Serial Correlogram Research Articles

Approximate Distributions for the Various Serial Correlograms

Saddlepoint methods are used to approximate the joint density of the serial correlogram up to lag m. Jacobian transformations also lead to approximations for the related partial correlogram and inverse correlogram. The approximations consider non-circularly and circularly defined models in both the null and the non-null settings. The distribution theory encompasses the standard non-circularly defined correlogram computed from least-squares residuals removing arbitrary fixed regressors. Connections of the general theory to the approximations given by Daniels and by Durbin in the circular setting are indicated. The double-saddlepoint density and distribution approximations are given for the conditional distribution of the non-circular lag m serial correlation given the previous lags from order 1 to m-1. This allows for the computation of p values in conditional inference when testing that the model is AR(m-1) versus AR(m). Numerical comparisons with the tests of Daniels and of Durbin suggest that their tests based on circularity assumptions are inadequate for short non-circular series but are in close agreement with the non-circular tests for moderately long series.

Microwave effects on input resistance and action potential firing of snail neurons.

Excitable tissues have been reported to respond to weak microwave (MW) fields, possibly by nonlinear perturbation of a cellular process such as ion conduction across membranes. We sought effects of MW (continuous wave, 2.45 GHz, specific absorption rates 12.5 or 125 mW/g) on input resistances and action potential (AP) intervals of neurons in ganglia of snails (Helix aspersa), at 20.9 +/- 0.1 degrees C. At 12.5 mW/g, input resistance did not change during irradiation, but increased (p < 0.05) afterward. At 125 mW/g, input resistance during irradiation was lower than in unirradiated controls. Serial correlograms changed marginally more frequently in MW experiments than in controls, but the changes had no consistent pattern. The AP firing rate was affected by MW, but the direction was not consistent across cells. When AP generation was modeled as being due to a neuronal input current, MW did not affect its mean, standard deviation, or autocorrelation. Unlike MW, temperature changes caused neurons to respond robustly and reversibly. Threshold for changing input resistance was 0.63 degree C. The data suggest that MW may enhance degenerative effects such as metabolic rundown or loss of ion channel patency, but do not indicate a specific mechanism for MW interaction with neurons.

Synaptic noise in spike trains of normal and denervated electroreceptor organs

The sequence of interspike intervals of the spontaneous activity in denervated electroreceptor organs of the catfish is analysed with several statistical techniques: visual inspection of dot displays, interval histograms, serial correlograms, tests for stationarity and trends, and tests for renewal properties, based on the spectrum of intervals. The interspike interval train of primary afferents can usually be treated as a renewal process. Following denervation, a number of non-renewal properties emerge. The interval histogram of the renewal spike trains can be fitted well with a gamma probability density function; non-renewal cases need a more complex approach. We propose that the stochastic fluctuations in interval duration arise from randomly occurring quantal depolarizations (Stein's model of stochastic neuronal excitation). Two important properties with regard to synaptic transduction are: afferent firing results from capture of a limited number of depolarizing quanta; and the quantal input rate and the threshold for firing appear to be correlated.

Changes in the firing properties of neurons in the dentate gyrus with denervation and reinnervation: Implications for behavioral recovery

The present study evaluates how the activity of neurons in the dentate gyrus of adult rats is affected by removal of the projection from the ipsilateral entorhinal cortex (EC) and by the reinnervation which follows this injury. We evaluated the average firing rate and characterized interstimulus interval (ISI) parameters for single units in the granule cell layer of the dentate gyrus in two ways: (I) by recording the activity of single neurons prior to and at 15 min and 2, 4, 6, and 8 h. following a unilateral EC lesion; and (II) by calculating average rates for samples of neurons at 2, 4, 6, 8, and 14 days postlesion. Of a sample of 31 neurons whose activity was recorded before and after an EC lesion, 27 (87%) showed decreased activity, and 4 (13%) showed increased activity. The average prelesion firing rate for all cells was 6.5 spikes/s, and the average rate decreased to 2.5 spikes/s at 15 min postlesion. The average firing rate remained depressed for the 8-h recording session, although it was not possible to maintain the recordings for all cells. Evaluations of ISI histograms revealed three general types: (a) a skewed distribution with a single peak; (b) a bimodal distribution with an early peak at intervals of a few ms and a later peak at approximately the same interval as the distributions with single peaks; (c) cells with low firing rates and more or less rectangular distributions. Cells producing each type of ISI histogram exhibited decreases in firing after EC lesions. However, the 4 neurons that exhibited increases in firing had relatively low firing rates prior to the lesion. There were no significant changes in the coefficient of variation or skewness of the ISI histograms following the lesions. The statistical dependency of successive ISIs as revealed by serial correlograms was relatively low in the prelesion sample, and showed no consistent change following the lesion. Comparison of the average firing rates of different samples of neurons at 2–14 days postlesion revealed that the average activity of neurons in the granule cell layer remained depressed at 2 and 4 days postlesion. However, the activity recovered to a level comparable to the prelesion control by 8 days postlesion. The time course of recovery of unit activity was comparable to the time course of sprouting as revealed by previous electrophysiological studies. Since sprouting of the dentate gyrus has previously been shown to be correlated with recovery of function, we discuss how the recovery of unit activity might play a role in the behavioral recovery.

The variability of the maintained discharge of cat dorsal lateral geniculate cells.

Maintained discharge in the presence of a steady background luminance was analysed from forty-eight cells in the A laminae of the dorsal lateral geniculate nucleus of cat. Cells were categorized as XG or YG and, in most cases, as on-or off-centre. The temporal contrast sensitivity function of twenty-seven of the cells was measured using drifting gratings of the optimal spatial frequency. The maintained discharge was characterized by several simple descriptors, including the interval distribution, mean firing rate, and coefficient of variability. Its temporal organization was revealed by two indicators of correlational properties, the normalized autocovariance and the serial correlogram, and more effectively, by the less familiar plot of the standard deviation of firing rate versus sample duration. The statistics revealing temporal organization of the maintained discharge indicated that the variability of firing was nearly, but not quite, derived from a renewal process. The maintained discharges of seven cells were studied for more than one luminance level. Mean luminance did not appear to have any consistent effect upon the statistics of the maintained discharge. The temporal filtering properties of lateral geniculate cells were deduced from a comparison of the temporal contrast sensitivities of geniculate neurones (Troy, 1983b) and retinal ganglion cells (Lennie, 1980). Analyses showed that the maintained discharge of retinal neurones passed through this filter could not account for the observed statistics of the maintained discharge of geniculate neurones. It is proposed that additional noise is added to the retinal signal at the level of the lateral geniculate. Models are presented to explain how the signals might be filtered in a way that does not also affect the added noise.

Statistics of the maintained discharge of cat retinal ganglion cells.

Action potentials were recorded from single fibres in the optic tracts of anaesthetized cats. Continuous records were obtained at various levels of scotopic and mesopic retinal illumination. In some cases, the light intensity was modulated by a pseudorandom Gaussian white-noise signal. The maintained discharge of on-centre neurones increased while the maintained discharge of off-centre neurons decreased with increased illumination of the receptive field centre. For both cell types, the coefficient of variation declined with increased rate of discharge. There was minimal short-term dependency in the firing patterns, and it was unaffected by the level of retinal illumination. Virtually all of the structure revealed by the normalized autocovariance functions could be attributed to the shape of the interval distributions. The first few coefficients of the serial correlogram were slightly negative. The magnitude of this negativity was not related to illumination. Long-term dependency in the firing pattern was also quite small; the standard deviations of the mean rate in samples of about 1 sec duration were only slightly less than would be predicted from the interval distributions. This dependency tended to increase at higher retinal illuminations. Neural discharges elicited by Gaussian modulation of the light were strikingly different from those elicited by steady light. Modulation caused the first coefficient of the serial correlogram to become more positive, while the next several coefficients became more negative. A corresponding pattern could be seen in the normalized autocovariance functions, and in the differences between the normalized autocovariance and normalized autoconvolution. Long-term dependency also increased dramatically, such that the standard deviations of mean rate were about 60% of what would be expected given the interval distributions observed. These results place a number of constraints upon the ways in which intrinsic noise in the retina may enter the visual processing network. Two alternative models consistent with the data are presented.

Retinal processing of intrinsic ad extrinsic noise.

1. Recordings were made from single ganglion cells in the isolated retinas of goldfish. Statistics of the maintained discharge were computed for steady-state firing in the dark, in the presence of a steady-adapting light confined essentially to the center of the receptive field, and in the presence of the same adapting light modulated by Gaussian white noise. 2. Steady adapting lights effected a significant initial change in firing rate and affected sensitivities to test probes. After a new minutes, however, the rate returned to a moderate level. There was no consistent relationship between firing in the dark and illuminated conditions, nor was there a consistent relationship between the values of the coefficient of variation of firing in the dark and in light, although some individual cells showed changes in these properties when illuminated. 3. There was no consistent change in the organization of the firing in dark and in steady light. Neither the normalized autocovariances nor the serial correlograms, indicators of short-term order, were significantly affected by light. Similarly, plots of the standard deviation of rate versus sample duration, an indicator of long-term structure, were not altered by illumination. The intrinsic noise thus appears unaffected by retinal illumination. 4. Gaussian modulation of an adapting light (extrinsic noise) increased the coefficient of variation; it also dramatically increased mean firing rate. This effect was observed in both red-on and red-off cells; it indicates a nonlinearity that is present even in the spatially linear X-like neurons. 5. Gaussian modulation of an adapting light made the short-duration values of the normalized autocovariances slightly more positive. Similarly, modulation made the first two or three coefficients of the serial correlogram more positive; this indicates low pass filtering of the extrinsic noise. 6. Gaussian modulation of an adapting light had no effect on the plots of standard deviation of rate versus sample duration other than simple translation due to increased variability. Since the form of these plots in the absence of modulation implies high-pass filtering of the intrinsic noise, the extrinsic noise must also be processed by the same (or a similar) high-pass filter. 7. A model is proposed in which extrinsic signals are band pass filtered by a low-pass and a high-pass filter in cascade. The intrinsic variability evident in the maintained discharge is apparently injected between the two filters. Alternative possibilities are discussed.

Analysis of bimodal interspike interval histograms of primary muscle spindle endings in active triceps surae muscles of cats.

A feature frequently observed in interspike interval histograms (IH) derived from stationary Ia fibre discharge patterns was a bimodality suggesting a mixed population composed of two sub-populations of possibly different origins. To verify this hypothesis a separation of these subpopulations was attempted by assuming a Gaussian distribution for the longer intervals. The success of such a separation depended on the distinctness of the histogram peaks and the relative sizes of each mode. Both factors in turn depended on the overall muscle length and, hence, on the mean spindle discharge rate. The smaller intervals were then isolated from the spike trains and submitted to further statistical analysis. By averaging overall muscle tension with respect to the smaller intervals, the latter could often be linked to tension trajectories which were of higher amplitude and faster time course than the trajectories obtained by averaging with respect to the rest of the spikes. In some cases, auto-correlation histograms of isolated small intervals as well as serial correlograms computed for all intervals indicated that some muscle spindle afferents responded sensitively to activity of single motor units. This would confirm recent results of Cameron et al. (1980).

Stochastic properties of gustatory impulse discharges in rat chorda tympani fibers.

1. The present study was intended to elucidate the role of temporal patterns of impulse discharges of the gustatory primary afferents in the coding of taste qualities by the use of simultaneous analyses of the across-neuron patterning (5) and the temporal patterning of impulses. 2. Impulse discharges of 43 rat chorda tympani fibers elicited by gustatory stimulation (0.1 M NaCl, 0.5 M sucrose, 0.01 N HCl, 0.02 M quinine hydrochloride, 0.3 M KCl, and 0.02 M saccharin sodium) were recorded. The temporal patterns of impulse discharges elicited by these stimuli were statistically analyzed both in an initial dynamic phase and a succeeding stationary phase of responses. In the dynamic phase, the time courses of firing frequency were studied; however, these were not clearly associated with the qualities of taste stimuli. In the stationary phase, the stochastic properties of impulse trains were studied regarding the impulse trains as a stochastic point process (30). In this study, interspike interval histograms (ISI histograms), joint interval histograms, serial correlograms, and autocorrelograms were computed. 3. In general, the distribution patterns of ISI histogram were not absolutely specific to the taste qualities. However, the gamma or the exponential distribution occurred most often with 0.1 M NaCl, and the bimodal or the skewed distribution was dominated with 0.5 M sucrose stimulation among the stimuli tested. The rhythmic discharges did not occur exclusively with the sweet taste stimulation, though they occurred more often with the sweet taste stimulation than with other taste stimulations. The joint interval histogram and the serial correlogram were used to examine the stochastic properties of impulse trains with particular reference to the time dependence in the impulse trains. Generally, the time dependence was not concerned with the taste qualities. 4. The chorda tympani fibers were classified into three types according to the magnitude of responses and the temporal patterns of impulse discharges. The neurons predominantly responsive to NaCl and unresponsive to sucrose were classified as type I neurons. The remaining neurons, which moderately responded to both NaCl and sucrose, were further categorized into type II neurons and type III neurons, depending on their temporal patterns of impulse discharge. The type II neurons tended to show the rhythmic or burstlike firing of impulses in response to more than one kind of taste stimuli. 5. The results showed that the taste quality was represented in the characteristic temporal patterning of impulses as well as in the across-neuron patterning of responses. The possible origin of the temporal discharge pattern and its significance in gustatory information processing were discussed on the basis of the neuron types described above.

Contaminated Renewal Processes and the Serial Correlogram

We derive the mean and variance of the sample serial correlation coefficients of a finite portion of a renewal process, the realization of which is contaminated by the addition or deletion of one point. This enables us to determine the asymptotic power of a test that the contaminated process is significantly different from a renewal process. In contrast to the signficant changes in serial correlation coefficient observed in simulations by Shiavi and Negin [1], our analysis shows that the expected differences are rather small. We discuss the work of ten Hoopen [2] which has a similar motivation.

Single neuron sequential interspike intervals: Measurement, teleprocessing, and analysis

Successive neuronal interspike intervals (ISI) were measured sequentially. Code numbers, each one characteristic of an experimental manipulation, were added to the measured ISI. The resulting file was sent automatically through MODEM and telephone to an UNIVAC 1110 computer by way of a microprocessor system. The UNIVAC computer was programmed to extract each code number from the ISI file and to create a descriptive index by use of a set of questions to the experimenter, each one depending on the code number encountered in the ISI file. Each element of the descriptive index contained, as pointer, the address of the very ISI where the manipulation started or ended. From these data, a classical spike rate versus time diagram as well as a sequential probability density function were computed and some spike train characteristics were automatically estimated from an autocorrelogram and a serial correlogram. An example is given to illustrate the results obtained with the system.

Firing rate of a retinal neuron are not predictable from interspike interval statistics

The intervals between successive action potentials (impulses, or "spikes") produced the maintained firing of a neuron (ISIs) are often treated as if they were independent on each other; that is, an impulse train is considered as a stationary renewal process. If this is so, the variability of the mean rate of firing impulses in a sequence of temporal windows should be predictable from the distribution of ISIs. This was found not to be the case for the maintained firing of retinal ganglion cells in goldfish. Although some evident nonstationarity sometimes resulted in greater variability of the observed rate distributions than those predicted (for relatively long temporal windows), as a general rule the observed rate distributions were considerable less dispersed than would be predicted by sampling of the ISI distributions. This was taken as evidence of long-term serial dependency between successive ISIs; however, two standard test for dependency (autocorrelations and serial correlograms failed to to reveal structure of sufficiently long duration to account for the effect noted.

The effects of recurrent inhibitory feedback in shaping discharge patterns of motoneurones excited by phasic muscle stretches

The spinal motoneurone-Renshaw cell circuitry, which constitutes an intricate negative feedback system, was investigated with respect to its significance for the shaping of motoneurone firing patterns excited by strong phasic inputs. Discharge patterns of single motoneurones were compared before and after opening of the recurrent inhibitory pathways by Renshaw cell blocking agents. Serial correlograms computed from motoneurone interspike intervals which were modulated by sinusoidal muscle stretch replicated the input periodicity, but were not changed in any consistent manner after Renshaw cell blockage. Longterm regularity and periodicity of motoneurone firing, i.e. the overall response characteristics, do not appear to be significantly determined by Renshaw cells under these conditions. The modulation of motoneurone interspike intervals was assessed by computing power spectra for corresponding instantaneous frequencies. The harmonic contents (2nd and 3rd harmonic of the driving frequency) of these spectra tended to decrease after Renshaw cell depression. The distortion of signal transmission in a single motoneurone channel is thus stronger with, than without, the recurrent inhibitory feedback. The implication of these findings for signal transmission from the spinal cord to the muscle is discussed.

Applications of queuing theory to some problems in neuronal circuitry*

This paper discusses mathematical models for neurons and neuron-pair networks. Models are developed in which the parameters are related to basic physiological properties. Single-neuron models are treated first. The membrane-potential decay is modeled as a linear function, making it analogous to the virtual waiting time in a queue. Both spatial and temporal summation are incorporated into the model. Networks consisting of two neurons are then analyzed. It is shown that even though each neuron generates a renewal process, the interaction of the spike trains produces a nonrenewal process. A feedback inhibitory network is found to generate a bursting pattern of spikes. Expressions for the interspike-interval density function and the serial correlogram are derived based on the points of regenerating in the process, and verified by computer simulation. Finally, the feedback neuron-pair model is applied to spike-train data from the hippocampus of a rabbit.

Marking Behaviour of Some Viverridae and Felidae Time-Interval Analysis of the Marking Pattern

[Several mammalian groups mark their surroundings by rubbing off their skin glands and/or by squirting urine. This pattern is thought to serve chemocommunication. In this study the marking behaviour of a number of captive Carnivora was ohserved. The significance of marking in these circumstances is discussed. 2. Marking is performed during a period of motor activity in series of fast, consecutive acts; it is accompanied, depending on the animal (species), by several, mostly orienting, acts. Composition (coherence) and sequence (transition probabilities) of this marking pattern are analysed for four animals, Netti (Genetta felina), Shiva (Prionailurus bengalensis), Ferdinand and Stuttgart ♀(Lcopardus geoffroyi). Coherence appeared to be susceptible to several factors, the sequence, however, appeared well fixed and uninfluenced by all factors investigated (season, time of day, human presence, other animals). Its functional significance is discussed and elucidated. Arguments are brought forward to show that some of the accompanying acts serve a visual display function. 3. Time-interval analysis has been carried out chiefly by computing arithmetic means, standard deviations and serial correlation coefficients of the intervals. Season, time of day, and extension of the bladder investigated in one animal influence frequency and interval; they do not, however, influence the variation coefficient and the serial correlogram. These last two results suggest a high stability of the system. Interdependency of the periodic features in the occurrence of some separate acts was found, indicating a relative coordination in the sense of VON HOLST (1939). The part-time integration of an act in a complex pattern does not preclude it from being performed independently or within the context of another pattern, as is best exemplified by sniffing; within the pattern, the closing act - in the present case marking - determines occurrence, duration and choice of those preceding it (Relative Hierarchy of Moods, LEYHATUSEN, 1965)., Several mammalian groups mark their surroundings by rubbing off their skin glands and/or by squirting urine. This pattern is thought to serve chemocommunication. In this study the marking behaviour of a number of captive Carnivora was ohserved. The significance of marking in these circumstances is discussed. 2. Marking is performed during a period of motor activity in series of fast, consecutive acts; it is accompanied, depending on the animal (species), by several, mostly orienting, acts. Composition (coherence) and sequence (transition probabilities) of this marking pattern are analysed for four animals, Netti (Genetta felina), Shiva (Prionailurus bengalensis), Ferdinand and Stuttgart ♀(Lcopardus geoffroyi). Coherence appeared to be susceptible to several factors, the sequence, however, appeared well fixed and uninfluenced by all factors investigated (season, time of day, human presence, other animals). Its functional significance is discussed and elucidated. Arguments are brought forward to show that some of the accompanying acts serve a visual display function. 3. Time-interval analysis has been carried out chiefly by computing arithmetic means, standard deviations and serial correlation coefficients of the intervals. Season, time of day, and extension of the bladder investigated in one animal influence frequency and interval; they do not, however, influence the variation coefficient and the serial correlogram. These last two results suggest a high stability of the system. Interdependency of the periodic features in the occurrence of some separate acts was found, indicating a relative coordination in the sense of VON HOLST (1939). The part-time integration of an act in a complex pattern does not preclude it from being performed independently or within the context of another pattern, as is best exemplified by sniffing; within the pattern, the closing act - in the present case marking - determines occurrence, duration and choice of those preceding it (Relative Hierarchy of Moods, LEYHATUSEN, 1965).]

Analysis of point process signals applied to motor unit firing patterns: I. Superposition of independent spike trains

The aim of the present study was to examine whether statistical methods common for the analysis of point process signals could be applied to the electromyogram, in order to extract information concerning the physiological mechanisms involved. This was carried out on the assumption that the electromyogram can be treated as the superposition result of a number of point process signals, each representing the firing pattern of one motor unit. No correlated activity between the different spike trains was assumed at this stage. A digital model for the superposition of event sequences was constructed, assigning to the individual sequences a Gaussian interval distribution. The effects of varying the number of spike trains participating in the superposition process, and changing the mean rates of firing were explored. The statistical methods used in the analysis were serial correlation, event autocorrelation, and power spectrum studies. It has been found that serial correlograms of the superimposed processes may be helpful in detecting the number of spike trains involved in the superposition, whereas power spectrum studies are useful in determining the mean rates of firing of the individual sequences.

Effect of skewness in three stochastic Pentad river flow models on crossing properties of synthesized data

Large samples are synthesized through autoregressive, fast fractional noise, and broken line models, based on a practically significant pentad time unit, for four stations in the British Wye catchment. Hydrologic characteristics such as the numbers, durations, and magnitudes of droughts and floods are assessed by means of the crossing properties at critical levels in the time series. If a Gaussian distribution is applied to the stochastic component, crossing properties other than surplus run lengths are unrealistic. Compatibility with historical properties is achieved by the incorporation of approximately twice the coefficient of skewness estimated from the original data through a transformation to a gamma function. Also there is agreement in serial correlograms and coefficients of skewness. In this way neither negative numbers nor outliers are generated through autoregressive models, but run lengths at extreme levels in data from all models need adjustment, and a closer fitting distribution function is desirable.

The effect of measurement errors on correlation estimates in interval sequences.

The serial correlogram (SCG) is used to determine the amount of dependence in spike-interval sequences. This communication demonstrates the effects of measurement errors [i.e., false alarms (FA's) and false dismissals (FD's) in spike-detection algorithms] on correlation coefficients when the sequence has a practical sample size.

A Theoretical Study of Serial Correlation of Spike Trains in A Second Order Neuron

Commonly, it is considered that in the nervous system the main bulk of information is coded in trains of action potentials so that information transfer is independent of the order of inter-spike intervals. Although the significance of the orderliness of events has been pointed out in many theoretical considerations of information transfer (Barlow, 1963; Bergstrom, 1969, 1972), direct empirical evidence in support of this concept has been difficult to obtain. As exceptions may be considered sensory signals elicited by periodic stimuli (Mountcastle et al., 1969). The question whether such properties of spike trains as described here contribute at all to the transfer of information in CNS remains open. It might be difficult to measure any relevant information code in a spike train with such a complicated and sensitive statistic as the serial correlogram. on the other hand, it seems justified to use serial correlation in selected cases in order to explore the functional structure of the neural pathways studied.

STAP-12: A library system for on-line assimilation and off-line analysis of event/time data

An open ended library system for neuronal spike train analysis is presented. The design is based on the experience with STAP-8, a spike train analysis program for the PDP-8/AX08 system. The system software and all I/O and analysis programs are written in assembly language for the standard PDP-12/A equipment. Single- or multi-channel assimilation of unit activity is possible by means of either AD-conversion of membrane potentials or event recording with Schmitt-trigger inputs. Multi-unit records of a single, non-selelctive electrode are sorted with respect to pre-defined threshold parameters. Data files (spike trains) with up to 2048 event times are saved on a LINC tape train library for off-line analysis. A set of 12 analysis programs is part of the basic STAP-12 system and covers the standard procedures, as interval histogram, autocorrelogram, crosscorrelogram, latency crosscorrelogram, auto- and crosscovariance estimates, serial correlogram, and Poisson parameter estimates. The user may extend the capacity of STAP-12, implementing his own specific programs.