Which Surrogate Works for Empirical Performance Modelling? A Case Study with Differential Evolution

It is not uncommon that meta-heuristic algorithms contain some intrinsic parameters, the optimal configuration of which is crucial for achieving their peak performance. However, evaluating the effectiveness of a configuration is expensive, as it involves many costly runs of the target algorithm. Perhaps surprisingly, it is possible to build a cheap-to-evaluate surrogate that models the algorithm's empirical performance as a function of its parameters. Such surrogates constitute an important building block for understanding algorithm performance, algorithm portfolio/selection, and the automatic algorithm configuration. In principle, many off-the-shelf machine learning techniques can be used to build surrogates. In this paper, we take the differential evolution (DE) as the baseline algorithm for proof-of-concept study. Regression models are trained to model the DE's empirical performance given a parameter configuration. In particular, we evaluate and compare four popular regression algorithms both in terms of how well they predict the empirical performance with respect to a particular parameter configuration, and also how well they approximate the parameter versus the empirical performance landscapes

Low-lying charmed and charmed-strange baryon states

In this work, we systematically study the mass spectra and strong decays of $1P$ and $2S$ charmed and charmed-strange baryons in the framework of nonrelativistic constituent quark models. With the light quark cluster-heavy quark picture, the masses are simply calculated by a potential model. The strong decays are studied by the Eichten-Hill-Quigg decay formula. Masses and decay properties of the well-established $1S$ and $1P$ states can be reproduced by our method. $\Sigma_c(2800)^{0,+,++}$ can be assigned as a $\Sigma_{c2}(3/2^-)$ or $\Sigma_{c2}(5/2^-)$ state. We prefer to interpret the signal $\Sigma_c(2850)^0$ as a $2S(1/2^+)$ state although at present we cannot thoroughly exclude the possibility that this is the same state as $\Sigma_c(2800)^0$. $\Lambda_c(2765)^+$ or $\Sigma_c(2765)^+$ could be explained as the $\Lambda_c^+(2S)$ state or $\Sigma^+_{c1}(1/2^-)$ state, respectively. We propose to measure the branching ratio of $\mathcal{B}(\Sigma_c(2455)\pi)/\mathcal{B}(\Sigma_c(2520)\pi)$ in future, which may disentangle the puzzle of this state. Our results support $\Xi_c(2980)^{0,+}$ as the first radial excited state of $\Xi_c(2470)^{0,+}$ with $J^P=1/2^+$. The assignment of $\Xi_c(2930)^0$ is analogous to $\Sigma_c(2800)^{0,+,++}$, \emph{i.e.}, a $\Xi^\prime_{c2}(3/2^-)$ or $\Xi^\prime_{c2}(5/2^-)$ state. In addition, we predict some typical ratios among partial decay widths, which are valuable for experimental search for these missing charmed and charmed-strange baryons.Comment: 16 pages, 3 figures, 13 tables. Accepted by Eur. Phys. J.

A high order unfitted finite element method for time-Harmonic Maxwell interface problems

In this paper, we propose a high order unfitted finite element method for solving time-harmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with possible hanging nodes. The $H^2$ regularity of the solution to Maxwell interface problems with $C^2$ interfaces in each subdomain is proved. Practical interface resolving mesh conditions are introduced under which the hp inverse estimates on three-dimensional curved domains are proved. Stability and hp a priori error estimate of the unfitted finite element method are proved. Numerical results are included to illustrate the performance of the method