Notes: The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. © 1998 American Institute of Physics.

Notes: Coloured light surrounding a white surface of about equal luminance makes the white surface appear illuminated with an unsaturated light of the complementary colour. In an attempt to discover the neurophysiological basis of such colour induction, we recorded from spectrally opponent cells of the parvocellular layers of the lateral geniculate nucleus (P-LGN) of anaesthetized macaques. Only cells with wide-band (W) spectral sensitivity in the short (S) or long wavelength (L) part of the spectrum (WS, WL) are excited by white spots of light centred on their receptive field. Cells with narrow-band (N) spectral sensitivity (NS, NL) and light-inhibited (L1) cells are inhibited by white light. Therefore, it is likely that the code for white is contained in a balanced excitation of the W cells. The effects of continuous illumination of remote surrounds with different wavelengths on the responses to achromatic light stimuli were investigated. Responses [on minus maintained discharge rate (MDR) or on-minus-off] were determined for white spots (1–3° diameter) flashed on the receptive field centre, presented either alone or in the presence of an annular surround of equal luminance (inner diameter 5°; outer diameter 20°). During red surround illumination the responses of WL cells to white spots tended to be reduced as were those of WS cells during blue surround illumination. Surround illumination with the opponent colour had more variable effects, neither WS nor WL cells showing a significant alteration of their mean response to white during surround illumination with opponent light. Response alterations were to a large extent due to changes in MDR, which increased in WS cells during blue surround illumination and in WL cells during red surround illumination. It is argued that the surround effects on centre responses are due to intraocular stray light rather than lateral connections in the retina. The surround effects also depended to some extent on the size of the test spot. L1 cells and the very rare parvocellular panchromatic on-cells showed no chromatic response changes during coloured surround illumination. Inasmuch as the excitation of WS cells, either alone or in combination with NS cell activation, is involved in coding for green and blue, and that of WL cells, in combination with NL cell activation, is involved in coding for red and yellow in perception, the shift of excitation towards one or the other W cell group indicates relatively more red or green signals in the white response, consistent with and in the same direction as colour induction. In addition, the summed population response of WS and WL cells is decreased during surround illumination with any colour including white. This is related to brightness decrease during surround illumination in perception.

Notes: [Auszug] Since the earliest demonstrations of chaos in physical nonlinear systems of three or more dimensions11'13, the question of its existence in biological systems, which are certainly nonlinear and multidimensional, naturally arose14'15. But in such cases one never has an accurate model for the ...

Notes: Summary The colour of an object is changed by surround colours so that the perceived colour is shifted in a direction complementary to the surround colour. To investigate the physiological mechanism underlying this phenomenon, we recorded from 260 neurons in the parvo-cellular lateral geniculate nucleus (P-LGN) of anaesthetized monkeys (Macaca fascicularis), and measured their responses to 1.0–2.0° diameter spots of equiluminant light of various spectral composition, centered over their receptive field (spectral response function, SRF). Five classes of colour opponent neurons and two groups of light inhibited cells were distinguished following the classification proposed by Creutzfeldt et al. (1979). In each cell we repeated the SRF measurement while an outer surround (inner diameter 5°, outer diameter 20°) was continuously illuminated with blue (452 nm) or red (664 nm) light of the same luminance as the center spots. The 1.0–1.5° gap between the center and the surround was illuminated with a dim white background light (0.5–1cd/m2). During blue surround illumination, neurons with an excitatory input from S-or M-cones (narrowand wide-band/short-wavelength sensitive cells, NSand WS-cells, respectively) showed a strong attenuation of responses to blue and green center spots, while their maintained discharge rate (MDR) increased. During red surround illumination the on-minus-off-responses of NS- and WS-cells showed a clear increment. L-cone excited WL-cells (wide-band/long-wavelength sensitive) showed a decrement of on-responses to red, yellow and green center spots during red surround illumination and, in the majority, also an increment of MDR. The response attenuation of narrow-band/long-wavelength sensitive (NL)-cellls was more variable, but their on-minus-off-responses were also clearly reduced in the average during red surrounds. Blue surround illumination affected WL-cell responses little and less consistently than those of NL-cells, but often broadened the SRF also in the WL-cells towards shorter wavelengths. The M-cone excited and S-cone suppressed WM-cells were strongly suppressed by blue but only little affected by red surround illumination. The changes of spectral responsiveness came out clearly in the group averages of the different cell classes, but snowed some variation between individual cells in each group. The zero-crossing wavelengths derived from on-minus-off-responses were also characteristically shifted towards wavelengths complementary to those of the surround. The direction of changes of spectral responsiveness of P-LGN-cells are thus consistent with psychophysical colour contrast and colour induction effects which imply that light of one spectral region in the surround reduces the contribution of light from that same spectral region in the (broad band or composite) object colour. Surrounds of any colour also decrease the brightness of a central coloured or achromatic light (darkness induction). We calculated the population response of P-LGN-units by summing the activity of all WS-, WM- and WL-cells and subtracting that of all NS- and NL-cells. The SRF of this population response closely resembled the spectral brightness function for equiluminous lights rather than the photopic luminosity function. With red or blue surrounds, this population SRF was lowered nearly parallel across the whole spectrum to about 0.7 of the amplitude of the control. In a psychophysical test on 4 observers we estimated the darkness induction of an equiluminous surround in a stimulus arrangement identical to the neurophysiological experiment, and found a brightness reduction for white, blue, green and red center stimuli to 0.5–0.7 of the brightness values without surround. This indicates that the neurophysiological results may be directly related to perception, and that P-LGN-cells not only signal for chroma but also for brightness, but in different combinations. The results indicate that both an additive (direct excitation or suppression of activity) and a multiplicative mechanism (change of gain control) must be involved in brightness and colour contrast perception. As mechanisms for the surround effects horizontal cell interactions appear not to be sufficient, and a direct adaptive effect on receptors feeding positive or negative (opponent) signals into the ganglion cells receptive fields by straylight from the surround must be seriously considered. This will be examined in the following companion paper. The results indicate that changes of spectral and brightness responses in a colour contrast situation sufficient to explain corresponding changes in perception are found already in geniculate neurons and their retinal afferents. This applies to mechanisms for colour constancy as well in as much as they are related to colour contrast.

Notes: Summary We report on experiments which were undertaken in an attempt to clarify mechanisms underlying the contrast effects of chromatic surround illumination on spectral responsiveness of cells in the parvocellular layers of the LGN (P-LGN-cells), that had been demonstrated under standard conditions in the preceding companion paper. The experiments were done in anesthetized macaques (Macaca fascicularis). In some neurons, S-potentials were recorded together with the post-synaptic action potentials, and all effects seen in P-LGN-cells were present already in their retinal afferents indicating their retinal origine. The responsiveness of the cells for center stimuli of different wavelengths and during illumination of the receptive field center or the outer surround was determined. Continuous outer surround illumination alered maintained dicharge rate (MDR), sensitivity and gain of P-LGN and retinal ganglion cells in the same way and empirically not distinguishable from direct illumination of the receptive field. Responses to surround flashes showed the same dependence on spectral composition as those to center flashes. Adaptation and excitation caused by outer surround illumination (inner diameter 5°, outer diameter 20°) were, in the average, ten times weaker than those exerted by light of the same spectral composition shone directly into the receptive field. Surround effects decreased proportional to r-2. Excitation by outer surround flashes was reduced by adaptation of the receptive field center in the same manner as responses to center flashes. The findings indicate that outer surround light has a direct excitatory and adaptive effect on the excitatory or inhibitory cones feeding into the receptive field. This indicates that straylight from the surround into the center could be responsible for the adaptive and excitatory effects of surround illumination. The straylight fraction from the remote surround into the receptive field must be higher, however, than that estimated from the psychophysically determined point spread function. It comes closer to earlier direct straylight measurements in excised eyes, but may be enhanced by chromatic aberration. If a surround of excitatory colour is flashed simultaneously with an excitatory center stimulus, additivity of center and surround excitation is observed only at low center intensities, while at higher center intensities the gain for center excitation is reduced similar to adaptive gain control. This could be explained by lateral interaction through horizontal connections in the retina, which decays within seconds, while adaptation of the cones feeding into the receptive field center is fully effective only after about 3 s. Our findings therefore suggest a two stage model for surround effects, a fast one mediated through horizontal connections controlling the gain of receptorbipolar transmission and a slow one through adaptation by straylight and controlling receptor gain. The fast process is receptor unspecific, i.e. pooling activity from all receptor types, while the second one is receptor specific. During real seeing both processes are simultaneous and complement each other because of continuous eye movements. Perceptual darkness and colour induction by remote surrounds are consistent with this model, which can also be applied to colour constancy. WM-cells (Yellow-minus-blue) show peculiar properties during surround or center illumination with blue light, suggestng an opponent mechanism different from that of other P-LGN-cells.

Notes: Abstract We report the results of a search for evidence of unstable periodic orbits in the sensory afferents of the facial cold receptors of the rat. Cold receptors are unique in that they exhibit a diversity of action potential firing patterns as well as pronounced transients in firing rate following rapid temperature changes. These characteristics are the result of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degree of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of complex activity. By detecting the existence of unstable periodic orbits, we demonstrate low-dimensional dynamical behavior whose characteristics depend on the temperature range, impulse pattern, and temperature transients.

Notes: Abstract We report the results of a search for evidence of periodic unstableorbits in the electroreceptors of the catfish. The function of thesereceptor organs is to sense weak external electric fields. Inaddition, they respond to the ambient temperature and to the ioniccomposition of the water. These quantities are encoded by receptorsthat make use of an internal oscillator operating at the level of themembrane potential. If such oscillators have three or more degreesof freedom, and at least one of which also exhibits a nonlinearity,they are potentially capable of chaotic dynamics. By detecting theexistence of stable and unstable periodic orbits, we demonstratebifurcations between noisy stable and chaotic behavior using theambient temperature as a parameter. We suggest that the techniquedeveloped herein be regarded as an additional tool for the analysisof data in sensory biology and thus can be potentially useful instudies of functional responses to external stimuli. We speculatethat the appearance of unstable orbits may be indicative of a stateof heightened sensory awareness by the animal.