David F. Anderson
Assistant Professor in Department of
(affiliate in Department of Statistics)
University of Wisconsin Madison
480 Lincoln Drive,
Madison WI 53706
Email: anderson at math dot wisc dot edu
Phone: (608) 263-4943
Office: Van Vleck 617.
- Developing and analyzing new computational
methods for the stochastic models that arise in the
biosciences. Lately, I am most interested in solving for
expectations or their derivatives with respect to system
parameters in the most efficient manner possible. This line of
research makes use of elements from both stochastic processes
and numerical analysis.
- Chemical reaction network theory in both the
deterministic and stochastic settings. A typical
question in this line of research is the following:
Given a (bio)chemical system with some network structure, what
are the possible dynamical behaviors of the system? Do
certain properties depend upon a specific choice of system
parameters? Solving these types of questions requires
elements from stochastic processes, dynamical systems, and
"chemical reaction network theory."
If you are a student considering a career in
Applied Mathematics, this link
may be useful.
Current graduate Students:
Former graduate Students:
Presentations (with slides)
Writings: journals and book
- David F. Anderson and Masanori Koyama, An asymptotic
relationship between coupling methods for stochastically
modeled population processes, submitted, 2014.
- David F. Anderson, Bard Ermentrout, and Peter
J. Thomas, Stochastic
Representations of Ion Channel Kinetics and Exact Stochastic
Simulation of Neuronal Dynamics, submitted, 2014.
- David F. Anderson, Desmond J. Higham, and Yu
Analysis of Multilevel Monte Carlo Tau-Leaping,
- David F. Anderson, Germán Enciso, and Matthew
D. Johnston, Stochastic
analysis of biochemical reaction networks with absolute
concentration robustness (official
web-link), with Supplementary
Material (including proofs, and statements of the most
general theorems), Journal of the
Royal Society Interface, Vol. 11, 20130943, February 12,
(Errata. In Definition 3.1
of the Supplementary Material it should be stated that the two
complexes are not equal. The linked Supplementary Material
above has this error corrected. Thanks to Robert Brijder
for pointing this out.)
- David F. Anderson, Joke Blom, Michel Mandjes,
Halldora Thorsdottir, and Koen De Turck, A functional central
limit theorem for a Markov-modulated infinite-server queue,
Methodology and Computing in Applied Probability, Springer,
DOI 10.1007/s11009-014-9405-8, 2014.
- Rishi Srivastava, David F. Anderson, and James
B. Rawlings, Comparison
of finite difference based methods to obtain sensitivities
of stochastic chemical kinetic models, Journal of
Chemical Physics, Vol. 138, No. 7, 074110, 2013.
- Elizabeth Skubak Wolf and David F. Anderson, A finite difference method
for estimating second order parameter sensitivities of
discrete stochastic chemical reaction networks, Journal
of Chemical Physics, Vol. 137, No. 22, 224112, 2012.
- David F. Anderson, An Efficient Finite Difference
Method for Parameter Sensitivities of Continuous Time Markov
Chains, SIAM Journal on Numerical Analysis, Vol. 50,
Issue 5, 2237 - 2258, 2012.
- David F. Anderson and Masanori Koyama, Weak error analysis of numerical
methods for stochastic models of population processes,
SIAM: Multiscale Modeling and Simulation, Vol. 10, No. 4, 1493
- 1524, 2012.
- David F. Anderson and Desmond J. Higham, Multi-level Monte Carlo for
continuous time Markov chains, with applications in
biochemical kinetics, SIAM: Multiscale Modeling and
Simulation, Vol. 10, No. 1, 146 - 179, 2012.
Matlab files for the implementation of MLMC on the
dimerization model given on page 169 of the MLMC paper can be
found here: MLMC_DIMER_public.zip.
- David F. Anderson, A proof of the Global
Attractor Conjecture in the single linkage class case,
SIAM J. Appl. Math., Vol. 71, No. 4, 2011.
- David F. Anderson, Boundedness of
trajectories for weakly reversible, single linkage class
reaction systems, Journal of Mathematical Chemistry,
Vol. 49, No. 10, 2275 - 2290, 2011.
- David F. Anderson and Thomas G. Kurtz, Continuous time Markov
chain models for chemical reaction networks, chapter in
Design and Analysis of
Biomolecular Circuits: Engineering Approaches to Systems and
Synthetic Biology, H. Koeppl et al. (eds.),
- David F. Anderson and Jonathan C. Mattingly, A weak trapezoidal method for
a class of stochastic differential equations,
Communications in Mathematical Sciences, Vol. 9, No. 1, 301 -
318, March 2011.
(Links for MATLAB code that implements the Weak
Trapezoidal algorithm for Example
5.1 and Example
5.2 from the manuscript.)
- David F. Anderson, Arnab Ganguly, and Thomas
G. Kurtz, Error
analysis of tau-leap simulation methods, Annals of
Applied Probability, Vol. 21, No. 6, 2226 - 2262,
- David F. Anderson, Gheorghe Craciun, and
Thomas G. Kurtz, Product-form
stationary distributions for deficiency zero chemical
reaction networks, Bulletin of Mathematical Biology,
Vol. 72, No. 8, 1947
- 1970, 2010.
- David F. Anderson and Anne Shiu, The dynamics of weakly
reversible population processes near facets, SIAM J.
Appl. Math., Vol. 70, No. 6, 1840 - 1858, January 2010.
- David F. Anderson, Global asymptotic stability
for a class of nonlinear chemical equations, SIAM J.
Appl. Math., Vol. 68, No. 5, pgs. 1464 - 1476, May 2008.
- David F. Anderson, Incorporating postleap checks
in tau-leaping, Journal of Chemical Physics, Vol 128,
No. 5, 054103, February 2008.
- David F. Anderson, A modified Next Reaction Method for
simulating chemical systems with time dependent propensities
and delays, Journal of Chemical Physics, Vol. 127, No.
21, 214107, December 2007.
- David F. Anderson and Jonathan C. Mattingly,
of Fluctuations in Biochemical Reaction Systems, II:
Nonlinear Chains, IET Systems Biology, 1(6), 313
- 325, November 2007.
- David F. Anderson, Jonathan C. Mattingly, H.
Frederik Nijhout, Michael Reed, Propagation
of Fluctuations in Biochemical Systems, I: Linear SSC
Networks, Bulletin of Mathematical Biology, Vol. 69, No.
6, 1791 - 1813, August 2007.
- H. Frederik Nijhout, Michael C. Reed, David
F. Anderson, Jonathan C. Mattingly, S. Jill James, and
Cornelia M. Ulrich,
Long-Range Allosteric Interactions between the Folate and
Methionine Cycles Stabilize DNA Methylation Reaction Rate,
Epigenetics, 1(2), 81 - 87, April/May 2006.
- David F. Anderson, Stochastic Perturbations
of Biochemical Reaction Systems, PhD Thesis, 2005.
Writings: unpublished notes.
- A short note on the Lyapunov
function for complex-balanced chemical reaction networks,