Jonathan Christopher Mattingly
Professor of Mathematics
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.
His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.
He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS.
His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.
He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS.
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012
 Chair of the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016
 Professor of Statistical Science, Statistical Science, Trinity College of Arts & Sciences 2012
Contact Information
 Background

Education, Training, & Certifications
 Ph.D., Princeton University 1998
 M.A., Princeton University 1996
 B.S., Yale University 1992

Duke Appointment History
 Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2006  2012
 Associate Professor, Statistical Science, Trinity College of Arts & Sciences 2008  2011
 Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2002  2005
 Recognition

In the News

JAN 8, 2018 Duke Research Blog 
NOV 28, 2016 
MAR 18, 2015 USA Today 
MAR 18, 2015 Chicago SunTimes 
MAR 17, 2015 
MAR 17, 2015 
NOV 26, 2014 WUNC 
NOV 12, 2014 Greensboro News & Record 
OCT 30, 2014 WFAECharlotte 
OCT 30, 2014 
OCT 29, 2014


Awards & Honors
 Fellow of the American Mathematical Society . American Mathematical Society. 2015
 Simons Visiting Professor . MSRI. 2015
 Institute of Mathematical Statistics Fellow. Institute of Mathematical Statistics. June 2012
 Faculty Early Career Development (CAREER) Program. National Science Foundation. 2005
 Sloan Research FellowshipMathematics. Alfred P. Sloan Foundation. 2005
 School of Mathematics/ Members. Institute for Advanced Study. 2002
 Expertise

Subject Headings
 Differential equations, Nonlinear
 Ergodic theory
 Evolution
 Fluid mechanics
 Folic Acid
 Invariant measures
 Lyapunov functions
 Malliavin calculus
 Mixing
 Models, Biological
 Nonequilibrium statistical mechanics
 Nonlinear Dynamics
 Probability Theory
 Random dynamical systems
 Stochastic Processes
 Stochastic analysis
 Stochastic differential equations
 Stochastic partial differential equations
 Turbulence
 Research

Selected Grants
 BIGDATA:F: Scalable Bayes uncertainty quantification with guarantees awarded by National Science Foundation 2015  2019
 Collaborative research: Propagation of dissipation: Stochastic stabilization in finite and infinite dimensions awarded by National Science Foundation 2016  2019
 Analysis and design of robust rare event simulation methods for protein folding and d awarded by University of Chicago 2013  2018
 Southeastern Probability Conference 2017: Special Edition Interacting Particle Systems with Applications in Biology, Ecology, and Statistical Physics awarded by National Science Foundation 2017  2018
 EMSW21RTG: awarded by National Science Foundation 2010  2017
 Multiscale Analysis of Dynamic Graphs awarded by Office of Naval Research 2012  2016
 FRG: Collaborative Proposal: awarded by National Science Foundation 2009  2013
 CAREER: Stochastic Analysis and Numerics in Partial Differential Equations and Extended Dynamical Systems awarded by National Science Foundation 2005  2011
 Analysis of Mechanisms of Biochemical Homeostasis awarded by National Science Foundation 2006  2010
 Publications & Artistic Works

Selected Publications

Conference Papers
 Mattingly, JC, and Suidan, TM. "Transition measures for the stochastic Burgers equation." 2008. Link to Item

Journal Articles
 Herschlag, G, Ravier, R, and Mattingly, JC. "Evaluating Partisan Gerrymandering in Wisconsin." (September 2, 2017). Open Access Copy Link to Item
 Bakhtin, Y, Hurth, T, Lawley, SD, and Mattingly, JC. "Smooth invariant densities for random switching on the torus (Submitted)." (August 1, 2017). Open Access Copy Link to Item
 Johndrow, JE, and Mattingly, JC. "Coupling and Decoupling to bound an approximating Markov Chain (Submitted)." (July 31, 2017). Open Access Copy Link to Item
 GlattHoltz, NE, Herzog, DP, and Mattingly, JC. "Scaling and Saturation in InfiniteDimensional Control Problems with Applications to Stochastic Partial Differential Equations." (June 30, 2017). Open Access Copy Link to Item
 GlattHoltz, N, Mattingly, JC, and Richards, G. "On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations." Journal of Statistical Physics 166, no. 34 (February 2017): 618649. Full Text Open Access Copy
 Hairer, M, and Mattingly, J. "The strong Feller property for singular stochastic PDEs (Submitted)." (2016). Open Access Copy Link to Item
 Tempkin, JOB, Koten, BV, Mattingly, JC, Dinner, AR, and Weare, J. "Trajectory stratification of stochastic dynamics." (2016). Open Access Copy Link to Item
 Bakhtin, Y, Hurth, T, and Mattingly, JC. "Regularity of invariant densities for 1D systems with random switching." Nonlinearity 28, no. 11 (October 1, 2015): 37553787. Full Text Open Access Copy
 Herzog, DP, and Mattingly, JC. "A practical criterion for positivity of transition densities." Nonlinearity 28, no. 8 (August 1, 2015): 28232845. Full Text Open Access Copy
 Herzog, D, and Mattingly, J. "Noiseinduced stabilization of planar flows II." Electronic Journal of Probability 20, no. 0 (2015). Full Text Open Access Copy
 Huckemann, S, Mattingly, J, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electronic Journal of Probability 20, no. 0 (2015). Full Text Open Access Copy
 Lawley, SD, Mattingly, JC, and Reed, MC. "Stochastic Switching in Infinite Dimensions with Applications to Random Parabolic PDE." SIAM Journal on Mathematical Analysis 47, no. 4 (January 2015): 30353063. Full Text Open Access Copy
 Luo, S, and Mattingly, JC. "Scaling limits of a model for selection at two scales." (2015). Open Access Copy Link to Item
 Mattingly, JC, and Pardoux, E. "Invariant measure selection by noise. An example." Discrete and Continuous Dynamical Systems 34, no. 10 (April 2014): 42234257. Full Text Open Access Copy
 Lawley, SD, Mattingly, JC, and Reed, MC. "Sensitivity to switching rates in stochastically switched odes." Communications in Mathematical Sciences 12, no. 7 (2014): 13431352. Full Text Open Access Copy
 Mattingly, JC, and Vaughn, C. "Redistricting and the Will of the People." arXiv preprint arXiv:1410.8796 (2014). (Academic Article) Open Access Copy
 Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 22382258. (Academic Article) Full Text Open Access Copy
 Luo, S, Reed, M, Mattingly, JC, and Koelle, K. "The impact of host immune status on the withinhost and population dynamics of antigenic immune escape." J R Soc Interface 9, no. 75 (October 7, 2012): 26032613. Full Text Open Access Copy Link to Item
 Athreyaz, A, Kolba, T, and Mattingly, JC. "Propagating lyapunov functions to prove noiseinduced stabilization." Electronic Journal of Probability 17 (2012). Full Text Open Access Copy
 Mattingly, JC, McKinley, SA, and Pillai, NS. "Geometric ergodicity of a beadspring pair with stochastic Stokes forcing." Stochastic Processes and their Applications 122, no. 12 (2012): 39533979. Full Text Open Access Copy
 Porporato, A, Kramer, PR, Cassiani, M, Daly, E, and Mattingly, J. "Local kinetic interpretation of entropy production through reversed diffusion." Phys Rev E Stat Nonlin Soft Matter Phys 84, no. 4 Pt 1 (October 2011): 041142. Full Text Open Access Copy Link to Item
 Anderson, DF, and Mattingly, JC. "A weak trapezoidal method for a class of stochastic differential equations." Communications in Mathematical Sciences 9, no. 1 (2011): 301318. Open Access Copy
 Hairer, M, Mattingly, JC, and Scheutzow, M. "Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations." Probability Theory and Related Fields 149, no. 1 (2011): 223259. Full Text Open Access Copy
 Hairer, M, and Mattingly, JC. "Yet Another Look at Harris' Ergodic Theorem for Markov Chains." SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS VI 63 (2011): 109+. Open Access Copy Link to Item
 Hairer, M, and Mattingly, JC. "A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs." Electronic Journal of Probability 16 (2011): 658738. Open Access Copy
 Koelle, K, Ratmann, O, Rasmussen, DA, Pasour, V, and Mattingly, J. "A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses." Proceedings of the Royal Society B: Biological Sciences 278, no. 1725 (2011): 37233730. Full Text Open Access Copy
 Mattingly, JC, Stuart, AM, and Tretyakov, MV. "Convergence of numerical timeaveraging and stationary measures via Poisson equations." SIAM Journal on Numerical Analysis 48, no. 2 (2010): 552577. Full Text Open Access Copy
 Hairer, M, and Mattingly, JC. "Slow energy dissipation in anharmonic oscillator chains." Communications on Pure and Applied Mathematics 62, no. 8 (2009): 9991032. Full Text Open Access Copy
 Hairer, M, Mattingly, JC, and Martin Hairer, . "Spectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equationsSpectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equations." Annals of Probability , no. 6 (2008): 9931032. (Academic Article)
 Iyer, G, and Mattingly, J. "A stochasticLagrangian particle system for the NavierStokes equations." Nonlinearity 21, no. 11 (2008): 25372553. Full Text
 Mattingly, J, and Anderson, D. "Propagation of fluctuations in biochemical systems, II: nonlinear chains." IET Systems Biology 1, no. 6 (November 1, 2007): 313325. Full Text
 Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: linear SSC networks." Bull Math Biol 69, no. 6 (August 2007): 17911813. Full Text Open Access Copy Link to Item
 Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: Linear SSC networks." BULLETIN OF MATHEMATICAL BIOLOGY 69, no. 6 (August 2007): 17911813. Full Text Link to Item
 Bakhtin, Y, and Mattingly, JC. "Malliavin calculus for infinitedimensional systems with additive noise." Journal of Functional Analysis 249, no. 2 (2007): 307353. Full Text
 Lamba, H, Mattingly, JC, and Stuart, AM. "An adaptive EulerMaruyama scheme for SDEs: Convergence and stability." IMA Journal of Numerical Analysis 27, no. 3 (2007): 479506. Full Text
 Mattingly, JC, Suidan, T, and VandenEijnden, E. "Simple systems with anomalous dissipation and energy cascade." Communications in Mathematical Physics 276, no. 1 (2007): 189220. Full Text
 Mattingly, JC, Suidan, TM, and VandenEijnden, E. "Anomalous dissipation in a stochastically forced infinitedimensional system of coupled oscillators." Journal of Statistical Physics 128, no. 5 (2007): 11451152. Full Text
 Nijhout, H, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "Erratum to H. Frederik Nijhout, et al. Epigenetics Volume 1, Issue 2; pp. 8187." Epigenetics 1, no. 3 (July 2006): 115115. Full Text
 Nijhout, HF, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "Longrange allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate." Epigenetics 1, no. 2 (April 2006): 8187. Link to Item
 Hairer, M, and Mattingly, JC. "Ergodicity of the 2D NavierStokes equations with degenerate stochastic forcing." Annals of Mathematics 164, no. 3 (2006): 9931032.
 Mattingly, JC, and Pardoux, É. "Malliavin calculus for the stochastic 2D NavierStokes equation." Communications on Pure and Applied Mathematics 59, no. 12 (2006): 17421790. Full Text Open Access Copy
 Bakhtin, Y, and Mattingly, JC. "Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations." Communications in Contemporary Mathematics 7, no. 5 (2005): 553582. Full Text
 Mattingly, JC, and Suidan, TM. "The small scales of the stochastic NavierStokes equations under rough forcing." JOURNAL OF STATISTICAL PHYSICS 118, no. 12 (January 2005): 343364. Full Text Link to Item
 Hairer, M, Mattingly, JC, and Pardoux, É. "Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations." Comptes Rendus Mathematique 339, no. 11 (December 2004): 793796. Full Text
 Hairer, M, and Mattingly, JC. "Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations." Comptes Rendus Mathematique 339, no. 12 (December 2004): 879882. Full Text
 Hairer, M, Mattingly, JC, and Pardoux, E. "Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier–Stokes equation." arXiv preprint math/0409057 (2004). (Academic Article)
 Mattingly, JC, Mattingly, JC, and Mattingly, JC. "On recent progress for the stochastic Navier Stokes equationsOn recent progress for the stochastic Navier Stokes equationsOn Recent Progress for the Stochastic Navier Stokes Equations." Journées "Équations aux Dérivées Partielles" XV (July 2003): viii+298. (Academic Article) Link to Item
 Mattingly, JC. "Contractivity and Ergodicity of the Random Map $\boldsymbol{\lowercase{x\,\mapsto\,x\theta}}$." Theory of Probability and Its Applications 47, no. 2 (2003): 333333. Full Text Open Access Copy
 Mattingly, JC. "The dissipative scale of the stochastics NavierStokes equation: Regularization and analyticity." Journal of Statistical Physics 108, no. 56 (December 1, 2002): 11571179. Full Text
 Mattingly, JC. "Exponential convergence for the stochastically forced NavierStokes equations and other partially dissipative dynamics." Communications in Mathematical Physics 230, no. 3 (November 1, 2002): 421462. Full Text
 Mattingly, J, Stuart, A, and Higham, D. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise." Stochastic Processes and their Applications 101, no. 2 (October 2002): 185232. Full Text
 Mattingly, JC, and Mattingly, JC. "Contractivity and ergodicity of the random map $x\mapstox\theta$." Теория вероятностей и ее применения 47, no. 2 (2002): 388397. Full Text Open Access Copy
 Mattingly, JC, and Stuart, AM. "Geometric ergodicity of some hypoelliptic diffusions for particle motions." Markov Processes and Related Fields 8 (2002): 199214. (Academic Article)
 E, W, Mattingly, JC, and Sinai, Y. "Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation." Communications in Mathematical Physics 224, no. 1 (November 2001): 83106. Full Text
 E, W, and Mattingly, JC. "Ergodicity for the NavierStokes equation with degenerate random forcing: Finitedimensional approximation." Communications on Pure and Applied Mathematics 54, no. 11 (November 2001): 13861402. Full Text Open Access Copy
 Mattingly, JC. "Ergodicity of 2D NavierStokes Equations with¶Random Forcing and Large Viscosity." Communications in Mathematical Physics 206, no. 2 (October 1, 1999): 273288. Full Text
 Mattingly, JC, and Sinai, YG. "An elementary proof of the existence and uniqueness theorem for the NavierStokes equations." Communications in Contemporary Mathematics 1, no. 4 (1999): 497516. Open Access Copy
 Holmes, PJ, Lumley, JL, Berkooz, G, Mattingly, JC, and Wittenberg, RW. "Lowdimensional models of coherent structures in turbulence." Physics Reports 287, no. 4 (August 1997): 337384. Full Text
 Bangia, S, Graves, CV, Herschlag, G, Kang, HS, Luo, J, Mattingly, JC, and Ravier, R. "Redistricting: Drawing the Line." Open Access Copy Link to Item
 Cooke, B, Herzog, DP, Mattingly, JC, McKinley, SA, and Schmidler, SC. "Geometric Ergodicity of Twodimensional Hamiltonian systems with a LennardJoneslike Repulsive Potential." Open Access Copy Link to Item
 Herschlag, G, Kang, HS, Luo, J, Graves, CV, Bangia, S, Ravier, R, and Mattingly, JC. "Quantifying Gerrymandering in North Carolina." Link to Item
 Herzog, DP, and Mattingly, JC. "Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials." Open Access Copy Link to Item
 Heymann, M, Teitsworth, SW, and Mattingly, JC. "Rare Transition Events in Nonequilibrium Systems with StateDependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices." Open Access Copy Link to Item
 Johndrow, JE, Mattingly, JC, Mukherjee, S, and Dunson, D. "Optimal approximating Markov chains for Bayesian inference." Open Access Copy Link to Item
 Johndrow, JE, and Mattingly, JC. "Error bounds for Approximations of Markov chains." Open Access Copy Link to Item
 Mattingly, JC, Pillai, NS, and Stuart, AM. "Diffusion limits of the random walk Metropolis algorithm in high dimensions." Annals of Applied Probability 22, no. 3: 881930. Full Text Open Access Copy Link to Item
 Munch, E, Turner, K, Bendich, P, Mukherjee, S, Mattingly, J, and Harer, J. "Probabilistic Fréchet Means for Time Varying Persistence Diagrams." Full Text Open Access Copy Link to Item

Other Articles
 Holmes, PJ, Mattingly, JC, and Wittenberg, RW. "Lowdimensional models of turbulence or, The dynamics of coherent structures." 19 (2001): 177215. Full Text

 Teaching & Mentoring

Recent Courses
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Stabilization and noise. Department Colloquium. Berekey Mathematics Department. November 12, 2015 2015
 Stochastic PDEs. Analysis of PDEs of Fluid Mechanics. October 2015 2015
 Ergodicity Finite and Infinite dimentional Markov Chains. CRMPIMS Summer School in Probability. McGill University. July 2015 2015
 Dynamics Days 2014. January 4, 2014 2014
 Stabilization by Noise. November 19, 2013 2013
 Uniqueness of the inviscid limit in a simple model damped/driven system.. November 5, 2013 2013
 Stochastic stabilization of OEDs.. September 6, 2013 2013
 Stochastic partial diﬀerential equations. August 1, 2013 2013
 Stabilization by noise. May 1, 2013 2013
 Stablization by Noise. February 14, 2013 2013
 Perspectives on Ergodicity. January 14, 2013 2013
 A Numerical Method for the SDEs from Chemical Equations. December 1, 2012 2012
 Minerva Lectures: Erodicity of Markov Processes: From Chains to SDEs to SPDEs. November 1, 2012 2012
 A Menagerie of Stabilization. July 1, 2012 2012
 Stochastic Stabilization. July 1, 2012 2012
 Building Lyapunov Functions (4 lectures). March 1, 2012 2012
 Noise Induced Stability. February 1, 2012 2012
 A Menagerie of Stochastic Stabilization. October 18, 2011 2011
 A menagerie of stochastic stabilization. August 1, 2011 2011
 Coarse–graining of many–body systems: analysis, computations and applications. July 1, 2011 2011
 Ergodicity of systems with singular interaction terms. November 18, 2010 2010
 Oberwolfach Seminar: The Ergodic Theory of Markov Processes. October 1, 2010 2010
 Malliavin Calculus to prove ergodic theorems for SPDEs. August 13, 2010 2010
 SPDE scaling limits of an Markov chain Montecarlo algorithm. June 28, 2010 2010
 The spread of randomness. June 1, 2010 2010
 How to prove an ergodic theorem. May 1, 2010 2010
 Coupling at infinity. March 30, 2010 2010
 Long time stochastic simiulation. March 15, 2010 2010
 Spectral Gaps in Wasserstien Distance. March 4, 2010 2010
 Trouble with a chain of stochastic oscillators. March 2, 2010 2010
 Hypoellipticity for SPDEs. March 1, 2010 2010
 Numerics of SDEs. February 24, 2010 2010
 Long Time Behavior of Stochastically Forced PDEs.. January 14, 2010 2010
 Ellipticity and Hypoellipticity for SPDEs *or* What is ellipticity in infinite dimensions anyway?. January 8, 2010 2010
 SPDE Limits of the Random Walk Metropolis Algorithm in High Dimensions. December 7, 2009 2009
 Stochastic fluctuations in bio chemical networks. November 9, 2009 2009
 Introduction to Ergodicity in Infinite Dimentions. July 1, 2009 2009
 What makes infinite dimensional Markov processes different ?. July 1, 2009 2009
 Stochastically forced fluid equations: Transfer between scales and ergodicity.. April 4, 2009 2009
 Trouble with a chain of stochastic oscillators. PACM. April 3, 2009 2009
 What makes the ergodic theory if Markov Chains in infinite dimensions different (and dificult) ?. March 3, 2009 2009
 Ergodicity, Energy Transfer, and Stochastic Partial Differential Equations. Columbia University. December 15, 2008 2008
 The Spread of Randomness: Ergodicity in Infinite Dimensions. December 15, 2008 2008
 The spread of randomness through dimensions. November 1, 2008 2008
 The spread of randomness through dimensions. November 1, 2008 2008
 Troubles with oscillators. October 1, 2008 2008
 What is different about the ergodic theory of stochastic PDEs (vs ODEs). October 1, 2008 2008
 Trouble with a chain of stochastic oscillators. September 1, 2008 2008
 Troubles with oscillators. August 1, 2008 2008
 The spread of randomness in infinite dimensions and ergodicity for SPDEs. June 1, 2008 2008
 Troubles with chains of anharmonic oscillators. June 1, 2008 2008
 Ergodicity of Degenerately forced SPDEs. May 27, 2008 2008
 Ergodicity of Degenerately forced SPDEs. May 1, 2008 2008

Outreach & Engaged Scholarship

Service to the Profession
 Associate editor Nonlinearity. December 2013 2013
 Organized invited session at SPA2013. August 2013 2013
 Co Organizer (with Amarjit Budhiraja ) : Seminar on Stochastic Processes 2013. March 2013 2013
 Local Orgnaizer (with Rick Durrett) : Woman in Probability III. October 2012 2012
 Assiciate Editor : Journal of Stochastic Partial Differential Equations. September 2012 2012
 SAMSI Stochastic Dynamics tradition workshop. November 2010 2010
 MFO week long school on ergodic theory. October 2010 2010
 SAMSI Opening Workshop for Stochastic Dynamics. August 2009 2009
 AMS Short Course Selelction Committee. 2009  2011 2009  2011
 local liaison/Organizer SAMSI year on stochastic dynamics. 2009  2010 2009  2010
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