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Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems.
Statistical mechanics of fluid mixtures
J.G. Kirkwood · 1935
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On the kinetic theory of rarefied gases
H. Grad · 1949
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A theory of cooperative phenomena
R. Kikuchi · 1951
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On the use of the normal approximation in the treatment of stochastic processes
P. Whittle · 1957
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A comparison of theoretical and empirical results for some stochastic population models
M.S. Bartlett, J.C. Gower, and P.H. Leslie · 1960
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The application of truncated hierarchy techniques in the solution of a stochastic linear differential equation
J.M. Richardson · 1964
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Mathematical Methods in Kinetic Theory
C. Cercignani · 1969
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Solutions of ordinary differential equations as limits of pure jump Markov processes
T.G. Kurtz · 1970
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Stochastic Differential Equations: Theory and Applications
L. Arnold · 1974
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Strong approximation theorems for density dependent Markov chains
T.G. Kurtz · 1978
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Geometric singular perturbation theory for ordinary differential equations
N. Fenichel · 1979
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Kinetic equations from Hamiltonian dynamics: Markovian limits
H. Spohn · 1980
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On the rationale of maximum-entropy methods
E.T. Jaynes · 1982
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Stochastic Systems
G. Adomian · 1983
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Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
T. Elmroth · 1983
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Random Vibrations of Elastic Systems
V.V. Bolotin · 1984
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The Boltzmann Equation and Its Applications
C. Cercignani · 1988
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The quasi-steady-state assumption: a case study in perturbation
L.A. Segel and M. Slemrod · 1989
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Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
G.W. Hammett and F.W. Perkins · 1990
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Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems
I. Csiszar · 1991
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Statistical mechanics of population: the lattice Lotka-Volterra model
H. Matsuda, N. Ogita, A. Sasaki, and K. Sato · 1992
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Conditional moment closure of turbulent reacting flow
R.W. Bilger · 1993
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Some applications of the method of moments for the homogeneous Boltzmann and Kac equations
L. Desvillettes · 1993
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Maximum entropy distribution and closure for Bose-Einstein and Fermi-Dirac radiation transport
J. Cernohorsky and S.A. Bludman · 1994
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Correlation equations and pair approximations for spatial ecologies
D.A. Rand · 1994
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Pathogen invasion and host extinction in lattice structured populations
K. Sato, H. Matsuda, and A. Sasaki · 1994
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Factorial moment expansion for stochastic systems
B. Blaszczyszyn · 1995
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A new perspective on the moment closure method
A.M. Hasofer and M. Grigoriu · 1995
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Geometric singular perturbation theory
C.K.R.T. Jones · 1995
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Note on the conditional moment closure in turbulent shear flows
A.Y. Klimenko · 1995
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Moment closure hierarchies for kinetic theories
C.D. Levermore · 1996
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On approximating the moments of the equilibrium distribution of a stochastic logistic model
J.H. Matis and T.R. Kiffe · 1996
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Using moment equations to understand stochastically driven spatial pattern formation in ecological systems
B. Bolker and S.W. Pacala · 1997
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Correlation models for childhood epidemics
M.J. Keeling, D.A. Rand, and A.J. Morris · 1997
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The evolution of cooperation in a lattice-structured population
M. Nakamaru, H. Matsuda, and Y. Iwasa · 1997
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An extended moment method in radiative transfer: the matrices of mean absorption and scattering coefficients
H. Struchtrup · 1997
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Studying and approximating spatio-temporal models for epidemic spread and control
J.A.N. Filipe and G.J. Gibson · 1998
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The Gaussian moment closure for gas dynamics
C.D. Levermore and W.J. Morokoff · 1998
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Moment realizability and the validity of the Navier-Stokes equations for rarefied gas dynamics
C.D. Levermore, W.J. Morokoff, and B.T. Nadiga · 1998
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Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal
B. Bolker and S.W. Pacala · 1999
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The nonlinear Fokker-Planck equation with state-dependent diffusion - A nonextensive maximum entropy approach
L. Borland, F. Pennini, A.R. Plastino, and A. Plastino · 1999
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The effects of local spatial structure on epidemiological invasions
M.J. Keeling · 1999
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Conditional moment closure for turbulent combustion
A.Y. Klimenko and R.W. Bilger · 1999
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Effects of immigration on some stochastic logistic models: a cumulant truncation analysis
J.H. Matis and T.R. Kiffe · 1999
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Correlation equations and pair approximations for spatial ecologies
D.A. Rand · 1999
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Moment methods for ecological processes in continuous space
B. Bolker, S.W. Pacala, and S.A. Levin · 2000
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Topological evolution of dynamical networks: global criticality from local dynamics
S. Bornholdt and T. Rohlf · 2000
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Relaxation projections and the method of moments
U. Dieckmann and R. Law · 2000
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Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation
O. Diekmann and J.A.P. Heesterbeek · 2000
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Multiplicative moments and measures of persistence in ecology
M.J. Keeling · 2000
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Moment approximations of individual-based models
R. Law and U. Dieckmann · 2000
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One-dimensional Riemann solvers and the maximum entropy closure
T.A. Brunner and J.P. Holloway · 2001
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Pair approximation for lattice models with multiple interaction scales
S.P. Ellner · 2001
Cited alongside, same era.
Comparing approximations to spatio-temporal models for epidemics with local spread
J.A.N. Filipe and G.J. Gibson · 2001
Cited alongside, same era.
Conditional moment closure (CMC) predictions of a turbulent methane-air jet flame
M.R. Roomina and R.W. Bilger · 2001
Cited alongside, same era.
A nonlinear dynamics perspective of moment closure for stochastic processes
J. Stark, P. Iannelli, and S. Baigent · 2001
Cited alongside, same era.
Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases
K.T.D. Eames and M.J. Keeling · 2002
Cited alongside, same era.
Foundations of Modern Probability
O. Kallenberg · 2002
Cited alongside, same era.
Contact processes on adaptive networks
A.-L. Do and T. Gross · 2009
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Partner switching stabilizes cooperation in coevolutionary prisoner’s dilemma
F. Feng, T. Wu, and L. Wang · 2009
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Stochastic Methods
C. Gardiner · 2009
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Moment-closure approximations for mass-action models
C.S. Gillespie · 2009
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Towards physically realizable and hyperbolic moment closures for kinetic theory
C.P. Groth and J.G. McDonald · 2009
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A motif-based approach to network epidemics
T. House, G. Davies, L. Danon, and M.J. Keeling · 2009
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An extension of the moment closure method
I. Nåsell · 2003
Cited alongside, same era.
Moment closure and the stochastic logistic model
I. Nåsell · 2003
Cited alongside, same era.
Regularization of Grad’s 13 moment equations: derivation and linear analysis
H. Struchtrup and M. Torrilhon · 2003
Cited alongside, same era.
The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
F. Golse and L. Saint-Raymond · 2004
Cited alongside, same era.
On moment closures for population dynamics in continuous space
D.J. Murrell, U. Dieckmann, and R. Law · 2004
Cited alongside, same era.
Extinction times and moment closure in the stochastic logistic process
T.J. Newman, J.B. Ferdy, and C. Quince · 2004
Cited alongside, same era.
C.H. Lee, K.-H. Kim, and P. Kim · 2009
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Derivation of the conditional moment closure equations for spray combustion
M. Mortensen and R.W. Bilger · 2009
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Time evolution of epidemic disease on finite and infinite networks
P.-A. Noël, B. Davoudi, R.C. Brunham, and L.J. Dubé amd B. Pourbohloul · 2009
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Heterogeneous pair approximation for voter models on networks
E. Pugliese and C. Castellano · 2009
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Contact switching as a control strategy for epidemic outbreaks
S. Risau-Gusman and D.H. Zanette · 2009
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Fluctuations and oscillations in a simple epidemic model
G. Rozhnova and A. Nunes · 2009
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Comparison of Markov chain and stochastic differential equation population models under higher-order moment closure approximation
A.J. Ekanayake and L.J.S. Allen · 2010
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A closure approximation technique for epidemic models
K. Hausken and J.F. Moxnes · 2010
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A Kinetic View of Statistical Physics
P.L. Krapivsky, S. Redner, and E. Ben-Naim · 2010
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Adaptive networks: coevolution of disease and topology
V. Marceau, P.-A. Noël, L. Hébert-Dufresne, A. Allard, and L.J. Dubé · 2010
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Enhanced vaccine control of epidemics in adpative networks
L.B. Shaw and I.B. Schwartz · 2010
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Moment closure in a Moran model with recombination
E. Baake and T. Hustedt · 2011
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Binomial moment equations for stochastic reaction systems
B. Barzel and O. Biham · 2011
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Analytical calculation of fragmentation transitions in adaptive networks
G.A. Böhme and T. Gross · 2011
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Cyclic dominance in adaptive networks
G. Demirel, P. Prizak, P.N. Reddy, and T. Gross · 2011
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Emergent bipartiteness in a society of knights and knaves
C.I. Del Genio and T. Gross · 2011
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High-accuracy approximation and binary-state dynamics on networks
J.P. Gleeson · 2011
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Higher moment analysis of a spatial stochastic process algebra
M.C. Guenther and J.T. Bradley · 2011
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Insights from unifying modern approximations to infections on networks
T. House and M.J. Keeling · 2011
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Effective degree network disease models
J. Lindquist, J. Ma, P. Van den Driessche, and F.H. Willeboordse · 2011
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A note on a paper by Erik Volz: SIR dynamics in random networks
J.C. Miller · 2011
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A multiscale maximum entropy moment closure for locally regulated space-time point process models of population dynamics
M. Raghib, N.A. Hill, and U. Dieckmann · 2011
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Maximum entropy moment-closure for stochastic systems on networks
T. Rogers · 2011
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Exact epidemic models on graphs using graph-automorphism driven lumping
P.L. Simon, M. Taylor, and I.Z. Kiss · 2011
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An effective degree model for epidemics on dynamic networks
M. Taylor, T.J. Taylor, and I.Z. Kiss · 2011
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Stochastic analysis of complex reaction networks using binomial moment equations
B. Barzel and O. Biham · 2012
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Differential equation approximations of stochastic network processes: an operator semigroup approach
A. Bátkai, I.Z. Kiss, E. Sikolya, and P.L. Simon · 2012
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Accuracy of mean-field theory for dynamics on real-world networks
J.P. Gleeson, S. Melnik, J.A. Ward, M.A. Porter, and P.J. Mucha · 2012
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New moment closures based on a priori distributions with applications to epidemic dynamics
I.Z. Kiss and P.L. Simon · 2012
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Time-scale and noise optimality in self-organized critical adaptive networks
C. Kuehn · 2012
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From Markovian to pairwise epidemic models and the performance of moment closure approximations
M. Taylor, P.L. Simon, D.M. Green, T. House, and I.Z. Kiss · 2012
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Endemic infections are always possible on regular networks
C.I. Del Genio and T. House · 2013
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Binary-state dynamics on complex networks: pair approximation and beyond
J.P. Gleeson · 2013
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Moment closures for performance models with highly non-linear rates
M.C. Guenther, A. Stefanek, and J.T. Bradley · 2013
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A mathematical framework for critical transitions: normal forms, variance and applications
C. Kuehn · 2013
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Towards realizable hyperbolic moment closures for viscous heat-conducting gas flows based on a maximum-entropy distribution
J.G. McDonald and C.P. Groth · 2013
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Kac’s program in kinetic theory
S. Mischler and C. Mouhot · 2013
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Entropy production moment closures and effective transport coefficients
T. Christen and F. Kassubek · 2014
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Moment-closure approximations for discrete adaptive networks
G. Demirel, F. Vazquez, G.A. Böhme, and T. Gross · 2014
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Epidemic spread in networks: Existing methods and current challenges
J.C. Miller and I.Z. Kiss · 2014
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Dynamical systems on networks: a tutorial
M.A. Porter and J.P. Gleeson · 2014
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Exploring the adaptive voter model dynamics with a mathematical triple jump
H. Silk, G. Demirel, M. Homer, and T. Gross · 2014
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Algebraic moment closure for population dynamics on discrete structures
T. House · 2015
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Multiple Time Scale Dynamics
C. Kuehn · 2015
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Exact and approximate moment closures for non-Markovian network epidemics
D.E. Pelinovsky and V. Zharnitsky · 2015
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