scholarly journals Revealing Spectrum Features of Stochastic Neuron Spike Trains

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1011
Author(s):  
Simone Orcioni ◽  
Alessandra Paffi ◽  
Francesca Apollonio ◽  
Micaela Liberti
Keyword(s):  
Power Spectra ◽  
Maximum Error ◽  
Peak Frequency ◽  
Spike Trains ◽  
Simple Expression ◽  
Channel Noise ◽  
Neuron Spike ◽  
Neurophysiological Studies ◽  
Spectral Peaks ◽  
Stochastic Neuron

Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra.

scholarly journals Temporal Properties of Posterior Parietal Neuron Discharges During Working Memory and Passive Viewing

2007 ◽  
Vol 97 (3) ◽  
pp. 2254-2266 ◽  
Author(s):  
Frederik C. Joelving ◽  
Albert Compte ◽  
Christos Constantinidis
Keyword(s):  
Working Memory ◽  
Posterior Parietal Cortex ◽  
Memory Task ◽  
Power Spectra ◽  
Low Frequency ◽  
Spatial Location ◽  
Spike Trains ◽  
Memory Condition ◽  
Temporal Properties ◽  
Posterior Parietal

Working memory is mediated by the discharges of neurons in a distributed network of brain areas. It was recently suggested that enhanced rhythmicity in neuronal activity may be critical for sustaining remembered information. To test whether working memory is characterized by unique temporal discharge patterns, we analyzed the autocorrelograms and power spectra of spike trains recorded from the posterior parietal cortex of monkeys performing a visuospatial working-memory task. We compared the intervals of active memory maintenance and fixation and repeated the same analysis in spike trains from monkeys never trained to perform any kind of memory task. The most salient effect we observed was a decrease of power in the 5- to 10-Hz frequency range during the presentation of visual stimuli. This pattern was observed both in the working-memory condition and the control condition, although it was more prominent in the former, where it persisted after cue presentation when the monkeys actively remembered the spatial location of the stimulus. Low-frequency power suppression resulted from relative refractory periods that were significantly longer in the working-memory condition and presumably emerged from local-circuit inhibition. We also detected a spectral peak in the 15- to 20-Hz range, although this was more prominent during fixation than during the stimulus and working-memory periods. Our results are in line with previous reports in prefrontal cortex and indicate that unique temporal patterns of single-neuron firing characterize persistent delay activity, although these do not involve the appearance of enhanced oscillations.

scholarly journals High-frequency electrical activity of the brain in patients with hemispheric ischemic stroke in combination with cognitive functions

2021 ◽  
Vol 25 (6) ◽  
pp. 12-18
Author(s):  
L. B. Novikova ◽  
K. M. Sharapova ◽  
O. E. Dmitrieva
Keyword(s):  
Ischemic Stroke ◽  
Mathematical Analysis ◽  
Depressive Disorders ◽  
Brain Activity ◽  
Power Spectra ◽  
Peak Frequency ◽  
Gamma Rhythm ◽  
Eeg Data ◽  
Background Eeg ◽  
The Brain

Abstract. The mathematical analysis of electroencephalography (EEG) provides information about the functional state of the brain, expands the understanding of the mechanisms of interaction between different areas of the brain, increases the possibilities of diagnostics and allows to put forward new tasks in the field of studying brain activity. Aim. To assess changes in the gamma-rhythm in patients with hemispheric ischemic stroke in the most acute and acute periods in comparison with cognitive and anxiety-depressive disorders. Material and methods. The study included 32 patients with hemispheric ischemic stroke. All patients underwent complex clinical, neurological, instrumental and laboratory studies. The study and recording of the EEG was carried out on the 1st and 21st days of the disease, lasting 20 minutes. The method of mathematical analysis was used to estimate the power spectra and the peak frequency of the gamma — rhythm of the background EEG. Results. As a result of the study, it was found that cognitive and anxiety-depressive disorders are detected already in the most acute and acute periods of ischemic stroke. In the mathematical analysis of the EEG statistically significant correlations between the gamma — rhythm index and cognitive, anxiety-depressive disorders in the frontal, central temporal areas are noted. Conclusion. The complex of examination of patients should include, in addition to clinical and neuropsychological research, mathematical analysis of EEG data.

Intracortical connections are not required for oscillatory activity in the visual cortex

1997 ◽  
Vol 14 (6) ◽  
pp. 963R-979R ◽  
Author(s):  
Geoffrey M. Ghose ◽  
Ralph D. Freeman
Keyword(s):  
Visual Cortex ◽  
Visual Information ◽  
Close Agreement ◽  
Power Spectra ◽  
Spike Trains ◽  
Cortical Layer ◽  
Oscillatory Activity ◽  
Complex Cells ◽  
Firing Rates ◽  
Simple And Complex Cells

Abstractarises from the integration of signals from strongly oscillatory cells within the LGN. The model also predicts the incidence of 50-Hz oscillatory cells within the cortex. Oscillatory discharge around 30 Hz is explained in a second model by the presence of intrinsically oscillatory cells within cortical layer 5. Both models generate spike trains whose power spectra and mean firing rates are in close agreement with experimental observations of simple and complex cells. Considered together, the two models can largely account for the nature and incidence of oscillatory discharge in the cat's visual cortex. The validity of these models is consistent with the possibility that oscillations are generated independently of intracortical interactions. Because these models rely on intrinsic stimulus-independent oscillators within the retina and cortex, the results further suggest that oscillatory activity within the cortex is not necessarily associated with the processing of high-order visual information.

scholarly journals Optimizing Time Histograms for Non-Poissonian Spike Trains

2011 ◽  
Vol 23 (12) ◽  
pp. 3125-3144 ◽  
Author(s):  
Takahiro Omi ◽  
Shigeru Shinomoto
Keyword(s):  
Goodness Of Fit ◽  
Optimization Method ◽  
Spike Trains ◽  
Time Axis ◽  
Squared Error ◽  
Neurophysiological Studies ◽  
Inhomogeneous Density ◽  
Integrated Squared Error ◽  
The Mean ◽  
The Given

The time histogram is a fundamental tool for representing the inhomogeneous density of event occurrences such as neuronal firings. The shape of a histogram critically depends on the size of the bins that partition the time axis. In most neurophysiological studies, however, researchers have arbitrarily selected the bin size when analyzing fluctuations in neuronal activity. A rigorous method for selecting the appropriate bin size was recently derived so that the mean integrated squared error between the time histogram and the unknown underlying rate is minimized (Shimazaki & Shinomoto, 2007 ). This derivation assumes that spikes are independently drawn from a given rate. However, in practice, biological neurons express non-Poissonian features in their firing patterns, such that the spike occurrence depends on the preceding spikes, which inevitably deteriorate the optimization. In this letter, we revise the method for selecting the bin size by considering the possible non-Poissonian features. Improvement in the goodness of fit of the time histogram is assessed and confirmed by numerically simulated non-Poissonian spike trains derived from the given fluctuating rate. For some experimental data, the revised algorithm transforms the shape of the time histogram from the Poissonian optimization method.

Bursting Dynamics of a Model Neuron Induced by Intrinsic Channel Noise

2003 ◽  
Vol 03 (03) ◽  
pp. L265-L274 ◽  
Author(s):  
Saul L. Ginzburg ◽  
Mark A. Pustovoit
Keyword(s):  
Model Neuron ◽  
Power Spectra ◽  
Channel Noise ◽  
Interspike Intervals ◽  
Membrane Area ◽  
Stochastic Nature ◽  
Bursting Neuron ◽  
Degree Of Coherence ◽  
Wide Range ◽  
Channel Currents

Irregular switching of ion channels is an inherent source of noise in real neurons. Taking into account the stochastic nature of calcium and fast potassium channel currents in the Plant model of a bursting neuron, we found noise-induced coherent bursting even in the case when the deterministic neuron is silent. The bursts keep their regularity in a wide range of membrane sizes. The measure of this coherence, the coefficient of variation of interspike intervals, passes through a minimum at the membrane area near 150 μ m 2. The degree of coherence obtained from power spectra of spike trains increases monotonously with decrease of membrane size.

scholarly journals Robust point-process Granger causality analysis in presence of exogenous temporal modulations and trial-by-trial variability in spike trains

2021 ◽  
Vol 17 (1) ◽  
pp. e1007675
Author(s):  
Antonino Casile ◽  
Rose T. Faghih ◽  
Emery N. Brown
Keyword(s):  
Granger Causality ◽  
Point Process ◽  
Temporal Structure ◽  
Temporal Variations ◽  
Spike Trains ◽  
Neuronal Firing ◽  
Connectivity Pattern ◽  
Relative Reduction ◽  
Neuronal Responses ◽  
Neurophysiological Studies

Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j’s point process likelihood obtained considering or removing neuron i. CIF’s hyper-parameters are set on a per-neuron basis by minimizing Akaike’s information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components.

AVALANCHE CORRELATION IN POWER SPECTRA WITH WIDE PEAKS

2007 ◽  
Vol 07 (03) ◽  
pp. L351-L366 ◽  
Author(s):  
ROBERTO EGGENHÖFFNER ◽  
EDVIGE CELASCO ◽  
MARCELLO CELASCO
Keyword(s):  
Spectral Power ◽  
Power Spectra ◽  
Present Theory ◽  
First Principle ◽  
Frequency Range ◽  
High Slope ◽  
Natural Systems ◽  
Spectral Peaks ◽  
Different Types

The occurrence of wide peaks in the frequency range spanning fifteen decades from mHz to above THz was reported in the power spectra of many natural systems. Mostly, these spectral peaks appear superimposed to the 1/f noise. Actually, two different types of spectral peaks were picked out: a first type characterized by wide peaks and high 1/f slope of the overall spectral behavior, the second one by narrow peaks spanning less than one frequency decade and low slopes. Here we highlight the role of correlation among avalanches as the main source of the wide noise peaks observed. The present theory is based on first principle statistics of elementary events clustered in time-amplitude correlated avalanches. A spectral power master equation suitable to explain peaked noise spectra arising from avalanche correlations is achieved analytically. Excellent agreement with our experiments in superconductors and many other observations in biological and natural systems are reported. Our statistical model shows that avalanche correlation gives wide peaks in the power spectrum superimposed to the 1/f behavior with high slope, a typical signature of avalanche processes.

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