David F. Anderson D. Anderson

Assistant Professor in Department of Mathematics

Affiliate Professor 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.

Research Interests: I use elements from probability theory, stochastic processes, and dynamical systems to solve whatever problem is of interest to me at the moment.  My current research interests are:

  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) in the most efficient manner possible.  This is sometimes referred to as solving the "weak problem."  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?  Solving these types of questions requires elements from stochastic processes, dynamical systems, and "chemical network theory."


 
Fall 2011 teaching:
        Math 605 --  Introduction to Stochastic Processes with Applications to Biology.
     
Spring 2012 teaching:
        Math 635 -- An introduction to Brownian Motion and Stochastic Calculus.

Fall 2012 teaching:
        Math 632 -- Introduction to Stochastic Processes (with a discrete state space).
        Math 831 -- Theory of Probability I.

Spring 2013 teaching:
        Math 832 -- Theory of Probability II.

Graduate Students: 
    Masanori Koyama.
    Beth Skubak

 
Recent Presentations (with slides)


Upcoming talks:
  1. SIAM Life Sciences,  San Diego, California.  August 7th - 10th, 2012.

Curriculum Vitae


Writings: (all are available on arxiv.org, even if this is not explicitly mentioned below)
  1. David F. Anderson, An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains, submitted.  Available on arxiv.org at arxiv.org/abs/1109.2890.
  2. David F. Anderson and Masanori Koyama, Weak error analysis of numerical methods for stochastic models of population processes, submitted. Available on arxiv.org at arxiv:1102.2922.

  3. 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.

  4. 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. 

  5. 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. 
     
  6. 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.

  7. 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.

  8. 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.  

  9. 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.

  10. 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.
  11. 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.

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

  13. 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.

  14. 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.

  15. 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.

  16. 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.
  17. David F. Anderson, Stochastic Perturbations of Biochemical Reaction Systems, PhD Thesis, 2005.


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