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} }
70 Citations
Evolution of Regenerative Ca-Ion Wave-Packet in Neuronal-Firing Fields: Quantum Path-Integral with Serial Shocks
- Physics
- 2016
The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which was applied to several classical physics systems, including statistical mechanics of neocortical…
Evolution of Regenerative Ca-Ion Wave-Packet in Neuronal-Firing Fields: Quantum Path-Integral with Serial Shocks
- Physics
- 2016
The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which has been applied to several classical physics systems, including statistical mechanics of neocortical…
The form of chaos in the noisy brain can manifest function
- PhysicsBehavioral and Brain Sciences
- 1996
Abstract I would like to emphasize the significance of chaotic dynamics at both local and macroscopic levels in the cortex. The basic notions dealt with in this commentary will be noise-induced…
Nonlinear nonequilibrium nonquantum nonchaotic statistical mechanics of neocortical interactions
- BiologyBehavioral and Brain Sciences
- 1996
The tentative conclusion that macroscopic neocortex may be considered (approximately) a linear near-equilibrium system is premature and does not correspond to tentative conclusions drawn from other studies of neocortex.
Options on Quantum Money: Quantum Path-Integral with Serial Shocks
- Physics
- 2017
The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which has been applied to several classical physics systems, including statistical mechanics of neocortical…
Is there chaos in the brain?
- Computer ScienceBehavioral and Brain Sciences
- 1996
Based on simulation studies and various experiments, it is suggested that the pointwise dimension of EEG time series may provide some valuable information about underlying neuronal generators.
Statistical mechanics of multiple scales of neocortical interactions
- Physics
- 1995
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…
Comparative reduction of theories — or over-simplification?
- BiologyBehavioral and Brain Sciences
- 1996
Rhythmic control provides a fundamentally different systems dynamics, one not provided by models that allow the emergence of continuous trajectories in the systems state space.
Quantum Variables in Finance and Neuroscience (Presentation Slides)
- Physics
- 2018
A path-integral algorithm, PATHINT, used previously for several systems, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Pilot quantum…
Multiscale neocortical dynamics, experimental EEG measures, and global facilitation of local cell assemblies
- Environmental ScienceBehavioral and Brain Sciences
- 1996
Abstract Multiscale dynamics, linear approximations, global boundary conditions, experimental verification, and global influences on local cell assemblies are considered in the context of Wright &…
References
SHOWING 1-10 OF 48 REFERENCES
Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory.
- Biology, Computer SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994
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.
- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995
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. Dynamics of synaptic modification
- Biology
- 1983
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.
- BiologyChaos
- 1993
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
- Physics
- 1995
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
- Physics
- 1992
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.
- BiologyPhysical review. A, Atomic, molecular, and optical physics
- 1991
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.
- PhysicsPhysical review. A, General physics
- 1987
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.
- Computer SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995
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.