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The construction of high-resolution shock-capturing schemes is vital in producing highly accurate gravitational waveforms from neutron star binaries. The entropy based flux limiting (EFL) scheme is able to perform fast converging binary neutron star merger simulations reaching up to fourth-order convergence in the gravitational waveform phase. In these results the EFL method was used only in the dynamical evolution of initial data constructed with the Lorene library. Here, we extend the use of the EFL method to the construction of eccentricity reduced initial data for neutron star binaries and present several new BNS simulations resulting from such initial data and show for the first time up to optimal fifth-order convergence in the gravitational waveform phase., Comment: 12 pages, 10 figures

A flight trajectory defines how exactly a quadrocopter moves in the three-dimensional space from one position to another. Automatic flight trajectory planning faces challenges such as high computational effort and a lack of precision. Hence, when low computational effort or precise control is required, programming the flight route trajectory manually might be preferable. However, this requires in-depth knowledge of how to accurately plan flight trajectories in three-dimensional space. We propose planning quadrocopter flight trajectories manually using the Programming by Demonstration (PbD) approach -- simply drawing the trajectory in the three-dimensional space by hand. This simplifies the planning process and reduces the level of in-depth knowledge required. We implemented the approach in the context of the Quadcopter Lab at Ulm University. In order to evaluate our approach, we compare the precision and accuracy of the trajectories drawn by a user using our approach as well as the required time with those manually programmed using a domain specific language. The evaluation shows that the Drawjectory workflow is, on average, 78.7 seconds faster without a significant loss of precision, shown by an average deviation 6.67 cm.

Modeling is often associated with complex and heavy tooling, leading to a negative perception among practitioners. However, alternative paradigms, such as everything-as-code or low-code, are gaining acceptance due to their perceived ease of use. This paper explores the dichotomy between these perceptions through the lens of ``modeler experience'' (MX). MX includes factors such as user experience, motivation, integration, collaboration \& versioning and language complexity. We examine the relationships between these factors and their impact on different modeling usage scenarios. Our findings highlight the importance of considering MX when understanding how developers interact with modeling tools and the complexities of modeling and associated tooling.

Purpose: Software modelling and Model-Driven Engineering (MDE) is traditionally studied from a technical perspective. However, one of the core motivations behind the use of software models is inherently human-centred. Models aim to enable practitioners to communicate about software designs, make software understandable, or make software easier to write through domain-specific modelling languages. Several recent studies challenge the idea that these aims can always be reached and indicate that human factors play a role in the success of MDE. However, there is an under-representation of research focusing on human factors in modelling. Methods: During a GI-Dagstuhl seminar, topics related to human factors in modelling were discussed by 26 expert participants from research and industry. Results: In breakout groups, five topics were covered in depth, namely modelling human aspects, factors of modeller experience, diversity and inclusion in MDE, collaboration and MDE, and teaching human-aware MDE. Conclusion: We summarise our insights gained during the discussions on the five topics. We formulate research goals, questions, and propositions that support directing future initiatives towards an MDE community that is aware of and supportive of human factors and values.

Lipidomics generates large data that makes manual annotation and interpretation challenging. Lipid chemical and structural diversity with structural isomers further complicates annotation. Although, several commercial and open-source software for targeted lipid identification exists, it lacks automated method generation workflows and integration with statistical and bioinformatics tools. We have developed the Comprehensive Lipidomic Automated Workflow (CLAW) platform with integrated workflow for parsing, detailed statistical analysis and lipid annotations based on custom multiple reaction monitoring (MRM) precursor and product ion pair transitions. CLAW contains several modules including identification of carbon-carbon double bond position(s) in unsaturated lipids when combined with ozone electrospray ionization (OzESI)-MRM methodology. To demonstrate the utility of the automated workflow in CLAW, large-scale lipidomics data was collected with traditional and OzESI-MRM profiling on biological and non-biological samples. Specifically, a total of 1497 transitions organized into 10 MRM-based mass spectrometry methods were used to profile lipid droplets isolated from different brain regions of 18-24 month-old Alzheimer's disease mice and age-matched wild-type controls. Additionally, triacyclglycerols (TGs) profiles with carbon-carbon double bond specificity were generated from canola oil samples using OzESI-MRM profiling. We also developed an integrated language user interface with large language models using artificially intelligent (AI) agents that permits users to interact with the CLAW platform using a chatbot terminal to perform statistical and bioinformatic analyses. We envision CLAW pipeline to be used in high-throughput lipid structural identification tasks aiding users to generate automated lipidomics workflows ranging from data acquisition to AI agent-based bioinformatic analysis., Comment: 53 pages, 4 main figures, 23 Supporting figures, 10 Supporting Tables

The current work is focused on the impact of the lithium stoichiometry on electrical conductivity, acoustic properties and high-temperature stability of single crystalline Li(Nb,Ta)O$_{3}$ at high temperatures. The crystals grown from Li-deficient melts were treated by the vapor transport equilibration (VTE) method, achieving near stoichiometric Li-content. It is shown, that the VTE-treated specimens generally exhibit lower conductivity at temperatures below 800 {\deg}C, which is attributed to the reduced number of Li-vacancies in near stoichiometric Li(Nb,Ta)O$_{3}$, provided that the Li-ion migration dominates the conductivity in this temperature range. Further, it is shown, that above 600-650 {\deg}C different mechanism increasingly contributes to the conductivity, which is consequently attributed to the electronic conduction. Further, it is shown that losses in LNT strongly increase above about 500 {\deg}C, which is interpreted to originate from conductivity-related relaxation mechanism. Finally, the thermal stability of Li(Nb,Ta)O$_{3}$ is evaluated by the measurement of the conductivity and resonance frequency as a function of time. It is found that during annealing at 700 {\deg}C for 350 hours, the resonance frequency of LiNbO$_{3}$ remains in a {\textpm} 100 ppm range of the initial value of 3.5 MHz., Comment: Submitted to Physica Status Solidi A: Applications and Materials Science on 21st December 2023

CONTEXT The R programming language has a huge and active community, especially in the area of statistical computing. Its interpreted nature allows for several interesting constructs, like the manipulation of functions at run-time, that hinder the static analysis of R programs. At the same time, there is a lack of existing research regarding how these features, or even the R language as a whole are used in practice. OBJECTIVE In this paper, we conduct a large-scale, static analysis of more than 50 million lines of real-world R programs and packages to identify their characteristics and the features that are actually used. Moreover, we compare the similarities and differences between the scripts of R users and the implementations of package authors. We provide insights for static analysis tools like the lintr package as well as potential interpreter optimizations and uncover areas for future research. METHOD We analyze 4230 R scripts submitted alongside publications and the sources of 19450 CRAN packages for over 350000 R files, collecting and summarizing quantitative information for features of interest. RESULTS We find a high frequency of name-based indexing operations, assignments, and loops, but a low frequency for most of R's reflective functions. Furthermore, we find neither testing functions nor many calls to R's foreign function interface (FFI) in the publication submissions. CONCLUSION R scripts and package sources differ, for example, in their size, the way they include other packages, and their usage of R's reflective capabilities. We provide features that are used frequently and should be prioritized by static analysis tools, like operator assignments, function calls, and certain reflective functions like load., Comment: 11+1 pages, 6 figures, 2 tables, accepted at MSR 2024

The entropy based flux-limiting (EFL) scheme is a novel approach designed to accurately resolve shocks and discontinuities in special and general relativistic hydrodynamics. By adaptively adjusting the numerical fluxes, the EFL method mitigates oscillations and preserves smooth transition across discontinuities in shock-dominated flows. Here, we extend the applicability of the EFL method beyond special/general relativistic hydrodynamics to scalar conservation laws and show how to treat systems without a thermodynamic entropy. This is an indication that the method has universal applicability to any system of partial differential equations that can be written in conservation form. We also present some further very challenging special/general relativistic hydrodynamics applications of the EFL method., Comment: 13 pages, 15 figures

Assume that a grocery item is sold 1'234 times on a given day. What should an ideal forecast have predicted for such a well-selling item, on average? More generally, when considering a given outcome value, should the empirical average of forecasted expectation values for that outcome ideally match it? Many people will intuitively answer the first question with "1'234, of course", and affirm the second. Perhaps surprisingly, such grouping of data by outcome induces a bias in the evaluation. An evaluation procedure that is aimed at verifying the absence of bias across velocities, when based on such segregation by outcome, therefore fools forecast evaluators and incentivizes forecasters to produce overly exaggerated (extreme) forecasts. Such anticipatory adjustments jeopardize forecast calibration and clearly worsen the forecast quality - this problem was named the "Forecaster's Dilemma" by Lerch et al. in 2017 (Statististical Science 32, 106). As a solution to check for bias across velocities, forecast evaluators should group pairs of forecasts and outcomes by the predicted values, and evaluate empirical mean outcomes per prediction bucket. Within a simple mathematical treatment for the number of items sold in a supermarket, the reader is walked through the dilemma and its circumvention., Comment: 6 pages

We provide a construction of binary pseudorandom sequences based on Hardy fields $\mathcal{H}$ as considered by Boshernitzan. In particular we give upper bounds for the well distribution measure and the correlation measure defined by Mauduit and S\'ark\"ozy. Finally we show that the correlation measure of order $s$ is small only if $s$ is small compared to the ``growth exponent'' of $\mathcal{H}$., Comment: 15 pages

The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0<\alpha<1$ were of recent interest. In the present paper we want to extend our considerations of the length of a random partition by providing a local limit theorem., Comment: 20 pages

We study the class of univariate polynomials $\beta_k(X)$, introduced by Carlitz, with coefficients in the algebraic function field $\mathbb F_q(t)$ over the finite field $\mathbb F_q$ with $q$ elements. It is implicit in the work of Carlitz that these polynomials form a $\mathbb F_q[t]$-module basis of the ring $\text{Int}(\mathbb F_q[t]) = \{f \in \mathbb F_q(t)[X] \mid f(\mathbb F_q[t]) \subseteq \mathbb F_q[t]\}$ of integer-valued polynomials on the polynomial ring $\mathbb F_q[t]$. This stands in close analogy to the famous fact that a $\mathbb Z$-module basis of the ring $\text{Int}(\mathbb Z)$ is given by the binomial polynomials $\binom{X}{k}$. We prove, for $k = q^s$, where $s$ is a non-negative integer, that $\beta_k$ is irreducible in $\text{Int}(\mathbb F_q[t])$ and that it is even absolutely irreducible, that is, all of its powers $\beta_k^m$ with $m>0$ factor uniquely as products of irreducible elements of this ring. As we show, this result is optimal in the sense that $\beta_k$ is not even irreducible if $k$ is not a power of $q$.

Attack graphs are a tool for analyzing security vulnerabilities that capture different and prospective attacks on a system. As a threat modeling tool, it shows possible paths that an attacker can exploit to achieve a particular goal. However, due to the large number of vulnerabilities that are published on a daily basis, they have the potential to rapidly expand in size. Consequently, this necessitates a significant amount of resources to generate attack graphs. In addition, generating composited attack models for complex systems such as self-adaptive or AI is very difficult due to their nature to continuously change. In this paper, we present a novel fragment-based attack graph generation approach that utilizes information from publicly available information security databases. Furthermore, we also propose a domain-specific language for attack modeling, which we employ in the proposed attack graph generation approach. Finally, we present a demonstrator example showcasing the attack generator's capability to replicate a verified attack chain, as previously confirmed by security experts., Comment: To appear at the 57th Hawaii International Conference on Social Systems (HICSS-57), Honolulu, Hawaii. 2024

Joint safety and security analysis of cyber-physical systems is a necessary step to correctly capture inter-dependencies between these properties. Attack-Fault Trees represent a combination of dynamic Fault Trees and Attack Trees and can be used to model and model-check a holistic view on both safety and security. Manually creating a complete AFT for the whole system is, however, a daunting task. It needs to span multiple abstraction layers, e.g., abstract application architecture and data flow as well as system and library dependencies that are affected by various vulnerabilities. We present an AFT generation tool-chain that facilitates this task using partial Fault and Attack Trees that are either manually created or mined from vulnerability databases. We semi-automatically create two system models that provide the necessary information to automatically combine these partial Fault and Attack Trees into complete AFTs using graph transformation rules.

Self-adaptive systems offer several attack surfaces due to the communication via different channels and the different sensors required to observe the environment. Often, attacks cause safety to be compromised as well, making it necessary to consider these two aspects together. Furthermore, the approaches currently used for safety and security analysis do not sufficiently take into account the intermediate steps of an adaptation. Current work in this area ignores the fact that a self-adaptive system also reveals possible vulnerabilities (even if only temporarily) during the adaptation. To address this issue, we propose a modeling approach that takes into account the different relevant aspects of a system, its adaptation process, as well as safety hazards and security attacks. We present several models that describe different aspects of a self-adaptive system and we outline our idea of how these models can then be combined into an Attack-Fault Tree. This allows modeling aspects of the system on different levels of abstraction and co-evolve the models using transformations according to the adaptation of the system. Finally, analyses can then be performed as usual on the resulting Attack-Fault Tree.

Gravitational wave astronomy pipelines rely on template waveform models for searches and parameter estimation purposes. For coalescing binary neutron stars (BNS), such models need to accurately reproduce numerical relativity (NR) up to merger, in order to provide robust estimate of the stars' equation of state - dependent parameters. In this work we present an improved version of the Effective One Body (EOB) model $\tt TEOBResumS$ for gravitational waves from BNS systems. Building upon recent post-Newtonian calculations, we include subleading order tidal terms in the waveform multipoles and EOB metric potentials, as well as add up to 5.5PN terms in the gyro-gravitomagnetic functions entering the spin-orbit sector of the model. In order to further improve the EOB-NR agreement in the last few orbital cycles before merger, we introduce next-to-quasicircular corrections in the waveform -- informed by a large number of BNS NR simulations -- and introduce a new NR-informed parameter entering the tidal sector of our conservative dynamics. The performance of our model is then validated against 14 new eccentricity reduced simulations of unequal mass, spinning binaries with varying equation of state. A time-domain phasing analysis and mismatch computations demonstrate that the new model overall improves over the previous version of $\tt TEOBResumS$. Finally, we present a closed-form frequency domain representation of the (tidal) amplitude and phase of the new model. This representation accounts for mass-ratio, aligned spin and (resummed) spin-quadrupole effects in the tidal phase and -- within the calibration region -- it is faithful to the original model., Comment: 17 pages, 6 figures

Dedicated model transformation languages are claimed to provide many benefits over the use of general purpose languages for developing model transformations. However, the actual advantages associated with the use of MTLs are poorly understood empirically. There is little knowledge and empirical assessment about what advantages and disadvantages hold and where they originate from. In a prior interview study, we elicited expert opinions on what advantages result from what factors and a number of factors that moderate the influence. We aim to quantitatively asses the interview results to confirm or reject the effects posed by different factors. We intend to gain insights into how valuable different factors are so that future studies can draw on these data for designing targeted and relevant studies. We gather data on the factors and quality attributes using an online survey. To analyse the data, we use universal structure modelling based on a structure model. We use significance values and path coefficients produced bz USM for each hypothesised interdependence to confirm or reject correlation and to weigh the strength of influence present. We analyzed 113 responses. The results show that the Tracing and Reuse Mechanisms are most important overall. Though the observed effects were generally 10 times lower than anticipated. Additionally, we found that a more nuanced view of moderation effects is warranted. Their moderating influence differed significantly between the different influences, with the strongest effects being 1000 times higher than the weakest. The empirical assessment of MTLs is a complex topic that cannot be solved by looking at a single stand-alone factor. Our results provide clear indication that evaluation should consider transformations of different sizes and use-cases. Language development should focus on providing transformation specific reuse mechanisms ., Comment: Submitted to EMSE as part of the Registered Reports track from ESEM 2022. arXiv admin note: text overlap with arXiv:2209.06570

In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented an adaptive estimate for the energy norm of the error in the conjugate gradient (CG) method. In this paper, we extend the estimate to algorithms for solving linear approximation problems with a general, possibly rectangular matrix that are based on applying CG to a system with a positive (semi-)definite matrix build from the original matrix. We show that the resulting estimate preserves its key properties: it can be very cheaply evaluated, and it is numerically reliable in finite-precision arithmetic under some mild assumptions. We discuss algorithms based on Hestenes-Stiefel-like implementation (often called CGLS and CGNE in the literature) as well as on bidiagonalization (LSQR and CRAIG), and both unpreconditioned and preconditioned variants. The numerical experiments confirm the robustness and very satisfactory behaviour of the estimate.

In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe the connections with mathematical topics such as equidistribution and discrepancy, metric number theory, normality, pseudorandomness, Diophantine equations, and the subsequence principle. In the final section of the paper we prove new results which provide necessary and sufficient conditions for the central limit theorem for subsequences, in the spirit of Nikishin's resonance theorem for convergence systems. More precisely, we characterize those sequences of random variables which allow to extract a subsequence satisfying a strong form of the central limit theorem., Comment: 58 pages. This is mostly a survey paper. The final section contains new results (with proofs). Version 2: minor corrections and updates. Version 3: corrected an error on p.8 (thanks to Jean-Francois Burnol for pointing out the error)

Using an adapted version of the SGRID code, we construct for the first time consistent quasi-equilibrium configurations for a binary system consisting of two neutron stars in which each is admixed with dark matter. The stars are modelled as a system of two non-interacting fluids minimally coupled to gravity. For the fluid representing baryonic matter the SLy equation of state is used, whereas the second fluid, which corresponds to dark matter, is described using the equation of state of a degenerate Fermi gas. We consider two different scenarios for the distribution of the dark matter. In the first scenario the dark matter is confined to the core of the star, whereas in the second scenario the dark matter extends beyond the surface of the baryonic matter, forming a halo around the baryonic star. The presence of dark matter alters the star's reaction to the companion's tidal forces, which we investigate in terms of the coordinate deformation and mass shedding parameters. The constructed quasi-equilibrium configurations mark the first step towards consistent numerical-relativity simulations of dark matter admixed neutron star binaries., Comment: 13 pages, 11 figures, v2: Added investigation of dependence on dark matter particle mass

Interpreting gravitational wave observations and understanding the physics of astrophysical compact objects such as black holes or neutron stars requires accurate theoretical models. Here, we present a new numerical relativity computer program, called Nmesh, that has the design goal to become a next generation program for the simulation of challenging relativistic astrophysics problems such as binary black hole or neutron star mergers. In order to efficiently run on large supercomputers, Nmesh uses a discontinuous Galerkin method together with a domain decomposition and mesh refinement that parallelizes and scales well. In this work, we discuss the various numerical methods we use. We also present results of test problems such as the evolution of scalar waves, single black holes and neutron stars, as well as shock tubes. In addition, we introduce a new positivity limiter that allows us to stably evolve single neutron stars without an additional artificial atmosphere, or other more traditional limiters., Comment: 44 pages, 17 figures

Forecast quality should be assessed in the context of what is possible in theory and what is reasonable to expect in practice. Often, one can identify an approximate upper bound to a probabilistic forecast's sharpness, which sets a lower, not necessarily achievable, limit to error metrics. In retail forecasting, a simple, but often unconquerable sharpness limit is given by the Poisson distribution. When evaluating forecasts using traditional metrics such as Mean Absolute Error, it is hard to judge whether a certain achieved value reflects unavoidable Poisson noise or truly indicates an overdispersed prediction model. Moreover, every evaluation metric suffers from precision scaling: Perhaps surprisingly, the metric's value is mostly defined by the selling rate and by the resulting rate-dependent Poisson noise, and only secondarily by the forecast quality. For any metric, comparing two groups of forecasted products often yields "the slow movers are performing worse than the fast movers" or vice versa, the na\"ive scaling trap. To distill the intrinsic quality of a forecast, we stratify predictions into buckets of approximately equal predicted value and evaluate metrics separately per bucket. By comparing the achieved value per bucket to benchmarks, we obtain an intuitive visualization of forecast quality, which can be summarized into a single rating that makes forecast quality comparable among different products or even industries. The thereby developed scaling-aware forecast rating is applied to forecasting models used on the M5 competition dataset as well as to real-life forecasts provided by Blue Yonder's Demand Edge for Retail solution for grocery products in Sainsbury's supermarkets in the United Kingdom. The results permit a clear interpretation and high-level understanding of model quality by non-experts., Comment: 39 pages, 11 figures; improved introduction and outlook

We present the second data release of gravitational waveforms from binary neutron star merger simulations performed by the Computational Relativity (CoRe) collaboration. The current database consists of 254 different binary neutron star configurations and a total of 590 individual numerical-relativity simulations using various grid resolutions. The released waveform data contain the strain and the Weyl curvature multipoles up to $\ell=m=4$. They span a significant portion of the mass, mass-ratio,spin and eccentricity parameter space and include targeted configurations to the events GW170817 and GW190425. CoRe simulations are performed with 18 different equations of state, seven of which are finite temperature models, and three of which account for non-hadronic degrees of freedom. About half of the released data are computed with high-order hydrodynamics schemes for tens of orbits to merger; the other half is computed with advanced microphysics. We showcase a standard waveform error analysis and discuss the accuracy of the database in terms of faithfulness. We present ready-to-use fitting formulas for equation of state-insensitive relations at merger (e.g. merger frequency), luminosity peak, and post-merger spectrum., Comment: 33 pages, 14 figures

Consider the problem of solving systems of linear algebraic equations $Ax=b$ with a real symmetric positive definite matrix $A$ using the conjugate gradient (CG) method. To stop the algorithm at the appropriate moment, it is important to monitor the quality of the approximate solution. One of the most relevant quantities for measuring the quality of the approximate solution is the $A$-norm of the error. This quantity cannot be easily computed, however, it can be estimated. In this paper we discuss and analyze the behaviour of the Gauss-Radau upper bound on the $A$-norm of the error, based on viewing CG as a procedure for approximating a certain Riemann-Stieltjes integral. This upper bound depends on a prescribed underestimate $\mu$ to the smallest eigenvalue of $A$. We concentrate on explaining a phenomenon observed during computations showing that, in later CG iterations, the upper bound loses its accuracy, and is almost independent of $\mu$. We construct a model problem that is used to demonstrate and study the behaviour of the upper bound in dependence of $\mu$, and developed formulas that are helpful in understanding this behavior. We show that the above mentioned phenomenon is closely related to the convergence of the smallest Ritz value to the smallest eigenvalue of $A$. It occurs when the smallest Ritz value is a better approximation to the smallest eigenvalue than the prescribed underestimate $\mu$. We also suggest an adaptive strategy for improving the accuracy of the upper bounds in the previous iterations., Comment: 30 pages, 8 figures

Forsythe formulated a conjecture about the asymptotic behavior of the restarted conjugate gradient method in 1968. We translate several of his results into modern terms, and generalize the conjecture (originally formulated only for symmetric positive definite matrices) to symmetric and nonsymmetric matrices. Our generalization is based on a two-sided or cross iteration with the given matrix and its transpose, which is based on the projection process used in the Arnoldi (or for symmetric matrices the Lanczos) algorithm. We prove several new results about the limiting behavior of this iteration, but the conjecture still remains largely open.

Background: Dedicated model transformation languages are claimed to provide many benefits over the use of general purpose languages for developing model transformations. However, the actual advantages and disadvantages associated with the use of model transformation languages are poorly understood empirically. There is little knowledge over what advantages and disadvantages hold in which cases and where they originate from. In a prior interview study, we elicited expert opinions on what advantages result from what factors surrounding model transformation languages as well as a number of moderating factors that moderate the influence. Objective: We aim to quantitatively asses the interview results to confirm or reject the influences and moderation effects posed by different factors and to gain insights into how valuable different factors are to the discussion. Method: We gather data on the factors and quality attributes using an online survey. To analyse the data and examine the hypothesised influences and moderations we use universal structure modelling based on a structural equation model. Universal structure modelling will produce significance values and path coefficients for each hypothesised and modelled interdependence between factors and quality attributes that can be used to confirm or reject correlation and to weigh the strength of influence present. Limitations: Due to the complexity and abstractness of the concepts under investigation, a measurement via reflective or formative indicators is not possible. Instead participants are queried about their assessment of concepts through a single item question. We further assume that positive and negative effects of a feature are more prominent if the feature is used more frequently., Comment: ESEM 2022: ACM/IEEE International Symposium on Empirical Software Engineering and Measurement - Registered Reports, September 19-23, 2022 Helsinki, Finland

Novices need to overcome initial barriers while programming cyber-physical systems behavior, like coding quadcopter missions, and should thus be supported by an adequately designed programming environment. Using multiple representations by including graphical previews is a common approach to ease coding and program understanding. However, novices struggle to map information of the code and graphical previews. Previous studies imply that mapping aids in a live programming environment might support novices while programming and foster a deeper understanding of the content. To implement these mapping aids in a domain independent way Source Location Tracking based on run-time information can be used. In our study, we tested N=82 participants while interacting and learning in an online programming environment. Using our 2x2 between-subject design study, we investigated the effects of two mapping aids: highlighting and dynamic linking on coding correctness including typical errors, and learning outcomes. Based on process data, successful strategies were analyzed. Combining both mapping aids compared to one aid resulted in higher performance. While highlights were more helpful for implementing the quadcopter missions, dynamic linking improved learning outcomes on the comprehension and application level . Traces of learning strategies were related to higher coding correctness and higher learning outcomes. Based on process data, users in the group with both aids had a higher chance of avoiding certain typical implementation mistakes. Implementing dynamic linking and highlighting through source location tracking is a promising approach to support novices to develop a better semantic understanding of the domain specific language. Depending on the coding tasks different mapping aids might be effective., Comment: 69 pages, submitted to the International Journal of Human Computer Studies, Andrea Vogt and Thomas Witte contributed equally to the manuscript

Let $(U_n)_{n\in \mathbb{N}}$ be a fixed linear recurrence sequence defined over the integers (with some technical restrictions). We prove that there exist effectively computable constants $B$ and $N_0$ such that for any $b,c\in \mathbb{Z}$ with $b> B$ the equation $U_n - b^m = c$ has at most two distinct solutions $(n,m)\in \mathbb{N}^2$ with $n\geq N_0$ and $m\geq 1$. Moreover, we apply our result to the special case of Tribonacci numbers given by $T_1= T_2=1$, $T_3=2$ and $T_{n}=T_{n-1}+T_{n-2}+T_{n-3}$ for $n\geq 4$. By means of the LLL-algorithm and continued fraction reduction we are able to prove $N_0=1.1\cdot 10^{37}$ and $B=e^{438}$. The corresponding reduction algorithm is implemented in Sage., Comment: 34 pages