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Electricity distribution companies are required to supply electric power, which conforms to accepted standards, that place limits on voltage fluctuations beyond nominal values. However, it is common for these fluctuations to exceed the specified standards. One solution to this problem is to install stand-alone root mean square (RMS) voltage regulators at the consumer site. Commonly available ac regulators typically have limitations such as slow response time, flattened sine wave output, low efficiency, and limited operating range. The linear ac voltage regulator is a relatively new type of solid-state, single-phase ac regulator for consumer-end, which addresses most of the abovementioned issues. It is based on a series transistor-array coupled with a line-frequency transformer that works seamlessly from boost-to buck-mode in the range of $0.8\text{--}1.1$ per-unit values of line voltage, without a need of any transformer configuration changes. However, previous prototypes exhibited reduced efficiency when the line voltage exceeded the nominal value. This article presents two alternative designs that achieve efficiencies of $\text{90}\text{--}{95\%}$ , usually required in commercial implementation. Analytical and experimental results of a multiwinding versus multitransformer-based prototypes of $\text{300}\,\text{VA}$ output capacity are presented.

The dynamics of a stochastic type-I Hodgkin-Huxley-like point neuron model exposed to inhibitory synaptic noise are investigated as a function of distance from spiking threshold and the inhibitory influence of the general anesthetic agent propofol. The model is biologically motivated and includes the effects of intrinsic ion-channel noise via a stochastic differential equation description as well as inhibitory synaptic noise modeled as multiple Poisson-distributed impulse trains with saturating response functions. The effect of propofol on these synapses is incorporated through this drug's principal influence on fast inhibitory neurotransmission mediated by γ-aminobutyric acid (GABA) type-A receptors via reduction of the synaptic response decay rate. As the neuron model approaches spiking threshold from below, we track membrane voltage fluctuation statistics of numerically simulated stochastic trajectories. We find that for a given distance from spiking threshold, increasing the magnitude of anesthetic-induced inhibition is associated with augmented signatures of critical slowing: fluctuation amplitudes and correlation times grow as spectral power is increasingly focused at 0 Hz. Furthermore, as a function of distance from threshold, anesthesia significantly modifies the power-law exponents for variance and correlation time divergences observable in stochastic trajectories. Compared to the inverse square root power-law scaling of these quantities anticipated for the saddle-node bifurcation of type-I neurons in the absence of anesthesia, increasing anesthetic-induced inhibition results in an observable exponent-0.5 for variance and-0.5 for correlation time divergences. However, these behaviors eventually break down as distance from threshold goes to zero with both the variance and correlation time converging to common values independent of anesthesia. Compared to the case of no synaptic input, linearization of an approximating multivariate Ornstein-Uhlenbeck model reveals these effects to be the consequence of an additional slow eigenvalue associated with synaptic activity that competes with those of the underlying point neuron in a manner that depends on distance from spiking threshold.

We present a theoretical modeling study that predicts that the EEG waveforms observed during the passage from wake through the stages of deepening natural sleep arise from the evolving interactions between symmetry-breaking transitions in the brain. These non-equilibrium transitions are brought on by modulations from naturally occurring neurotransmitters, primarily acetylcholine and GABA, whose concentrations vary dynamically during sleep. In particular, we find that the slow-wave oscillations of deepest nonREM sleep are fundamentally chaotic in nature, arising spontaneously from a competitive interaction between Turing (spatial) and Hopf (temporal) instabilities. We show that by introducing an activity-based regulation of inhibitory gap-junction diffusion, the sleeping cortex can move towards the edge of chaos defined by the boundary between the disordered slow-wave state and a pathologically ordered seizure-like state. We suggest that such self-organization could allow the brain to dwell in a state that is optimized for pruning and consolidation of memories.

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale l≈10μm is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999)], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length Bl, with B≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q(->) in favor of low-frequency spatial modes Q(->) using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

The Wilson–Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions—sudden qualitative changes in the state of a dynamical system emerging from a bifurcation—accessible to the Wilson–Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing–Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein–Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

In this chapter we investigate a range of dynamic behaviors accessible to a continuum model of the cerebral cortex placed close to the anesthetic phase transition. If the anesthetic transition from the high-firing (conscious) to the low-firing (comatose) state can be modeled as a jump between two equilibrium states of the cortex, then we can draw an analogy with the vapor-to-liquid phase transition of the van der Waals gas of classical thermodynamics. In this analogy, specific volume (inverse density) of the gas maps to cortical activity, with pressure and temperature being the analogs of anesthetic concentration and subcortical excitation. It is well known that at the thermodynamic critical point, large fluctuations in specific volume are observed; we find analogous critically-slowed fluctuations in cortical activity at its critical point. Unlike the van der Waals system, the cortical model can also exhibit nonequilibrium phase transitions in which the homogeneous equilibrium can destabilize in favor of slow global oscillations (Hopf temporal instability), stationary structures (Turing spatial instability), and chaotic spatiotemporal activity patterns (Hopf–Turing interactions). We comment on possible physiological and pathological interpretations for these dynamics. In particular, the turbulent state may correspond to the cortical slow oscillation between “up” and “down” states observed in nonREM sleep and clinical anesthesia.

We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable ${h}_{e},$ the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for ${h}_{e}.$ The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (``coma''), corresponding to a strong inhibitory anesthetic effect, ${h}_{e}$ is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, ${h}_{e}$ can take on three values, two of which are stable; we label the stable solutions as ``active'' (enhanced firing) and ``quiescent'' (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, ${h}_{e}$ again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates (``seizure''). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the ${h}_{e}$ signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by B\"uhrer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1 Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning.

It is a well established clinical observation that, at low concentrations, most anesthetic agents produce a surge in brain activity that occurs around the time of loss of consciousness. At higher concentrations, brain activity slows, and eventually tends towards electrical silence. A second surge in EEG power occurs during the return to consciousness. These induction and recovery biphasic power surges were first explained in terms of a first-order switching transition between distinct active and quiescent neural states, but subsequent modeling by other researchers has demonstrated that biphasic surges can also be generated by a smooth, graduated transition between normal and suppressed levels of cortical activity. In this chapter we examine the contrasting predictions of the switching model versus the continuous model for anesthetic induction. If the continuous non-switching picture is correct, then the return path to recovery will retrace the trajectory for induction, so the biphasic peaks should occur at identical drug concentrations. In contrast, the switching model predicts that there must be a hysteresis separation between the entry and recovery EEG power maxima, and that the patient will awaken at a lower drug concentration than that required to put her to sleep.

Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input? We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases, the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM.

We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor–capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the low-firing state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.

It is a simple observation that the function of the central nervous system changes abruptly at certain critical brain concentrations of the anesthetic drug. This can be viewed as analogous to “state transitions” in systems of interacting particles, which have been extensively studied in the physical sciences. Theoretical models of the electroencephalogram (EEG) are in semi-quantitative agreement with experimental data and show some features suggestive of anesthetic-induced state transitions (critical slowing, the biphasic effect, increase in spatial correlations, and entropy changes). However, the EEG is only an indirect marker of the (unknown) networks of cortical connectivity that are required for the formation of consciousness. It is plausible that anesthetic-induced alteration in cortical and corticothalamic network topology prevents the formation of a giant component in the neuronal population network, and hence induces unconsciousness.

One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for ${D}_{2}$, the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda et al. [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of ${D}_{2}\ensuremath{\approx}0.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$. We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of ${D}_{2}$ cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the spatial variations in brain activity patterns detected with the BOLD (blood oxygen--level--dependent) signal detected with magnetic resonance imaging, and may provide a natural substrate for synchronous gamma-band rhythms observed across separated EEG (electroencephalogram) electrodes.

In this paper we use a continuum model in two spatial dimensions to study the dynamics of the cortex during natural sleep, including explicitly the effects of two key neuromodulators. The model predicts that a number of states could be available to the cortex. We identify two of these with slow-wave sleep and rapid eye movement (REM) sleep, and focus on the transition between the two. Eigenvalue analysis of the linearized model, together with simulations on a two-dimensional grid, show that a number of oscillatory states exist; the occurrence of these is particularly dependent upon the duration in time of the inhibitory postsynaptic potential. These oscillatory states are similar to the cortical slow oscillation and certain types of seizure. Power spectra are evaluated for different parameter sets and compare favorably with experiment. Grid simulations show that transitions between cortical states (e.g., slow-wave to REM) can be seeded at any point in space by random fluctuations in subcortical input.

Inflight calibration of the near and thermal infrared channels of the AVHRR (advanced very high resolution radiometer) proceeds by linearly interpolating between a pair of reference radiances: the zero-radiance of deep space, and the calculable radiance of a passive blackbody honeycomb target (internal calibration target, ICT) whose temperature is measured with a cluster of four embedded PRTs (platinum resistance thermometers). Traditionally, the ICT temperature has been taken to be the equally-weighted average of the four PRT readings. The authors present evidence to show that equal weighting is not optimal, and describe how to compute revised weightings which improve calibration accuracies by /spl sim/0.13 K during times of rapid temperature change.

In our two recent papers [M.L. Steyn-Ross et al., Phys. Rev. E 60, 7299 (1999); 64, 011917 (2001)] we presented clinical evidence for a general anesthetic-induced phase change in the cerebral cortex, and showed how the significant features of the cortical phase change (biphasic power surge, spectral energy redistribution, ``heat capacity'' divergence), could be explained using a stochastic single-macrocolumn model of the cortex. The model predictions were based on rather strong ``adiabatic'' assumptions which assert that the mean-field excitatory and inhibitory macrocolumn voltages are ``slow'' variables whose equilibration times are much longer than those of the input ``currents'' that drive the macrocolumn. In the present paper we test the adiabatic assumption by running numerical simulations of the stochastic differential equations. These simulations confirm the number and nature of the steady-state solutions, the growth of fluctuation power at transition, and the redistribution of spectral energy towards lower frequencies. We use spectral entropy to quantify these changes in the power spectral density, and to show that the spectral entropy should decrease markedly at the point of transition. This prediction agrees with recent clinical findings by Vierti\"o-Oja and colleagues [J. Clinical Monitoring Computing 16, 60 (2000)]. Our modeling work shows that there is an inverse relationship between spectral entropy H and correlation time T of the soma-voltage fluctuations: $H\ensuremath{\propto}\ensuremath{-}(\mathrm{ln}T).$ In a theoretical analysis we prove that this proportionality becomes exact for an ideal Lorentzian process. These findings suggest that by monitoring the changes in EEG correlation time, it should be possible to track changes in the state of patient consciousness.

In a recent paper the authors developed a stochastic model for the response of the cerebral cortex to a general anesthetic agent. The model predicted that there would be an anesthetic-induced phase change at the point of transition into unconsciousness, manifested as a divergence in the electroencephalogram spectral power, and a change in spectral energy distribution from being relatively broadband in the conscious state to being strongly biased towards much lower frequencies in the unconscious state. Both predictions have been verified in recent clinical measurements. In the present paper we extend the model by calculating the equilibrium distribution function for the cortex, allowing us to establish a correspondence between the cortical phase transition and the more familiar thermodynamic phase transitions. This correspondence is achieved by first identifying a cortical free energy function, then by postulating that there exists an inverse relationship between an anesthetic effect and a quantity we define as cortical excitability, which plays a role analogous to temperature in thermodynamic phase transitions. We follow standard thermodynamic theory to compute a cortical entropy and a cortical "heat capacity," and we investigate how these will vary with anesthetic concentration. The significant result is the prediction that the entropy will decrease discontinuously at the moment of induction into unconsciousness, concomitant with a release of "latent heat" which should manifest as a divergence in the analogous heat capacity. There is clear clinical evidence of heat capacity divergence in historical anesthetic-effect measurements performed in 1977 by Stullken et al. [Anesthesiology 46, 28 (1977)]. The discontinuous step change in cortical entropy suggests that the cortical phase transition is analogous to a first-order thermodynamic transition in which the comatose-quiescent state is strongly ordered, while the active cortical state is relatively disordered.

The PSSC teaching film, ‘‘Frames of Reference,’’ was made in 1960, and was one of the first audio‐visual attempts at showing how your physical ‘‘point of view,’’ or frame of reference, necessarily alters both your perceptions and your observations of motion. The gentle humor and original demonstrations made a lasting impact on many audiences, and with its recent re‐release as part of the AAPT Cinema Classics videodisc it is timely that we should review both the message and the methods of the film. An annotated script and photographs from the film are presented, followed by extension material on rotating frames which teachers may find appropriate for use in their classrooms: constructions, demonstrations, an example, and theory.

We present evidence for the hypothesis that transitions between the low- and high-firing states of the cortical slow oscillation correspond to neuronal phase transitions. By analyzing intracellular recordings of the membrane potential during the cortical slow oscillation in rats, we quantify the temporal fluctuations in power and the frequency centroid of the power spectrum in the period of time before "down" to "up" transitions. By taking appropriate averages over such events, we present these statistics as a function of time before transition. The results demonstrate an increase in fluctuation power and time scale broadly consistent with the slowing of systems close to phase transitions. The analysis is complicated and limited by the difficulty in identifying when transitions begin, and removing dc trends in membrane potential.

Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other., Author Summary We develop and demonstrate a model that allows us to examine how the predictions of spiking and rate-based models of neurons and their interactions are related. First, the behavior of a chain of neurons is explored by simulating each spiking neuron and spike-mediated interactions between neurons individually. Second, the same chain is studied using approximations based on the firing rate of the neurons. The predictions for these two approaches are closely compared and it is found that the simpler, rate-based approach captures the major system behaviors of the spike-based approach, namely spiking rates and modulations in those rates. Strong interactions between these modes take place when the frequency of one mode is an integer or half-integer multiple of the frequency of the other mode.

This thesis examines a stochastic model for the electrical behavior of the cerebral cortex under the influence of a general anesthetic agent. The modeling element is the macrocolumn, an organized assembly of ∼10 5 cooperating neurons within a small cylindrical volume (∼1 mm 3 ) of the cortex. The state variables are h e and h i , the mean-field average soma voltages for the populations of excitatory and inhibitory neurons comprising the macrocolumn; the random fluctuations of h e about steady state are taken as the source of the scalp-measured EEG (electroencephalogram) signal. The effect of GABAergic anesthetic (e.g., propofol) is incorporated as a lengthening of the inhibitory postsynaptic impulse response. After performing a linear stability analysis of the anesthetic-determined distribution of soma voltage steady states, we obtain a model prediction of a pair of first-order discontinuities in soma voltage occurring at hysteretically separated critical values of anesthetic concentration: the first jump corresponding to induction (loss of consciousness), and the second corresponding to emergence (return of consciousness). Significant changes in EEGcharacteristics are predicted in the vicinity of both critical points: (1) strong increase in cortical power (“biphasic” effect); (2) pronounced spectral shift toward lower frequencies with concomitant decrease in spectral entropy; (3) pronounced increase in correlation time of EEG fluctuations (“critical slowing down”). There is excellent clinical support for all three predictions. When NMDA voltage-gated receptors are included in the model, we find a prediction of a double biphasic peak for a slow GABAergic induction of anesthesia, and this finding has also been confirmed in a recent report in the anesthesiology literature.

We examine in detail the calibration procedures for the advanced very high resolution radiometer (AVHRR) infrared channels. The AVHRR literature states that the linear mapping used to convert radiometric count to scene radiance is satisfactory for channel 3, but is only approximately correct for channels 4 and 5 since these channels have a slight curvature in their respective radiance-versus-count response functions, so a nonlinearity correction (NLC) is applied. Traditionally, these adjustments have been tabulated as brightness temperature corrections; we find that when expressed as radiance corrections, the NLCs can be written in a particularly simple form which depends only on the temperature of the internal calibration target. This new formulation eliminates the need to interpolate within the tables of temperature NLCs and permits the correction to be applied prior to conversion to equivalent brightness temperature, rather than after. Examination of the calibration records for 48 NOAA 11 passes sampled over a full year revealed several significant features: (1) For low Sun elevation angles relative to the satellite, sunlight can apparently leak into the optical path of the AVHRR, distorting the in-flight calibration data for channel 3, producing errors in apparent scene temperature as large as 2°C. (2) There is a clear demarcation between the calibration slopes for day and night operation of the satellite. (3) The thermal step that occurs when the spacecraft crosses the night-day boundary into full sunlight leads to transient calibration errors which decay to zero with a time constant of about 40 s. At the peak of the transient, the apparent scene temperature can be depressed by over 1°C in channel 3, and by up to 0.4°C in channels 4 and 5. Quality control measures and techniques for compensating for calibration problems are discussed.

A novel mechanism is proposed for optical bistability utilizing the population trapping which may occur in a coherent superposition of sublevels in a three-level system. The resulting bistability does not require atomic saturation and is insensitive to Doppler and laser bandwidth effects.

The quantum theory of a coherently driven optical cavity with an intracavity Raman active medium is presented. This system is shown to give rise to laser action at the Stokes frequency. A Fokker-Planck equation is derived for the Stokes mode and shown to assume the same form as that for the usual laser. The limiting noise in this Raman laser arose from the spontaneous decay of a pump photon into a Stokes photon and a phonon.

We present a model for a linear amplifier which adds phase-dependent noise to the input signal. This is achieved by preparing the internal modes of the amplifier in a squeezed vacuum. Such a scheme could be used to amplify a squeezed-signal quadrature with reduced added noise compared with conventional schemes. The model discussed could be realized as nondegenerate parametric amplification.