Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Models of stochastic $$\hbox {Ca}^{2+}$$ spiking

Complexity and limited knowledge render it impractical to write down the equations describing a cellular system completely. Cellular biophysics uses hypotheses-based modelling instead. How can we set up models with predictive power beyond the experimental examples used to develop them? The two textbook systems of cellular biophysics, $$\hbox {Ca}^{2+}$$ Ca 2 + signalling and neuronal membrane potential dynamics, both face this question. Both systems also have a non-equilibrium feature in common: on different time scales and for different observables, they exhibit stochastic spiking, i.e., sequences of stereotypical events that are separated by statistically distributed intervals, the interspike intervals (ISI). Here we review recent progress on the description of $$\hbox {Ca}^{2+}$$ Ca 2 + spikes in terms of blips, puffs and cellular $$\hbox {Ca}^{2+}$$ Ca 2 + spikes and focus on stochastic models that can explain the statistics of the single ISIs, in particular its mean and variance and the cell-to-cell variability of these statistics. We also review models of the stochastic integrate-and-fire type and measures like the spike-train power spectrum or the serial correlation coefficient that are used to describe neuronal spike trains. These concepts from computational neuroscience might be applicable for understanding long-term memory effects in $$\hbox {Ca}^{2+}$$ Ca 2 + spiking that extend beyond a single ISI, such as cumulative refractoriness.

A study on continuous inspection of markov processs with a clearance interval

Dodge’s continuous sampling plan-1 (CSP-1) with clearance interval zero may be inefficient if there is serial correlation between successive units which are Markov dependent and a clearance interval greater than zero is appropriate. For such a situation, the average outgoing quality limit (AOQL) expression has been obtained and, when the serial correlation coefficient of the Markov chain is assumed to be known a priori, it is numerically demonstrated that smaller AOQL values are achieved numerically for values of the clearance interval from 1 to 4, by improving the performance of CSP-1.

Assessment of drought across central Sudan using UNEP dryness ratio

The objective of this paper is to improve our perception of drought in central Sudan. This has been realized by detailing the changes that occurred in the dryness ratio (rainfall/potential evapotranspiration) of the United Nations Environment Programme (UNEP) during the period 1941–2005. Eight representative stations of the area were selected and their dryness ratios examined on annual and monthly bases. A trend towards intensifying and more recurrent drought has been found. This trend is particularly significant in the arid areas. Statistically significant increase in areal coverage of drought has occurred. Substantial changes took place in the severity and frequency of drought between 1941–1970 and 1971–2005 over the whole area. Moreover, the early to mid-1970s, mid-1980s, early 1990s and early 2000s were determined as common drought years and were among the driest 10 years. The analysis also revealed high and generally increasing inter-annual variability of the dryness ratio. There is not a dominant short-term persistence in the data, as assessed by the lag-one serial correlation coefficient. Early forecast of the moisture condition during the rest of the season could merely be accomplished at small scale in the area. These results indicate that drought in the study area is irregular.

NEAR-INTEGRATED RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES

We determine the limiting behavior of near-integrated first-order random coefficient autoregressive RCA(1) time series. It is shown that the asymptotics of the finite-dimensional distributions crucially depends on how the critical value 1 is approached, which determines whether the process is near-stationary, has a unit root, or is mildly explosive. %In a second part, we derive the limit distribution of the serial correlation coefficient in the near stationary and the mildly explosive settings under very general conditions on the parameters. The results obtained are in accordance with those available for first-order autoregressive time series and can hence serve as an addition to existing literature in the area.

Einige Bemerkungen zur Berechnung des Autokorrelationskoeffizienten in der Zeitreihenanalyse / Some Remarks on the Calculation of the Serial Correlation Coefficient in the Analysis of Time Series

ZusammenfassungIn der Zeitreihenanalyse wird der Autokorrelationskoeffizient anders berechnet als der gewöhnliche Korrelationskoeffizient. Es wird der Unterschied zwischen den beiden Versionen untersucht, und zwar hauptsächlich im Sinn der deskriptiven Statistik. Es stellt sich heraus, daß die Version der Zeitreihenanalyse tendenziell dem Absolutbetrag nach kleiner ausfällt als der gewöhnliche Korrelationskoeffizient. Dieses Resultat wird durch asymptotische Überlegungen und einige einfache Modell-Zeitreihen gestützt. Als Stichprobenfunktionen betrachtet werden einige Tatsachen betreffend die Autokovarianz abgeleitet, die jedoch ein komplizierteres Verhalten zeigen.