David F. Anderson
Vilas Distinguished Achievement Professor of Mathematics

David Anderson pic 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:
  1. 2024 -- Graduate Student Aidan Howells earned his PhD on Feb. 27th.
  2. 2022 -- Named a Simons Fellow.
  3. 2021 -- Graduate Student Tung Nguyen earned his PhD on May 3rd.
  4. 2021 -- Tung Nguyen has been awarded the GSSC Fellowship, which will support him for the Spring semester of 2021! 
  5. 2020 -- Graduate Student Chaojie Yuan earned his PhD on May 5th.
  6. 2019 -- Graduate Student Kurt Ehlert earned his PhD on December 13th.
  7. 2018 -- Appointed Vilas Distinguished Achievement Professor.
  8. 2018 -- Graduate student Jinsu Kim earned his PhD on May 8th.
  9. 2016 -- Vilas Associates Award.
  10. 2015 -- Graduate student Yu Sun earned his PhD on December 15th.
  11. 2014 -- Awarded the IMA Prize in Mathematics from the Institute for Mathematics and its Applications (IMA).
  12. 2014 -- Graduate student Elizabeth Wolf earned her PhD on May 14th.
  13. 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
  1. David F. Anderson, Timo Seppalainen, and Benedek Valko, Introduction to Probability, University of Cambridge Press, 2017.

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

Journal articles and book chapters
  1. David F. Anderson and Aidan S Howells, Parametric Sensitivity Analysis for Models of Reaction Networks within Interacting Compartments, submitted, 2024.

  2. David F. Anderson and Badal Joshi, Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed, Theoretical Computer Science, Vol. 1025, 114983, 2024.

  3. 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.

  4. David F. Anderson and Aidan S. Howells, Stochastic reaction networks within interacting compartments, Bulletin of Mathematical Biology, Volume 85, number 87, 2023.

  5. 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.

  6. 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.

  7. David F. Anderson and Kurt W. Ehlert, Conditional Monte Carlo for reaction networks, SIAM J. Sci. Comput., Vol. 44, No. 2, A993 - A1019, 2022.

  8. 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.

  9. David F. Anderson, Badal Joshi, and Abhishek Deshpande, On reaction network implementations of neural networks, Royal Society Interface, Vol. 18, 20210031, 2021.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. Nataliya G. Batina, Christopher J. Crnich, David F. Anderson, and Dorte D.V. Dopfer, Identifying Conditions for Elimination and Epidemic Potential of Methicillin-resistant Staphylococcus aureus in Nursing Homes, Antimicrobial Resistance & Infection Control, Vol. 5, Issue 32, 2016.

  27. 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

  28. 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.

  29. 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.

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. 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.

  36. 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.)

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. 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.)

  42. 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. 

  43. 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. 
     
  44. 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.

  45. 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.)

  46. 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.  

  47. 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.

  48. 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.

  49. 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.

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

  51. 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.

  52. 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.

  53. 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.

  54. 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.
  1. A short note on the Lyapunov function for complex-balanced chemical reaction networks, 2014.