The Extreme Ultraviolet and X-Ray Sun in Time: High-Energy Evolutionary Tracks of a Solar-Like Star

Aims. We aim to describe the pre-main sequence and main-sequence evolution of X-ray and extreme-ultaviolet radiation of a solar mass star based on its rotational evolution starting with a realistic range of initial rotation rates. Methods. We derive evolutionary tracks of X-ray radiation based on a rotational evolution model for solar mass stars and the rotation-activity relation. We compare these tracks to X-ray luminosity distributions of stars in clusters with different ages. Results. We find agreement between the evolutionary tracks derived from rotation and the X-ray luminosity distributions from observations. Depending on the initial rotation rate, a star might remain at the X-ray saturation level for very different time periods, approximately from 10 Myr to 300 Myr for slow and fast rotators, respectively. Conclusions. Rotational evolution with a spread of initial conditions leads to a particularly wide distribution of possible X-ray luminosities in the age range of 20 to 500 Myrs, before rotational convergence and therefore X-ray luminosity convergence sets in. This age range is crucial for the evolution of young planetary atmospheres and may thus lead to very different planetary evolution histories.Comment: 4 pages, 4 figures, accepted for publication in A&

A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification

$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an $R$-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new $k$NN algorithm and its improvements to other version of $k$NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional $k$NN algorithm, the proposed manifold version $k$NN shows promising potential for classifying manifold-distributed data.Comment: 32 pages, 12 figures, 7 table