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Spectral methods for neural characterization using generalized quadratic models
 in Adv in Neural Info Proc Sys 26
, 2013
"... We describe a set of fast, tractable methods for characterizing neural responses to highdimensional sensory stimuli using a model we refer to as the generalized quadratic model (GQM). The GQM consists of a lowrank quadratic function followed by a point nonlinearity and exponentialfamily noise. T ..."
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Cited by 7 (4 self)
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We describe a set of fast, tractable methods for characterizing neural responses to highdimensional sensory stimuli using a model we refer to as the generalized quadratic model (GQM). The GQM consists of a lowrank quadratic function followed by a point nonlinearity and exponentialfamily noise
A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily
"... Often, researchers wish to analyze nonlinear dynamic discretetime stochastic models. This chapter provides a toolkit for solving such models easily, building on loglinearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the me ..."
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Cited by 216 (2 self)
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to use the method of undetermined coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing the solution with a matrix quadratic equation and solving it, and to provide frequencydomain techniques to calculate the second order properties
Quadratic Expansions of Spectral Functions
, 2000
"... A function, F , on the space of n n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument, that is F (A) = F (UAU T ) for every orthogonal U and symmetric A in its domain. Spectral functions are in onetoone correspondence with the symmetric functions ..."
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Cited by 6 (4 self)
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on R n : those that are invariant under arbitrary swapping of their arguments. In this paper we show that a spectral function has a quadratic expansion around a point A if and only if its corresponding symmetric function has quadratic expansion around (A) (the vector of eigenvalues). We also give a
LINE SPECTRAL PROPERTIES OF QUADRATIC MODELS
"... Line Spectrum Pair (LSP) decomposition is a technique developed for robust representation of the coefficients of a Linear Predictive (LP) model. It has favourable properties with respect to root loci and quantisation noise. In this article, we will explore the properties of LSP polynomials when they ..."
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they are used to represent quadratic models of form A 2 (z) and A(z)z −m A(z −1). The quadratic models show intriguing properties in LSP decomposition, which can be used to develop a Levinsontype algorithm. 1.
Spectral Analysis for Neural Signals
"... (Mitra P, ed) pp. [xxxx]. Washington, DC: Society for Neuroscience. All articles and their graphics are under the copyright of their respective authors. Cover graphics and design © 2008 Society for Neuroscience. ..."
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(Mitra P, ed) pp. [xxxx]. Washington, DC: Society for Neuroscience. All articles and their graphics are under the copyright of their respective authors. Cover graphics and design © 2008 Society for Neuroscience.
Spectral
"... numerical schemes for timedependent convection with viscosity dependent on temperature. ..."
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numerical schemes for timedependent convection with viscosity dependent on temperature.
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