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Background: Programming is a fundamental skill in computer science and software engineering specifically. Mastering it is a challenge for novices, which is evidenced by numerous errors that students make during programming assignments. Objective: In our study, we want to identify common programming errors in CS2 courses and understand how students evolve over time. Method: To this end, we conducted a longitudinal study of errors that students of a CS2 course made in subsequent programming assignments. Specifically, we manually categorized 710 errors based on a modified version of an established error framework. Result: We could observe a learning curve of students, such that they start out with only few syntactical errors, but with a high number of semantic errors. During the course, the syntax and semantic errors almost completely vanish, but logical errors remain consistently present. Conclusion: Thus, students have only little trouble with learning the programming language, but need more time to understand and express concepts in a programming language.

As software pervades more and more areas of our professional and personal lives, there is an ever-increasing need to maintain software, and for programmers to be able to efficiently write and understand program code. In the first study of its kind, we analyze fixation-related potentials (FRPs) to explore the online processing of program code patterns that are ambiguous to programmers, but not the computer (so-called atoms of confusion), and their underlying neurocognitive mechanisms in an ecologically valid setting. Relative to unambiguous counterparts in program code, atoms of confusion elicit a late frontal positivity with a duration of about 400 to 700 ms after first looking at the atom of confusion. As the frontal positivity shows high resemblance with an event-related potential (ERP) component found during natural language processing that is elicited by unexpected but plausible words in sentence context, we take these data to suggest that the brain engages similar neurocognitive mechanisms in response to unexpected and informative inputs in program code and in natural language. In both domains, these inputs lead to an update of a comprehender's situation model that is essential for information extraction from a quickly unfolding input.

\textit{Background}: Large language models (LLMs) have become a paramount interest of researchers and practitioners alike, yet a comprehensive overview of key considerations for those developing LLM-based systems is lacking. This study addresses this gap by collecting and mapping the topics practitioners discuss online, offering practical insights into where priorities lie in developing LLM-based applications. \textit{Method}: We collected 189 videos from 2022 to 2024 from practitioners actively developing such systems and discussing various aspects they encounter during development and deployment of LLMs in production. We analyzed the transcripts using BERTopic, then manually sorted and merged the generated topics into themes, leading to a total of 20 topics in 8 themes. \textit{Results}: The most prevalent topics fall within the theme Design \& Architecture, with a strong focus on retrieval-augmented generation (RAG) systems. Other frequently discussed topics include model capabilities and enhancement techniques (e.g., fine-tuning, prompt engineering), infrastructure and tooling, and risks and ethical challenges. \textit{Implications}: Our results highlight current discussions and challenges in deploying LLMs in production. This way, we provide a systematic overview of key aspects practitioners should be aware of when developing LLM-based applications. We further pale off topics of interest for academics where further research is needed.

In this note we introduce a notion of dichotomy which generalizes the classical concept of exponential dichotomy and the recent notion of Bohl dichotomy. A key attribute is the discussion of the sets of subspaces of the state space on which the dichotomy estimates are uniform. Two main results are a dichotomy spectral theorem based on our notion of dichotomy which is uniform on subspaces and a formula for the dichotomy spectral intervals which is new for the Bohl dichotomy spectrum as well as for the classical exponential dichotomy spectrum.

Retrieval-augmented generation (RAG) is an umbrella of different components, design decisions, and domain-specific adaptations to enhance the capabilities of large language models and counter their limitations regarding hallucination and outdated and missing knowledge. Since it is unclear which design decisions lead to a satisfactory performance, developing RAG systems is often experimental and needs to follow a systematic and sound methodology to gain sound and reliable results. However, there is currently no generally accepted methodology for RAG evaluation despite a growing interest in this technology. In this paper, we propose a first blueprint of a methodology for a sound and reliable evaluation of RAG systems and demonstrate its applicability on a real-world software engineering research task: the validation of configuration dependencies across software technologies. In summary, we make two novel contributions: (i) A novel, reusable methodological design for evaluating RAG systems, including a demonstration that represents a guideline, and (ii) a RAG system, which has been developed following this methodology, that achieves the highest accuracy in the field of dependency validation. For the blueprint's demonstration, the key insights are the crucial role of choosing appropriate baselines and metrics, the necessity for systematic RAG refinements derived from qualitative failure analysis, as well as the reporting practices of key design decision to foster replication and evaluation.

We present here the current state of a collection of promising ultraviolet technologies in preparation for the Habitable Worlds Observatory. Working with experts representing a significant number of groups working in the ultraviolet, we summarize some of the leading science drivers, present an argument for a 100 nm blue wavelength cutoff, and gather current state of the art of UV technologies. We present the state of the art of contamination control, a crucial piece of the UV instrument plan. We explore next steps with individual technologies, as well as present paths forward with systems level testing and development.

Aspera is a NASA Astrophysics Pioneers SmallSat mission designed to study diffuse OVI emission from the warm-hot phase gas in the halos of nearby galaxies. Its payload consists of two identical Rowland Circle-type long-slit spectrographs, sharing a single MicroChannel plate detector. Each spectrograph channel consists of an off-axis parabola primary mirror and a toroidal diffraction grating optimized for the 1013-1057 Angstroms bandpass. Despite the simple configuration, the optical alignment/integration process for Aspera is challenging due to tight optical alignment tolerances, driven by the compact form factor, and the contamination sensitivity of the Far-Ultraviolet optics and detectors. In this paper, we discuss implementing a novel multi-phase approach to meet these requirements using state-of-the-art optical metrology tools. For coarsely positioning the optics we use a blue-laser 3D scanner while the fine alignment is done with a Zygo interferometer and a custom computer-generated hologram. The detector focus requires iterative in-vacuum alignment using a Vacuum UV collimator. The alignment is done in a controlled cleanroom facility at the University of Arizona., Comment: Manuscript submitted for Proceedings of Astronomical Telescopes + Instrumentation 2024, Paper no. 13093-9

Thin film interference is integral to modern photonics and optoelectronics, e.g. allowing for precise design of high performance optical filters, efficiency enhancements in photovoltaics and light-emitting devices, as well as the realization of microlasers and high-performance photodetectors. However, interference inevitably leads to a change of spectral characteristics with angle, which is generally undesired and can limit the usefulness of thin-film coatings and devices. Here, we introduce a strategy to overcome this fundamental limit in optics by utilizing and tuning the exciton-polariton modes arising in ultra-strongly coupled microcavities. We demonstrate optical filters with narrow pass bands that shift by less than their half width (<15 nm) even at extreme angles. Our filters cover the entire visible range and surpass comparable metal-dielectric-metal filters in all relevant metrics. By expanding this strategy to strong coupling with the photonic sidebands of dielectric multilayer stacks, we also obtain filters with high extinction ratios and up to 98% peak transmission. Based on these findings, we realize ultrathin and flexible narrowband filter films, monolithically integrate our filters with organic photodiodes, and demonstrate polarization-sensitive polariton filters. These results illustrate how strong coupling provides additional degrees of freedom in thin film optics that will enable a multitude of exciting new applications in micro-optics, sensing, and biophotonics.

Background: Programming skills are advantageous to navigate today's society, so it is important to teach them to students. However, failure rates for programming courses are high, and especially students who fall behind early in introductory programming courses tend to stay behind. Objective: To catch these students as early as possible, we aim to develop an early warning system, so we can offer the students support, for example, in the form of syntax drill-and-practice exercises. Method: To develop the early warning system, we assess different cognitive skills of students of an introductory programming course. On several points in time over the course, students complete tests that measure their ability to develop a mental model of programming, language skills, attention, and fluid intelligence. Then, we evaluated to what extent these skills predict whether students acquire programming skills. Additionally, we assess how syntax drill-and-practice exercises improve how students acquire programming skill. Findings: Most of the cognitive skills can predict whether students acquire programming skills to a certain degree. Especially the ability to develop an early mental model of programming and language skills appear to be relevant. Fluid intelligence also shows predictive power, but appears to be comparable with the ability to develop a mental model. Furthermore, we found a significant positive effect of the syntax drill-and-practice exercises on the success of a course. Implications: Our first suggestion of an early warning system consists of few, easy-to-apply tests that can be integrated in programming courses or applied even before a course starts. Thus, with the start of a programming course, students who are at high risk of failing can be identified and offered support, for example, in the form of syntax drill-and-practice exercises to help students to develop programming skills., Comment: 20 pages, 8 figures

Background: In times when the ability to program is becoming increasingly important, it is still difficult to teach students to become successful programmers. One remarkable aspect are recent findings from neuro-imaging studies, which suggest a consistent role of language competency of novice programmers when they learn programming. Thus, for effectively teaching programming, it might be beneficial to draw from linguistic research, especially from foreign language acquisition. Objective: The goal of this study is to investigate the feasibility of this idea, such that we can enhance learning programming by activating language learning mechanisms. Method: To this end, we conducted an empirical study, in which we taught one group of students an artificial language, while another group received an introduction into Git as control condition, before we taught both groups basic programming knowledge in a programming course. Result: We observed that the training of the artificial language can be easily integrated into our curriculum. Furthermore, we observed that language learning strategies were activated and that participants perceived similarities between learning the artificial language and the programming language. However, within the context of our study, we did not find a significant benefit for programming competency when students learned an artificial language first. Conclusion: Our study lays the methodological foundation to explore the use of natural language acquisition research and expand this field step by step. We report our experience here to guide research and to open up the possibilities from the field of linguistic research to improve programming acquisition., Comment: 13 pages, 5 figures

We consider the shape optimization of flow fields for electrochemical cells. Our goal is to improve the cell by modifying the shape of its flow field. To do so, we introduce simulation models of the flow field with and without the porous transport layer. The latter is less detailed and used for shape optimization, whereas the former is used to validate our obtained results. We propose three objective functions based on the uniformity of the flow and residence time as well as the wall shear stress. After considering the respective optimization problems separately, we use techniques from multi-criteria optimization to treat the conflicting objective functions systematically. Our results highlight the potential of our approach for generating novel flow field designs for electrochemical cells.

Bohl dichotomy is a notion of hyperbolicity for linear nonautonomous difference equations that is weaker than the classical concept of exponential dichotomy. In the class of systems with bounded invertible coefficient matrices which have bounded inverses, we study the relation between the set $\mathrm{BD}$ of systems with Bohl dichotomy and the set $\mathrm{ED}$ of systems with exponential dichotomy. It can be easily seen from the definition of Bohl dichotomy that $\mathrm{ED} \subseteq \mathrm{BD}$. Using a counterexample we show that the closure of $\mathrm{ED}$ is not contained in $\mathrm{BD}$. The main result of this paper is the characterization $\operatorname{int}\mathrm{BD} = \mathrm{ED}$. The proof uses upper triangular normal forms of systems which are dynamically equivalent and utilizes a diagonal argument to choose subsequences of perturbations each of which is constructed with the Millionshikov Rotation Method. An Appendix describes the Millionshikov Rotation Method in the context of nonautonomous difference equations as a universal tool.

Background: Despite similar education and background, programmers can exhibit vast differences in efficacy. While research has identified some potential factors, such as programming experience and domain knowledge, the effect of these factors on programmers' efficacy is not well understood. Aims: We aim at unraveling the relationship between efficacy (speed and correctness) and measures of programming experience. We further investigate the correlates of programmer efficacy in terms of reading behavior and cognitive load. Method: For this purpose, we conducted a controlled experiment with 37~participants using electroencephalography (EEG) and eye tracking. We asked participants to comprehend up to 32 Java source-code snippets and observed their eye gaze and neural correlates of cognitive load. We analyzed the correlation of participants' efficacy with popular programming experience measures. Results: We found that programmers with high efficacy read source code more targeted and with lower cognitive load. Commonly used experience levels do not predict programmer efficacy well, but self-estimation and indicators of learning eagerness are fairly accurate. Implications: The identified correlates of programmer efficacy can be used for future research and practice (e.g., hiring). Future research should also consider efficacy as a group sampling method, rather than using simple experience measures., Comment: 12 pages, 7 figures, To be published at Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE '22)

For nonautonomous linear difference equations with bounded coefficients on $\mathbb{N}$ which have a bounded inverse, we introduce two different notions of spectra and discuss their relation to the well-known exponential dichotomy spectrum. The first new spectral notion is called Bohl spectrum and is based on an extended notion of the concept of Bohl exponents. The second new spectral notion is called Bohl dichotomy spectrum and is based on a relaxed version of exponential dichotomy called Bohl dichotomy. We prove spectral theorems and show that the Bohl dichotomy spectrum is the closure of the Bohl spectrum and also a subset of the exponential dichotomy spectrum. We discuss the spectra of upper triangular systems and how they relate to the spectra of their diagonal entries. An example illustrates the subtle differences between the different notions of spectra.

Using Maxwell's mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} = \frac{\partial \mathbf{D}}{\partial t} + \mathbf{j}$, $\operatorname{div} \mathbf{D} = \varrho$, $\operatorname{div} \mathbf{B} = 0$, which together with the constituting relations $\mathbf{D} = \varepsilon_0 \mathbf{E}$, $\mathbf{B} = \mu_0 \mathbf{H}$, form what we call today Maxwell's equations. Main tools are the divergence, curl and gradient integration theorems and a version of Poincare's lemma formulated in vector calculus notation. Remarks on the history of the development of electrodynamic theory, quotations and references to original and secondary literature complement the paper.

Egyptologists and historians of mathematics around 1930 did an admirable job in showing that problem 14 of the newly discovered Moscow Papyrus from around 1850 BCE amounts to a general and exact calculation of the volume of a truncated pyramid (frustum). They were less successful in giving tentative explanations of what convinced the Egyptians of its correctness. In particular, they never looked into the possibility of dissecting three identical copies of the frustum and recomposing them into three boxes of differing sizes whose volumes can be easily calculated. This is surprising because the formula at which the historians arrived seems to suggest this procedure. About 2000 years after the Egyptians, the Chinese scholar Liu Hui did exactly this for the almost identical problem from the Nine Chapters. If those historians of mathematics around 1930 had known Liu Hui's algorithm they could have easily drawn tentative conclusions also for the Egyptian case. The present paper suggests that it was their knowledge of rigorous Euclidean geometry and of relatively modern algebra which distorted the judgment of those historians, something which could not have been the case for Liu Hui. Their failure seems to have discouraged later Egyptologists to look for explanations or to even point to Liu Hui when his work had become known. Thus a chance was missed to use the great intuitive and pedagogic potential of a remarkable piece of Egyptian mathematics. This paper is not a contribution to the historiography of Egyptian mathematics for which the author is no specialist but argues primarily on a methodological level using secondary historical sources. The paper is partly inspired by a more recent publication of Paul Shutler (2009) who suggests an intuitive and historically possible proof also for the special, and mathematically crucial case of the second formula, which is related to the full pyramid.

Motivated by sequential detection of transient signals in high dimensional data stream, we study the performance of EWMA, MA, CUSUM, and GLRT charts for detecting a transient signal in multivariate data streams in terms of the power of detection (POD) under the constraint of false detecting probability (FDP) at the stationary state. Approximations are given for FDP and POD. Comparisons show that the EWMA chart performs equally well as the GLRT chart when the signal strength is unknown, while its design is free of signal length and easy to update. In addition, the MEWMA chart with hard-threshold performs better when the signal only appears in a small portion of the channels. Dow Jones 30 industrial stock prices are used for illustration.

Determining whether a configurable software system has a performance bug or it was misconfigured is often challenging. While there are numerous debugging techniques that can support developers in this task, there is limited empirical evidence of how useful the techniques are to address the actual needs that developers have when debugging the performance of configurable software systems; most techniques are often evaluated in terms of technical accuracy instead of their usability. In this paper, we take a human-centered approach to identify, design, implement, and evaluate a solution to support developers in the process of debugging the performance of configurable software systems. We first conduct an exploratory study with 19 developers to identify the information needs that developers have during this process. Subsequently, we design and implement a tailored tool, adapting techniques from prior work, to support those needs. Two user studies, with a total of 20 developers, validate and confirm that the information that we provide helps developers debug the performance of configurable software systems.

Many software systems can be tuned for multiple objectives (e.g., faster runtime, less required memory, less network traffic or energy consumption, etc.). Optimizers built for different objectives suffer from "model disagreement"; i.e., they have different (or even opposite) insights and tactics on how to optimize a system. Model disagreement is rampant (at least for configuration problems). Yet prior to this paper, it has barely been explored. This paper shows that model disagreement can be mitigated via VEER, a one-dimensional approximation to the N-objective space. Since it is exploring a simpler goal space, VEER runs very fast (for eleven configuration problems). Even for our largest problem (with tens of thousands of possible configurations), VEER finds as good or better optimizations with zero model disagreements, three orders of magnitude faster (since its one-dimensional output no longer needs the sorting procedure). Based on the above, we recommend VEER as a very fast method to solve complex configuration problems, while at the same time avoiding model disagreement., Comment: 27 pages, 7 figures, 4 tables, accepted by EMSE