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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]\u2013type 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]\u2013type 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]\u2013type 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]\u2013type -noise, including applications to animal models and possible impact on quantum foundations.<\/jats:p>","DOI":"10.1162\/neco_a_01067","type":"journal-article","created":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T21:42:04Z","timestamp":1521754924000},"page":"1830-1929","source":"Crossref","is-referenced-by-count":0,"title":["Hidden Quantum Processes, Quantum Ion Channels, and 1\/<i>f<sup>\u03b8<\/sup><\/i>-Type Noise"],"prefix":"10.1162","volume":"30","author":[{"given":"Alan","family":"Paris","sequence":"first","affiliation":[{"name":"NeuroLogic Laboratory, Institute for Simulation and Training, University of Central Florida, Orlando, FL 32826, U.S.A."}]},{"given":"Azadeh","family":"Vosoughi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32826, U.S.A."}]},{"given":"Stephen A.","family":"Berman","sequence":"additional","affiliation":[{"name":"College of Medicine, University of Central Florida, Orlando, FL 32826, U.S.A."}]},{"given":"George","family":"Atia","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32826, U.S.A."}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(76)90201-2"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195184017"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1973.sp010410"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1101\/lm.960510"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1002\/bip.20698"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neulet.2009.11.039"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4090-5"},{"key":"B8","volume-title":"Creative evolution","author":"Bergson H.","year":"1998"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1038\/35102067"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1021\/ba-1994-0235.ch017"},{"key":"B11","volume-title":"Wholeness and the implicate order","author":"Bohm D.","year":"1980"},{"key":"B12","volume-title":"Quantum theory","author":"Bohm D.","year":"1989"},{"key":"B13","volume-title":"The undivided universe","author":"Bohm D.","year":"1993"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0320-4"},{"key":"B15","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780195301069.001.0001","volume-title":"Rhythms of the brain","author":"G. 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