Comment on the Adiabatic Condition

The experimental observation of effects due to Berry's phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum mechanics. Since Berry's original paper in 1984, the spin 1/2 coupled with rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematically sound.Comment: 9 page

Detection of a variable ultra-fast outflow in the Narrow Line Seyfert 1 galaxy PG 1448+273

Relativistically blueshifted absorption features of highly ionised ions, the so-called ultra-fast outflows (UFOs), have been detected in the X-ray spectra of a number of accreting supermassive black holes. If these features truly originate from accretion disc winds accelerated to more than 10 per cent of the speed of light, their energy budget is very significant and they can contribute to or even drive galaxy-scale feedback from active galactic nuclei (AGN). However, the UFO spectral features are often weak due to high ionisation of the outflowing material, and the inference of the wind physical properties can be complicated by other spectral features in AGN such as relativistic reflection. Here we study a highly accreting Narrow Line Seyfert 1 galaxy PG 1448+273. We apply an automated, systematic routine for detecting outflows in accreting systems and achieve an unambiguous detection of a UFO in this AGN. The UFO absorption is observed in both soft and hard X-ray bands with the XMM-Newton observatory. The velocity of the outflow is (26900 +- 600) km/s (~0.09c), with an ionisation parameter of log ({\xi} / erg cm s^-1)=4.03_{-0.08}^{+0.10} and a column density above 10^23 cm^-2. At the same time, we detect weak warm absorption features in the spectrum of the object. Our systematic outflow search suggests the presence of further multi-phase wind structure, but we cannot claim a significant detection considering the present data quality. The UFO is not detected in a second, shorter observation with XMM-Newton, indicating variability in time, observed also in other similar AGN.Comment: Accepted for publication in MNRAS. 14 pages, 11 figures, 1 tabl

Locating the Source of Diffusion in Large-Scale Networks

How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.Comment: To appear in Physical Review Letters. Includes pre-print of main paper, and supplementary materia