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.

The angiographic findings of cortical nodular hyperplasia, adenolipoma, and intracaval extension of recurrent pheochromocytoma were correlated with the pathological findings. Adenolipoma was angiographically similar to other adrenal neoplasms, adding difficulties to its differential diagnosis. Two cases of cortical nodular hyperplasia showed possibly pathognomonic patterns of discrete vascular cortical accumulations of contrast media which represent capillary malformations within the hyperplastic nodules. Intracaval extension of recurrent pheochromocytoma was found to be similar to other tumors which invade veins.

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E ects of fringe elds in separation dipoles D1 D2 and low-quadrupoles Q1-Q3 of LHC interaction regions in collision optics are investigated by means of stepwise ray-tracing in terms of aberrations, beam envelopes and other detunings. E ects of the longitudinal distribution of b10 error coe cient are next investigated in a similar way for assessment and comparison.

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.