## Calculating Macroscopic Consequences of Microscopic Interactions

*09 Jul 2023 12:00*

[A placeholder while I organize my thoughts]

See also: Statistical mechanics (especially, perhaps, non-equilibrium statistical mechanics); cellular automata (especially their continuum limits); evolutionary theory; economics; sociology; simulation modeling; statistical emulators for simulation models; large deviations of stochastic processes; emergence; Mroi-Zwanzig formalism; mean-field games and mean-field control;

- Recommended:
- David Cai, Louis Tao and David W. McLaughlin, "An embedded network
approach for scale-up of fluctuation-driven systems with preservation of spike
information", Proceedings of the
National Academy of Sciencces (USA)
**101**(2004): 14288--14293 [Interesting, but I really needed to read their prior paper on their coarse-graining method (below) to evaluate this.] - Dror Givon, Raz Kupferman and Andrew Stuart, "Extracting
macroscopic dynamics: model problems and algorithms", Nonlinearity
**17**(2004): R55--R127 [PDF preprint] - Clark Glymour, "When Is a Brain Like the Planet?",
Philosophy of
Science
**74**(2007): 330--347 - Olof Gonerup and Martin Nilsson Jacobi, "A method for inferring hierarchical dynamics in stochastic processes", nlin.AO/0703034
- Martin Nilsson Jacobi, "Quotient Manifold Projections and Hierarchical Dynamics in Smooth Dynamical Systems" [Lie-algebraic techniques for determining when a low-dimensional projection of a high-dimensional dynamical system will itself be a self-contained dynamical system. I heard Martin talk about it, and it's very cool stuff.]
- Martin Nilsson Jacobi, Olof Goernerup, "A dual eigenvector condition for strong lumpability of Markov chains", arxiv:0710.1986
- Thomas Schelling, Micromotives and Macrobehavior

- To read:
- David Andrieux, "Bounding the coarse graining error in hidden Markov dynamics", arxiv:1104.1025
- Masano Aoki
- New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects
- Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents

- Karen Ball, Tom Kurtz, Lea Popovic and Greg Rempala, "Asymptotic analysis of multiscale approximations to reaction networks", math.PR/0508015
- Robert W. Batterman
- "The tyranny of scales", phil-sci/8678
- A Middle Way: A Non-Fundamental Approach to Many-Body Physics

- Sven Banisch, Ricardo Lima, Tanya Araújo, "Aggregation and Emergence in Agent-Based Models: A Markov Chain Approach", arxiv:1207.2255
- David Cai, Louis Tao, Michael Shelley and David McLaughlin, "An
effective kinetic representation of fluctuation-driven neuronal networks with
application to simple and complex cells in visual cortex", Proceedings of the
National Academy of Sciences (USA)
**101**(2004): 7757--7762 - Nicolas Champagnat, Régis Ferrière, Sylvie Méléard, "Individual-based probabilistic models of adaptive evolution and various scaling approximations", arxiv:math/0510453
- R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler,
F. Warner and S. W. Zucker, "Geometric diffusions as a tool for harmonic
analysis and structure definition of data"
- "Diffusion maps", Proceedings of the
National Academy of Sciences
**102**(2005): 7426--7431 - "Multiscale methods", Proceedings of the
National Academy of Sciences
**102**(2005): 7432--7437

- "Diffusion maps", Proceedings of the
National Academy of Sciences
- Andreas Degenhard and Javier Rodriguez-Laguna, "Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations," cond-mat/0106156
- Manh Hong Duong, Mark A. Peletier, Upanshu Sharma, "Coarse-graining and fluctuations: Two birds with one stone", arxiv:1404.1466
- Radek Erban, Ioannis G. Kevrekidis and Hans G. Othmer, "An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal", physics/0505179
- G. Flores Hidalgo and Y. W. Milla, "Dressed (Renormalized) Coordinates in a Nonlinear System", physics/0410238
- Navot Israeli and Nigel Goldenfeld, "Coarse-graining of cellular automata, emergence, and the predictability of complex systems", nlin.CG/0508033
- Shalev Itzkovitz, Reuven Levitt, Nadav Kashtan, Ron Milo, Michael Itzkovitz and Uri Alon, "Coarse-Graining and Self-Dissimilarity of Complex Networks", q-bio.MN/0405011
- Artemy Kolchinsky, Luis M. Rocha, "Prediction and Modularity in Dynamical Systems", arxiv:1106.3703
- Daniel Korenblum and David Shalloway, "Macrostate data clustering",
Physical Review E
**67**(2003): 056704 - Peter Kotelenez, Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations [blurb]
- Peter M. Kotelenez and Thomas G. Kurtz, "Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type", Probability Theory and Related Fields
**146**(2010): 189--222 - Frederic Legoll and Tony Lelievre, "Some remarks on free energy and coarse-graining", arxiv:1008.3792
- Nadia Loy, Andrea Tosin, "Markov jump processes and collision-like models in the kinetic description of multi-agent systems",
Communications in Mathematical Sciences
**18**(2020): 1539--1568, arxiv:1905.11343 - Andrew J. Majda, Rafail V. Abramov and Marcus J. Grote, Information Theory and Stochastic for Multiscale Nonlinear Systems [PDF draft?]
- A. Majda, I. Timofeyev and E. Vanden-Eijnden, "Stochastic models for selected slow variables in large deterministic systems", Nonlinearity
**19**(2006): 769 - M. Marques-Pita and L. M. Rocha, "Schema Redescription in Cellular Automata: Revisiting Emergence in Complex Systems", arxiv:1102.1691, pp. 233--240 in The 2011 IEEE Symposium on Artificial Life
- Brian A. Maurer, "Statistical mechanics of complex ecological
aggregates", Ecological
Complexity
**2**(2005): 71--85 - Igor Mezic, "Spectral Properties of Dynamical Systems, Model
Reduction and Decompositions", Nonlinear
Dynamics
**41**(2005): 309--325 - Sung Joon Moon and Ioannis G. Kevrekidis, "An equation-free approach to coupled oscillator dynamics: the Kuramoto model example", nlin.AO/0502016 [An approach to predicting the behavior of macroscopic, coarse-grained variables, which is equation-free in the sense that it "circumvent[s] the derivation of explicit dynamical equations (approximately) governing [their] evolution", substituting rather "short burts of appropriately initialized simulations of the 'fine-scale', detailed" model. This sounds like an interesting idea, applicable e.g. to agent-based models, but I need to read the paper to see if/how it actually works.]
- Sung Joon Moon, R Ghanem, I. G. Kevrekidis, "An equation-free approach to coupled oscillator dynamics", nlin.AO/0509022
- Sung Joon Moon, B. Nabet, Naomi E. Leonard, Simon A. Levin, and I. G. Kevrekidis, "Heterogeneous animal group models and their group-level alignment dynamics; an equation-free approach", q-bio.QM/0606021
- Boaz Nadler, Stephane Lafon, Ronald R. Coifman and Ioannis
G. Kevrekidis
- "Diffusion maps, spectral clustering and reaction coordinates of dynamical systems", math.NA/0503445
- "Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators", math.NA/0506090

- Catherine J. Penington, Barry D. Hughes, and Kerry A. Landman, "Building macroscale models from microscale probabilistic models: A general probabilistic approach for nonlinear diffusion and multispecies phenomena", Physical Review E
**84**(2011): 041120 - Liang Qiao, Radek Erban, C. T. Kelley and Ioannis G. Kevrekidis, "Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation", q-bio.QM/0606006
- A. J. Roberts
- "Normal form transforms separate slow and fast modes in stochastic dynamical systems", arxiv:math.DS/0701623
- "Resolve the multitude of microscale interactions to model stochastic partial differential equations", math.DS/0506533

- Wolfgang Stadje, "The evolution of aggregated Markov chains",
Statistics and
Probability Letters
**74**(2005): 303--311 ["Given a stationary two-sided Markov chain ... with finite state space ... and a partition ... we consider the aggregated sequence defined by [applying the partition], which is also stationary but in general not Markovian. We present a tractable way to determine the transition probabilities of [the aggregated process], either given a finite part of its past or given its infinite past. These probabilities are linked to the Radon-Nikodym derivative of [the density of an exponentially-decaying sum of aggregated values, conditional on the unaggregated process] with respect to [the unconditional distribution of the exponentially-decaying sum]".] - Panagiotis Stinis, "A comparative study of two stochastic mode reduction methods", math.NA/0509028
- Thomas N. Thiem, Felix P. Kemeth, Tom Bertalan, Carlo R. Laing and Ioannis G. Kevrekidis, "Global and Local Reduced Models for Interacting, Heterogeneous Agents", Chaos
**31**(2021): 073139, arxiv:2105.09398 - Ji-Feng Yang, "Renormalization group equations as 'decoupling' theorems", hep-th/0507024