We study the evolution of a stochastic helical magnetic field generated in the early Universe after the electroweak phase transition, using standard magnetohydrodynamics (MHD). We find how the coherence length ξ, magnetic energy EM and magnetic helicity H evolve with time. We show that the self-similarity of the magnetic power spectrum alone implies that ξ ∼ t1/2. This in turn implies that magn...

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This note gives a closed form expression for the linear transform computed by an optimally trained linear heteroencoder network of arbitrary topology trained to minimize squared error. The transform can be thought of as a restricted rank version of the basic linear least-squares regression (discrete Wiener filter) between input and output. The rank restriction is set by the “bottleneck” size of...