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.

Predictions of diotic tone-in-noise detection based on a nonlinear optimal combination of energy, envelope, and fine-structure cues.

Tone-in-noise detection has been studied for decades; however, it is not completely understood what cue or cues are used by listeners for this task. Model predictions based on energy in the critical band are generally more successful than those based on temporal cues, except when the energy cue is not available. Nevertheless, neither energy nor temporal cues can explain the predictable variance for all listeners. In this study, it was hypothesized that better predictions of listeners' detection performance could be obtained using a nonlinear combination of energy and temporal cues, even when the energy cue was not available. The combination of different cues was achieved using the logarithmic likelihood-ratio test (LRT), an optimal detector in signal detection theory. A nonlinear LRT-based combination of cues was proposed, given that the cues have Gaussian distributions and the covariance matrices of cue values from noise-alone and tone-plus-noise conditions are different. Predictions of listeners' detection performance for three different sets of reproducible noises were computed with the proposed model. Results showed that predictions for hit rates approached the predictable variance for all three datasets, even when an energy cue was not available.

Detection of brain stimuli using Ramanujan periodicity transforms.

OBJECTIVE: The ability to efficiently match the frequency of the brain's response to repetitive visual stimuli in real time is the basis for reliable SSVEP-based brain-computer-interfacing (BCI). APPROACH: The detection of different stimuli is posed as a composite hypothesis test, where SSVEPs are assumed to admit a sparse representation in a Ramanujan periodicity transform (RPT) dictionary. For the binary case, we develop and analyze the performance of an RPT detector based on a derived generalized likelihood ratio test. Our approach is extended to multi-hypothesis multi-electrode settings, where we capture the spatial correlation between the electrodes using pre-stimulus data. We also introduce a new metric for evaluating SSVEP detection schemes based on their achievable efficiency and discrimination rate tradeoff for given system resources. MAIN RESULTS: We obtain exact distributions of the test statistic in terms of confluent hypergeometric functions. Results based on extensive simulations with both synthesized and real data indicate that the RPT detector substantially outperforms spectral-based methods. Its performance also surpasses the calibration-free state-of-the-art canonical correlation analysis (CCA) and filter bank CCA (FBCCA) methods with respect to accuracy and sample complexity in short data lengths regimes crucial for real-time applications. The proposed approach is asymptotically optimal as it closes the gap to a perfect measurement bound as the data length increases. In contrast to existing supervised methods which are highly data-dependent, the RPT detector only uses pre-stimulus data to estimate the per-subject spatial correlation, thereby dispensing with considerable overhead associated with data collection for a large number of subjects and stimuli. SIGNIFICANCE: Our work advances the theory and practice of emerging real-time BCI and affords a new framework for comparing SSVEP detection schemes across a wider spectrum of operating regimes.

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.