochastic kernels
with
Ronald Coifman
IMA Journal of Applied Mathematics
doi.org/10.1093/imamat/hxy065
-
arXiv:1707.00682
Stretching convex domains to capture many lattice points
International Mathematics Research Notices
doi.org/10.1093/imrn/rny102
-
arXiv:1706.04170
Triangles capturing many lattice points
with
Stefan Steinerberger
Mathematika
doi.org/10.1112/S0025579318000219
-
arXiv:1704.02962
The Stability of the First Neumann Laplacian Eigenfunction
Under Domain Deformations and Applications
Applied and Computational Harmonic Analysis
doi.org/10.1016/j.acha.2019.05.001
-
arXiv:1608.03628
Time Coupled Diffusion Maps
with
Matthew Hirn
Applied and Computational Harmonic Analysis
doi.org/10.1016/j.acha.2017.11.003
-
arXiv:1607.05235
Extracting Geography from Trade Data
with
Yuke Li, Tianhao Wu, Stefan
Steinerberger
Physica A
doi.org/10.1016/j.physa.2017.01.037
Notes
Some short notes on various topics
-
some-math-for-numerics.pdf
- Introductory note about some key mathematical ideas used in
numerical methods
- Discusses asymptotic series, Richardson extrapolation, contraction mapping,
and simple iteration
-
stirlings-approximation.pdf
- Elementary proof of Stirling's approximation up to constant
- Discusses concave functions, trapezoid rule, midpoint rule
-
euler-maclaurin.pdf
- Informal and precise statements of Euler-Maclaurin formula
- Preliminaries about asymptotic series, Richardson extrapolation, Taylor's theorem, Trapezoid rule
-
gaussian-quadrature.pdf
- Introduction to Gaussian quadrature
- Introduces Legendre polynomials, Gaussian quadrature remainder formula, numerical example
-
chebyshev-interpolation.pdf
- Introduction to polynomial interpolation
- Includes polynomial interpolation remainder formula, Chebyshev polynomials, Chebyshev nodes
-
de-moivre-thm.pdf
- Sketch of de Moivre's central limit theorem
- Uses Binomial distribution, Stirling's formula, Reimann sum
Mentoring
- Graduate
- Undergraduate
- Summer research 2023
- Summer research 2020
- Summer research 2018
Teaching
- Spring 2024
- High Dimensional Probability, MTH 669, Oregon State University
- Winter 2024
- Probability Theory II, MTH 665, Oregon State University
- Fall 2023
- Probability Theory, MTH 664, Oregon State University
- Spring 2023
- Advanced Calculus II, MTH 312, Oregon State University
- Probability III, MTH 465/565, Oregon State University
- Winter 2023
- Probability II, MTH 464/564, Oregon State University
- Fall 2021
- Numerical methods, MAT 321/APC 321, Princeton University
- Fall 2020
-
Numerical methods, MAT 321/APC 321, Princeton University
- Spring 2021
- Linear Algebra with Applications, MAT 202, Princeton University
- Fall 2018
- Calculus II, MATH 115, Yale University