scholarly journals Neocortical Dynamics at Multiple Scales: EEG Standing Waves, Statistical Mechanics, and Physical Analogs

2010 ◽  
Author(s):  
Lester Ingber ◽  
Paul L. Nunez
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Standing Waves ◽  
Neocortical Dynamics

Nonlinear Periodic Systems: Bands and Localization

2009 ◽  
Author(s):  
Alexander Vakakis
Keyword(s):  
Traveling Waves ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Near Field ◽  
Standing Waves ◽  
Nonlinear Resonance ◽  
Nonlinear Effects ◽  
Periodic Media ◽  
Spatially Extended ◽  
Nonlinear Standing Waves

We consider the dynamics of nonlinear mono-coupled periodic media. When coupling dominates over nonlinearity near-field standing waves and spatially extended traveling waves exist, inside stop and pass bands, respectively, of the nonlinear system. Nonlinear standing waves are analytically studied using a nonlinear normal mode formulation, whereas nonlinear traveling waves are analyzed by the method of multiple scales. When the nonlinear effects are of the same order with the coupling ones a completely different picture emerges, since nonlinear resonance interactions are unavoidable. As a result, infinite families of strongly and weakly localized nonlinear standing waves appear with frequencies lying in pass or stop bands of the corresponding linear periodic medium. Moreover, in the limit of weak coupling these solutions develop sensitive dependence on initial conditions, and the possibility of spatial chaos in the system exists. Some additional results on chaotic dynamics in linear periodic media with strongly nonlinear disorders are reviewed.

scholarly journals Hybrid Classical-Quantum Fitting Attention States to Statistical Mechanics of Neocortical Interactions

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Wave Packets ◽  
Quantum Systems ◽  
Quantum Model ◽  
Quantum Processes ◽  
Multivariate Statistical ◽  
Synaptic Interactions ◽  
Classical Quantum ◽  
Random Shocks

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the Principal Investigator (PI). However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The PI's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

scholarly journals Hybrid Classical-Quantum Fitting Attention States to Statistical Mechanics of Neocortical Interactions

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Wave Packets ◽  
Quantum Systems ◽  
Quantum Model ◽  
Quantum Processes ◽  
Multivariate Statistical ◽  
Synaptic Interactions ◽  
Classical Quantum ◽  
Random Shocks

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the Principal Investigator (PI). However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The PI's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

scholarly journals Hybrid Classical-Quantum Fitting Attention States to Statistical Mechanics of Neocortical Interactions

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Wave Packets ◽  
Quantum Systems ◽  
Quantum Model ◽  
Quantum Processes ◽  
Multivariate Statistical ◽  
Synaptic Interactions ◽  
Classical Quantum ◽  
Random Shocks

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the Principal Investigator. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The Principal Investigator's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

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