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A dearth of close-in planets orbiting rapid rotators was reported almost a decade ago. According to this view only slowly spinning stars with rotation periods longer than 5-10 days would host planets with orbital periods shorter than 2 or 3 days. This Letter brings an enlarged and more detailed analysis that led us to the question: Is there really a dearth in that distribution or is it a dearth of data? For this new analysis, we combined different samples of Kepler and TESS stars with confirmed planets or planet candidates with measured stellar rotation periods, using Gaia data to perform an in-depth selection of 1013 planet-hosting main-sequence stars. With the newer, enlarged, and more refined data, the reported dearth of close-in planets orbiting rapid rotators tends to disappear, thus suggesting that it may reflect a scarcity of data in the prior analysis. A two sample statistical test strongly supports our results, showing that the distribution of close-in planets orbiting rapid rotators is almost indistinguishable from that for close-in planets orbiting slow rotators., Comment: 6 pages, 2 figures, 1 table, accepted for publication in ApJ Letters

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($\ge(4.1\pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$\pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated., Comment: Letter and Supplemental Material, 6 figures, 8 pages

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global convergence analysis of the proposed method is established under suitable conditions, and some preliminary numerical experiments are given to illustrate its performance.

Magnetic skyrmions are mesmerizing spin textures with peculiar topological and dynamical properties, typically the product of competing interactions in ferromagnets, and with great technological potential [1-5]. Researchers have long wondered whether analogous electric skyrmions might exist in ferroelectrics, maybe featuring novel behaviors and possibilities for electric and mechanical control. The results thus far are modest, though: an electric equivalent of the most typical magnetic skyrmion (which would rely on a counterpart of the Dzyaloshinskii-Moriya interaction) seems all but impossible; further, the exotic ferroelectric orders observed or predicted to date [6-8] rely on very specific nano-structures (composites, superlattices), which limits the generality and properties (e.g., mobility) of the possible associated skyrmions. Here we propose an original approach to write electric skyrmions in simple ferroelectric lattices in a customary manner. Our second-principles simulations [9] of columnar ferroelectric nano-domains, in prototype compound PbTiO3 , show that it is possible to harness the Bloch-type internal structure of the domain wall [10] and hence create a genuine skyrmion. We check that the object thus obtained displays the usual skyrmion-defining features; further, it also presents unusual ones, including a symmetry-breaking skyrmion-skyrmion transition driven by strain, various types of topological transformations induced by external fields and temperature, and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating electric textures with non-trivial topologies, using standard experimental tools and materials, effectively inaugurating the field of electric skyrmions., Comment: 5 pages and 3 figures

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Holder-like condition and the other is for functions that satisfies a Smale condition, which includes a substantial class of analytic functions. Some preliminaries numerical experiments illustrating the applicability of the proposed method for medium and large problems are also presented.

This paper analyzes the iteration-complexity of a generalized alternating direction method of multipliers (G-ADMM) for solving linearly constrained convex problems. This ADMM variant, which was first proposed by Bertsekas and Eckstein, introduces a relaxation parameter $\alpha \in (0,2)$ into the second ADMM subproblem. Our approach is to show that the G-ADMM is an instance of a hybrid proximal extragradient framework with some special properties, and, as a by product, we obtain ergodic iteration-complexity for the G-ADMM with $\alpha\in (0,2]$, improving and complementing related results in the literature. Additionally, we also present pointwise iteration-complexity for the G-ADMM.

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant as an instance of a hybrid proximal extragradient framework applied to a specific monotone inclusion problem.