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We report the discovery of short-period photometric variability and modulated Zeeman-split hydrogen emission in SDSSJ125230.93-023417.72 (EPIC 228939929), a variable white dwarf star observed at long cadence in \textit{K2} Campaign 10. The behavior is associated with a magnetic ($B=5.0$ MG) spot on the stellar surface, making the $317.278$-second period a direct measurement of the stellar rotation rate. This object is therefore the fastest-rotating apparently isolated (without a stellar companion) white dwarf yet discovered, and the second found to exhibit chromospheric Balmer emission after GD 356, in which the emission has been attributed to a unipolar inductor mechanism driven by a possible rocky planet. We explore the properties and behavior of this object, and consider whether its evolution may hold implications for white dwarf mergers and their remnants., Comment: 11 pages, 6 figures, 3 tables. Accepted for publication in ApJ

We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopedic review and lecture notes: we try to present a coherent and self-contained picture of the basics of this field, to explain the ideas and tricks, to show how the predictions of the theory compare with (simulation) experiments, and to bring together scattered results. Technical details are given explicitly in an appendix. In order to avoid distraction we concentrate the references in a final section. In addition this paper contains some new results: (i) explicit solutions of the macroscopic equations that describe the error evolution for on-line and batch learning rules, (ii) an analysis of the dynamics of arbitrary macroscopic observables (for complete and incomplete trainingsets), leading to a general Fokker-Planck equation, and (iii) the macroscopic laws describing batch learning with complete training sets. We close the paper with a preliminary expose of ongoing research on the dynamics of learning for the case where the training set is incomplete (i.e. where the number of examples scales linearly with the network size)., Comment: 56 pages LaTex with Postscript figures included in text