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The evolution in latitude of sunspots is a key feature of the cyclic solar dynamo. Here, we present the results of a spectroscopic and spectropolarimetric monitoring campaign on the young (∼20 Myr old) early G star HIP 89829, in order to investigate potential evolution in the distribution of the star's spots and magnetic features. Our analysis of this G5V star spans eight epochs, from June 2010 to August 2015. The techniques of Doppler imaging and Zeeman–Doppler imaging were used to create brightness maps for each epoch and magnetic maps for two epochs. The brightness images show the star to have stable spot features with two main spot latitudes – a polar spot, often seen on young rapidly rotating stars such as this, and another highly unusual group of large spot features around the 20° and 30° latitudes. These lower spot latitudes appear to be rather stable over the 5 yr of observations. We included a solar-type differential rotation law into the imaging process and measured near-solid-body rotation for epochs where sufficient data exist for this analysis. The magnetic features show a dominant poloidal and a weaker toroidal magnetic field for both Stokes V epochs, which is unusual for a star with a rapid rotation period of 0.57 d. We conclude that HIP 89829 is an active young solar-type star with long-lived spots and near-solid-body rotation. [ABSTRACT FROM AUTHOR]

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of extremal solutions for the BP equations, and we use them to fix a fraction of spins in their ground state configuration. At the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size. This in turn makes the associated optimization problem highly non trivial in the critical region. Using the bounds on the BP messages provided by the extremal solutions we design a new and very easy to implement BP scheme which is able to output a large number of stable fixed points. On one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time. On the other hand we found that the number of fixed points of the BP algorithm grows with the system size in the critical region. This unexpected feature poses new relevant questions about the physics of this class of models. [ABSTRACT FROM AUTHOR]

The early, active history of our Sun is still not fully understood. Observations of the magnetic fields on active young solar-type stars allow us an insight into the early evolution of our Sun. Here we present Doppler and Zeeman–Doppler images of the young late-F star HIP 71933 (HD 129181) at multiple epochs to add to the growing data about the evolution of magnetic cycles in solar-type stars. Spectroscopic data were obtained over seven epochs spanning 10 yr of observations, with two epochs including spectropolarimetric data. The brightness maps at all epochs show a consistent spot activity in a non-uniform ring at a latitude of approximately +60° with no polar spot present in any epoch. The two magnetic field maps taken ∼2 yr apart show a strong poloidal field configuration with most of the poloidal field energy in the dipolar configuration. The magnetic maps show no evidence of a polarity reversal. We were able to measure the differential rotation from one of the seven epochs using the brightness data finding a dΩ of 0.325 ± 0.01 rad d−1. The values for the rotational period and differential rotation found for HIP 71933 are consistent with values found for other late-F or early-G stars. The dominant poloidal features and the limited spots at the pole are unusual for a rapidly rotating star but not unique. [ABSTRACT FROM AUTHOR]