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We present the measurement of the two-neutrino double-$\beta$ decay rate of $^{76}$Ge performed with the GERDA Phase II experiment. With a subset of the entire GERDA exposure, 11.8 kg$\cdot$yr, the half-life of the process has been determined: $T^{2\nu}_{1/2} = (2.022 \pm 0.018_{stat} \pm 0.038_{sys})\times10^{21}$ yr. This is the most precise determination of the $^{76}$Ge two-neutrino double-$\beta$ decay half-life and one of the most precise measurements of a double-$\beta$ decay process. The relevant nuclear matrix element can be extracted: $M^{2\nu}_{\text{eff}} = (0.101\pm0.001).$, Comment: 7 pages, 4 figures, 2 tables

We search for tri-nucleon decays of $^{76}$Ge in the dataset from the GERmanium Detector Array (GERDA) experiment. Decays that populate excited levels of the daughter nucleus above the threshold for particle emission lead to disintegration and are not considered. The ppp-, ppn-, and pnn-decays lead to $^{73}$Cu, $^{73}$Zn, and $^{73}$Ga nuclei, respectively. These nuclei are unstable and eventually proceed by the beta decay of $^{73}$Ga to $^{73}$Ge (stable). We search for the $^{73}$Ga decay exploiting the fact that it dominantly populates the 66.7 keV $^{73m}$Ga state with half-life of 0.5 s. The nnn-decays of $^{76}$Ge that proceed via $^{73m}$Ge are also included in our analysis. We find no signal candidate and place a limit on the sum of the decay widths of the inclusive tri-nucleon decays that corresponds to a lower lifetime limit of 1.2x10$^{26}$ yr (90% credible interval). This result improves previous limits for tri-nucleon decays by one to three orders of magnitude., Comment: 8 pages, 9 figures, 3 tables

Companies like OpenAI, Google DeepMind, and Anthropic have the stated goal of building artificial general intelligence (AGI) - AI systems that perform as well as or better than humans on a wide variety of cognitive tasks. However, there are increasing concerns that AGI would pose catastrophic risks. In light of this, AGI companies need to drastically improve their risk management practices. To support such efforts, this paper reviews popular risk assessment techniques from other safety-critical industries and suggests ways in which AGI companies could use them to assess catastrophic risks from AI. The paper discusses three risk identification techniques (scenario analysis, fishbone method, and risk typologies and taxonomies), five risk analysis techniques (causal mapping, Delphi technique, cross-impact analysis, bow tie analysis, and system-theoretic process analysis), and two risk evaluation techniques (checklists and risk matrices). For each of them, the paper explains how they work, suggests ways in which AGI companies could use them, discusses their benefits and limitations, and makes recommendations. Finally, the paper discusses when to conduct risk assessments, when to use which technique, and how to use any of them. The reviewed techniques will be obvious to risk management professionals in other industries. And they will not be sufficient to assess catastrophic risks from AI. However, AGI companies should not skip the straightforward step of reviewing best practices from other industries., Comment: 44 pages, 13 figures, 9 tables

The new generation of laser-based solid-state lighting (SSL) white light sources requires new material systems capable of withstanding, diffusing and converting high intensity laser light. State-of-the-art systems use a blue light emitting diode (LED) or laser diode (LD) in combination with color conversion materials, such as yellow emitting Ce-doped phosphors or red and green emitting quantum dots (QD), to produce white light. However, for laser-based high-brightness illumination in particular, thermal management is a major challenge, and in addition, a light diffuser is required to diffuse the highly focused laser beam. Here, we present a hybrid material system that simultaneously enables efficient, uniform light distribution and color conversion of a blue LD, while ensuring good thermal management even at high laser powers of up to 5W. A highly open porous (> 99%) framework structure of hollow SiO$_2$ microtubes is utilized as an efficient light diffuser that can drastically reduce speckle contrast. By further functionalizing the microtubes with halide perovskite QDs (SiO$_2$@CsPbBr$_3$ as model system) color conversion from UV to visible light is achieved. Under laser illumination, the open porous structure prevents heat accumulation and thermal quenching of the QDs. By depositing an ultrathin (~ 5.5 nm) film of poly(ethylene glycol dimethyl acrylate) (pEGDMA) via initiated chemical vapor deposition (iCVD), the luminescent stability of the QDs against moisture is enhanced. The demonstrated hybrid material system paves the way for the design of advanced and functional laser light diffusers and converters that can meet the challenges associated with laser-based SSL applications., Comment: Corresponding authors: Fabian Sch\"utt, Huayna Terraschke

Clustering is an important tool for data exploration where the goal is to subdivide a data set into disjoint clusters that fit well into the underlying data structure. When dealing with sensitive data, privacy-preserving algorithms aim to approximate the non-private baseline while minimising the leakage of sensitive information. State-of-the-art privacy-preserving clustering algorithms tend to output clusters that are good in terms of the standard metrics, inertia, silhouette score, and clustering accuracy, however, the clustering result strongly deviates from the non-private KMeans baseline. In this work, we present a privacy-preserving clustering algorithm called DPM that recursively separates a data set into clusters based on a geometrical clustering approach. In addition, DPM estimates most of the data-dependent hyper-parameters in a privacy-preserving way. We prove that DPM preserves Differential Privacy and analyse the utility guarantees of DPM. Finally, we conduct an extensive empirical evaluation for synthetic and real-life data sets. We show that DPM achieves state-of-the-art utility on the standard clustering metrics and yields a clustering result much closer to that of the popular non-private KMeans algorithm without requiring the number of classes., Comment: The first two authors equally contributed to this work

Advanced AI models hold the promise of tremendous benefits for humanity, but society needs to proactively manage the accompanying risks. In this paper, we focus on what we term "frontier AI" models: highly capable foundation models that could possess dangerous capabilities sufficient to pose severe risks to public safety. Frontier AI models pose a distinct regulatory challenge: dangerous capabilities can arise unexpectedly; it is difficult to robustly prevent a deployed model from being misused; and, it is difficult to stop a model's capabilities from proliferating broadly. To address these challenges, at least three building blocks for the regulation of frontier models are needed: (1) standard-setting processes to identify appropriate requirements for frontier AI developers, (2) registration and reporting requirements to provide regulators with visibility into frontier AI development processes, and (3) mechanisms to ensure compliance with safety standards for the development and deployment of frontier AI models. Industry self-regulation is an important first step. However, wider societal discussions and government intervention will be needed to create standards and to ensure compliance with them. We consider several options to this end, including granting enforcement powers to supervisory authorities and licensure regimes for frontier AI models. Finally, we propose an initial set of safety standards. These include conducting pre-deployment risk assessments; external scrutiny of model behavior; using risk assessments to inform deployment decisions; and monitoring and responding to new information about model capabilities and uses post-deployment. We hope this discussion contributes to the broader conversation on how to balance public safety risks and innovation benefits from advances at the frontier of AI development., Comment: Update July 11th: - Added missing footnote back in. - Adjusted author order (mistakenly non-alphabetical among the first 6 authors) and adjusted affiliations (Jess Whittlestone's affiliation was mistagged and Gillian Hadfield had SRI added to her affiliations) Updated September 4th: Various typos

With the implementation of the new EU regulation 2022/1426 regarding the type-approval of the automated driving system (ADS) of fully automated vehicles, scenario-based testing has gained significant importance in evaluating the performance and safety of advanced driver assistance systems and automated driving systems. However, the exploration and generation of concrete scenarios from a single logical scenario can often lead to a number of similar or redundant scenarios, which may not contribute to the testing goals. This paper focuses on the the goal to reduce the scenario set by clustering concrete scenarios from a single logical scenario. By employing clustering techniques, redundant and uninteresting scenarios can be identified and eliminated, resulting in a representative scenario set. This reduction allows for a more focused and efficient testing process, enabling the allocation of resources to the most relevant and critical scenarios. Furthermore, the identified clusters can provide valuable insights into the scenario space, revealing patterns and potential problems with the system's behavior., Comment: accepted IEEE ITSC 2023

This article argues that frontier artificial intelligence (AI) developers need an internal audit function. First, it describes the role of internal audit in corporate governance: internal audit evaluates the adequacy and effectiveness of a company's risk management, control, and governance processes. It is organizationally independent from senior management and reports directly to the board of directors, typically its audit committee. In the IIA's Three Lines Model, internal audit serves as the third line and is responsible for providing assurance to the board, while the Combined Assurance Framework highlights the need to coordinate the activities of internal and external assurance providers. Next, the article provides an overview of key governance challenges in frontier AI development: dangerous capabilities can arise unpredictably and undetected; it is difficult to prevent a deployed model from causing harm; frontier models can proliferate rapidly; it is inherently difficult to assess frontier AI risks; and frontier AI developers do not seem to follow best practices in risk governance. Finally, the article discusses how an internal audit function could address some of these challenges: internal audit could identify ineffective risk management practices; it could ensure that the board of directors has a more accurate understanding of the current level of risk and the adequacy of the developer's risk management practices; and it could serve as a contact point for whistleblowers. In light of rapid progress in AI research and development, frontier AI developers need to strengthen their risk governance. Instead of reinventing the wheel, they should follow existing best practices. While this might not be sufficient, they should not skip this obvious first step., Comment: 42 pages, 2 figures, 2 tables

Particulate air pollution is taking a huge toll on modern society, being associated with more than three million deaths per year. In addition, airborne infectious microorganism can spread dangerous diseases, further elevating the problem. A common way to mitigate the risks of airborne particles is by air filtration. However, conventional air filters usually do not provide any functionality beyond particle removal. They are unable to inactivate accumulated contaminants and therefore need periodic maintenance and replacement to remain operational and safe. This work presents a multifunctional, self-cleaning air filtration system which utilizes a novel graphene-enhanced air filter medium (GeFM). The hybrid network of the GeFM combines the passive structure-based air filtration properties of an underlying ceramic network with additional active features based on the functional properties of a graphene thin film. The GeFM is able to capture >95 % of microorganisms and particles larger than 1 $\mu$m and can be repetitively Joule-heated to >300 {\deg}C for several hours without signs of degradation. Hereby, built-up organic particulate matter and microbial contaminants are effectively decomposed, regenerating the GeFM. Additionally, the GeFM provides unique options to monitor the filter's air troughput and loading status during operation. The active features of the GeFM can drastically improve filter life-time and safety, offering great potential for the development of safer and more sustainable air filtration solutions to face the future challenges of air pollution and pandemics., Comment: * Corresponding authors: Prof. Dr. Rainer Adelung (ra@tf.uni-kiel.de) and Dr.-Ing. Fabian Sch\"utt (fas@tf.uni-kiel.de)

A number of leading AI companies, including OpenAI, Google DeepMind, and Anthropic, have the stated goal of building artificial general intelligence (AGI) - AI systems that achieve or exceed human performance across a wide range of cognitive tasks. In pursuing this goal, they may develop and deploy AI systems that pose particularly significant risks. While they have already taken some measures to mitigate these risks, best practices have not yet emerged. To support the identification of best practices, we sent a survey to 92 leading experts from AGI labs, academia, and civil society and received 51 responses. Participants were asked how much they agreed with 50 statements about what AGI labs should do. Our main finding is that participants, on average, agreed with all of them. Many statements received extremely high levels of agreement. For example, 98% of respondents somewhat or strongly agreed that AGI labs should conduct pre-deployment risk assessments, dangerous capabilities evaluations, third-party model audits, safety restrictions on model usage, and red teaming. Ultimately, our list of statements may serve as a helpful foundation for efforts to develop best practices, standards, and regulations for AGI labs., Comment: 38 pages, 8 figures, 8 tables

We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application is the completion of the classification of Enriques surfaces with finite automorphism groups started by Kondo, Nikulin, Martin and Katsura-Kondo-Martin., Comment: 32 pages; (epi)journal version

We determine the optimal H\"older exponent in Massari's regularity theorem for sets with variational mean curvature in $\mathrm{L}^p$. In fact, we obtain regularity with improved exponents and at the same time provide sharp counterexamples.

Scenario generation is one of the essential steps in scenario-based testing and, therefore, a significant part of the verification and validation of driver assistance functions and autonomous driving systems. However, the term scenario generation is used for many different methods, e.g., extraction of scenarios from naturalistic driving data or variation of scenario parameters. This survey aims to give a systematic overview of different approaches, establish different categories of scenario acquisition and generation, and show that each group of methods has typical input and output types. It shows that although the term is often used throughout literature, the evaluated methods use different inputs and the resulting scenarios differ in abstraction level and from a systematical point of view. Additionally, recent research and literature examples are given to underline this categorization., Comment: accepted at IEEE IV 2023

An essential requirement for scenario-based testing the identification of critical scenes and their associated scenarios. However, critical scenes, such as collisions, occur comparatively rarely. Accordingly, large amounts of data must be examined. A further issue is that recorded real-world traffic often consists of scenes with a high number of vehicles, and it can be challenging to determine which are the most critical vehicles regarding the safety of an ego vehicle. Therefore, we present the inverse universal traffic quality, a criticality metric for urban traffic independent of predefined adversary vehicles and vehicle constellations such as intersection trajectories or car-following scenarios. Our metric is universally applicable for different urban traffic situations, e.g., intersections or roundabouts, and can be adjusted to certain situations if needed. Additionally, in this paper, we evaluate the proposed metric and compares its result to other well-known criticality metrics of this field, such as time-to-collision or post-encroachment time., Comment: accepted at IEEE IV 2023

Organizations that develop and deploy artificial intelligence (AI) systems need to take measures to reduce the associated risks. In this paper, we examine how AI companies could design an AI ethics board in a way that reduces risks from AI. We identify five high-level design choices: (1) What responsibilities should the board have? (2) What should its legal structure be? (3) Who should sit on the board? (4) How should it make decisions and should its decisions be binding? (5) What resources does it need? We break down each of these questions into more specific sub-questions, list options, and discuss how different design choices affect the board's ability to reduce risks from AI. Several failures have shown that designing an AI ethics board can be challenging. This paper provides a toolbox that can help AI companies to overcome these challenges., Comment: 21 pages, 2 figures, 2 tables

Conversion of light into heat is essential for a broad range of technologies such as solar thermal heating, catalysis and desalination. Three-dimensional (3D) carbon nanomaterial-based aerogels have shown to hold great promise as photothermal transducer materials. However, till now, their light-to-heat conversion is limited by surface-near absorption, resulting in a strong heat localization only at the illuminated surface region, while most of the aerogel volume remains unused. We present an innovative fabrication concept for highly porous (>99.9%) photothermal hybrid aeromaterials, that enable an ultra-rapid and volumetric photothermal response with an enhancement by a factor of around 2.5 compared to the pristine variant. The hybrid aeromaterial is based on strongly light-scattering framework structures composed of interconnected hollow silicon dioxide (SiO${_2}$) microtubes, which are functionalized with extremely low amounts (in order of a few ${\mu}$g cm${^-}$${^3}$) of reduced graphene oxide (rGO) nanosheets, acting as photothermal agents. Tailoring the density of rGO within the framework structure enables us to control both, light scattering and light absorption, and thus the volumetric photothermal response. We further show that by rapid and repeatable gas activation these transducer materials expand the field of photothermal applications, like untethered light-powered and -controlled microfluidic pumps and soft pneumatic actuators.

Hydrogel-based soft actuators can operate in sensitive environments, bridging the gap of rigid machines interacting with soft matter. However, while stimuli-responsive hydrogels can undergo extreme reversible volume changes of up to ~90%, water transport in hydrogel actuators is in general limited by their poroelastic behavior. For poly(N-isopropylacrylamide) (PNIPAM) the actuation performance is even further compromised by the formation of a dense skin layer. Here we show, that incorporating a bioinspired microtube graphene network into a PNIPAM matrix with a total porosity of only 5.4 % dramatically enhances actuation dynamics by up to ~400 % and actuation stress by ~4000 % without sacrificing the mechanical stability, overcoming the water transport limitations. The graphene network provides both untethered light-controlled and electrically-powered actuation. We anticipate that the concept provides a versatile platform for enhancing the functionality of soft matter by combining responsive and two-dimensional materials, paving the way towards designing soft intelligent matter., Comment: Shared First-authorship: Margarethe Hauck and Lena Marie Saure

The emerging interest in tin-halide perovskites demands a robust understanding of the fundamental properties of these materials starting from the earliest steps of their synthesis. In a first-principles work based on time-dependent density-functional theory, we investigate the structural, energetic, electronic, and optical properties of 14 tin-iodide solution complexes formed by the SnI$_2$ unit tetracoordinated with molecules of common solvents, which we classify according to their Gutmann's donor number. We find that all considered complexes are energetically stable and their formation energy expectedly increases with the donating ability of the solvent. The energies of the frontier states are affected by the choice of the solvent with their absolute values decreasing with the donor number. The occupied orbitals are predominantly localized on the tin-iodide unit while the unoccupied ones are distributed also on the solvent molecules. Owing to this partial wave-function overlap, the first optical excitation is generally weak, although the spectral weight is red-shifted by the solvent molecules being coordinated to SnI$_2$ in comparison to the reference obtained for this molecule alone. Comparisons with results obtained on the same level of theory on Pb-based counterparts corroborate our analysis. The outcomes of this study provide quantum-mechanical insight into the fundamental properties of tin-iodide solution complexes. This knowledge is valuable in the research on lead-free halide perovskites and their precursors.

Large language models (LLMs) represent a major advance in artificial intelligence (AI) research. However, the widespread use of LLMs is also coupled with significant ethical and social challenges. Previous research has pointed towards auditing as a promising governance mechanism to help ensure that AI systems are designed and deployed in ways that are ethical, legal, and technically robust. However, existing auditing procedures fail to address the governance challenges posed by LLMs, which display emergent capabilities and are adaptable to a wide range of downstream tasks. In this article, we address that gap by outlining a novel blueprint for how to audit LLMs. Specifically, we propose a three-layered approach, whereby governance audits (of technology providers that design and disseminate LLMs), model audits (of LLMs after pre-training but prior to their release), and application audits (of applications based on LLMs) complement and inform each other. We show how audits, when conducted in a structured and coordinated manner on all three levels, can be a feasible and effective mechanism for identifying and managing some of the ethical and social risks posed by LLMs. However, it is important to remain realistic about what auditing can reasonably be expected to achieve. Therefore, we discuss the limitations not only of our three-layered approach but also of the prospect of auditing LLMs at all. Ultimately, this article seeks to expand the methodological toolkit available to technology providers and policymakers who wish to analyse and evaluate LLMs from technical, ethical, and legal perspectives., Comment: 22 pages, 2 figures. AI Ethics (2023)

Organizations that develop and deploy artificial intelligence (AI) systems need to manage the associated risks - for economic, legal, and ethical reasons. However, it is not always clear who is responsible for AI risk management. The Three Lines of Defense (3LoD) model, which is considered best practice in many industries, might offer a solution. It is a risk management framework that helps organizations to assign and coordinate risk management roles and responsibilities. In this article, I suggest ways in which AI companies could implement the model. I also discuss how the model could help reduce risks from AI: it could identify and close gaps in risk coverage, increase the effectiveness of risk management practices, and enable the board of directors to oversee management more effectively. The article is intended to inform decision-makers at leading AI companies, regulators, and standard-setting bodies., Comment: 22 pages, 2 figures

SchNetPack is a versatile neural networks toolbox that addresses both the requirements of method development and application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural networks as well as a PyTorch implementation of molecular dynamics. An optional integration with PyTorch Lightning and the Hydra configuration framework powers a flexible command-line interface. This makes SchNetPack 2.0 easily extendable with custom code and ready for complex training task such as generation of 3d molecular structures.

The ability to detect liquid argon scintillation light from within a densely packed high-purity germanium detector array allowed the GERDA experiment to reach an exceptionally low background rate in the search for neutrinoless double beta decay of $^{76}$Ge. Proper modeling of the light propagation throughout the experimental setup, from any origin in the liquid argon volume to its eventual detection by the novel light read-out system, provides insight into the rejection capability and is a necessary ingredient to obtain robust background predictions. In this paper, we present a model of the GERDA liquid argon veto, as obtained by Monte Carlo simulations and constrained by calibration data, and highlight its application for background decomposition.

The proposed EU AI Act is the first comprehensive attempt to regulate AI in a major jurisdiction. This article analyses Article 9, the key risk management provision in the AI Act. It gives an overview of the regulatory concept behind Article 9, determines its purpose and scope of application, offers a comprehensive interpretation of the specific risk management requirements, and outlines ways in which the requirements can be enforced. This article is written with the aim of helping providers of high-risk systems comply with the requirements set out in Article 9. In addition, it can inform revisions of the current draft of the AI Act and efforts to develop harmonised standards on AI risk management.

Comparing representations of complex stimuli in neural network layers to human brain representations or behavioral judgments can guide model development. However, even qualitatively distinct neural network models often predict similar representational geometries of typical stimulus sets. We propose a Bayesian experimental design approach to synthesizing stimulus sets for adjudicating among representational models efficiently. We apply our method to discriminate among candidate neural network models of behavioral face dissimilarity judgments. Our results indicate that a neural network trained to invert a 3D-face-model graphics renderer is more human-aligned than the same architecture trained on identification, classification, or autoencoding. Our proposed stimulus synthesis objective is generally applicable to designing experiments to be analyzed by representational similarity analysis for model comparison.

A major challenge in the safety assessment of automated vehicles is to ensure that risk for all traffic participants is as low as possible. A concept that is becoming increasingly popular for testing in automated driving is scenario-based testing. It is founded on the assumption that most time on the road can be seen as uncritical and in mainly critical situations contribute to the safety case. Metrics describing the criticality are necessary to automatically identify the critical situations and scenarios from measurement data. However, established metrics lack universality or a concept for metric combination. In this work, we present a multidimensional evaluation model that, based on conventional metrics, can evaluate scenes independently of the scene type. Furthermore, we present two new, further enhanced evaluation approaches, which can additionally serve as universal metrics. The metrics we introduce are then evaluated and discussed using real data from a motion dataset.

Soft and flexible conductors are essential in the development of soft robots, wearable electronics, as well as electronic tissue and implants. However, conventional soft conductors are inherently characterized by a large change in conductance upon mechanical deformation or under alternating environmental conditions, e.g., humidity, drastically limiting their application potential and performance. Here, we demonstrate a novel concept for the development of strain-invariant, fatigue resistant and highly water stable soft conductor. By combining different thin film technologies in a three-dimensional fashion, we develop nano- and micro-engineered, multi-layered (< 50 nm), ultra-lightweight (< 15 mg/cm$^3$) foam-like composite framework structures based on PEDOT:PSS and PTFE. The all-organic composite framework structures are characterized by conductivities of up to 184 S/m, remaining strain-invariant between 80 % compressive and 25 % tensile strain. We further show, that the multi-layered composites are characterized by properties that surpass that of framework structures based on the individual materials. Both, the initial electrical and mechanical properties of the composite framework structures are retained during long-term cycling, even after 2000 cycles at 50 % compression. Furthermore, the PTFE functionalization renders the framework structure highly hydrophobic, resulting in stable electrical properties, even when immersed in water for up to 30 days. The here presented concept overcomes the previous limitations of strain-invariant soft conductors and demonstrates for the first time a versatile approach for the development of innovative multi-scaled and multi-layered functional materials, for applications in soft electronics, energy storage and conversion, sensing, catalysis, water and air purification, as well as biomedicine., Comment: Corresponding authors: Dr.-Ing. Fabian Sch\"utt (fas@tf.uni-kiel.de) and Dr.-Ing. Stefan Schr\"oder (ssch@tf.uni-kiel.de); Shared senior authorship: Dr.-Ing. Fabian Sch\"utt and Dr.-Ing. Stefan Schr\"oder

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing., Comment: Submitted as a roadmap article to Modelling and Simulation in Materials Science and Engineering; Address any correspondence to Vikram Gavini (vikramg@umich.edu) and Danny Perez (danny_perez@lanl.gov)

A search for Beyond the Standard Model double-$\beta$ decay modes of $^{76}$Ge has been performed with data collected during the Phase II of the GERmanium Detector Array (GERDA) experiment, located at Laboratori Nazionali del Gran Sasso of INFN (Italy). Improved limits on the decays involving Majorons have been obtained, compared to previous experiments with $^{76}$Ge, with half-life values on the order of 10$^{23}$ yr. For the first time with $^{76}$Ge, limits on Lorentz invariance violation effects in double-$\beta$ decay have been obtained. The isotropic coefficient $\mathring{a}_\text{of}^{(3)}$, which embeds Lorentz violation in double-$\beta$ decay, has been constrained at the order of $10^{-6}$ GeV. We also set the first experimental limits on the search for light exotic fermions in double-$\beta$ decay, including sterile neutrinos.

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 12, if the minimal resolution of $X$ is not a supersingular K3 surface. We also provide a family of explicit examples, valid in any characteristic., Comment: 21 pages

The CP2K program package, which can be considered as the swiss army knife of atomistic simulations, is presented with a special emphasis on ab-initio molecular dynamics using the second-generation Car-Parrinello method. After outlining current and near-term development efforts with regards to massively parallel low-scaling post-Hartree-Fock and eigenvalue solvers, novel approaches on how we plan to take full advantage of future low-precision hardware architectures are introduced. Our focus here is on combining our submatrix method with the approximate computing paradigm to address the immanent exascale era., Comment: 7 pages, 2 figures

A visual system has to learn both which features to extract from images and how to group locations into (proto-)objects. Those two aspects are usually dealt with separately, although predictability is discussed as a cue for both. To incorporate features and boundaries into the same model, we model a layer of feature maps with a pairwise Markov random field model in which each factor is paired with an additional binary variable, which switches the factor on or off. Using one of two contrastive learning objectives, we can learn both the features and the parameters of the Markov random field factors from images without further supervision signals. The features learned by shallow neural networks based on this loss are local averages, opponent colors, and Gabor-like stripe patterns. Furthermore, we can infer connectivity between locations by inferring the switch variables. Contours inferred from this connectivity perform quite well on the Berkeley segmentation database (BSDS500) without any training on contours. Thus, computing predictions across space aids both segmentation and feature learning, and models trained to optimize these predictions show similarities to the human visual system. We speculate that retinotopic visual cortex might implement such predictions over space through lateral connections., Comment: Submitted to NeurIPS 2022

Verification and validation are major challenges for developing automated driving systems. A concept that gets more and more recognized for testing in automated driving is scenario-based testing. However, it introduces the problem of what scenarios are relevant for testing and which are not. This work aims to find relevant, interesting, or critical parameter sets within logical scenarios by utilizing Bayes optimization and Gaussian processes. The parameter optimization is done by comparing and evaluating six different metrics in two urban intersection scenarios. Finally, a list of ideas this work leads to and should be investigated further is presented., Comment: Proceedings of the 8th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2022)

We give an overview of the affine surface area, its properties and its history.

In recent years, the prediction of quantum mechanical observables with machine learning methods has become increasingly popular. Message-passing neural networks (MPNNs) solve this task by constructing atomic representations, from which the properties of interest are predicted. Here, we introduce a method to automatically identify chemical moieties (molecular building blocks) from such representations, enabling a variety of applications beyond property prediction, which otherwise rely on expert knowledge. The required representation can either be provided by a pretrained MPNN, or learned from scratch using only structural information. Beyond the data-driven design of molecular fingerprints, the versatility of our approach is demonstrated by enabling the selection of representative entries in chemical databases, the automatic construction of coarse-grained force fields, as well as the identification of reaction coordinates.

Semantic segmentation is a core ability required by autonomous agents, as being able to distinguish which parts of the scene belong to which object class is crucial for navigation and interaction with the environment. Approaches which use only one time-step of data cannot distinguish between moving objects nor can they benefit from temporal integration. In this work, we extend a backbone LatticeNet to process temporal point cloud data. Additionally, we take inspiration from optical flow methods and propose a new module called Abstract Flow which allows the network to match parts of the scene with similar abstract features and gather the information temporally. We obtain state-of-the-art results on the SemanticKITTI dataset that contains LiDAR scans from real urban environments. We share the PyTorch implementation of TemporalLatticeNet at https://github.com/AIS-Bonn/temporal_latticenet ., Comment: Accepted IEEE International Conference on Robotics and Automation (ICRA) 2022, Code available at https://github.com/AIS-Bonn/temporal_latticenet

Consider two half-spaces $H_1^+$ and $H_2^+$ in $\mathbb{R}^{d+1}$ whose bounding hyperplanes $H_1$ and $H_2$ are orthogonal and pass through the origin. The intersection $\mathbb{S}_{2,+}^d:=\mathbb{S}^d\cap H_1^+\cap H_2^+$ is a spherical convex subset of the $d$-dimensional unit sphere $\mathbb{S}^d$, which contains a great subsphere of dimension $d-2$ and is called a spherical wedge. Choose $n$ independent random points uniformly at random on $\mathbb{S}_{2,+}^d$ and consider the expected facet number of the spherical convex hull of these points. It is shown that, up to terms of lower order, this expectation grows like a constant multiple of $\log n$. A similar behaviour is obtained for the expected facet number of a homogeneous Poisson point process on $\mathbb{S}_{2,+}^d$. The result is compared to the corresponding behaviour of classical Euclidean random polytopes and of spherical random polytopes on a half-sphere., Comment: 21 pages, 5 figures