Not just a bad metaphor, but a little piece of a big bad metaphor.

Besides failing for the reasons Brette gives, codes fail to help us understand brain function because codes imply algorithms that compute outputs without reference to the signals' meanings. Algorithms cannot be found in the brain, only manipulations that operate on meaningful signals and that cannot be described as computations, that is, sequences of predefined operations.

γ-Aminobutyric Acid Type A Receptor Potentiation Inhibits Learning in a Computational Network Model.

BACKGROUND: Propofol produces memory impairment at concentrations well below those abolishing consciousness. Episodic memory, mediated by the hippocampus, is most sensitive. Two potentially overlapping scenarios may explain how γ-aminobutyric acid receptor type A (GABAA) potentiation by propofol disrupts episodic memory-the first mediated by shifting the balance from excitation to inhibition while the second involves disruption of rhythmic oscillations. We use a hippocampal network model to explore these scenarios. The basis for these experiments is the proposal that the brain represents memories as groups of anatomically dispersed strongly connected neurons. METHODS: A neuronal network with connections modified by synaptic plasticity was exposed to patterned stimuli, after which spiking output demonstrated evidence of stimulus-related neuronal group development analogous to memory formation. The effect of GABAA potentiation on this memory model was studied in 100 unique networks. RESULTS: GABAA potentiation consistent with moderate propofol effects reduced neuronal group size formed in response to a patterned stimulus by around 70%. Concurrently, accuracy of a Bayesian classifier in identifying learned patterns in the network output was reduced. Greater potentiation led to near total failure of group formation. Theta rhythm variations had no effect on group size or classifier accuracy. CONCLUSIONS: Memory formation is widely thought to depend on changes in neuronal connection strengths during learning that enable neuronal groups to respond with greater facility to familiar stimuli. This experiment suggests the ability to form such groups is sensitive to alteration in the balance between excitation and inhibition such as that resulting from administration of a γ-aminobutyric acid-mediated anesthetic agent.

Neuronal spike train entropy estimation by history clustering.

Neurons send signals to each other by means of sequences of action potentials (spikes). Ignoring variations in spike amplitude and shape that are probably not meaningful to a receiving cell, the information content, or entropy of the signal depends on only the timing of action potentials, and because there is no external clock, only the interspike intervals, and not the absolute spike times, are significant. Estimating spike train entropy is a difficult task, particularly with small data sets, and many methods of entropy estimation have been proposed. Here we present two related model-based methods for estimating the entropy of neural signals and compare them to existing methods. One of the methods is fast and reasonably accurate, and it converges well with short spike time records; the other is impractically time-consuming but apparently very accurate, relying on generating artificial data that are a statistical match to the experimental data. Using the slow, accurate method to generate a best-estimate entropy value, we find that the faster estimator converges to this value more closely and with smaller data sets than many existing entropy estimators.

Network model of top-down influences on local gain and contextual interactions in visual cortex.

The visual system uses continuity as a cue for grouping oriented line segments that define object boundaries in complex visual scenes. Many studies support the idea that long-range intrinsic horizontal connections in early visual cortex contribute to this grouping. Top-down influences in primary visual cortex (V1) play an important role in the processes of contour integration and perceptual saliency, with contour-related responses being task dependent. This suggests an interaction between recurrent inputs to V1 and intrinsic connections within V1 that enables V1 neurons to respond differently under different conditions. We created a network model that simulates parametrically the control of local gain by hypothetical top-down modification of local recurrence. These local gain changes, as a consequence of network dynamics in our model, enable modulation of contextual interactions in a task-dependent manner. Our model displays contour-related facilitation of neuronal responses and differential foreground vs. background responses over the neuronal ensemble, accounting for the perceptual pop-out of salient contours. It quantitatively reproduces the results of single-unit recording experiments in V1, highlighting salient contours and replicating the time course of contextual influences. We show by means of phase-plane analysis that the model operates stably even in the presence of large inputs. Our model shows how a simple form of top-down modulation of the effective connectivity of intrinsic cortical connections among biophysically realistic neurons can account for some of the response changes seen in perceptual learning and task switching.

γ-Aminobutyric acid receptor type A receptor potentiation reduces firing of neuronal assemblies in a computational cortical model.

BACKGROUND: The understanding of how general anesthetics act on individual cells and on global brain function has increased significantly during the last decade. What remains poorly understood is how anesthetics act at intermediate scales. Several major theories emphasize the importance of neuronal groups, sets of strongly connected neurons that fire in a time-locked fashion, in all aspects of brain function, particularly as a necessary substrate of consciousness. The authors have undertaken computer modeling to determine how ã-aminobutyric acid receptor type A (GABAA) receptor potentiating agents such as propofol may influence the dynamics of neuronal group formation and ongoing activity. METHODS: A computer model of a cortical network with connections modified by synaptic plasticity was examined. At baseline, the model spontaneously formed neuronal groups. Direct effects of GABAA receptor potentiation and indirect effects on input drive were then examined to study their effects on this process. RESULTS: Potentiation of GABAA inhibition and input drive reduction reduced the firing frequency of inhibitory and excitatory neurons in a dose-dependent manner. The diminution in spiking rates led to dramatic reductions in the firing frequency of neuronal groups. Simulated electroencephalographic output from the model at baseline exhibits gamma and theta rhythmicity. The direct and indirect GABAA effects reduce the amplitude of these underlying rhythms and modestly slow the gamma rhythm. CONCLUSIONS: GABAA facilitation both directly and indirectly inhibits the ability of neurons to form groups spontaneously. A lack of group formation is consistent with some theories of anesthetic-induced loss of memory formation and consciousness.

Quantitative tools for examining the vocalizations of juvenile songbirds.

The singing of juvenile songbirds is highly variable and not well stereotyped, a feature that makes it difficult to analyze with existing computational techniques. We present here a method suitable for analyzing such vocalizations, windowed spectral pattern recognition (WSPR). Rather than performing pairwise sample comparisons, WSPR measures the typicality of a sample against a large sample set. We also illustrate how WSPR can be used to perform a variety of tasks, such as sample classification, song ontogeny measurement, and song variability measurement. Finally, we present a novel measure, based on WSPR, for quantifying the apparent complexity of a bird's singing.

Quantitative descriptions of generalized arousal, an elementary function of the vertebrate brain.

We review a concept of the most primitive, fundamental function of the vertebrate CNS, generalized arousal (GA). Three independent lines of evidence indicate the existence of GA: statistical, genetic, and mechanistic. Here we ask, is this concept amenable to quantitative analysis? Answering in the affirmative, four quantitative approaches have proven useful: (i) factor analysis, (ii) information theory, (iii) deterministic chaos, and (iv) application of a Gaussian equation. It strikes us that, to date, not just one but at least four different quantitative approaches seem necessary for describing different aspects of scientific work on GA.

A continuous entropy rate estimator for spike trains using a K-means-based context tree.

Entropy rate quantifies the change of information of a stochastic process (Cover & Thomas, 2006). For decades, the temporal dynamics of spike trains generated by neurons has been studied as a stochastic process (Barbieri, Quirk, Frank, Wilson, & Brown, 2001; Brown, Frank, Tang, Quirk, & Wilson, 1998; Kass & Ventura, 2001; Metzner, Koch, Wessel, & Gabbiani, 1998; Zhang, Ginzburg, McNaughton, & Sejnowski, 1998). We propose here to estimate the entropy rate of a spike train from an inhomogeneous hidden Markov model of the spike intervals. The model is constructed by building a context tree structure to lay out the conditional probabilities of various subsequences of the spike train. For each state in the Markov chain, we assume a gamma distribution over the spike intervals, although any appropriate distribution may be employed as circumstances dictate. The entropy and confidence intervals for the entropy are calculated from bootstrapping samples taken from a large raw data sequence. The estimator was first tested on synthetic data generated by multiple-order Markov chains, and it always converged to the theoretical Shannon entropy rate (except in the case of a sixth-order model, where the calculations were terminated before convergence was reached). We also applied the method to experimental data and compare its performance with that of several other methods of entropy estimation.

Mathematical analysis of locomotor behavior by mice in a radial maze.

We investigated the effects of beta-estradiol on the locomotor behavior of female mice in a radial maze. Data comprising the total distance traveled during each arm entry were obtained from video records of six consecutive daily recording sessions. Distributions of these data were bimodal for both ovariectomized control and beta-estradiol-treated ovariectomized subjects. Data were fit with the sum of two gamma probability distributions. Three parameters of the analytic fits were useful for quantifying the effect of beta-estradiol on locomotor behavior: (i) the sampling distance (median of the total distance traveled during each arm entry in the short-distance peak of a bimodal distribution), (ii) the committed distance (median of the total per-arm-entry distance traveled in the long-distance peak), and (iii) the partition distance (distance represented by the minimum between the two peaks). Analysis showed that for sampling-distance arm entries beta-estradiol typically had little if any significant effect on female locomotor behavior, whereas it significantly increased the total distance traveled during committed-distance arm entries on the first 2 days of exposure to the empty maze. beta-Estradiol also increased the ability of females to discriminate between empty maze arms and arms that contained intact or castrated male mice and partially prevented loss of this capacity after removal of the males.

Theories and measures of consciousness: an extended framework.

A recent theoretical emphasis on complex interactions within neural systems underlying consciousness has been accompanied by proposals for the quantitative characterization of these interactions. In this article, we distinguish key aspects of consciousness that are amenable to quantitative measurement from those that are not. We carry out a formal analysis of the strengths and limitations of three quantitative measures of dynamical complexity in the neural systems underlying consciousness: neural complexity, information integration, and causal density. We find that no single measure fully captures the multidimensional complexity of these systems, and all of these measures have practical limitations. Our analysis suggests guidelines for the specification of alternative measures which, in combination, may improve the quantitative characterization of conscious neural systems. Given that some aspects of consciousness are likely to resist quantification altogether, we conclude that a satisfactory theory is likely to be one that combines both qualitative and quantitative elements.

Control of neuronal discharge timing by afferent fiber number and the temporal pattern of afferent impulses.

We employ computer simulations to explore the effect of different temporal patterns of afferent impulses on the evoked discharge of a model cerebellar Purkinje cell. We show that the frequency and temporal correlation of impulses across afferent fibers determines which of four regimes of discharge activity is evoked. In the uncorrelated, here Poissonian, case, (i) cell discharge is determined by the total stimulation rate and temporal patterns of discharge are the same for different combinations of afferent fiber number and mean impulse rate per fiber giving the same total stimulation. Alternatively, if temporal correlations are present in the stimulus, (ii) for stimulation frequencies of 4 to at least 64 Hz there is a narrow range of afferent fiber number for which every stimulus pulse (composed of a single impulse on each afferent fiber) evokes a single action potential. In this case cell discharge is frequency locked to the stimulus with a concomitant reduction in discharge variability. (iii) For lower fiber numbers and thus discharge frequencies lower than the locking frequency, the variability of cell discharge is typically independent of afferent impulse timing, whereas, (iv) at higher fiber numbers and thus higher discharge frequencies, the reverse is true. We conclude that in case (iii) the cell acts as an integrator and discharge is determined by the stimulation rate, whereas in case (iv) the cell acts as a coincidence detector and the timing of discharge is determined by the temporal pattern of afferent stimulation. We discuss our results in terms of their significance for neuronal activity at the network level and suggest that the reported effects of varying stimulus timing and afferent convergence can be expected to obtain also with other principal cell types within the central nervous system.

Estimating the temporal interval entropy of neuronal discharge.

To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.

Modelling criteria: Not just for robots.

Webb's scheme for classifying behavioral models is applicable to a wide range of theories and simulations, nonrobotic as well as robotic. It is suggested that a meta-analysis of existing models, characterized according to the proposed scheme, could identify regions of the seven-dimensional modelling space that are particularly likely to lead to new insights in understanding behavior.