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While linear autoencoders can be defined over any field, only real-valued linear autoencoders have been studied so far.
A key innovation here is due to the use of real-valued linear model instead of complex-valued linear (or widely linear) model.
It is in fact a linear function and therefore a vector in the dual space F*(P) of real-valued linear functions on F(P).
Weston [4] proved a Hahn-Banach extension theorem in which a real-valued linear functional is dominated by a real-valued convex function.
In contrast, a time domain solution would require many time steps per period 2 π / ω and consequently the solution of a large number of real-valued linear systems.
The prototype filter used in this work is a near perfect reconstruction (NPR), real-valued linear phase (symmetric) FIR low-pass filter with length L p and support region m∈{0,1,…,L p −1}.
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These two vectors are the real valued linear combinations of the ± π 2 basis vectors.
Our chief assumption relates to the specification of the conditional mean function, namely: E Y i = h μ i Generally, h is a known function which maps our real valued linear predictor into the interval (0,1).
Assays with a correlation coefficient higher than 0.99 in the estimated vs. real value linear regression (Table 1) were able to discriminate clearly between all adjacent points of the 9-point methylation curves.
which is real-valued.
The NAG model represents a real valued, non-linear and non-continuous optimization problem.
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