Discovery of a Second Nova Eruption of V2487 Ophiuchi

A directed search for previously-undiscovered nova eruptions was conducted in the astronomical plate archives at Harvard College Observatory and Sonneberg Observatory. We found that an eruption of V2487 Oph (Nova Oph 1998) occurred on 1900 June 20. V2487 Oph was previously classified as a classical nova, which we identified as a probable recurrent nova based on its large expansion velocities and the presence of high excitation lines in the outburst spectrum. The event was recorded on Harvard plate AM 505, at a B magnitude of 10.27 +/- 0.11, which is near peak. The outburst can only be seen on one plate, but the image has a characteristic dumbbell shape (caused by a double exposure) that is identical to the other star images on the plate, and thus is not a plate defect. We conclude that this is in fact a previously-undiscovered nova outburst of V2487 Oph, confirming our prediction that it is a recurrent nova. We also examine the discovery efficiency for eruptions of the system and conclude that a randomly-timed outburst has, on average, a 30% chance of being discovered in the past century. Using this, we deduce a recurrence time for V2487 Oph of approximately 18 years, which implies that the next eruption is expected around 2016.Comment: 18 pages, 2 figures, to be published in the Astronomical Journa

Randomized Smoothing for Stochastic Optimization

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic optimization procedures, both in expectation and with high probability, that have optimal dependence on the variance of the gradient estimates. To the best of our knowledge, these are the first variance-based rates for non-smooth optimization. We give several applications of our results to statistical estimation problems, and provide experimental results that demonstrate the effectiveness of the proposed algorithms. We also describe how a combination of our algorithm with recent work on decentralized optimization yields a distributed stochastic optimization algorithm that is order-optimal.Comment: 39 pages, 3 figure