David F. Anderson D. Anderson

Assistant Professor in Department of Mathematics

(affiliate in Department of Statistics)

Contact Information:

Department of Mathematics
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.

Current Research Interests:

  1. 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. 

  2. 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 these 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."

Google Scholar Profile



If you are a student considering a career in Applied Mathematics, this link may be useful. 

Spring 2014 Teaching:
        Math 431, Lecture 01 -- Introduction to the theory of probability.

        Math 431, Lecture 03 -- Introduction to the theory of probability.


Current graduate Students: 
    Elizabeth Skubak Wolf
    Yu Sun

Former graduate Students:
    Masanori Koyama   


Recent Presentations (with slides)

Curriculum Vitae


Writings: journals and book chapters.
  1. David F. Anderson and Masanori Koyama, An asymptotic relationship between coupling methods for stochastically modeled population processes, submitted, 2014.

  2. David F. Anderson, Bard Ermentrout, and Peter J. Thomas, Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics, submitted, 2014.

  3. David F. Anderson, Desmond J. Higham, and Yu Sun, Complexity Analysis of Multilevel Monte Carlo Tau-Leaping, submitted, 2013.

  4. 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.

  5. 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, accepted for publication to Methodology and Computing in Applied Probability, 2014.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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. 

  12. 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. 
     
  13. 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.

  14. 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.

  15. 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.  

  16. 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.

  17. 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.

  18. 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.

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

  20. 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.

  21. 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.

  22. 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.

  23. 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.

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


Writings: unpublished notes.

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