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| The '''linear-nonlinear-Poisson (LNP) cascade model''' is a simplified functional model of neural spike responses.<ref name="chichilnisky01">Chichilnisky, E. J., [http://www.stat.columbia.edu/~liam/teaching/neurostat-spr07/papers/Chichilnisky-2001.pdf A simple white noise analysis of neuronal light responses.] Network: Computation in Neural Systems 12:199–213. (2001)</ref><ref name="simoncelli">Simoncelli, E. P., Paninski, L., Pillow, J. & Swartz, O. (2004). [http://www.cns.nyu.edu/~eero/ABSTRACTS/simoncelli03c-abstract.html Characterization of Neural Responses with Stochastic Stimuli] in (Ed. M. Gazzaniga) ''The Cognitive Neurosciences 3rd edn'' (pp 327–338) MIT press.</ref><ref name="schwartz06">Schwartz O., Pillow J. W., Rust N. C., & Simoncelli E. P. (2006). Spike-triggered neural characterization. ''Journal of Vision'' 6:484–507</ref> It has been successfully used to describe the response characteristics of neurons in early sensory pathways, especially the visual system. The LNP model is generally implicit when using reverse correlation or the [[spike-triggered average]] to characterize neural responses with white-noise stimuli.
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| [[Image:LNPModelDiagram.png|right|thumb|300px|The Linear-Nonlinear-Poisson Cascade Model]]
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| There are three stages of the LNP cascade model. The first stage consists of a linear filter, or linear [[receptive field]], which describes how the neuron integrates stimulus intensity over space and time. The output of this filter then passes through a nonlinear function, which gives the neuron's instantaneous spike rate as its output. Finally, the spike rate is used to generate spikes according to an inhomogeneous [[Poisson process]].
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| The linear filtering stage performs [[dimensionality reduction]], reducing the high-dimensional spatio-temporal stimulus space to a low-dimensional feature space, within which the neuron computes its response. The nonlinearity converts the filter output to a (non-negative) spike rate, and accounts for nonlinear phenomena such as spike threshold (or rectification) and response saturation. The Poisson spike generator converts the continuous spike rate to a series of spike times, under the assumption that the probability of a spike depends only on the instantaneous spike rate.
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| == Mathematical formulation ==
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| ===single-filter LNP===
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| Let <math>\mathbf{x}</math> denote the spatio-temporal stimulus vector at a particular instant, and
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| <math>\mathbf{k}</math> denote a linear filter (the neuron's linear receptive field), which is a vector with the same number of elements as <math>\mathbf{x}</math>. Let <math>f</math> denote the nonlinearity, a scalar function with non-negative output. Then the LNP model specifies that, in the limit of small time bins, | |
| : <math>P(\textrm{spike}) \propto f(\mathbf{k} \cdot \mathbf{x})</math>.
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| For finite-sized time bins, this can be stated precisely as the probability of observing ''y'' spikes in a single bin:
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| : <math> P(y \textrm{~spikes}) = \frac{\left(\Delta \lambda\right)^y}{y!} e^{- \Delta \lambda}</math>
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| : where <math> \lambda = f(\mathbf{k}\cdot\mathbf{x})</math>, and <math>\Delta</math> is the bin size.
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| ===Multi-filter LNP===
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| For neurons sensitive to multiple dimensions of the stimulus space, the linear stage of the LNP model can be generalized to a bank of linear filters, and the nonlinearity becomes a function of multiple inputs. Let <math>\mathbf{k_1}, \mathbf{k_2}, \ldots, \mathbf{k_n}</math> denote the set of linear filters that capture a neuron's stimulus dependence. Then the multi-filter LNP model is described by
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| : <math>P(\textrm{spike}) \propto f(\mathbf{k_1}\!\cdot\!\mathbf{x},\; \mathbf{k_2}\!\cdot\!\mathbf{x},\; \ldots,\; \mathbf{k_n}\!\cdot\!\mathbf{x})</math>
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| or
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| : <math>P(\textrm{spike}) \propto f(K\mathbf{x}),</math>
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| where <math>K</math> is a matrix whose columns are the filters <math>\mathbf{k_i}</math>.
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| == Estimation ==
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| The parameters of the LNP model consist of the linear filters <math>\{{k_i}\}</math> and the nonlinearity <math>f</math>. The estimation problem (also known as the problem of ''neural characterization'') is the problem of determining these parameters from data consisting of a time-varying stimulus and the set of observed spike times. Techniques for estimating the LNP model parameters include: | |
| * moment-based techniques, such as the [[spike-triggered average]] or [[spike-triggered covariance]]<ref name="chichilnisky01"/><ref name="simoncelli"/><ref name="schwartz06"/><ref name="brenner00">Brenner, N., Bialek, W., & de Ruyter van Steveninck, R. R. (2000).</ref>
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| * with information-maximization or [[maximum likelihood]] techniques.
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| == Related models ==
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| * The LNP model provides a simplified, mathematically tractable approximation to more biophysically detailed [[Biological neuron model|single-neuron models]] such as the [[integrate-and-fire]] or [[Hodgkin–Huxley model]].
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| * If the nonlinearity <math>f</math> is a fixed invertible function, then the LNP model is a [[generalized linear model]]. In this case, <math>f</math> is the inverse link function.
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| * An alternative to the LNP model for neural characterization is the [[Volterra series|Volterra kernel]] or [[Wiener kernel]] series expansion, which arises in classical nonlinear systems-identification theory.<ref>Marmarelis & Marmerelis, 1978. ''Analysis of Physiological Systems: The White Noise Approach.'' London: Plenum Press.</ref> These models approximate a neuron's input-output characteristics using a polynomial expansion analogous to the [[Taylor series]], but do not explicitly specify the spike-generation process.
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| ==See also==
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| *[[Random neural network]]
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| *[[Spike-triggered average]]
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| *[[Spike-triggered covariance]]
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| ==References==
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| <references/>
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| [[Category:Computational neuroscience]]
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| [[Category:Stochastic models]]
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Younger males are much less likely to have ingrained routines, unyielding mindsets, and rigid expectations of what they want from their companion. They usually tend to be open-minded about her profession, journey, and places to live. Change is not the impediment for them that it is for more mature males.
A simple Google search will assist to further assistance my declare. And you can attempt it with me, if you like. Are there more dating websites for older women looking for more youthful males or much more for more mature males looking for younger ladies? The previous much outweigh the latter, from what I can see.
You should alter the subject of your discussions. Inquire about her job, hobbies, what kind of songs she likes... Woman is intelligent, assured and experienced, so do not talk about about age. You ought to be assured as well.
And 1 other stage with older women dating men. Males peak sexually a lot more youthful than ladies, and by age forty are probably passing their primary. Women are just obtaining there. This may have, for some women, an influence on their choice for more youthful males. Based on the guy's attitude. Some older men can't see women as equal sexual companions. Again, the more subservient location. The lady's passions are not acknowledged for what they are.
Again, you would also want your adore, relationship and relationship companion to carry on to offer you more of the emotional requirements as and at when necessary.
Yes, on the whole, older women do discover more youthful men appealing. That is my claim. Now read to the end and tell me if you agree (fingers crossed, you will).
When you day older women you should be ready for a real partnership. It is time to allow go of the video games. If you are a participant or someone who likes to toy with a girl's emotions then older women are most likely not for you. However, if you are looking for a deep relationship exactly where you can make a good connection with a lady then an more mature woman may just be the correct option.
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