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Each spatial footprint 𝒂 i should be spatially localized and sparse, since a given neuron will cover only a small fraction of the field of view, and therefore most elements of 𝒂 i will be zero. Thus, we need to incorporate spatial locality and sparsity constraints on A ( Discount Fashion Style Newest Fashionalbe Deep V Collar Viscose Plus Size Print Women Long Dress Great Deals For Sale Genuine For Sale Free Shipping Extremely VbI67
). We discuss details further below.

Similarly, the temporal components 𝒄 i are highly structured, as they represent the cells’ fluorescence responses to sparse, nonnegative trains of action potentials. Following ( Vogelstein et al., 2010 ; Pnevmatikakis et al., 2016 ), we model the calcium dynamics of each neuron 𝒄 i with a stable autoregressive (AR) process of order p ,

(3)

where s i ( t ) 0 is the number of spikes that neuron fired at the t -th frame. (Note that there is no further noise input into c i ( t ) beyond the spike signal s i ( t ) .) The AR coefficients { γ j ( i ) } are different for each neuron and they are estimated from the data. In practice, we usually pick p = 2 , thus incorporating both a nonzero rise and decay time of calcium transients in response to a spike; then Cheap Sale Great Deals Nicekicks PHYANIC Spring Sneakers Air Mesh Shoes For Women Laceup The Cheapest Cheap Online Free Shipping Discounts S2kjr9I
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:

d x = λ / ( 2 N A ) {\displaystyle dx=\lambda /(2*NA)}

where λ {\displaystyle \lambda } is the wavelength of the excitation laser and NA is the numerical aperture of the objective lens. The Abbe diffraction limit holds if the incoming wave front is parallel. In reality, however, the laser beam profile is Gaussian. Therefore, in order to the calculate the achievable resolution, formulas for truncated Gaussian beams have to be used. [48]

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Has one optional argument:

If , the count will only include unique instances. This is the SQL equivalent of . The default value is .

Returns the maximum value of the given expression.

Returns the minimum value of the given expression.

Returns the standard deviation of the data in the provided expression.

By default, StdDev returns the population standard deviation. However, if sample=True , the return value will be the sample standard deviation.

SQLite

SQLite doesn’t provide out of the box. An implementation is available as an extension module for SQLite. Consult the SQlite documentation for instructions on obtaining and installing this extension.

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Computes the sum of all values of the given expression.

Returns the variance of the data in the provided expression.

By default, Variance returns the population variance. However, if sample=True , the return value will be the sample variance.

SQLite

SQLite doesn’t provide out of the box. An implementation is available as an extension module for SQLite. Consult the SQlite documentation for instructions on obtaining and installing this extension.

This section provides reference material for query-related tools not documented elsewhere.

objects

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