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Stephen A. Berman

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Publisher: Journals Gateway

*Neural Computation*(2018) 30 (7): 1830–1929.

Published: 01 July 2018

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In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations. Abstract In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from and channel kinetics, in order to identify the source of –type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately –type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous –type Lorentzian weights, in which the spectral exponent is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to –type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond –type -noise, including applications to animal models and possible impact on quantum foundations.