To investigate the directionality of neural interactions as assessed by electrophysiology, we adapted methods of structural analysis from the field of econometrics. In particular, within the framework of autoregressive modelling of the data, we considered quantitative measures of linear relationship between multiple time series adopting the Wiener-Granger concept of causality. The techniques were evaluated with local field potential measurements from the cat visual system. Here, several issues had to be addressed. First, out of several statistical tests of the stationarity of local field potentials considered, those based on the Kolmogorov-Smirnov and on the reverse arrangement statistics proved to be most powerful. The application of those tests to the experimental data showed that the large part of the local field potentials can be considered stationary on a time scale of 1 s. Second, out of the several investigated methods for the determination of an optimal order of the autoregressive model, the Akaike Information Criterion had the most suitable properties. The identified order of the model, across different repetitions of the trials, was consistently 5-8. Third, although the individual segments of field potentials used for the analysis were relatively short, the methods of structural analysis applied produced reliable results, confirming findings of simulations of data with similar properties. Furthermore the features of the estimated models were consistent among trials, so that the analysis of average measures of interaction appears to be a viable approach to investigate the relationship between the recording sites. In summary, the statistical methods considered have proved to be suitable for the study of the directionality of neuronal interactions.

The study of the cooperativity among cortical areas is essential to our understanding of brain functioning. Here we investigated the relative contributions of top-down and bottom-up directed interactions between area 17 and area 7 of the cat visual system. Bipolar local field potentials were recorded while the animals performed a go/no-go task or were in a quiet resting state. The data were analyzed by applying measures of interaction based on the Wiener-Granger causality concept. We found that during the visual task top-down directed interactions were of a similar magnitude as the bottom-up component. Second, interareal couplings tended to increase in conditions requiring a discriminative effort. Third, during behaviors not dominated by visual processing non-directed interactions increased.

We use methods of nonlinear dynamics to describe the effect of periodic inhibition on the patterns of action potentials generated by regular spiking rat cortical neuron in vitro. Both direct measurements and our mathematical model reveal that chaotic patterns of discharge can be evoked at certain frequencies of inhibitory stimulation. We use detailed biophysical simulation of a cortical neuron to explain the firing patterns in terms of known membrane ionic conductances.There is a small voltage difference across the outer membrane of every living cell [1]. Neurons make use of this membrane voltage to perform their computations and to communicate with one another. One very common neuronal communication signal is the action potential, a brief regenerative voltage spike that can travel long distances along the cell membrane without attenuation [2]. The time between spikes (interspike interval duration) may encode information, since the form and distribution of these intervals reflect excitatory and inhibitory signals reaching the nerve cells.In this paper, we investigate the effect of periodic inhibitory pulses on the output pattern of rat cortical neurons that usually generate a regular train of spikes in response to intracellular injection of a constant stimulating current. The experiments were performed in a brain slice preparation, and also in a simulated cortical pyramidal neuron. We analyze the data using methods of nonlinear dynamics, which are emerging as powerful tools for understanding the behavior of biological systems [3]. We develop and enhance an approach of Glass and Guevara et al. [4], which they used to describe the changes in instantaneous firing rate of embryonic chicken heart cells.Slices of somatosensory cortex from Sprague-Dawley rat were prepared by standard procedures [5]. We used sharp electrodes to record membrane potentials from neurons (n = 20) in the first third of the cortex adjacent to cerebral white matter. Intracellular injection of constant current evoked regular spiking behavior in these neurons. To simulate inhibitory input we superimposed negative rectangular current pulses of 5 ms duration at time t t ,i= 1, 2,... (c.f. Fig. 1 tive to the preceding spike. When we applied the current pulse soon after a spike, we observed a shortening of the interspike interval, while late application lengthened the interval, as shown in Figure 1. The effect of a stimulus arriving at time r, after the preceding spike, on the interspike interval length T, was described in terms of phase. The phase of the applied stimulus is defined as tJT 0 , where T 0 is the unperturbed interspike interval (c.f. Figure 1). Plotting T/T 0 versus yields the phase response curve (see Fig. 2) which shows how the interspike interval length depends on the exact arrival time of the stimulus. From the phase ; of the last stimulus, the phase of the next stimulus i + 1 can be predicted by a Poincare map P: 0,--0 1 + j. This claim can be confirmed from Fig. 1, which shows that the following relation holds:D...

This paper investigates empirically how similarity of demand structures -approximated by similarity of income distributions -affects trade patterns along both the extensive and intensive margin.

No abstract