Recording from two neurons: second-order stimulus reconstruction from spike trains and population coding.

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, 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. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Synergy in a neural code.

We show that the information carried by compound events in neural spike trains-patterns of spikes across time or across a population of cells-can be measured, independent of assumptions about what these patterns might represent. By comparing the information carried by a compound pattern with the information carried independently by its parts, we directly measure the synergy among these parts. We illustrate the use of these methods by applying them to experiments on the motion-sensitive neuron H1 of the fly's visual system, where we confirm that two spikes close together in time carry far more than twice the information carried by a single spike. We analyze the sources of this synergy and provide evidence that pairs of spikes close together in time may be especially important patterns in the code of H1.

On the application of information theory to neural spike trains.

The nervous system represents time-dependent signals in sequences of discrete action potentials or spikes are identical so that information is carried only in the spike arrival times. We show how to quantify this information, in bits, free from any assumptions about which features of the spike train or input waveform are most important. We apply this approach to the analysis of experiments on a variety of systems, including some where we confront severe sampling problems, and discuss some to the results obtained and hopes for future extensions.

Reproducibility and variability in neural spike trains.

To provide information about dynamic sensory stimuli, the pattern of action potentials in spiking neurons must be variable. To ensure reliability these variations must be related, reproducibly, to the stimulus. For H1, a motion-sensitive neuron in the fly's visual system, constant-velocity motion produces irregular spike firing patterns, and spike counts typically have a variance comparable to the mean, for cells in the mammalian cortex. But more natural, time-dependent input signals yield patterns of spikes that are much more reproducible, both in terms of timing and of counting precision. Variability and reproducibility are quantified with ideas from information theory, and measured spike sequences in H1 carry more than twice the amount of information they would if they followed the variance-mean relation seen with constant inputs. Thus, models that may accurately account for the neural response to static stimuli can significantly underestimate the reliability of signal transfer under more natural conditions.

[Diagnosis of acute myocardial infarct in corrected orthogonal electrocardiogram]. / Uber die Erkennung des akuten Herzinfarkts im korrigierten orthogonalen Elektrokardiogramm

In 450 patients of a guarded ward for coronary diseases apart from the 15 conventional ECG-leads three corrected orthogonal leads after Frank were registered. In 141 cases an infarction could be confirmed. Using an observation of the course a recognition of the infarctions was always possible in the conventional as well as the corrected orthogonal ECG. In not penetrating infarctions a very careful analysis of the electrocardiograms and of the controls of the course is necessary, since the changes of the final ventricular deflection in the corrected orthogonal deviation system are less expressed than in the conventional leads. Thus, the corrected orthogonal electrocardiogram seems to be suitable for screening investigations concerning the recognition of a myocardial infarction.