Information Losses in Neural Classifiers from Sampling

This paper considers the subject of information losses arising from the finite datasets used in the training of neural classifiers. It proves a relationship between such losses as the product of the expected total variation of the estimated neural model with the information about the feature space contained in the hidden representation of that model. It then bounds this expected total variation as a function of the size of randomly sampled datasets in a fairly general setting, and without bringing in any additional dependence on model complexity. It ultimately obtains bounds on information losses that are less sensitive to input compression and in general much smaller than existing bounds. The paper then uses these bounds to explain some recent experimental findings of information compression in neural networks which cannot be explained by previous work. Finally, the paper shows that not only are these bounds much smaller than existing ones, but that they also correspond well with experiments.Comment: To be published in IEEE TNNL

Analytical treatment for the development of electromagnetic cascades in intense magnetic fields

In a strong magnetic field, a high-energy photon can be absorbed and then produce an electron-positron pair. The produced electron/positron will in turn radiate a high-energy photon via synchrotron radiation, which then initiates a cascade. We built a one-dimensional Monte-Carlo code to study the development of the cascade especially after it reaches the saturated status, when almost all the energy of the primary particles transfers to the photons. The photon spectrum in this status has a cut-off due to the absorption by magnetic fields, which is much sharper than the exponential one. Below the cut-off, the spectral energy distribution (SED) manifest itself as a broken power-law with a spectral index of $0.5$ and $0.125$, respectively, below and above the broken energy. The SED can be fitted by a simple analytical function, which is solely determined by the product of the cascade scale $R$ and the magnetic field perpendicular to the motion of the particle B_{\perp}, with an accuracy better than 96\%. The similarity of the spectrum to that from the cascade in an isotropic black-body photon field is also studied.Comment: 7 pages, 7 figures, minor changes. Version to appear in PR

Recent advances in femtosecond laser-assisted cataract surgery

Perfect vision and fewer complications is our goal in cataract surgery, femtosecond laser-assisted cataract surgery hold the promise. Applications of femtosecond laser technology for capsulotomy, nuclear fragmentation and corneal incision in cataract surgery bring a new level of accuracy, reproducibility and predictability over the current cataract surgery. The femtosecond laser produces capsulotomies that are more precise, accurate, reproducible, and stronger than those created with the conventional manual technique, and further helps maintain proper positioning of the IOL. Femtosecond laser in nuclear fragmentation lead to a lower effective phacoemulsification time, and the corneal incision is more stable. But currently there are some complications and a clear learning curve associated with the use of femtosecond lasers for cataract surgery. The long-term safety and visual outcomes still need further investigation