A Comprehensive Study of Automatic Program Repair on the QuixBugs Benchmark

Automatic program repair papers tend to repeatedly use the same benchmarks. This poses a threat to the external validity of the findings of the program repair research community. In this paper, we perform an empirical study of automatic repair on a benchmark of bugs called QuixBugs, which has been little studied. In this paper, 1) We report on the characteristics of QuixBugs; 2) We study the effectiveness of 10 program repair tools on it; 3) We apply three patch correctness assessment techniques to comprehensively study the presence of overfitting patches in QuixBugs. Our key results are: 1) 16/40 buggy programs in QuixBugs can be repaired with at least a test suite adequate patch; 2) A total of 338 plausible patches are generated on the QuixBugs by the considered tools, and 53.3% of them are overfitting patches according to our manual assessment; 3) The three automated patch correctness assessment techniques, RGT_Evosuite, RGT_InputSampling and GT_Invariants, achieve an accuracy of 98.2%, 80.8% and 58.3% in overfitting detection, respectively. To our knowledge, this is the largest empirical study of automatic repair on QuixBugs, combining both quantitative and qualitative insights. All our empirical results are publicly available on GitHub in order to facilitate future research on automatic program repair

High-Dimensional L2L_2Boosting: Rate of Convergence

Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of $L_2$Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called \textquotedblleft post-Boosting\textquotedblright. This is a post-selection estimator which applies ordinary least squares to the variables selected in the first stage by $L_2$Boosting. Another variant is \textquotedblleft Orthogonal Boosting\textquotedblright\ where after each step an orthogonal projection is conducted. We show that both post-$L_2$Boosting and the orthogonal boosting achieve the same rate of convergence as LASSO in a sparse, high-dimensional setting. We show that the rate of convergence of the classical $L_2$Boosting depends on the design matrix described by a sparse eigenvalue constant. To show the latter results, we derive new approximation results for the pure greedy algorithm, based on analyzing the revisiting behavior of $L_2$Boosting. We also introduce feasible rules for early stopping, which can be easily implemented and used in applied work. Our results also allow a direct comparison between LASSO and boosting which has been missing from the literature. Finally, we present simulation studies and applications to illustrate the relevance of our theoretical results and to provide insights into the practical aspects of boosting. In these simulation studies, post-$L_2$Boosting clearly outperforms LASSO.Comment: 19 pages, 4 tables; AMS 2000 subject classifications: Primary 62J05, 62J07, 41A25; secondary 49M15, 68Q3

Holographic recording of laser-induced plasma

We report on a holographic probing technique that allows for measurement of free-electron distribution with fine spatial detail. Plasma is generated by focusing a femtosecond pulse in air. We also demonstrate the capability of the holographic technique of capturing the time evolution of the plasma-generation process

Precision spectroscopy and density-dependent frequency shifts in ultracold Sr

By varying the density of an ultracold $^{88}$Sr sample from $10^9$ cm$^{-3}$ to $> 10^{12}$ cm$^{-3}$, we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the $^1S_0$ - $^3P_1$ optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the $^{88}$Sr $^1S_0 - ^3P_1$ optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is ($434 829 121 312 334 \pm 20_{stat} \pm 33_{sys}$) Hz.Comment: 4 pages, 4 figures, 1 table. submitte

L2-Boosting for Economic Applications

In the recent years more and more highdimensional data sets, where the number of parameters p is high compared to the number of observations n or even larger, are available for applied researchers. Boosting algorithms represent one of the major advances in machine learning and statistics in recent years and are suitable for the analysis of such data sets. While Lasso has been applied very successfully for highdimensional data sets in Economics, boosting has been underutilized in this field, although it has been proven very powerful in fields like Biostatistics and Pattern Recognition. We attribute this to missing theoretical results for boosting. The goal of this paper is to fill this gap and show that boosting is a competitive method for inference of a treatment effect or instrumental variable (IV) estimation in a high-dimensional setting. First, we present the L2Boosting with componentwise least squares algorithm and variants which are tailored for regression problems which are the workhorse for most Econometric problems. Then we show how L2Boosting can be used for estimation of treatment effects and IV estimation. We highlight the methods and illustrate them with simulations and empirical examples. For further results and technical details we refer to (?) and (?) and to the online supplement of the paper

Dynamics of filament formation in a Kerr medium

We have studied the large-scale beam breakup and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission, and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines (constellation), then filaments form on the constellations, and finally the filaments release a fraction of their energy through conical emission. We observed a phase transition to a faster filamentation rate at the onset of conical emission. We attribute this to the interaction of conical emissions with the constellation which creates additional filaments. Numerical simulations show good agreement with the experimental results