David F. Anderson D. Anderson

Associate Professor
Department of Mathematics


Email: anderson@math.wisc.edu
Phone: (608) 263-4943
Office: Van Vleck 617.

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.

Recent news:

  1. I was recently awarded the IMA Prize in Mathematics from the Institute for Mathematics and its Applications (IMA).
  2. My former graduate student, Masanori Koyama, is now a postdoc at Kyoto University.
  3. My former graduate student, Beth Skubak Wolf, is now an assistant professor at St. Mary's College.

Curriculum Vitae
Google Scholar Profile

Teaching (Fall 2015): Math 605 - Stochastic methods in biology.

Office hours (Fall 2015):

Current graduate Students: 
Yu Sun
Jinsu Kim
Kurt Ehlert

Former graduate Students:
Masanori Koyama   
Elizabeth Skubak Wolf

Recent Presentations (with slides)


UW-Madison Probability Seminar
UW-Madison Networks Seminar
 
Writings.

Books
  1. David F. Anderson and Thomas G. Kurtz, Stochastic Analysis of Biochemical Systems, Springer, 2015.


Journal articles and book chapters
  1. David F. Anderson, Desmond J. Higham, and Yu Sun, Computational complexity analysis for Monte Carlo approximations of classically scaled population processes, submitted, 2015.

  2. 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, accepted to American Journal of Infection Control, 2015.

  3. David F. Anderson, Desmond J. Higham, and Yu Sun, Multilevel Monte Carlo for stochastic differential equations with small noise, submitted, 2015.

  4. 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.

  5. 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.
  6. David F. Anderson and Masanori Koyama, An asymptotic relationship between coupling methods for stochastically modeled population processes, accepted for publication to IMA Journal of Numerical Analysis, 2014.
  7. 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.
  8. 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.
  9. 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.)
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.

  16. 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. 

  17. 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. 
     
  18. 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.
  19. 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.)
  20. 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.  

  21. 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.

  22. 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.
  23. 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.

  24. David F. Anderson, Incorporating postleap checks in tau-leaping, Journal of Chemical Physics, Vol 128, No. 5, 054103, February 2008.

  25. 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.

  26. 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.

  27. 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.

  28. 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.
  29. David F. Anderson, Stochastic Perturbations of Biochemical Reaction Systems, PhD Thesis, 2005.


 Unpublished notes.

  1.     A short note on the Lyapunov function for complex-balanced chemical reaction networks, 2014.