Kalman filter control of a model of spatiotemporal cortical dynamics

Journal of Neural Engineering

Volumn 5, Issue 1, 2008, Pages 1-8

  Schiff, Steven J ^a   Sauer, Tim ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISEASES; ELECTRIC FIELDS; KALMAN FILTERS;

NONLINEAR METHOD; SPATIOTEMPORAL CORTICAL DYNAMICS; WAVE PATTERNS;

NONLINEAR SYSTEMS;

ALGORITHM; ARTICLE; BRAIN CORTEX; CALCULATION; DYNAMICS; ELECTRIC FIELD; ENERGY; FILTER; KALMAN FILTER; MATHEMATICAL ANALYSIS; NONLINEAR SYSTEM; PARAMETER; PHYSICS; PRIORITY JOURNAL; SIGNAL DETECTION;

ALGORITHMS; CEREBRAL CORTEX; COMPUTER SIMULATION; HUMANS; LINEAR MODELS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS;

EID: 40549143057     PISSN: 17412560     EISSN: 17412552     Source Type: Journal    
DOI: 10.1088/1741-2560/5/1/001     Document Type: Article

References (25)

1. Evensen G 1994 Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics J. Geophys. Res. 99 10143-62
2. Evensen G and Van Leeuwen P J 2000 An ensemble Kalman smoother for non-linear dynamics Mon. Weather Rev. 128 1852-67
3. Gauss C F 1857 Theory of the Motion of the Heavenly Bodies Moving About the Sun in Conic Sections trans. ed C F Davis (Boston: Little, Brown and Company)
4. Gluckman B J, Nguyen H, Weinstein S L and Schiff S J 2001 Adaptive electric field suppression of epileptic seizures J. Neurosci. 21 590-600
5. Hansen J and Penland C 2007 On stochastic parameter estimation using data assimilation Physica D 230 88-98
6. Holmes P, Lumley J L and Berkooz G 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge: Cambridge University Press)
7. Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S J and Wu J Y 2004 Spiral waves in mammalian neocortex J. Neurosci. 24 9897-902
8. Hunt B, Kostelich E J and Szunyogh I 2007 Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter Physica D 230 112-26
9. Julier S J and Uhlmann J K 1997a A consistent, debiased method for converting between polar and Cartesian coordinate systems SPIE 3086 110-21
10. Julier S J and Uhlmann J K 1997b A new extension of the Kalman filter to nonlinear systems SPIE 3068 182-93
11. Kalman R E 1960 A new approach to linear filtering and prediction problems Trans. ASME D 82 35-45
12. Park E-H, Barreto E, Gluckman B J, Schiff S J and So P 2005 A model of the effects of applied electric fields on neuronal synchronization J. Comp. Neurosci. 19 53-70
13. Pinto D J and Ermentrout G B 2001a Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses SIAM J. Appl. Math. 62 206-25
14. Pinto D J and Ermentrout G B 2001b Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses SIAM J. Appl. Math. 62 226-43
15. Rubino D, Robbins K A and Hatsopoulos N G 2006 Propagating waves mediate information transfer in the motor cortex Nat. Neurosci. 9 1549-57
16. Schiff S J, Huang X and Wu J Y 2007 Dynamical evolution of spatiotemporal patterns in mammalian middle cortex Phys. Rev. Lett. 98 178102
17. Schiff S J, Jerger K, Duong D H, Chang T, Spano M L and Ditto W L 1994 Controlling chaos in the brain Nature 370 615-20
18. Simon D 2006 Optimal State Estimation (Hoboken: Wiley-Interscience)
19. Smith T R, Moehlis J and Holmes P 2005 Low-dimensional models for turbulent plane Couette flow in a minimal flow unit J. Fluid Mech. 538 71-110
20. Voss H, Timmer J and Kurths J 2004 Nonlinear dynamical system identification from uncertain and indirect measurements Int. J. Bif. Chaos 14 1905-33
21. Wan E A, Merwe R and Nelson A T 2000 Dual estimation and the unscented transformation Advances in Neural Information Processing Systems vol 12 ed S Solla, T Leen and K-R Müller (Cambridge, MA: MIT Press) pp 666-72
22. Wiener N 1964 Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Cambridge, MA: MIT Press)
23. Wilson H R and Cowan J D 1972 Excitatory and inhibitory interactions in localized populations of model neurons Biophys. J. 12 1-24
24. Wilson H R and Cowan J D 1973 A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue Kybernetik 13 55-80
25. Xu W, Huang X, Takagaki K and Wu J-Y 2007 Compression and reflection of visually evoked cortical waves Neuron 55 119-29