Martin J. Mohlenkamp
Associate Professor
Department of Mathematics
College of Arts & Sciences
Ohio University
See my mathematical geneology.
Contact Information
- Solid mail:
Department of Mathematics /
Morton Hall 321 /
1 Ohio University /
Athens OH 45701 USA
- E-mail:
mohlenka@ohio.edu
- Office: 315-B Morton Hall
- Phone: (740) 593-1259
- Fax: (740) 593-9805
- For office hours check one of the courses I am currently teaching.
Teaching
Courses
Resources
- Wavelet Materials
- I have organized some wavelet
materials for a short course I taught in 2004.
- Good Problems
-
We have developed a method to gently teach mathematical writing.
Good Problems: teaching mathematical writing
D. Bundy, E. Gibney, J. McColl, M. Mohlenkamp, K. Sandberg,
B. Silverstein, P. Staab, and M. Tearle.
University of Colorado APPM
preprint #466, August 15, 2001.
Up-to-date materials through a Student's Guide.
Research
General Interests
- Fast Algorithms: How to get a computer to give you the (right)
answer as quickly as possible.
- Numerical Analysis: How to adapt a continuous problem (from
physics, for example) into something a computer can solve
(preferably with a fast algorithm).
- Applied Mathematics: How to bring the power of Mathematics to bear
on problems from other fields (often using Numerical Analysis).
- (Computational) Harmonic Analysis: How to represent the world
efficiently in terms of waves (and wavelets).
- Mathematics: How to see the beautiful structures all around us.
We are running an
Applied and Computational Mathematics Seminar.
Students
- Ryan Botts
- PhD 2010. Recovery and Analysis of
Regulatory Networks from Expression Data Using Sums of Separable
Functions
Projects and Publications
The Multiparticle Schrodinger Equation
It is notoriously difficult to compute numerical solutions to this
basic governing equation in quantum mechanics. This project is big
enough that it needs its own web page. See also
the press
release.
- Approximating a Wavefunction as an Unconstrained Sum
of Slater Determinants.
- Gregory Beylkin, Martin J. Mohlenkamp, and Fernando Perez.
Journal of Mathematical Physics, 49(3):032107, 2008.
(Copyright 2008 American Institute of Physics. This article
may be found at http://link.aip.org/link/?JMP/49/032107. It
can also be downloaded here for personal
use only; any other use requires prior permission of the
author and the American Institute of Physics.)
- Convergence of Green Iterations for Schrodinger Equations.
- Martin J. Mohlenkamp and Todd Young.
in Recent Advances in Computational Science: Selected
Papers from the International Workshop on
Computational Sciences and Its Education.
P. Jorgensen, X. Shen, C-W. Shu, N. Yan, editors.
World Scientific, 2008.
(preprint)
- A Center-of-Mass Principle for the Multiparticle Schrodinger
Equation.
- Martin J. Mohlenkamp.
Journal of Mathematical Physics, 51(2):022112-1--15, 2010.
(Copyright 2010 American Institute of Physics. This article
may be found at http://link.aip.org/link/?JMP/51/022112.
It can also be downloaded here for personal
use only; any other use requires prior permission of the
author and the American Institute of Physics.)
- Capturing the Inter-electron Cusp using a Geminal Layer on
an Unconstrained Sum of Slater Determinants.
- Martin J. Mohlenkamp
SIAM Journal on Applied Mathematics, 72(6):1742-1771, 2012
(link; reprint.)
- Function Space Requirements for the Single-Electron Functions
within the Multiparticle Schrodinger Equation
-
Martin J. Mohlenkamp
(submitted September 11 2012; revised April 30 2013;
preprint.)
Multivariate Regression
Regression is the art of building a function that approximately
matches the data, and gives a reasonable value at new data locations.
In this work we build a regression method that scales linearly with
the dimension, and so can be used in high dimensions.
- Multivariate Regression and Machine Learning with Sums of
Separable Functions.
- Gregory Beylkin, Jochen Garcke, and Martin J. Mohlenkamp.
SIAM Journal on Scientific Computing, 31(3): 1840-1857
(2009).
(link;
preprint.)
- Learning to Predict Physical Properties using Sums
of Separable Functions.
- Mayeul d'Avezac, Ryan Botts, Martin J. Mohlenkamp,
and Alex Zunger
SIAM Journal on Scientific Computing, 33(6): 3381-3401 (2011)
(link; reprint.)
Numerical Analysis in High Dimensions
It is a common experience in numerical analysis to develop a very nice
algorithm in dimension one or two, discover it is painfully slow in
dimension three or above, and then give up and go work on other nice
algorithms in dimension one or two. The cause of this is clear:
computational costs grow exponentially with dimension. We now have a
technique to bypass this Curse of Dimensionality in both low
(2-4) and high (hundreds) dimensional settings.
- Numerical Operator Calculus in Higher Dimensions.
- Gregory Beylkin and Martin J. Mohlenkamp.
Proceedings of the National Academy of Sciences,
99(16):10246-10251, August 6, 2002.
(University of Colorado APPM
preprint #476
August 2, 2001; Abstract
and final journal version.)
- Algorithms for Numerical Analysis in High Dimensions
- Gregory Beylkin and Martin J. Mohlenkamp
SIAM Journal on Scientific Computing, 26(6):2133-2159,
2005.
(University of Colorado APPM preprint #519, February 2004;
(preprint).)
- Musings on Multilinear Fitting
- Martin J. Mohlenkamp
Linear Algebra and its Applications, 438(2): 834-852, 2013.
(final version; preprint.)
Trigonometric Identities
Although it seems like there should be nothing new in
trigonometry, we stumbled upon some rather cute identities for
sine of the sum of several variables.
- Trigonometric Identities and Sums of Separable Functions
- Martin J. Mohlenkamp and Lucas Monzon
The Mathematical Intelligencer, 27(2):65--69, 2005.
(preprint;
An earlier version is available as:
An Identity for Sine of the Sum of Several Variables.
Martin J. Mohlenkamp and Lucas Monzon.
University of Colorado APPM
preprint #480, October 24, 2001.)
Spectral Projectors
- Fast Spectral Projection Algorithms for Density-Matrix
Computations.
- Gregory Beylkin, Nicholas Coult, Martin J. Mohlenkamp.
Journal of Computational Physics, 152(1):32-54, 10 June
1999.
(ID jcph.1999.6215;
University of Colorado APPM
preprint #392, August 12, 1998.)
Spherical Harmonics
My thesis was a Fast Transform for Spherical Harmonics.
(Like an FFT, but for the sphere.) Completed in the spring of
1997 under the direction of R.R. Coifman at Yale University.
(Abstract, Thesis itself (.ps))
- A Fast Transform for Spherical Harmonics
- Martin J. Mohlenkamp
Journal of Fourier Analysis and Applications,
5(2/3):159-184, 1999.
(preprint)
- libftsh
- is a software library
implementing the transform.
I have also created
A User's Guide to Spherical Harmonics
for those new to the area.
Resources
- Are you plagued and annoyed by chain letters? Here is an
anti-chain letter that absolves you of all bad luck
from not sending other chain letters. If you want to
you can distribute it to others.
Martin J. Mohlenkamp
Last modified: Tue Apr 30 15:29:54 EDT 2013
