How intrinsic neuronal heterogeneity shapes the cross-correlation functions between spike trains

Germ cells of aquatic organisms are complex systems whose growth and development depends on many factors, one of which is the composition of the aquatic environment. We used parameters in our analysis from aggregate data available from published literature. They are data of the transmembrane potential of the germinal cells of Misgurnus fossilis (Linnaeus, 1758) at the development stage from 180th to 360th minutes. Embryos were incubated in an environment with nickel, cobalt, tin, and zinc ions and without them. Plotted lines of the transmembrane potential were digitized and calibrated at intervals of 10 minutes. Rows of numerical values of the transmembrane potentials were obtained. These rows were used for calculation of autocorrelation and cross-cross-correlation functions. It was established that the transmembrane potential describes nonperiodic and quasi-periodic oscillations. The higher statistically significant values of the autocorrelation coefficients were observed in the first lags. Autocorrelation analysis indicates that the periods of oscillations of the transmembrane potential increase with the action of nickel, cobalt, tin and zinc on the germ. The phenomena and processes that occur in the germ cell are well reflected at the initial stages of the auto-correction and are lost when the magnitude of the lag increases. The degree of similarity of transmembrane potentials with the help of cross-correlation analysis is quantitatively characterized. The distribution of fluctuations of cross-correlation functions with complex dynamics, which arise with time shifts both in the forward and reverse directions, were established. It is established that for large values of time shifts, the cross-correlation coefficient is a low-informative indicator, since information about the influence of the factor on the living system is lost. A graph for a given time shift was constructed. The connection between the nodes is the magnitude of the cross-correlation coefficients between the vapor of the transmembrane potentials, which indicate the degree of similarity of the bioelectric processes. Graphs will be used for qualitative and quantitative study of system dynamics. The obtained results confirm the existence of a close relationship between environmental nickel, cobalt, tin, and zinc and the oscillation of transmembrane potential during early embryogenesis.

Download Full-text

Development of technologies for reducing the error of traditional algorithms of correlation analysis of noisy signals

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2020-6-9-16 ◽

2020 ◽

pp. 9-16

Author(s):

Telman A. Aliev ◽

Naila F. Musaeva ◽

Narmin E. Rzayeva ◽

Ana I. Mammadova

Keyword(s):

Correlation Analysis ◽

Correlation Functions ◽

Cross Correlation ◽

Observation Time ◽

Noisy Signal ◽

Factors Affecting ◽

Useful Signal ◽

Noisy Signals ◽

Traditional Technologies ◽

The Cross

The authors analyze the factors affecting the errors in the estimates of the correlation functions of the noisy signals when using traditional calculation algorithms. It is shown that the sum noise of the noisy signal in many cases consists of the noise caused by external factors and the noise caused by the initiation of various defects during the operation of control objects. For this reason, in order to eliminate the error in the results of the correlation analysis of noisy signals, it is necessary to create algorithms and technologies for determining the estimate of the noise variance and the cross-correlation functions between the useful signal and the noise. For this purpose, appropriate algorithms and technologies are proposed that open up the possibility of reducing the error of traditional technologies for determining the estimates of correlation functions. With the purpose of reducing the error of the results of correlation analysis, a technology is proposed for determining the approximate equivalent samples of the noise of the noisy signals. It is shown that using the equivalent noise samples, it is possible to obtain results that are identical to the results of using real samples of the noise in the correlation analysis of the same signals. Moreover, by extracting the equivalent noise samples from the noisy signal, the equivalent samples of the useful signal are also determined, which allow determining the estimates equivalent to the estimates of the correlation functions of the useful signal. At the same time, having equivalent noise samples and useful signal samples, the estimates of the cross-correlation function between the useful signal and the noise are determined. The study have shown that despite certain errors in the equivalent samples compared to the true samples, with a sufficient observation time using equivalent samples, the error of traditional technologies for the correlation analysis of noisy signals can be significantly reduced. These technologies can also be used to correct errors in the results of the analysis of experimental data in information-measuring and other measuring complexes and systems, which will significantly improve their metrological characteristics.

Download Full-text

Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions

Neural Computation ◽

10.1162/neco.2008.08-08-847 ◽

2009 ◽

pp. 090202092741069-23 ◽

Cited By ~ 1

Author(s):

Michael Krumin ◽

Shy Shoham

Keyword(s):

Correlation Functions ◽

Cross Correlation ◽

Spike Trains

Download Full-text

Estimating Membrane Voltage Correlations From Extracellular Spike Trains

Journal of Neurophysiology ◽

10.1152/jn.000889.2002 ◽

2003 ◽

Vol 89 (4) ◽

pp. 2271-2278 ◽

Cited By ~ 23

Author(s):

Jessy D. Dorn ◽

Dario L. Ringach

Keyword(s):

Correlation Coefficient ◽

Cross Correlation ◽

Spike Trains ◽

Membrane Voltage ◽

Upper And Lower Bounds ◽

Nominal Data ◽

Order Of Magnitude ◽

The Mean ◽

The Cross ◽

Measure Of Association

The cross-correlation coefficient between neural spike trains is a commonly used tool in the study of neural interactions. Two well-known complications that arise in its interpretation are 1) modulations in the correlation coefficient may result solely from changes in the mean firing rate of the cells and 2) the mean firing rates of the neurons impose upper and lower bounds on the correlation coefficient whose absolute values differ by an order of magnitude or more. Here, we propose a model-based approach to the interpretation of spike train correlations that circumvents these problems. The basic idea of our proposal is to estimate the cross-correlation coefficient between the membrane voltages of two cells from their extracellular spike trains and use the resulting value as the degree of correlation (or association) of neural activity. This is done in the context of a model that assumes the membrane voltages of the cells have a joint normal distribution and spikes are generated by a simple thresholding operation. We show that, under these assumptions, the estimation of the correlation coefficient between the membrane voltages reduces to the calculation of a tetrachoric correlation coefficient (a measure of association in nominal data introduced by Karl Pearson) on a contingency table calculated from the spike data. Simulations of conductance-based leaky integrate-and-fire neurons indicate that, despite its simplicity, the technique yields very good estimates of the intracellular membrane voltage correlation from the extracellular spike trains in biologically realistic models.

Download Full-text

Double, triple and quadruple-line spectroscopic binary candidates within the Gaia-ESO Survey

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317005567 ◽

2017 ◽

Vol 12 (S330) ◽

pp. 329-330

Author(s):

Thibault Merle ◽

Sophie Van Eck ◽

Alain Jorissen ◽

Mathieu Van der Swaelmen ◽

Gregor Traven ◽

...

Keyword(s):

Correlation Functions ◽

Cross Correlation ◽

Spectroscopic Binary ◽

Data Release ◽

The Galaxy ◽

Different Populations ◽

The Cross

AbstractThe Gaia-ESO Survey (GES, Gilmore et al. 2012) provides a unique opportunity to detect spectroscopically multiplicity among different populations of the Galaxy using the cross-correlation functions (CCFs). We present here the GES internal Data Release 4 (iDR4) results of the detection of double, triple and quadruple-line spectroscopic binary candidates (SBs) and discuss some peculiar systems.

Download Full-text

Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions

Neural Computation ◽

10.1162/neco.2009.08-08-847 ◽

2009 ◽

Vol 21 (6) ◽

pp. 1642-1664 ◽

Cited By ~ 26

Author(s):

Michael Krumin ◽

Shy Shoham

Keyword(s):

Correlation Functions ◽

Point Processes ◽

Cross Correlation ◽

Spike Trains ◽

Correlation Structure ◽

Distributed Processes ◽

New Strategy ◽

Neuronal Stimulation ◽

Analytical Formulas ◽

Rate Processes

Emerging evidence indicates that information processing, as well as learning and memory processes, in both the network and single-neuron levels are highly dependent on the correlation structure of multiple spike trains. Contemporary experimental as well as theoretical studies that involve quasi-realistic neuronal stimulation thus require a method for controlling spike train correlations. This letter introduces a general new strategy for generating multiple spike trains with exactly controlled mean firing rates and correlation structure (defined in terms of auto- and cross-correlation functions). Our approach nonlinearly transforms random gaussian-distributed processes with a predistorted correlation structure into nonnegative rate processes, which are then used to generate doubly stochastic Poisson point processes with the required correlation structure. We show how this approach can be used to generate stationary or nonstationary spike trains from small or large groups of neurons with diverse auto- and cross-correlation structures. We analyze and derive analytical formulas for the high-order correlation structure of generated spike trains and discuss the limitations of this approach.

Download Full-text