Symmetry breakdown of stochastic potential by noise cross-correlations among colored noise sources

2011 ◽  
Vol 83 (2) ◽  
pp. 235-243 ◽  
Author(s):  
I. A. Knyaz’
Keyword(s):  
Colored Noise ◽  
Noise Sources ◽  
Symmetry Breakdown ◽  
Cross Correlations

Stochastic Hodgkin-Huxley Equations with Colored Noise Terms in the Conductances

2013 ◽  
Vol 25 (1) ◽  
pp. 46-74 ◽  
Author(s):  
Marifi Güler
Keyword(s):  
Colored Noise ◽  
Open Channel ◽  
Small Cells ◽  
Spontaneous Firing ◽  
Spike Generation ◽  
Membrane Area ◽  
Transmembrane Voltage ◽  
Cross Correlations ◽  
Firing Efficiency ◽  
Voltage Gated Ion Channels

The excitability of cells is facilitated by voltage-gated ion channels. These channels accommodate a multiple number of gates individually. The possible impact of that gate multiplicity on the cell's function, specifically when the membrane area is of limited size, was investigated in the author's prior work (Güler, 2011 ). There, it was found that a nontrivially persistent correlation takes place between the transmembrane voltage fluctuations (also between the fluctuations in the gating variables) and the component of open channel fluctuations attributed to the gate multiplicity. This nontrivial phenomenon was found to be playing a major augmentative role for the elevation of excitability and spontaneous firing in small cells. In addition, the same phenomenon was found to be enhancing spike coherence significantly. Here we extend Fox and Lu's ( 1994 ) stochastic Hodgkin-Huxley equations by incorporating colored noise terms into the conductances there to obtain a formalism capable of capturing the addressed cross-correlations. Statistics of spike generation, spike coherence, firing efficiency, latency, and jitter from the articulated set of equations are found to be highly accurate in comparison with the corresponding statistics from the exact microscopic Markov simulations. This way, it is demonstrated vividly that our formulation overcomes the inherent inadequacy of the Fox and Lu equations. Finally, a recently proposed diffusion approximation method (Linaro, Storace, & Giugliano, 2011 ) is taken into consideration, and a discussion on its character is pursued.

scholarly journals Connecting beamforming and kernel-based noise source inversion

2020 ◽  
Vol 224 (3) ◽  
pp. 1607-1620
Author(s):  
Daniel C Bowden ◽  
Korbinian Sager ◽  
Andreas Fichtner ◽  
Małgorzata Chmiel
Keyword(s):  
Waveform Inversion ◽  
Great Promise ◽  
Source Inversion ◽  
Noise Sources ◽  
Full Waveform ◽  
Data Driven Approach ◽  
Cross Correlations ◽  
Selection For ◽  
Window Selection ◽  
Synthetic Models

SUMMARY Beamforming and backprojection methods offer a data-driven approach to image noise sources, but provide no opportunity to account for prior information or iterate through an inversion framework. In contrast, recent methods have been developed to locate ambient noise sources based on cross-correlations between stations and the construction of finite-frequency kernels, allowing for inversions over multiple iterations. These kernel-based approaches show great promise, both in mathematical rigour and in results, but are less physically intuitive and interpretable. Here we show that these apparently two different classes of methods, beamforming and kernel-based inversion, are achieving exactly the same result in certain circumstances. This paper begins with a description of a relatively simple beamforming or backprojection algorithm, and walks through a series of modifications or enhancements. By including a rigorously defined physical model for the distribution of noise sources and therefore synthetic correlation functions, we come to a framework resembling the kernel-based iterative approaches. Given the equivalence of these approaches, both communities can benefit from bridging the gap. For example, inversion frameworks can benefit from the numerous image enhancement tools developed by the beamforming community. Additionally, full-waveform inversion schemes that require a window selection for the comparisons of misfits can more effectively target particular sources through a windowing in a beamform slowness domain, or might directly use beamform heatmaps for the calculation of misfits. We discuss a number of such possibilities for the enhancement of both classes of methods, testing with synthetic models where possible.

scholarly journals Estimation of Phase Noise in Oscillators with Colored Noise Sources

2013 ◽  
Vol 17 (11) ◽  
pp. 2160-2163 ◽  
Author(s):  
M. Reza Khanzadi ◽  
Rajet Krishnan ◽  
Thomas Eriksson
Keyword(s):  
Phase Noise ◽  
Colored Noise ◽  
Noise Sources

scholarly journals Interspike interval correlations in neuron models with adaptation and correlated noise

2021 ◽  
Vol 17 (8) ◽  
pp. e1009261
Author(s):  
Lukas Ramlow ◽  
Benjamin Lindner
Keyword(s):  
Correlation Coefficient ◽  
Serial Correlation ◽  
Colored Noise ◽  
Interspike Interval ◽  
Correlated Noise ◽  
Spike Frequency Adaptation ◽  
Noise Sources ◽  
Integrate And Fire ◽  
Weak Noise ◽  
Serial Correlation Coefficient

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.

On the link between Beamforming and Kernel-based Source Inversion

2020 ◽  
Author(s):  
Daniel Bowden ◽  
Korbinian Sager ◽  
Andreas Fichtner ◽  
Małgorzata Chmiel
Keyword(s):  
Prior Information ◽  
Time Window ◽  
Great Promise ◽  
Source Inversion ◽  
Finite Frequency ◽  
Noise Sources ◽  
Data Driven Approach ◽  
Gradient Based ◽  
Cross Correlations ◽  
A Current

<p>Beamforming and backprojection methods offer a data-driven approach to image noise sources, but provide no opportunity to account for prior information or iterate through an inversion framework. In contrast, recent methods have been developed to locate ambient noise sources based on cross-correlations between stations and the construction of finite-frequency kernels, allowing for inversions over multiple iterations (i.e., Tromp et al., 2010, Ermert et al. 2017, Sager et al. 2018). These kernel-based approaches show great promise, both in mathematical rigour and in results, but may remain difficult to understand or implement for the wider community. Here we show that these two different classes of methods, beamforming and kernel-based inversion, are achieving exactly the same result in certain circumstances. This means existing beamforming and backprojection methods can also incorporate prior information in a mathematically correct manner.</p><p>We start with a description of a relatively simple beamforming or backprojection algorithm, based on time-domain shifting and measurement of waveform coherence. Only by changing the order of steps, we begin to resemble the kernel-based approaches. By adding a physical model for the distribution of noise sources, and therefore synthetic correlation functions, we can extend backprojection to an iterative, gradient-based inversion scheme. Adjoint methods and a direct simulation of correlation wavefields can later be used to increase computational efficiency, but we stress that these are not needed to understand the approach.</p><p>Given the equivalence of these approaches between these two communities, both sides can benefit from bridging the gap. For example, for kernel-based inversion schemes, a current challenge lies in defining the misfit and time window over which a correlation will be scored; a windowing function based on beamform images offers a more intuitive way to identify significant contributions in the noise wavefield, exploiting more than just the direct surface-wave arrivals.</p>

Rapid Global Finite-Frequency Ambient Noise Source Inversion

2020 ◽  
Author(s):  
Jonas Igel ◽  
Laura Ermert ◽  
Andreas Fichtner
Keyword(s):  
Ambient Noise ◽  
Noise Source ◽  
Computational Cost ◽  
User Interaction ◽  
Real Data ◽  
Source Distribution ◽  
Source Inversion ◽  
Finite Frequency ◽  
Noise Sources ◽  
Cross Correlations

<p>Common assumptions in ambient noise seismology such as Green’s function retrieval and equipartitioned wavefields are often not met in the Earth. Full waveform ambient noise tomography methods are free of such assumptions, as they implement knowledge of the time- and space-dependent ambient noise source distribution, whilst also taking finite-frequency effects into account. Such methods would greatly simplify near real-time monitoring of the sub-surface. Additionally, the distribution of the secondary microseisms could act as a new observable of the ocean state since its mechanism is well understood (e.g. Ardhuin et al., 2011).</p><p>To efficiently forward-model global noise cross-correlations we implement (1) pre-computed high-frequency wavefields obtained using, for example, AxiSEM (Nissen-Meyer et al., 2014), and (2) spatially variable grids, both of which greatly reduce the computational cost. Global cross-correlations for any source distribution can be computed within a few seconds in the microseismic frequency range (up to 0.2 Hz). Similarly, we can compute the finite-frequency sensitivity kernels which are then used to perform a gradient-based iterative inversion of the power-spectral density of the noise source distribution. We take a windowed logarithmic energy ratio of the causal and acausal branches of the cross-correlations as measurement, which is largely insensitive to unknown 3D Earth structures.</p><p>Due to its parallelisation on a cluster, our inversion tool is able to rapidly invert for the global microseismic noise source distribution with minimal required user interaction. Synthetic and real data inversions show promising results for noise sources in the North Atlantic with the structure and spatial distribution resolved at scales of a few hundred kilometres. Finally, daily noise sources maps could be computed by combining our inversion tool with a daily data download and processing toolkit.</p>

scholarly journals Improving cross-correlations of ambient noise using an rms-ratio selection stacking method

2020 ◽  
Vol 222 (2) ◽  
pp. 989-1002
Author(s):  
Jinyun Xie ◽  
Yingjie Yang ◽  
Yinhe Luo
Keyword(s):  
Short Duration ◽  
Ambient Noise ◽  
Signal To Noise Ratio ◽  
Ambient Noise Tomography ◽  
Noise Sources ◽  
Time Duration ◽  
Crust And Upper Mantle ◽  
Phase Velocities ◽  
Noise Data ◽  
Cross Correlations

SUMMARY Stacking of ambient noise correlations is a crucial step to extract empirical Green's functions (EGFs) between station pairs. The traditional method is to linearly stack all short-duration cross-correlation functions (CCFs) over a long period of time to obtain final stacks. It requires at least several months of ambient noise data to obtain reliable phase velocities at periods of several to tens of seconds from CCFs. In this study, we develop a new stacking method named root-mean-square ratio selection stacking (RMSR_SS) to reduce the time duration required for the recovery of EGFs from ambient noise. In our RMSR_SS method, rather than stacking all short-duration CCFs, we first judge if each of the short-duration CCF constructively contributes to the recovery of EGFs or not. Then, we only stack those CCFs which constructively contribute to the convergence of EGFs. By applying our method to synthetic noise data, we demonstrate how our method works in enhancing the signal-to-noise ratio of CCFs by rejecting noise sources which do not positively contribute to the recovery of EGFs. Then, we apply our method to real noise data recorded in western USA. We show that reliable and accurate phase velocities can be measured from 15-d long ambient noise data using our RMSR_SS method. By applying our method to ambient noise tomography (ANT), we can reduce the deployment duration of seismic stations from several months or years to a few tens of days, significantly improving the efficiency of ANT in imaging crust and upper-mantle structures.

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