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.

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.

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.

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.

Neurons in the nervous system exhibit an outstanding variety of morphological and physiological properties. However, close to threshold, this remarkable richness may be grouped succinctly into two basic types of excitability, often referred to as type I and type II. The dynamical traits of these two neuron types have been extensively characterized. It would be interesting, however, to understand the information-processing consequences of their dynamical properties. To that end, here we determine the differences between the stimulus features inducing firing in type I and type II neurons. We work with both realistic conductance-based models and minimal normal forms. We conclude that type I neurons fire in response to scale-free depolarizing stimuli. Type II neurons, instead, are most efficiently driven by input stimuli containing both depolarizing and hyperpolarizing phases, with significant power in the frequency band corresponding to the intrinsic frequencies of the cell.

As subjects perceive the sensory world, different stimuli elicit a number of neural representations. Here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. As an example, the subjective distance between different locations in space is calculated from the activity of rodent's hippocampal place cells and lateral septal cells. Such a distance is compared to the real distance between locations. As the number of sampled neurons increases, the subjective distance shows a tendency to resemble the metrics of real space.

The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between stimuli and responses. The information loss is quantified. Whenever the probabilities are only slightly distorted, the information loss is shown to be quadratic in the distortion.

A novel definition of the stimulus-specific information is presented, which is particularly useful when the stimuli constitute a continuous and metric set, as, for example, position in space. The approach allows one to build the spatial information distribution of a given neural response. The method is applied to the investigation of putative differences in the coding of position in hippocampus and lateral septum.