Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented which builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low variance Gaussian process. It is found that, in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale which is set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies, with little modification, to point process spectra, and is of utility in studying a point process driven by a continuous stimulus. While the material discussed is of general applicability to point processes attention will be confined to sequences of neuronal action potentials (spike trains) which were the motivation for this work.Comment: 33 pages, 9 figure

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio

Exploring the potential impact of relational coherence on persistent rule-following : the first study

Rule-governed behavior and derived relational responding have both been identified as important variables in human learning. Recent developments in the relational frame theory (RFT) have outlined a number of key variables of potential importance when analyzing the dynamics involved in derived relational responding. Recent research has explored the impact of one of these variables, level of derivation, on persistent rule-following and implicated another, coherence, as possibly important. However, no research to date has examined the impact of coherence on persistent rule-following directly. Across two experiments, coherence was manipulated through the systematic use of performance feedback, and its impact was examined on persistent rule-following. A training procedure based on the implicit relational assessment procedure (IRAP) was used to establish novel combinatorially entailed relations that manipulated the feedback provided on the trained relations (A-B and B-C) in Experiment 1, and on the untrained, derived relations (A-C) in Experiment 2. One of these relations was then inserted into the rule for responding on a subsequent contingency-switching match-to-sample (MTS) task to assess rule persistence. While no significant differences were found in Experiment 1, the provision or non-provision of feedback had a significant differential impact on rule-persistence in Experiment 2. Specifically, participants in the Feedback group resurged back to the original rule for significantly more responses after demonstrating contingency-sensitive responding than did the No-Feedback group, after the contingency reversal. The results highlight the subtle complexities that appear to be involved in persistent rule-following in the face of reversed reinforcement contingencies

How behavioral constraints may determine optimal sensory representations

The sensory-triggered activity of a neuron is typically characterized in terms of a tuning curve, which describes the neuron's average response as a function of a parameter that characterizes a physical stimulus. What determines the shapes of tuning curves in a neuronal population? Previous theoretical studies and related experiments suggest that many response characteristics of sensory neurons are optimal for encoding stimulus-related information. This notion, however, does not explain the two general types of tuning profiles that are commonly observed: unimodal and monotonic. Here, I quantify the efficacy of a set of tuning curves according to the possible downstream motor responses that can be constructed from them. Curves that are optimal in this sense may have monotonic or non-monotonic profiles, where the proportion of monotonic curves and the optimal tuning curve width depend on the general properties of the target downstream functions. This dependence explains intriguing features of visual cells that are sensitive to binocular disparity and of neurons tuned to echo delay in bats. The numerical results suggest that optimal sensory tuning curves are shaped not only by stimulus statistics and signal-to-noise properties, but also according to their impact on downstream neural circuits and, ultimately, on behavior.Comment: 24 pages, 9 figures (main text + supporting information