David F. Anderson
Vilas Distinguished Achievement Professor of
Mathematics
617 Van Vleck Hall
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, Wi 53706
email: anderson@math.wisc.edu
Teaching (Fall, 2024): Math 733.
Research Interests. My research lies
at the interface of mathematics and biology, and encompasses two
distinct arenas of exploration: (1) mathematical systems biology,
and (2) algorithm design and numerical analysis for the stochastic
models arising in systems biology.
Group News:
- 2024 -- Graduate Student Aidan Howells earned his PhD on Feb.
27th.
- 2022 -- Named a Simons
Fellow.
- 2021 -- Graduate Student Tung Nguyen earned his PhD on May
3rd.
- 2021 -- Tung Nguyen has been awarded the GSSC Fellowship,
which will support him for the Spring semester of 2021!
- 2020 -- Graduate Student Chaojie Yuan earned his PhD on May
5th.
- 2019 -- Graduate Student Kurt Ehlert earned his PhD on
December 13th.
- 2018 -- Appointed Vilas Distinguished Achievement Professor.
- 2018 -- Graduate student Jinsu Kim earned his PhD on May 8th.
- 2016 -- Vilas Associates Award.
- 2015 -- Graduate student Yu Sun earned his PhD on December
15th.
- 2014 -- Awarded the IMA
Prize in Mathematics from the Institute for Mathematics and
its Applications (IMA).
- 2014 -- Graduate student Elizabeth Wolf earned her PhD on May
14th.
- 2013 -- Graduate student Masanori Koyama earned his Phd on
December 16th.
Curriculum Vitae
Google
Scholar Profile
Current graduate Students:
Jingyi Ma
Former graduate Students:
Masanori Koyama,
PhD in December, 2013.
Elizabeth Wolf, PhD in May, 2014.
Yu Sun, PhD in December, 2015.
Jinsu Kim, PhD in May, 2018.
Kurt Ehlert, PhD in December, 2019.
Chaojie
Yuan, PhD in May, 2020.
Tung Nguyen,
PhD in May, 2021.
Aidan Howells,
PhD in February, 2024.
Writings.
Books
- David F. Anderson, Timo Seppäläinen, and Benedek Valko, Introduction to Probability,
University of Cambridge Press, 2017.
- David F. Anderson and Thomas G. Kurtz, Stochastic
Analysis of Biochemical Systems, Springer, 2015.
Journal articles and book chapters
- David F. Anderson and Aidan S Howells, Parametric
Sensitivity Analysis for Models of Reaction Networks within
Interacting Compartments, submitted, 2024.
- David F. Anderson and Badal Joshi, Chemical
mass-action systems as analog computers: implementing
arithmetic computations at specified speed, submitted,
2024.
- David F. Anderson, Daniele Cappelletti, Wai-Tong Louis Fan,
and Jinsu Kim, A new path method for
exponential ergodicity of Markov processes on Z^d, with
applications to stochastic reaction networks, submitted,
2023.
- David F. Anderson and Aidan S. Howells, Stochastic
reaction networks within interacting compartments,
Bulletin of Mathematical Biology, Volume 85, number 87, 2023.
- David F. Anderson and Jinsu Kim, Mixing times for two
classes of stochastically modeled reaction networks,
Mathematical Biosciences and Engineering, Vol. 20, Issue 3,
4690-4713, 2023.
- David F. Anderson and Tung Nguyen, Prevalence of deficiency zero reaction
networks in an Erdos-Rényi framework, Journal of Applied
Probability, Vol 59, issue 2, 384-398, 2022.
- David F. Anderson and Kurt W. Ehlert, Conditional Monte Carlo for reaction
networks, SIAM J. Sci. Comput., Vol. 44, No. 2, A993 -
A1019, 2022.
- David F. Anderson and Tung D. Nguyen, Deficiency zero for random reaction
networks under a stochastic block model framework, Journal
of Mathematical Chemistry, Vol. 59, 2063 - 2097, 2021.
- David F. Anderson, Badal Joshi, and Abhishek Deshpande, On reaction network implementations of
neural networks, Royal Society Interface, Vol. 18,
20210031, 2021.
- David F. Anderson, James D. Brunner, Gheorghe Craciun, and
Matthew D. Johnston, On classes of
reaction networks and their associated polynomial dynamical
systems, Journal of Mathematical Chemistry, Volume 58,
1895 - 1925, 2020.
- David F. Anderson and Chaojie Yuan, Variance of finite
difference methods for reaction networks with non-Lipschitz
rate functions, Volume 58, Number 6, 3125-3143, SIAM
Journal on Numerical Analysis, 2020.
- David F. Anderson, Daniele Cappelletti, Jinsu Kim, and Tung
Nguyen, Tier
structure of strongly endotactic reaction networks (Link),
Stochastic Processes and their Applications, Volume 130, Issue
12, 7218-7259, 2020.
- David F. Anderson, Daniele Cappelletti, and Jinsu Kim, Stochastically
modeled weakly reversible reaction networks with a single
linkage class, Journal of Applied Probability, Volume 57,
Issue 3, 792 - 810, 2020.
- David F. Anderson, David Schnoerr, and Chaojie Yuan, Time-dependent product-form Poisson
distributions for reaction networks with higher order
complexes, Journal of Mathematical Biology, Volume 80,
1919-1951, 2020.
Official version can be found at http://link.springer.com/article/10.1007/s00285-020-01485-y.
- David F. Anderson, Daniele Cappelletti, Andres Ortiz-Munoz,
and Erik Winfree, Stochastic
chemical reaction networks for approximating arbitrary
probability distributions, Theoretical Computer Science,
Vol. 801, 64-95, 2020.
- David F. Anderson and Daniele Cappelletti, Discrepancies
between extinction events and boundary equilibria in reaction
networks, Journal of Mathematical Biology, Vol. 79, Issue
4, 1253 - 1277, 2019. Springer
link.
- David F. Anderson and Tung D. Nguyen, Results
on stochastic reaction networks with non-mass action kinetics,
Mathematical Biosciences and Engineering, Vol. 16, Issue 4,
2118-2140, 2019.
- David F. Anderson and Chaojie Yuan,
Low variance couplings for stochastic models of intracellular
processes with time-dependent rate functions, Bulletin of
Mathematical Biology Vol. 81, Issue 8, 2902 - 2930, 2019.
- David F. Anderson, Desmond J. Higham, Saul C. Leite, and Ruth
J. Williams, On constrained
Langevin Equations and (Bio)Chemical Reaction Networks,
SIAM Multiscale Modeling & Simulation, Vol. 17, No. 1, 2019.
- David F. Anderson and Jinsu Kim, Some network conditions
for positive recurrence of stochastically modeled reaction
networks, SIAM J. Appl. Math., Vol. 78, Issue 5,
2692-2713, 2018.
- David F. Anderson, Daniele Cappelletti, Masanori Koyama, and
Thomas G. Kurtz, Non-explosivity
of stochastically modeled reaction networks that are complex
balanced, Bulletin of Mathematical Biology, Vol. 80, Issue
10, 2561-2579, 2018.
- David F. Anderson, Desmond J. Higham, and Yu Sun, Computational complexity
analysis for Monte Carlo approximations of classically scaled
population processes, SIAM Multiscale Modeling &
Simulation, Vol. 16, No. 3, pp. 1206-1226, 2018.
- David F. Anderson, Radek Erban, Tomislav Plesa, and
Konstantinos C. Zygalakis, Noise control for
molecular computing, Journal of the Royal Society
Interface, journal
weblink, Vol. 15, No. 144, 2018.
- David F. Anderson, Robert Brijder, Gheorghe Craciun, and
Matthew D. Johnston, Conditions
for extinction events in chemical reaction networks with
discrete state spaces, Journal of Mathematical Biology,
Vol. 76, Issue 6, 1535 - 1558, 2018.
- David F. Anderson, Daniele Cappelletti, and Thomas G. Kurtz, Finite time distributions of
stochastically modeled chemical systems with absolute
concentration robustness, SIAM J. Applied Dynamical
Systems, Vol. 16, No. 3, 1309 - 1339, 2017.
- Nataliya G. Batina, Christopher J. Crnich, David F. Anderson,
and Dörte D.V. Döpfer, Identifying
Conditions for Elimination and Epidemic Potential of
Methicillin-resistant Staphylococcus aureus in Nursing Homes,
Antimicrobial Resistance & Infection Control, Vol. 5, Issue
32, 2016.
- David F. Anderson and Simon L. Cotter, Product-form
stationary distributions for deficiency zero networks with
non-mass action kinetics, Bulletin of Mathematical
Biology, Vol. 78, Issue 12, 2016. Erratum in
Example 1. Open access link: http://rdcu.be/xKY9
- 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, Vol. 18, Issue
1, 153-168, 2016.
- Nataliya G. Batina, Christopher J. Crnich, David F. Anderson,
and Dörte D.V. Döpfer, Models
to Predict Prevalence and Transition Dynamics of
Methicillin-resistant Staphylococcus aureus in Community
Nursing Homes, American Journal of Infection Control, Vol.
44, No. 5, 507 - 514, 2016.
- David F. Anderson, Desmond J. Higham, and Yu Sun, Multilevel Monte Carlo for
stochastic differential equations with small noise, SIAM
Journal on Numerical Analysis, Vol. 54, No. 2, 505 - 529, 2016.
- David F. Anderson, Gheorghe Craciun, Manoj Gopalkrishnan, and
Carsten Wiuf, Lyapunov
functions, stationary distributions, and non-equilibrium
potential for reaction networks, Bulletin of Mathematical
Biology, Vol. 77, Issue 9, 1744 - 1767, 2015.
- David F. Anderson and Elizabeth Skubak Wolf, Hybrid
Pathwise Sensitivity Methods for Discrete Stochastic Models of
Chemical Reaction Systems, Journal of Chemical Physics,
Vol. 142, 034103, 2015.
- David F. Anderson and Masanori Koyama, An asymptotic
relationship between coupling methods for stochastically
modeled population processes, IMA Journal of Numerical
Analysis, Vol. 35, No. 4, 1757 - 1778, 2015.
- David F. Anderson, Bard Ermentrout, and Peter J. Thomas, Stochastic Representations
of Ion Channel Kinetics and Exact Stochastic Simulation of
Neuronal Dynamics, Journal for Computational Neuroscience,
Vol. 38, Issue 1, 67-82, 2015.
- David F. Anderson, Desmond J. Higham, and Yu Sun, Complexity of Multilevel Monte
Carlo Tau-Leaping, SIAM Journal on Numerical Analysis,
Vol. 52, Issue 6, 3106–3127, 2014.
- 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,
2014.
(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.)
- 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, Multilevel 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.
(Errata. On page 176, there should
be a plus sign in front of the counting processes associated
with the 6th reaction channel.)
- David F. Anderson, A proof of the Global Attractor
Conjecture in the single linkage class case, SIAM J. Appl.
Math., Vol. 71, No. 4, 1487-1508, 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.), Springer, 2011.
- 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, 2011.
- 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, Propagation
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.
Unpublished notes.
- A short note on the Lyapunov
function for complex-balanced chemical reaction networks,
2014.