We present a novel analytical approach for studying neural encoding. As a first step we model a neural sensory system as a communication channel. Using the method of typical sequence in this context, we show that a coding scheme is an almost bijective relation between equivalence classes of stimulus/response pairs. The analysis allows a quantitative determination of the type of information encoded in neural activity patterns and, at the same time, identification of the code with which that information is represented. Due to the high dimensionality of the sets involved, such a relation is extremely difficult to quantify. To circumvent this problem, and to use whatever limited data set is available most efficiently, we use another technique from information theory— quantization. We quantize the neural responses to a reproduction set of small finite size. Amongmany possible quantizations, we choose one which preserves as much of the informativeness of the original stimulus/response relation as possible, through the use of an information-based distortion function. This method allows us to study coarse but highly informative approximations of a coding scheme model, and then to refine them automatically when more data become available.

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewallike processes with the same spike-time histogram.

y to describe the main, usual form (or forms) of communication. We should take the approach of the moderately bright investigator, and leave the discovery of exceptional facts for later on. Further, we should try to quantify how much is communicated in each situation, because only a quantitative comparison allows to assess different codes, especially if they share part of the content of what is being communicated. Information theory [1] has been developed precisely to quantify communication, and is therefore quintessential to an appraisal of neural codes. Applying information theory to neural activity (rather than to the synthetic communication systems for which it was developed) is however riddled with practical problems and subtleties, which must be clarified before reporting experimental results. In this chapter, we do not consider other means of neuronal communication than the emission of action potentials, or spikes, and regard them as selfsimilar all-or-none even

The present study introduces information-geometric measures to analyze neural ring patterns by taking not only the second-order but also higher-order interactions among neurons into ac-count. Information geometry provides useful tools and concepts for this purpose, including the orthogonality of coordinate pa-rameters and the Pythagoras relation in the Kullback-Leibler di-vergence. Based on this orthogonality, we show anovel method to analyze spike ring patterns by decomposing the interactions of neurons of various orders. As a result, purely pairwise, triple-wise, and higher-order interactions are singled out. We also demonstrate the bene ts of our proposal by using real neural data, recorded in the prefrontal and parietal cortices of mon-keys. 1

Neurons in the visual cortex receive a large amount of input from recurrent connections, yet the functional role of these connections remains unclear. Here we explore networks with strong recurrence in a computational model and show that short-term depression of the synapses in the recurrent loops implements an adaptive filter. This allows the visual system to respond reliably to deteriorated stimuli yet quickly to high-quality stimuli. For low-contrast stimuli, the model predicts long response latencies, whereas latencies are short for high-contrast stimuli. This is consistent with physiological data showing that in higher visual areas, latencies can increase more than 100 ms at low contrast compared to high contrast. Moreover, when presented with briefly flashed stimuli, the model predicts stereotypical responses that outlast the stimulus, again consistent with physiological findings. The adaptive properties of the model suggest that the abundant recurrent connections found in visual cortex serve to adapt the network’s time constant in accordance with the stimulus and normalizes neuronal signals such that processing is as fast as possible while maintaining reliability.

processing and spectrotemporal reverse

is taken from the final draft rather than from the publisher’s PDF version. The original publication is available at www.springerlink.com.

We are given a neural spike train with spike times t1,..., tn and we want to discover something about the temporal resolution over which these spike times were generated. Jitter methods [4, 10, 1] are one way to begin approaching this problem. They are all based on the following intuitive approach:

The time histogram is a fundamental tool for representing the inhomogeneous density of event occurrences such as neuronal firings. The shape of a histogram critically depends on the size of the bins that partition the time axis. In most neurophysiological studies, however, researchers have arbitrarily selected the bin size when analyzing fluctuations in neuronal activity. A rigorous method for selecting the appropriate bin size was recently derived so that the mean integrated squared error between the time histogram and the unknown underlying rate is minimized (Shimazaki & Shinomoto, 2007). This derivation assumes that spikes are independently drawn from a given rate. However, in practice, biological neurons express non-Poissonian features in their firing patterns, such that the spike occurrence depends on the preceding spikes, which inevitably deteriorate the optimization. In this letter, we revise the method for selecting the bin size by considering the possible non-Poissonian features. Improvement in the goodness of fit of the time histogram is assessed and confirmed by numerically simulated non-Poissonian spike trains derived from the given fluctuating rate. For some experimental data, the revised algorithm transforms the shape of the time histogram from the Poissonian optimization method.

This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the Hodgkin-Huxley description, which is somehow the canonical description for the “biological neuron”. We discuss some models reducing