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Many systems are topologically trivial in the bulk, but still have non-trivial wavefunctions locally in the Brillouin zone. For example, in a small-gap Dirac material the Berry curvature is strongly peaked, but cancels over the full Brillouin zone, while in semimetals and in nodal superconductors there may be a lower-dimensional winding topology associated to the nodes. Experimentally, it is difficult to directly observe such topology. We consider general bulk Hamiltonians with nodes and chiral symmetry, extending to them the method developed in Dutreix et al. [Nature, 574(7777):219-222 (2019)], which in particular detected the winding around Dirac cones in graphene using charge modulations around an impurity. We apply our method to nodal superconductors in 2d, in presence of a (non)magnetic impurity, measured by standard or spin-polarized STM tip. We derive general conditions on the impurity scattering and on the STM tip, expressed in terms of their preference among the two chiralities, for when the measurement near the impurity captures the winding difference between any chosen pair of (Bogoliubon) Dirac cones. We emphasize the robustness of observing vortices in momentum space, in contrast to dislocations in real space, in STM data. Testing the conditions on the topological nodal superconductor proposed for monolayer NbSe2 under an in-plane magnetic field, we find that spin-polarized STM on a magnetic impurity can detect the winding of each of the 12 nodes. We conclude that a judicious choice of impurity can be a powerful tool to determine topological quantities in 2d superconducting systems as well as any nodal chiral system., Comment: 17 pages, 6 figures

The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are only convergence results for some specific cases in one spatial dimension. The aim of this manuscript is therefore to prove that the Dirichlet-Neumann method converges for a class of semilinear elliptic equations on Lipschitz continuous domains in two and three spatial dimensions. This is achieved by first proving a new result on the convergence of nonlinear iterations in Hilbert spaces and then applying this result to the Steklov-Poincar\'e formulation of the Dirichlet-Neumann method.

Software analytics (SA) is frequently proposed as a tool to support practitioners in software engineering (SE) tasks. We have observed that several secondary studies on SA have been published. Some of these studies have overlapping aims and some have even been published in the same calendar year. This presents an opportunity to analyze the congruence or divergence of the conclusions in these studies. Such an analysis can help identify broader generalizations beyond any of the individual secondary studies. We identified five secondary studies on the use of SA for SE. These secondary studies cover primary research from 2000 to 2021. Despite the overlapping objectives and search time frames of these secondary studies, there is negligible overlap of primary studies between these secondary studies. Thus, each of them provides an isolated view, and together, they provide a fragmented view, i.e., there is no ``common picture'' of the area. Thus, we conclude that an overview of the literature identified by these secondary studies would be useful in providing a more comprehensive overview of the topic.

Recently, their has been development of an abstract approach to the Robin--Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. However, previously this setting has not been applicable to initial-boundary value problems. The aim of this short note is therefore to demonstrate that this general framework can be applied to such problems as well.

A method for assessing the quality of electronic material properties of thin-film metal oxide semiconductor field-effect transistors (MOSFETs) is presented. By investigating samples with MOCVD-grown MoS${_2}$ channels exposed to atmospheric conditions, the existence of electron traps in MoS${_2}$ and at the interface between the gate insulator and the thin-film MoS${_2}$ are revealed. Differential conductance and capacitance data of the transistor channels are plotted as 3D surfaces on a base plane spanned by the measurement frequency versus the gate voltage. The existence of defects is confirmed by comparison with ideal results from a theoretical model., Comment: 24 pages

We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically computationally challenging due to the martingale constraint, however, by extending the state space we can identify them with problems that exhibit a certain sequential martingale structure. Our method exploits such structures in combination with entropic regularisation, enabling fast computation of optimal solutions and allowing us to solve problems with a large number of marginals. We demonstrate the method by using it for computing robust price bounds for different options, such as lookback options and Asian options.

Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was only achieved for monotone increasing generalized quantifiers. In this paper, we modify the fundamental semantical guideline of dependence logic to create a framework that adequately handles both monotone and non-monotone generalized quantifiers. We demonstrate that this new logic can interpret dependence logic and possesses the same expressive power as existential second-order logic (ESO) on the level of formulas. Additionally, we establish truth conditions for generalized quantifiers and prove that the extended logic remains conservative over first-order logic with generalized quantifiers and is able to express the branching of continuous generalized quantifiers.

The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann--Neumann methods that have better convergence properties and require less computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov--Poincar\'e operators.

Understanding adaptive human driving behavior, in particular how drivers manage uncertainty, is of key importance for developing simulated human driver models that can be used in the evaluation and development of autonomous vehicles. However, existing traffic psychology models of adaptive driving behavior either lack computational rigor or only address specific scenarios and/or behavioral phenomena. While models developed in the fields of machine learning and robotics can effectively learn adaptive driving behavior from data, due to their black box nature, they offer little or no explanation of the mechanisms underlying the adaptive behavior. Thus, a generalizable, interpretable, computational model of adaptive human driving behavior is still lacking. This paper proposes such a model based on active inference, a behavioral modeling framework originating in computational neuroscience. The model offers a principled solution to how humans trade progress against caution through policy selection based on the single mandate to minimize expected free energy. This casts goal-seeking and information-seeking (uncertainty-resolving) behavior under a single objective function, allowing the model to seamlessly resolve uncertainty as a means to obtain its goals. We apply the model in two apparently disparate driving scenarios that require managing uncertainty, (1) driving past an occluding object and (2) visual time sharing between driving and a secondary task, and show how human-like adaptive driving behavior emerges from the single principle of expected free energy minimization., Comment: 33 pages, 13 figures

Information about autonomic nervous system (ANS) activity may be valuable for personalized atrial fibrillation (AF) treatment but is not easily accessible from the ECG. In this study, we propose a new approach for ECG-based assessment of respiratory modulation in AV nodal refractory period and conduction delay. A 1-dimensional convolutional neural network (1D-CNN) was trained to estimate respiratory modulation of AV nodal conduction properties from 1-minute segments of RR series, respiration signals, and atrial fibrillatory rates (AFR) using synthetic data that replicates clinical ECG-derived data. The synthetic data were generated using a network model of the AV node and 4 million unique model parameter sets. The 1D-CNN was then used to analyze respiratory modulation in clinical deep breathing test data of 28 patients in AF, where a ECG-derived respiration signal was extracted using a novel approach based on periodic component analysis. We demonstrated using synthetic data that the 1D-CNN can predict the respiratory modulation from RR series alone ($\rho$ = 0.805) and that the addition of either respiration signal ($\rho$ = 0.830), AFR ($\rho$ = 0.837), or both ($\rho$ = 0.855) improves the prediction. Results from analysis of clinical ECG data of 20 patients with sufficient signal quality suggest that respiratory modulation decreased in response to deep breathing for five patients, increased for five patients, and remained similar for ten patients, indicating a large inter-patient variability., Comment: 20 pages, 7 figures, 5 tables

We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and time-dependent Steklov--Poincar\'e operators. The convergence analysis is conducted without assuming restrictive regularity assumptions on the solutions or the numerical iterates. We also prove that these continuous convergence results extend to the discrete case obtained when combining domain decompositions with space-time finite elements., Comment: arXiv admin note: text overlap with arXiv:2210.13868

Context: It is an enigma that agile projects can succeed 'without requirements' when weak requirements engineering is a known cause for project failures. While agile development projects often manage well without extensive requirements test cases are commonly viewed as requirements and detailed requirements are documented as test cases. Objective: We have investigated this agile practice of using test cases as requirements to understand how test cases can support the main requirements activities, and how this practice varies. Method: We performed an iterative case study at three companies and collected data through 14 interviews and two focus groups. Results: The use of test cases as requirements poses both benefits and challenges when eliciting, validating, verifying, and managing requirements, and when used as a documented agreement. We have identified five variants of the test-cases-as-requirements practice, namely de facto, behaviour-driven, story-test driven, stand-alone strict and stand-alone manual for which the application of the practice varies concerning the time frame of requirements documentation, the requirements format, the extent to which the test cases are a machine executable specification and the use of tools which provide specific support for the practice of using test cases as requirements. Conclusions: The findings provide empirical insight into how agile development projects manage and communicate requirements. The identified variants of the practice of using test cases as requirements can be used to perform in-depth investigations into agile requirements engineering. Practitioners can use the provided recommendations as a guide in designing and improving their agile requirements practices based on project characteristics such as number of stakeholders and rate of change.

It is a conundrum that agile projects can succeed 'without requirements' when weak requirements engineering is a known cause for project failures. While Agile development projects often manage well without extensive requirements documentation, test cases are commonly used as requirements. We have investigated this agile practice at three companies in order to understand how test cases can fill the role of requirements. We performed a case study based on twelve interviews performed in a previous study. The findings include a range of benefits and challenges in using test cases for eliciting, validating, verifying, tracing and managing requirements. In addition, we identified three scenarios for applying the practice, namely as a mature practice, as a de facto practice and as part of an agile transition. The findings provide insights into how the role of requirements may be met in agile development including challenges to consider., Comment: Proceedings of XP 2015: 27-39

Weak alignment of requirements engineering (RE) with verification and validation (VV) may lead to problems in delivering the required products in time with the right quality. For example, weak communication of requirements changes to testers may result in lack of verification of new requirements and incorrect verification of old invalid requirements, leading to software quality problems, wasted effort and delays. However, despite the serious implications of weak alignment research and practice both tend to focus on one or the other of RE or VV rather than on the alignment of the two. We have performed a multi-unit case study to gain insight into issues around aligning RE and VV by interviewing 30 practitioners from 6 software developing companies, involving 10 researchers in a flexible research process for case studies. The results describe current industry challenges and practices in aligning RE with VV, ranging from quality of the individual RE and VV activities, through tracing and tools, to change control and sharing a common understanding at strategy, goal and design level. The study identified that human aspects are central, i.e. cooperation and communication, and that requirements engineering practices are a critical basis for alignment. Further, the size of an organisation and its motivation for applying alignment practices, e.g. external enforcement of traceability, are variation factors that play a key role in achieving alignment. Our results provide a strategic roadmap for practitioners improvement work to address alignment challenges. Furthermore, the study provides a foundation for continued research to improve the alignment of RE with VV.

[Context and motivation] When developing software, coordination between different organizational units is essential in order to develop a good quality product, on time and within budget. Particularly, the synchronization between requirements and verification processes is crucial in order to assure that the developed software product satisfies customer requirements. [Question/problem] Our research question is: what are the current challenges in aligning the requirements and verification processes? [Principal ideas/results] We conducted an interview study at a large software development company. This paper presents preliminary findings of these interviews that identify key challenges in aligning requirements and verification processes. [Contribution] The result of this study includes a range of challenges faced by the studied organization grouped into the categories: organization and processes, people, tools, requirements process, testing process, change management, traceability, and measurement. The findings of this study can be used by practitioners as a basis for investigating alignment in their organizations, and by scientists in developing approaches for more efficient and effective management of the alignment between requirements and verification., Comment: Requirements Engineering: Foundation for Software Quality: 16th International Working Conference, REFSQ 2010, Essen, Germany, June 30-July 2, 2010. Proceedings 16 (pp. 128-142). Springer Berlin Heidelberg