Hemispheric asymmetries in cortical grey matter of gyri and sulci in modern human populations from South America.

Structural asymmetries of brain regions associated with lateralised functions have been extensively studied. However, there are fewer morphometric analyses of asymmetries of the gyri and sulci of the entire cortex. The current study assessed cortical asymmetries in a sample of healthy adults (N = 175) from an admixed population from South America. Grey matter volume and surface area of 66 gyri and sulci were quantified on T1 magnetic resonance images. The departure from zero of the differences between left and right hemispheres (L-R), a measure of directional asymmetry (DA), the variance of L-R, and an index of fluctuating asymmetry (FA) were evaluated for each region. Significant departures from perfect symmetry were found for most cortical gyri and sulci. Regions showed leftward asymmetry at the population level in the frontal lobe and superior lateral parts of the parietal lobe. Rightward asymmetry was found in the inferior parietal, occipital, frontopolar, and orbital regions, and the cingulate (anterior, middle, and posterior-ventral). Despite this general pattern, several sulci showed the opposite DA compared to the neighbouring gyri, which remarks the need to consider the neurobiological differences in gyral and sulcal development in the study of structural asymmetries. The results also confirm the absence of DA in most parts of the inferior frontal gyrus and the precentral region. This study contributes with data on populations underrepresented in the databases used in neurosciences. Among its findings, there is agreement with previous results obtained in populations of different ancestry and some discrepancies in the middle frontal and medial parietal regions. A significant DA not reported previously was found for the volume of long and short insular gyri and the central sulcus of the insula, frontomarginal, transverse frontopolar, paracentral, and middle and posterior parts of the cingulate gyrus and sulcus, gyrus rectus, occipital pole, and olfactory sulcus, as well as for the volume and area of the transverse collateral sulcus and suborbital sulcus. Also, several parcels displayed significant variability in the left-right differences, which can be partially attributable to developmental instability, a source of FA. Moreover, a few gyri and sulci displayed ideal FA with non-significant departures from perfect symmetry, such as subcentral and posterior cingulate gyri and sulci, inferior frontal and fusiform gyri, and the calcarine, transverse collateral, precentral, and orbital sulci. Overall, these results show that asymmetries are ubiquitous in the cerebral cortex.

The Emergence of the Normal Distribution in Deterministic Chaotic Maps.

The central limit theorem states that, in the limits of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to attain a stable distribution. The condition of independence, however, only holds in real systems as an approximation. To extend the theorem to more general situations, previous studies have derived a version of the central limit theorem that also holds for variables that are not independent. Here, we present numerical results that characterize how convergence is attained when the variables being summed are deterministically related to one another through the recurrent application of an ergodic mapping. In all the explored cases, the convergence to the limit distribution is slower than for random sampling. Yet, the speed at which convergence is attained varies substantially from system to system, and these variations imply differences in the way information about the deterministic nature of the dynamics is progressively lost as the number of summands increases. Some of the identified factors in shaping the convergence process are the strength of mixing induced by the mapping and the shape of the marginal distribution of each variable, most particularly, the presence of divergences or fat tails.

Inferring a Property of a Large System from a Small Number of Samples.

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.

Bridging physiological and perceptual views of autism by means of sampling-based Bayesian inference.

Theories for autism spectrum disorder (ASD) have been formulated at different levels, ranging from physiological observations to perceptual and behavioral descriptions. Understanding the physiological underpinnings of perceptual traits in ASD remains a significant challenge in the field. Here we show how a recurrent neural circuit model that was optimized to perform sampling-based inference and displays characteristic features of cortical dynamics can help bridge this gap. The model was able to establish a mechanistic link between two descriptive levels for ASD: a physiological level, in terms of inhibitory dysfunction, neural variability, and oscillations, and a perceptual level, in terms of hypopriors in Bayesian computations. We took two parallel paths-inducing hypopriors in the probabilistic model, and an inhibitory dysfunction in the network model-which lead to consistent results in terms of the represented posteriors, providing support for the view that both descriptions might constitute two sides of the same coin.

Statistical Properties of Color Matching Functions.

In trichromats, color vision entails the projection of an infinite-dimensional space (the one containing all possible electromagnetic power spectra) onto the three-dimensional space that modulates the activity of the three types of cones. This drastic reduction in dimensionality gives rise to metamerism, that is, the perceptual chromatic equivalence between two different light spectra. The classes of equivalence of metamerism are revealed by color-matching experiments in which observers adjust the intensity of three monochromatic light beams of three preset wavelengths (the primaries) to produce a mixture that is perceptually equal to a given monochromatic target stimulus. Here we use the linear relation between the color matching functions and the absorption probabilities of each type of cone to find particularly useful triplets of primaries. As a second goal, we also derive an analytical description of the trial-to-trial variability and the correlations of color matching functions stemming from Poissonian noise in photon capture. We analyze how the statistical properties of the responses to color-matching experiments vary with the retinal composition and the wavelengths of peak absorption probability, and compare them with experimental data on subject-to-subject variability obtained previously.

Time- and frequency-resolved covariance analysis for detection and characterization of seizures from intracraneal EEG recordings.

The amount of power in different frequency bands of the electroencephalogram (EEG) carries information about the behavioral state of a subject. Hence, neurologists treating epileptic patients monitor the temporal evolution of the different bands. We propose a covariance-based method to detect and characterize epileptic seizures operating on the band-filtered EEG signal. The algorithm is unsupervised and performs a principal component analysis of intra-cranial EEG recordings, detecting transient fluctuations of the power in each frequency band. Its simplicity makes it suitable for online implementation. Good sampling of the non-ictal periods is required, while no demands are imposed on the amount of data during ictal activity. We tested the method with 32 seizures registered in 5 patients. The area below the resulting receiver-operating characteristic curves was 87% for the detection of seizures and 91% for the detection of recruited electrodes. To identify the behaviorally relevant correlates of the physiological signal, we identified transient changes in the variance of each band that were correlated with the degree of loss of consciousness, the latter assessed by the so-called Consciousness Seizure Scale, summarizing the performance of the subject in a number of behavioral tests requested during seizures. We concluded that those crisis with maximal impairment of consciousness tended to exhibit an increase in variance approximately 40 s after seizure onset, with predominant power in the theta and alpha bands and reduced delta and beta activity.

The subjective metric of remembered colors: A Fisher-information analysis of the geometry of human chromatic memory.

In order to explore the metric structure of the space of remembered colors, a computer game was designed, where players with normal color vision had to store a color in memory, and later retrieve it by selecting the best match out of a continuum of alternatives. All tested subjects exhibited evidence of focal colors in their mnemonic strategy. We found no concluding evidence that the focal colors of different players tended to cluster around universal prototypes. Based on the Fisher metric, for each subject we defined a notion of distance in color space that captured the accuracy with which similar colors where discriminated or confounded when stored and retrieved from memory. The notions of distance obtained for different players were remarkably similar. Finally, for each player, we constructed a new color scale, in which colors are memorized and retrieved with uniform accuracy.

Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples.

Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here, we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables-the one with minimal entropy-is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain a consistent estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between the two variables, without seeking to model the specific way in which they are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states in which the large-entropy variable registers coincidences.

Novel Perceptually Uniform Chromatic Space.

Chromatically perceptive observers are endowed with a sense of similarity between colors. For example, two shades of green that are only slightly discriminable are perceived as similar, whereas other pairs of colors, for example, blue and yellow, typically elicit markedly different sensations. The notion of similarity need not be shared by different observers. Dichromat and trichromat subjects perceive colors differently, and two dichromats (or two trichromats, for that matter) may judge chromatic differences inconsistently. Moreover, there is ample evidence that different animal species sense colors diversely. To capture the subjective metric of color perception, here we construct a notion of distance in color space based on the physiology of the retina, and is thereby individually tailored for different observers. By applying the Fisher metric to an analytical model of color representation, we construct a notion of distance that reproduces behavioral experiments of classical discrimination tasks. We then derive a coordinate transformation that defines a new chromatic space in which the Euclidean distance between any two colors is equal to the perceptual distance, as seen by one individual subject, endowed with an arbitrary number of color-sensitive photoreceptors, each with arbitrary absorption probability curves and appearing in arbitrary proportions.

Information-Theoretical Analysis of the Neural Code in the Rodent Temporal Lobe.

In the study of the neural code, information-theoretical methods have the advantage of making no assumptions about the probabilistic mapping between stimuli and responses. In the sensory domain, several methods have been developed to quantify the amount of information encoded in neural activity, without necessarily identifying the specific stimulus or response features that instantiate the code. As a proof of concept, here we extend those methods to the encoding of kinematic information in a navigating rodent. We estimate the information encoded in two well-characterized codes, mediated by the firing rate of neurons, and by the phase-of-firing with respect to the theta-filtered local field potential. In addition, we also consider a novel code, mediated by the delta-filtered local field potential. We find that all three codes transmit significant amounts of kinematic information, and informative neurons tend to employ a combination of codes. Cells tend to encode conjunctions of kinematic features, so that most of the informative neurons fall outside the traditional cell types employed to classify spatially-selective units. We conclude that a broad perspective on the candidate stimulus and response features expands the repertoire of strategies with which kinematic information is encoded.

Assessing the Relevance of Specific Response Features in the Neural Code.

The study of the neural code aims at deciphering how the nervous system maps external stimuli into neural activity-the encoding phase-and subsequently transforms such activity into adequate responses to the original stimuli-the decoding phase. Several information-theoretical methods have been proposed to assess the relevance of individual response features, as for example, the spike count of a given neuron, or the amount of correlation in the activity of two cells. These methods work under the premise that the relevance of a feature is reflected in the information loss that is induced by eliminating the feature from the response. The alternative methods differ in the procedure by which the tested feature is removed, and the algorithm with which the lost information is calculated. Here we compare these methods, and show that more often than not, each method assigns a different relevance to the tested feature. We demonstrate that the differences are both quantitative and qualitative, and connect them with the method employed to remove the tested feature, as well as the procedure to calculate the lost information. By studying a collection of carefully designed examples, and working on analytic derivations, we identify the conditions under which the relevance of features diagnosed by different methods can be ranked, or sometimes even equated. The condition for equality involves both the amount and the type of information contributed by the tested feature. We conclude that the quest for relevant response features is more delicate than previously thought, and may yield to multiple answers depending on methodological subtleties.

Derivation of Human Chromatic Discrimination Ability from an Information-Theoretical Notion of Distance in Color Space.

The accuracy with which humans detect chromatic differences varies throughout color space. For example, we are far more precise when discriminating two similar orange stimuli than two similar green stimuli. In order for two colors to be perceived as different, the neurons representing chromatic information must respond differently, and the difference must be larger than the trial-to-trial variability of the response to each separate color. Photoreceptors constitute the first stage in the processing of color information; many more stages are required before humans can consciously report whether two stimuli are perceived as chromatically distinguishable. Therefore, although photoreceptor absorption curves are expected to influence the accuracy of conscious discriminability, there is no reason to believe that they should suffice to explain it. Here we develop information-theoretical tools based on the Fisher metric that demonstrate that photoreceptor absorption properties explain about 87% of the variance of human color discrimination ability, as tested by previous behavioral experiments. In the context of this theory, the bottleneck in chromatic information processing is determined by photoreceptor absorption characteristics. Subsequent encoding stages modify only marginally the chromatic discriminability at the photoreceptor level.

Bursting Neurons in the Hippocampal Formation Encode Features of LFP Rhythms.

Burst spike patterns are common in regions of the hippocampal formation such as the subiculum and medial entorhinal cortex (MEC). Neurons in these areas are immersed in extracellular electrical potential fluctuations often recorded as the local field potential (LFP). LFP rhythms within different frequency bands are linked to different behavioral states. For example, delta rhythms are often associated with slow-wave sleep, inactivity and anesthesia; whereas theta rhythms are prominent during awake exploratory behavior and REM sleep. Recent evidence suggests that bursting neurons in the hippocampal formation can encode LFP features. We explored this hypothesis using a two-compartment model of a bursting pyramidal neuron driven by time-varying input signals containing spectral peaks at either delta or theta rhythms. The model predicted a neural code in which bursts represented the instantaneous value, phase, slope and amplitude of the driving signal both in their timing and size (spike number). To verify whether this code is employed in vivo, we examined electrophysiological recordings from the subiculum of anesthetized rats and the MEC of a behaving rat containing prevalent delta or theta rhythms, respectively. In both areas, we found bursting cells that encoded information about the instantaneous voltage, phase, slope and/or amplitude of the dominant LFP rhythm with essentially the same neural code as the simulated neurons. A fraction of the cells encoded part of the information in burst size, in agreement with model predictions. These results provide in-vivo evidence that the output of bursting neurons in the mammalian brain is tuned to features of the LFP.

Thalamic neuron models encode stimulus information by burst-size modulation.

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Information-theoretical analysis of the statistical dependencies among three variables: Applications to written language.

We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two variables is or is not mediated by a third variable. These concepts are applied to the analysis of written texts. We find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words, but also, on the presence or absence of nearby pairs of words. We identify the words enclosing the key semantic concepts of the text, the triplets of words with high pairwise and triple interactions, and the words that mediate the pairwise interactions between other words.

Effects of spike-triggered negative feedback on receptive-field properties.

Sensory neurons are often described in terms of a receptive field, that is, a linear kernel through which stimuli are filtered before they are further processed. If information transmission is assumed to proceed in a feedforward cascade, the receptive field may be interpreted as the external stimulus' profile maximizing neuronal output. The nervous system, however, contains many feedback loops, and sensory neurons filter more currents than the ones representing the transduced external stimulus. Some of the additional currents are generated by the output activity of the neuron itself, and therefore constitute feedback signals. By means of a time-frequency analysis of the input/output transformation, here we show how feedback modifies the receptive field. The model is applicable to various types of feedback processes, from spike-triggered intrinsic conductances to inhibitory synaptic inputs from nearby neurons. We distinguish between the intrinsic receptive field (filtering all input currents) and the effective receptive field (filtering only external stimuli). Whereas the intrinsic receptive field summarizes the biophysical properties of the neuron associated to subthreshold integration and spike generation, only the effective receptive field can be interpreted as the external stimulus' profile maximizing neuronal output. We demonstrate that spike-triggered feedback shifts low-pass filtering towards band-pass processing, transforming integrator neurons into resonators. For strong feedback, a sharp resonance in the spectral neuronal selectivity may appear. Our results provide a unified framework to interpret a collection of previous experimental studies where specific feedback mechanisms were shown to modify the filtering properties of neurons.

Dynamics and reliability of bistable neurons driven with time-dependent stimuli.

The reliability of a spiking neuron depends on the frequency content of the driving input signal. Previous studies have shown that well above threshold, regularly firing neurons generate reliable responses when the input signal resonates with the firing frequency of the cell. Instead, well below threshold, reliable responses are obtained when the input frequency resonates with the subthreshold oscillations of the neuron. Previous theories, however, provide no clear prediction for the input frequency giving rise to maximally reliable spiking at threshold, which is probably the most relevant firing regime in mammalian cortex under physiological conditions. In particular, when the firing onset is governed by a subcritical Hopf bifurcation, the frequency of subthreshold oscillations often differs from the firing rate at threshold. The predictions of previous studies, hence, cannot be smoothly merged at threshold. Here we explore the behavior of reliability in bistable neurons near threshold using three types of driving stimuli: constant, periodic, and stochastic. We find that the two natural frequencies of the system, associated with the two coexisting attractors, provide a rich variety of possible locking modes with the external signal. Reliability is determined by the sensitivity to noise of each locking mode and by the transition probabilities between modes. Noise increases the amount of spike time jitter, and minimal jitter is obtained for input frequencies coinciding with the suprathreshold firing rate of the cell. In addition, noise may either enhance or inhibit transitions between the two attractors, depending on the input frequency. The dual role played by noise in bistable systems implies that reliability is determined by a delicate balance between spike time jitter and the rate of transitions between attractors.

When and why noise correlations are important in neural decoding.

Information may be encoded both in the individual activity of neurons and in the correlations between their activities. Understanding whether knowledge of noise correlations is required to decode all the encoded information is fundamental for constructing computational models, brain-machine interfaces, and neuroprosthetics. If correlations can be ignored with tolerable losses of information, the readout of neural signals is simplified dramatically. To that end, previous studies have constructed decoders assuming that neurons fire independently and then derived bounds for the information that is lost. However, here we show that previous bounds were not tight and overestimated the importance of noise correlations. In this study, we quantify the exact loss of information induced by ignoring noise correlations and show why previous estimations were not tight. Further, by studying the elementary parts of the decoding process, we determine when and why information is lost on a single-response basis. We introduce the minimum decoding error to assess the distinctive role of noise correlations under natural conditions. We conclude that all of the encoded information can be decoded without knowledge of noise correlations in many more situations than previously thought.

Linking dynamical and functional properties of intrinsically bursting neurons.

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts. There presented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.

Spike-triggered covariance: geometric proof, symmetry properties, and extension beyond Gaussian stimuli.

The space of sensory stimuli is complex and high-dimensional. Yet, single neurons in sensory systems are typically affected by only a small subset of the vast space of all possible stimuli. A proper understanding of the input-output transformation represented by a given cell therefore requires the identification of the subset of stimuli that are relevant in shaping the neuronal response. As an extension to the commonly-used spike-triggered average, the analysis of the spike-triggered covariance matrix provides a systematic methodology to detect relevant stimuli. As originally designed, the consistency of this method is guaranteed only if stimuli are drawn from a Gaussian distribution. Here we present a geometric proof of consistency, which provides insight into the foundations of the method, in particular, into the crucial role played by the geometry of stimulus space and symmetries in the stimulus-response relation. This approach leads to a natural extension of the applicability of the spike-triggered covariance technique to arbitrary spherical or elliptic stimulus distributions. The extension only requires a subtle modification of the original prescription. Furthermore, we present a new resampling method for assessing statistical significance of identified relevant stimuli, applicable to spherical and elliptic stimulus distributions. Finally, we exemplify the modified method and compare it to other prescriptions given in the literature.