We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.
In this paper, we investigate the bifurcations of solutions to a class of degenerate constrained optimization problems. This study was motivated by the Information Bottleneck and Information Distortion problems, which have been used to successfully cluster data in many different applications. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer. This leads to a challenging annealing optimization problem, which we recast as a fixed-point dynamics problem of a gradient flow of a related dynamical system. The gradient system possesses an SN symmetry due to its invariance in relabeling representative classes. Its flow hence passes through a series of bifurcations with specific symmetry breaks. Here, we show that the dynamical system related to the Information Bottleneck problem has an additional spurious symmetry that requires more-challenging analysis of the symmetry-breaking bifurcation. For the Information Bottleneck, we determine that when bifurcations occur, they are only of pitchfork type, and we give conditions that determine the stability of the bifurcating branches. We relate the existence of subcritical bifurcations to the existence of first-order phase transitions in the corresponding distortion function as a function of the annealing parameter, and provide criteria with which to detect such transitions.
In this paper we propose a model for the lateral connectivity of orientation-selective cells in the visual cortex based on information-theoretic considerations. We study the properties of the input signal to the visual cortex and find new statistical structures which have not been processed in the retino-geniculate pathway. Applying the idea that the system optimizes the representation of incoming signals, we derive the lateral connectivity that will achieve this for a set of local orientation-selective patches, as well as the complete spatial structure of a layer of such patches. We compare the results with various physiological measurements.
Introduction Classical studies of biological sensory systems use the following main technique: sensory stimuli are drawn from a pre-determined distribution P(stim) and presented to the animal; the ensemble associated with sensory response is collected and used to characterize the conditional distribution P(stim|resp) (or parameters thereof) as a model of sensory system function. However, most of the standard statistical tool used in neuroscience to estimate P(stim|resp) are valid under a very fundamental condition – that the samples used to estimate P(stim|resp) are drawn from the same distribution. This is obviously not the case in most studies of sensory system, where the samples are drawn explicitly from a different distribution, P(stim) (the sampling distribution), selected by the scientist. We demonstrate here that in this case the observed conditional distribution is P*(stim|resp) = P(stim|resp) *P(stim) and expectations estimated with this dataset are parameters of P*, not P. To characterize the actual functional properties of the system, one needs to use estimators developed within unequal probability sampling theory [1]. We apply one of these estimators, the HorvitzThompson estimator of the mean mHT = Σi xi/P(xi), to observations {xi} from the cricket cercal sensory system and illustrate the ensuing changes in apparent functionality (Figure 1).
The state of economic thought in the contemporary world is presented in brief, as well as its prospects related to the development of science and technology. With regard to the anniversary of the Economic Thought Journal it is pointed out: how the Journal started; its development, activities and impact on the economic society in Bulgaria; purposefulness and main themes of publications; reviews of authors and readers.
What is the meaning associated with a single action potential in a neural spike train? The answer depends on the way the question is formulated. One general approach toward formulating this question involves estimating the average stimulus waveform preceding spikes in a spike train. Many different algorithms have been used to obtain such estimates, ranging from spike-triggered averaging of stimuli to correlation-based extraction of “stimulus-reconstruction” kernels or spatiotemporal receptive fields. We demonstrate that all of these approaches miscalculate the stimulus feature selectivity of a neuron. Their errors arise from the manner in which the stimulus waveforms are aligned to one another during the calculations. Specifically, the waveform segments are locked to the precise time of spike occurrence, ignoring the intrinsic “jitter” in the stimulus-to-spike latency. We present an algorithm that takes this jitter into account. “Dejittered” estimates of the feature selectivity of a neuron are more accurate (i.e., provide a better estimate of the mean waveform eliciting a spike) and more precise (i.e., have smaller variance around that waveform) than estimates obtained using standard techniques. Moreover, this approach yields an explicit measure of spike-timing precision. We applied this technique to study feature selectivity and spike-timing precision in two types of sensory interneurons in the cricket cercal system. The dejittered estimates of the mean stimulus waveforms preceding spikes were up to three times larger than estimates based on the standard techniques used in previous studies and had power that extended into higher-frequency ranges. Spike timing precision was ∼5 ms.
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