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Spike-triggered Covariance
Spike-triggered covariance (STC) analysis is a tool for characterizing a neuron's response properties using the covariance of stimuli that elicit spikes from a neuron. STC is related to the spike-triggered average (STA), and provides a complementary tool for estimating linear filters in a linear-nonlinear-Poisson (LNP) cascade model. Unlike STA, the STC can be used to identify a multi-dimensional feature space in which a neuron computes its response. STC analysis identifies the stimulus features affecting a neuron's response via an eigenvector decomposition of the spike-triggered covariance matrix.Brenner, N., Bialek, W., & de Ruyter van Steveninck, R.R. (2000). Schwartz, O., Chichilnisky, E. J., & Simoncelli, E. P. (2002). Bialek, W. & de Ruyter van Steveninck, R. (2005). Arxiv preprint q-bio/0505003.Schwartz O., Pillow J. W., Rust N. C., & Simoncelli E. P. (2006). Spike-triggered neural characterization. ''Journal of Vision'' 6:484-507 Eigenvectors with eigenvalues significant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret because it is not normalized and hence depends on the magnitudes of the variables. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation. A distinction must be made between (1) the covariance of two random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spike-triggered Average
The spike-triggered averaging (STA) is a tool for characterizing the response properties of a neuron using the spikes emitted in response to a time-varying stimulus. The STA provides an estimate of a neuron's linear receptive field. It is a useful technique for the analysis of electrophysiological data. Mathematically, the STA is the average stimulus preceding a spike.de Boer and Kuyper (1968) Triggered Correlation. ''IEEE Transact. Biomed. Eng.'', 15:169-179Marmarelis, P. Z. and Naka, K. (1972). White-noise analysis of a neuron chain: an application of the Wiener theory. ''Science'', 175:1276-1278Chichilnisky, E. J. (2001). A simple white noise analysis of neuronal light responses. ''Network: Computation in Neural Systems'', 12:199-213Simoncelli, E. P., Paninski, L., Pillow, J. & Swartz, O. (2004)."Characterization of neural responses with stochastic stimuli" In M. Gazzaniga (Ed.) ''The Cognitive Neurosciences, III'' (pp. 327-338). MIT press. To compute the STA, the stimulus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance Matrix
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the x and y directions contain all of the necessary information; a 2 \times 2 matrix would be necessary to fully characterize the two-dimensional variation. The covariance matrix of a random vector \mathbf is typically denoted by \operatorname_ or \Sigma. Definition Throughout this article, boldfaced unsubsc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Components Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volterra Series
The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. In the Volterra series the output of the nonlinear system depends on the input to the system at ''all'' other times. This provides the ability to capture the "memory" effect of devices like capacitors and inductors. It has been applied in the fields of medicine (biomedical engineering) and biology, especially neuroscience. It is also used in electrical engineering to model intermodulation distortion in many devices, including power amplifiers and frequency mixers. Its main advantage lies in its generality: it can represent a wide range of systems. Thus it is sometimes considered a non-parametric model. In mathematics, a Volterra series de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Series
In mathematics, the Wiener series, or Wiener G-functional expansion, originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series. For this reason it is also known as the Wiener–Hermite expansion. The analogue of the coefficients are referred to as Wiener kernels. The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise. This property allows the terms to be identified in applications by the ''Lee–Schetzen method''. The Wiener series is important in nonlinear system identification. In this context, the series approximates the functional relation of the output to the entire history of system input at any time. The Wiener series has been applied mostly to the identification of biological systems, especially in neuroscience. The name Wiener series ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Neuroscience
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field. Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics, and it is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
