Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise.

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-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 [Formula: see text]-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 [Formula: see text]-type Lorentzian weights, in which the spectral exponent [Formula: see text] 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 [Formula: see text]-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 [Formula: see text]-type -noise, including applications to animal models and possible impact on quantum foundations.

A New Statistical Model of Electroencephalogram Noise Spectra for Real-Time Brain-Computer Interfaces.

OBJECTIVE: A characteristic of neurological signal processing is high levels of noise from subcellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model that has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 to over 30 Hz, and has approximately 1/fθ behavior in the midfrequencies without infinities. METHODS: We validate this model using three approaches. First, we show how GVZM PSDs can arise in a population of ion channels at maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. RESULTS: In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely used SSVEP estimators. CONCLUSION: The GVZM noise model can be a useful and reliable technique for EEG signal processing. SIGNIFICANCE: Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces, which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.

Optimal causal filtering for 1 /fα-type noise in single-electrode EEG signals.

Understanding the mode of generation and the statistical structure of neurological noise is one of the central problems of biomedical signal processing. We have developed a broad class of abstract biological noise sources we call hidden simplicial tissues. In the simplest cases, such tissue emits what we have named generalized van der Ziel-McWhorter (GVZM) noise which has a roughly 1/fα spectral roll-off. Our previous work focused on the statistical structure of GVZM frequency spectra. However, causality of processing operations (i.e., dependence only on the past) is an essential requirement for real-time applications to seizure detection and brain-computer interfacing. In this paper we outline the theoretical background for optimal causal time-domain filtering of deterministic signals embedded in GVZM noise. We present some of our early findings concerning the optimal filtering of EEG signals for the detection of steady-state visual evoked potential (SSVEP) responses and indicate the next steps in our ongoing research.