No abstract

Pulse-type weakly electric fishes communicate through electrical discharges with a stereotyped waveform, varying solely the interval between pulses according to the information being transmitted. This simple codification mechanism is similar to the one found in various known neuronal circuits, which renders these animals as good models for the study of natural communication systems, allowing experiments involving behavioral and neuroethological aspects. Performing analysis of data collected from more than one freely swimming fish is a challenge since the detected electric organ discharge (EOD) patterns are dependent on each animal's position and orientation relative to the electrodes. However, since each fish emits a characteristic EOD waveform, computational tools can be employed to match each EOD to the respective fish. In this paper we describe a computational method able to recognize fish EODs from dyads using normalized feature vectors obtained by applying Fourier and dual-tree complex wavelet packet transforms. We employ support vector machines as classifiers, and a continuity constraint algorithm allows us to solve issues caused by overlapping EODs and signal saturation. Extensive validation procedures with Gymnotus sp. showed that EODs can be assigned correctly to each fish with only two errors per million discharges.

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels -measured by a chi-squared averaged over the whole experiment -is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons.

Is the characterization of biological systems as complex systems in the mathematical sense a fruitful assertion? In this paper we argue in the affirmative, although obviously we do not attempt to confront all the issues raised by this question. We use the fly's visual system as an example and analyse our experimental results of one particular neuron in the fly's visual system from this point of view. We find that the motionsensitive 'H1' neuron, which converts incoming signals into a sequence of identical pulses or 'spikes', encodes the information contained in the stimulus into an alphabet composed of a few letters. This encoding occurs on multilayered sets, one of the features attributed to complex systems. The conversion of intervals between consecutive occurrences of spikes into an alphabet requires us to construct a generating partition. This entails a oneto-one correspondence between sequences of spike intervals and words written in the alphabet. The alphabet dynamics is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike intervals, such as models using Poisson statistics, whose dynamics is monofractal. We embed the support of the probability measure, which describes the distribution of words written in this alphabet, in a two-dimensional space, whose topology can be reproduced by an M-shaped map. This map has positive Lyapunov exponents, indicating a chaotic-like encoding.