Discontinuities in recurrent neural networks

This paper studies the computational power of various discontinuous real computational models that are based on the classical analog recurrent neural network (ARNN). This ARNN consists of finite number of neurons; each neuron computes a polynomial net-function and a sigmoid-like continuous activation-function. The authors introducePostprint (published version

Resonant Inverse Compton Scattering Spectra from Highly-magnetized Neutron Stars

Hard, non-thermal, persistent pulsed X-ray emission extending between 10 keV and $\sim 150$ keV has been observed in nearly ten magnetars. For inner-magnetospheric models of such emission, resonant inverse Compton scattering of soft thermal photons by ultra-relativistic charges is the most efficient production mechanism. We present angle-dependent upscattering spectra and pulsed intensity maps for uncooled, relativistic electrons injected in inner regions of magnetar magnetospheres, calculated using collisional integrals over field loops. Our computations employ a new formulation of the QED Compton scattering cross section in strong magnetic fields that is physically correct for treating important spin-dependent effects in the cyclotron resonance, thereby producing correct photon spectra. The spectral cut-off energies are sensitive to the choices of observer viewing geometry, electron Lorentz factor, and scattering kinematics. We find that electrons with energies $\lesssim 15$ MeV will emit most of their radiation below 250 keV, consistent with inferred turnovers for magnetar hard X-ray tails. More energetic electrons still emit mostly below 1 MeV, except for viewing perspectives sampling field line tangents. Pulse profiles may be singly- or doubly-peaked dependent upon viewing geometry, emission locale, and observed energy band. Magnetic pair production and photon splitting will attenuate spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The resonant Compton spectra are strongly polarized, suggesting that hard X-ray polarimetry instruments such as X-Calibur, or a future Compton telescope, can prove central to constraining model geometry and physics.Comment: 43 pages, 12 figures; accepted for publication in ApJ; v3 fixes typos and updates some reference

Correlation between magnetic interactions and domain structure in A1 FePt ferromagnetic thin films

We have investigated the relationship between the domain structure and the magnetic interactions in a series of FePt ferromagnetic thin films of varying thickness. As-made films grow in the magnetically soft and chemically disordered A1 phase that may have two distinct domain structures. Above a critical thickness $d_{cr}\sim 30$ nm the presence of an out of plane anisotropy induces the formation of stripes, while for $d<d_{cr}$ planar domains occur. Magnetic interactions have been characterized using the well known DCD-IRM remanence protocols, $\delta M$ plots, and magnetic viscosity measurements. We have observed a strong correlation between the domain configuration and the sign of the magnetic interactions. Planar domains are associated with positive exchange-like interactions, while stripe domains have a strong negative dipolar-like contribution. In this last case we have found a close correlation between the interaction parameter and the surface dipolar energy of the stripe domain structure. Using time dependent magnetic viscosity measurements, we have also estimated an average activation volume for magnetic reversal, $\langle V_{ac}\rangle \sim 1.37\times 10^{4}$ nm$^{3},$ which is approximately independent of the film thickness or the stripe period.Comment: 25 pages, 11 figure