Path-integral evolution of chaos embedded in noise: Duffing neocortical analog

@article{Ingber1996PathintegralEO,
  title={Path-integral evolution of chaos embedded in noise: Duffing neocortical analog},
  author={Lester Ingber and Ramesh Srinivasan and Paul L. Nunez},
  journal={Mathematical and Computer Modelling},
  year={1996},
  volume={23},
  pages={43-53}
}
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70 Citations
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8
Methods Citations
14

70 Citations

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References

SHOWING 1-10 OF 48 REFERENCES
Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory.
  • Ingber
  • Biology, Computer Science
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
TLDR
A recently developed C-language code, PATHINT, provides a non-Monte Carlo technique for calculating the dynamic evolution of arbitrary-dimension nonlinear Lagrangians, such as derived for the two-variable SMNI problem.
Statistical mechanics of neocortical interactions: High-resolution path-integral calculation of short-term memory.
  • Ingber, Núñez
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
High-resolution path-integral calculations of a previously developed model of short-term memory in neocortex are presented, made possible with supercomputer resources, and supported by coarser estimates made by Ingber.
Statistical mechanics of neocortical interactions. I. Basic formulation
Statistical mechanics of neocortical interactions. Dynamics of synaptic modification
TLDR
The formation, stability, and interaction of spatial-temporal patterns of columnar firings are explicitly calculated, to test hypothesized mechanisms relating to information processing.
Implications of recording strategy for estimates of neocortical dynamics with electroencephalography.
TLDR
A large scale, quasilinear theory of neocortical dynamics in which standing wave phenomenon occur with predicted frequencies in the general range of EEG, and a relatively simple nonlinear physical system consisting of a linear string with attached nonlinear springs.
Statistical mechanics of multiple scales of neocortical interactions
INTRODUCTION General philosophy In many complex systems, as spatial-temporal scales of observation are increased, new phenomena arise by virtue of synergistic interactions among smaller-scale…
PHASE TRANSITIONS IN THE HUMAN BRAIN: SPATIAL MODE DYNAMICS
Pattern formation and switching between self-organized states are often associated with instabilities in open, nonequilibrium systems. We describe an experiment which shows that systematically…
Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography.
  • Ingber
  • Biology
    Physical review. A, Atomic, molecular, and optical physics
  • 1991
TLDR
The SMNI model is shown to be consistent with EEG data during selective attention tasks and with neocortical mechanisms describing short-term memory previously published using this approach, and strong quantitative support for an accurate intuitive picture is given.
Numerical evaluation of path-integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients.
  • Wehner, Wolfer
  • Physics
    Physical review. A, General physics
  • 1987
TLDR
A path-integral solution to truly nonlinear Fokker-Planck equations is derived and this discrete formulation provides a basis for an efficient numerical algorithm and is applied with excellent results to several example problems where exact solutions can be calculated.
Path-integral evolution of multivariate systems with moderate noise.
  • Ingber
  • Computer Science
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
Anon Monte Carlo path-integral algorithm that is particularly adept at handling nonlinearLagrangians is extended to multivariate systems and is particularly accurate for systems with moderate noise.
...
1
2
3
4
5
...