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Many physical processes can be expressed through partial differential equations (PDEs). Real-world measurements of such processes are often collected at irregularly distributed points in space, which can be effectively represented as graphs; however, there are currently only a few existing datasets. Our work aims to make advancements in the field of PDE-modeling accessible to the temporal graph machine learning community, while addressing the data scarcity problem, by creating and utilizing datasets based on PDEs. In this work, we create and use synthetic datasets based on PDEs to support spatio-temporal graph modeling in machine learning for different applications. More precisely, we showcase three equations to model different types of disasters and hazards in the fields of epidemiology, atmospheric particles, and tsunami waves. Further, we show how such created datasets can be used by benchmarking several machine learning models on the epidemiological dataset. Additionally, we show how pre-training on this dataset can improve model performance on real-world epidemiological data. The presented methods enable others to create datasets and benchmarks customized to individual requirements. The source code for our methodology and the three created datasets can be found on https://github.com/github-usr-ano/Temporal_Graph_Data_PDEs., Comment: Currently under review

In 2003, Ozsv\'ath, Szab\'o, and Rasmussen introduced the $\tau$ invariant for knots, and in 2011, Sarkar published a computational shortcut for the $\tau$ invariant of knots that can be represented by diagonal grid diagrams. Previously, the only knots known to have diagonal grid diagram representations were torus knots. We prove that all such knots are positive knots, and we produce an example of a knot with a diagonal grid diagram representation which is not a torus knot., Comment: 6 pages, 5 figures

Undulators are X-ray sources that are widely utilised in advanced synchrotron radiation sources and freeelectron laser facilities. Due to sustainability and energy efficiency, the development focuses on small-scale, high-field, and especially compact undulators with short period lengths ($\leq$ 10 mm) and narrow magnetic gaps ($\leq$ 4 mm). Therefore, hightemperature superconducting (HTS) tapes, which can provide a high critical current density and high critical magnetic fields at higher temperatures, are extensively used and investigated at the Karlsruhe Institute of Technology. A new concept of superconducting undulators (SCUs) was introduced and further developed by laser-scribing a meander pattern into the superconducting layer to achieve a quasi-sinusoidal current path through the HTS tape. Here we present the complete and final design of such a compact SCU, in particular our latest results regarding the design of the liner with its tapering in the warm region, as well as the cryogenic cooling concept.

Quantifying interaction strengths between state variables in dynamical systems is essential for understanding ecological networks. Within the empirical dynamic modeling approach, multivariate S-map infers the interaction Jacobian from time series data without assuming specific dynamical models. This approach enables the non-parametric statistical inference of interspecific interactions through state space reconstruction. However, deviations in the biological interpretation and numerical implementation of the interaction Jacobian from its mathematical definition pose challenges. We mathematically reintroduce the interaction Jacobian using differential quotients, uncovering two problems: (1) the mismatch between the interaction Jacobian and its biological meaning complicates comparisons between interspecific and intraspecific interactions; (2) the interaction Jacobian is not fully implemented in the parametric Jacobian numerically derived from given parametric models, especially using ordinary differential equations. As a result, model-based evaluations of S-map methods become inappropriate. To address these problems, (1) we propose adjusting the diagonal elements of the interaction Jacobian by subtracting 1 to resolve the comparability problem between inter- and intraspecific interaction strengths. Simulations of population dynamics showed that this adjustment prevents overestimation of intraspecific interaction strengths. (2) We introduce an alternative parametric Jacobian and then cumulative interaction strength (CIS), providing a more rigorous benchmark for evaluating S-map methods. Furthermore, we demonstrated that the numerical gap between CIS and the existing parametric Jacobian is substantial in realistic scenarios, suggesting CIS as preferred benchmark. These solutions offer a clearer framework for developing non-parametric approaches in ecological time series analysis., Comment: 39 pages, 5 figures and 2 tables

While the pretraining of Foundation Models (FMs) for remote sensing (RS) imagery is on the rise, models remain restricted to a few hundred million parameters. Scaling models to billions of parameters has been shown to yield unprecedented benefits including emergent abilities, but requires data scaling and computing resources typically not available outside industry R&D labs. In this work, we pair high-performance computing resources including Frontier supercomputer, America's first exascale system, and high-resolution optical RS data to pretrain billion-scale FMs. Our study assesses performance of different pretrained variants of vision Transformers across image classification, semantic segmentation and object detection benchmarks, which highlight the importance of data scaling for effective model scaling. Moreover, we discuss construction of a novel TIU pretraining dataset, model initialization, with data and pretrained models intended for public release. By discussing technical challenges and details often lacking in the related literature, this work is intended to offer best practices to the geospatial community toward efficient training and benchmarking of larger FMs.

This paper presents a novel approach to multi-robot planning and collaboration. We demonstrate a cognitive strategy for robots in human-robot teams that incorporates metacognition, natural language communication, and explainability. The system is embodied using the HARMONIC architecture that flexibly integrates cognitive and control capabilities across the team. We evaluate our approach through simulation experiments involving a joint search task by a team of heterogeneous robots (a UGV and a drone) and a human. We detail the system's handling of complex, real-world scenarios, effective action coordination between robots with different capabilities, and natural human-robot communication. This work demonstrates that the robots' ability to reason about plans, goals, and attitudes, and to provide explanations for actions and decisions are essential prerequisites for realistic human-robot teaming., Comment: Submitted to ICRA 2025 Conference, Atlanta, GA, USA

We present HARMONIC, a framework for implementing cognitive robots that transforms general-purpose robots into trusted teammates capable of complex decision-making, natural communication and human-level explanation. The framework supports interoperability between a strategic (cognitive) layer for high-level decision-making and a tactical (robot) layer for low-level control and execution. We describe the core features of the framework and our initial implementation, in which HARMONIC was deployed on a simulated UGV and drone involved in a multi-robot search and retrieval task., Comment: Accepted for presentation at ICRA@40. 23-26 September 2024, Rotterdam, Netherlands

Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in sensitive applications such as medical imaging. Recent works by Arndt et al (2023 Inverse Problems 39 125018, 2024 Inverse Problems 40 045021) addressed this gap by analyzing a data-driven reconstruction method based on invertible residual networks (iResNets). They revealed that, under reasonable assumptions, this approach constitutes a convergent regularization scheme. However, the performance of the reconstruction method was only validated on academic toy problems and small-scale iResNet architectures. In this work, we address this gap by evaluating the performance of iResNets on two real-world imaging tasks: a linear blurring operator and a nonlinear diffusion operator. To do so, we extend some of the theoretical results from Arndt et al to encompass nonlinear inverse problems and offer insights for the design of large-scale performant iResNet architectures. Through numerical experiments, we compare the performance of our iResNet models against state-of-the-art neural networks, confirming their efficacy. Additionally, we numerically investigate the theoretical guarantees of this approach and demonstrate how the invertibility of the network enables a deeper analysis of the learned forward operator and its learned regularization.

In image-based reinforcement learning (RL), policies usually operate in two steps: first extracting lower-dimensional features from raw images (the "recognition" step), and then taking actions based on the extracted features (the "decision" step). Extracting features that are spuriously correlated with performance or irrelevant for decision-making can lead to poor generalization performance, known as observational overfitting in image-based RL. In such cases, it can be hard to quantify how much of the error can be attributed to poor feature extraction vs. poor decision-making. In order to disentangle the two sources of error, we introduce the notions of recognition regret and decision regret. Using these notions, we characterize and disambiguate the two distinct causes behind observational overfitting: over-specific representations, which include features that are not needed for optimal decision-making (leading to high decision regret), vs. under-specific representations, which only include a limited set of features that were spuriously correlated with performance during training (leading to high recognition regret). Finally, we provide illustrative examples of observational overfitting due to both over-specific and under-specific representations in maze environments as well as the Atari game Pong.

ArborX is a performance portable geometric search library developed as part of the Exascale Computing Project (ECP). In this paper, we explore a collaboration between ArborX and a cosmological simulation code HACC. Large cosmological simulations on exascale platforms encounter a bottleneck due to the in-situ analysis requirements of halo finding, a problem of identifying dense clusters of dark matter (halos). This problem is solved by using a density-based DBSCAN clustering algorithm. With each MPI rank handling hundreds of millions of particles, it is imperative for the DBSCAN implementation to be efficient. In addition, the requirement to support exascale supercomputers from different vendors necessitates performance portability of the algorithm. We describe how this challenge problem guided ArborX development, and enhanced the performance and the scope of the library. We explore the improvements in the basic algorithms for the underlying search index to improve the performance, and describe several implementations of DBSCAN in ArborX. Further, we report the history of the changes in ArborX and their effect on the time to solve a representative benchmark problem, as well as demonstrate the real world impact on production end-to-end cosmology simulations., Comment: Submitted to IJHPCA

The integration of Large Language Models (LLMs) with Knowledge Graphs (KGs) offers significant synergistic potential for knowledge-driven applications. One possible integration is the interpretation and generation of formal languages, such as those used in the Semantic Web, with SPARQL being a core technology for accessing KGs. In this paper, we focus on measuring out-of-the box capabilities of LLMs to work with SPARQL and more specifically with SPARQL SELECT queries applying a quantitative approach. We implemented various benchmarking tasks in the LLM-KG-Bench framework for automated execution and evaluation with several LLMs. The tasks assess capabilities along the dimensions of syntax, semantic read, semantic create, and the role of knowledge graph prompt inclusion. With this new benchmarking tasks, we evaluated a selection of GPT, Gemini, and Claude models. Our findings indicate that working with SPARQL SELECT queries is still challenging for LLMs and heavily depends on the specific LLM as well as the complexity of the task. While fixing basic syntax errors seems to pose no problems for the best of the current LLMs evaluated, creating semantically correct SPARQL SELECT queries is difficult in several cases., Comment: peer reviewed publication at NLP4KGc @ Semantics 2024, see https://sites.google.com/view/3rdnlp4kgc

Restoring limb motor function in individuals with spinal cord injury (SCI), stroke, or amputation remains a critical challenge, one which affects millions worldwide. Recent studies show through surface electromyography (EMG) that spared motor neurons can still be voluntarily controlled, even without visible limb movement . These signals can be decoded and used for motor intent estimation; however, current wearable solutions lack the necessary hardware and software for intuitive interfacing of the spared degrees of freedom after neural injuries. To address these limitations, we developed a wireless, high-density EMG bracelet, coupled with a novel software framework, MyoGestic. Our system allows rapid and tailored adaptability of machine learning models to the needs of the users, facilitating real-time decoding of multiple spared distinctive degrees of freedom. In our study, we successfully decoded the motor intent from two participants with SCI, two with spinal stroke , and three amputees in real-time, achieving several controllable degrees of freedom within minutes after wearing the EMG bracelet. We provide a proof-of-concept that these decoded signals can be used to control a digitally rendered hand, a wearable orthosis, a prosthesis, or a 2D cursor. Our framework promotes a participant-centered approach, allowing immediate feedback integration, thus enhancing the iterative development of myocontrol algorithms. The proposed open-source software framework, MyoGestic, allows researchers and patients to focus on the augmentation and training of the spared degrees of freedom after neural lesions, thus potentially bridging the gap between research and clinical application and advancing the development of intuitive EMG interfaces for diverse neural lesions., Comment: 23 pages, 8 figures

Matter-wave interferometry with molecules is intriguing both because it demonstrates a fundamental quantum phenomenon and because it opens avenues to quantum-enhanced measurements in physical chemistry. One great challenge in such experiments is to establish matter-wave beam splitting mechanisms that are efficient and applicable to a wide range of particles. In the past, continuous standing light waves in the visible spectral range were used predominantly as phase gratings, while pulsed vacuum ultraviolet light found applications in photo-ionisation gratings. Here, we explore the regime of continuous, intense deep-ultraviolet ($\rm >1 MW/cm^2$, $\rm 266\,nm$) light masks, where a rich variety of photo-physical and photo-chemical phenomena and relaxation pathways must be considered. The improved understanding of the mechanisms in this interaction opens new potential pathways to protein interferometry and to matter-wave enhanced sensing of molecular properties., Comment: 11 pages, 8 figures. Supplemental information is included

This paper presents an in-depth examination of checkpoint-restart mechanisms in High-Performance Computing (HPC). It focuses on the use of Distributed MultiThreaded CheckPointing (DMTCP) in various computational settings, including both within and outside of containers. The study is grounded in real-world applications running on NERSC Perlmutter, a state-of-the-art supercomputing system. We discuss the advantages of checkpoint-restart (C/R) in managing complex and lengthy computations in HPC, highlighting its efficiency and reliability in such environments. The role of DMTCP in enhancing these workflows, especially in multi-threaded and distributed applications, is thoroughly explored. Additionally, the paper delves into the use of HPC containers, such as Shifter and Podman-HPC, which aid in the management of computational tasks, ensuring uniform performance across different environments. The methods, results, and potential future directions of this research, including its application in various scientific domains, are also covered, showcasing the critical advancements made in computational methodologies through this study., Comment: 9 pages, 4 figures

We show that matter-wave diffraction off a single standing laser wave can be used as an accurate measurement scheme for photophysical molecular parameters. These include state-dependent optical polarizabilities and photon-absorption cross sections, the relaxation rates for fluorescence, internal conversion, and intersystem crossing, as well as ionization or cleavage probabilities. We discuss how the different photophysical processes manifest as features of the interference pattern, and we determine the accuracy of molecular parameters estimated from a realistic measurement with finite particle numbers. The analysis is based on an analytic calculation in Wigner representation, which accounts for the laser-induced coherent and incoherent dynamics, for the finite longitudinal and transverse coherence in the matter-wave beam, the gravitational and Coriolis acceleration, and an imperfect standing laser wave., Comment: 18 pages, 6 figures; corresponds to published version

The Resource Description Framework (RDF) is a fundamental technology in the Semantic Web, enabling the representation and interchange of structured data. However, RDF lacks the capability to express negated statements in a generic way. As a result, exchanging negative information on a Web scale is thus far restricted to specific cases and predefined statements. The ability to negate (virtually) any RDF statement allows for a comprehensive way to refute, deny or otherwise invalidate claims on a Web scale. Via an intermediate step of a diagrammatic approach to logical expressions called Peirce graphs, we introduce RDF Surfaces, an extension of RDF that incorporates the concept of classic negation, known from first-order logic. Overall, RDF Surfaces provides an abstract, visual approach to negation within the Semantic Web, offering a more general and widely applicable approach than previous attempts at incorporating negation. Aside from a (traditional) programmatic syntax, RDF Surfaces can also be represented visually by means of diagrams inspired by Peirce graphs. We demonstrate negation via RDF Surfaces and how to reason upon it in illustrative use cases drawn from the domains of academic publishing and eHealth. We hope this vision paper attracts new implementers and opens the discussion to its formal specification.

We introduce a structured illumination technique for dark-field x-ray microscopy optimized for three-dimensional imaging of ordered materials at sub-micrometer length scales. Our method utilizes a coded aperture to spatially modulate the incident x-ray beam on the sample, enabling the reconstruction of the sample's 3D structure from images captured at various aperture positions. Unlike common volumetric imaging techniques such as tomography, our approach casts a scanning x-ray silhouette of a coded aperture for depth resolution along the axis of diffraction, eliminating any need for sample rotation or rastering, leading to a highly stable imaging modality. This modification provides robustness against geometric uncertainties during data acquisition, particularly for achieving sub-micrometer resolutions where geometric uncertainties typically limit resolution. We introduce the image reconstruction model and validate our results with experimental data on an isolated twin domain within a bulk single crystal of an iron pnictide obtained using a dark-field x-ray microscope. This timely advancement aligns with the enhanced brightness upgrade of the world's synchrotron radiation facilities, opening unprecedented opportunities in imaging., Comment: 20 pages, 5 figures

We introduce the Riskman ontology & shapes for representing and analysing information about risk management for medical devices. Risk management is concerned with taking necessary precautions so a medical device does not cause harms for users or the environment. To date, risk management documentation is submitted to notified bodies (for certification) in the form of semi-structured natural language text. We propose to use classes from the Riskman ontology to logically model risk management documentation and to use the included SHACL constraints to check for syntactic completeness and conformity to relevant standards. In particular, the ontology is modelled after ISO 14971 and the recently published VDE Spec 90025. Our proposed methodology has the potential to save many person-hours for both manufacturers (when creating risk management documentation) as well as notified bodies (when assessing submitted applications for certification), and thus offers considerable benefits for healthcare and, by extension, society as a whole.

Lower limb amputations and neuromuscular impairments severely restrict mobility, necessitating advancements beyond conventional prosthetics. While motorized bionic limbs show promise, their effectiveness depends on replicating the dynamic coordination of human movement across diverse environments. In this paper, we introduce a model for human behavior in the context of bionic prosthesis control. Our approach leverages human locomotion demonstrations to learn the synergistic coupling of the lower limbs, enabling the prediction of the kinematic behavior of a missing limb during tasks such as walking, climbing inclines, and stairs. We propose a multitasking, continually adaptive model that anticipates and refines movements over time. At the core of our method is a technique called multitask prospective rehearsal, that anticipates and synthesizes future movements based on the previous prediction and employs a corrective mechanism for subsequent predictions. Our evolving architecture merges lightweight, task-specific modules on a shared backbone, ensuring both specificity and scalability. We validate our model through experiments on real-world human gait datasets, including transtibial amputees, across a wide range of locomotion tasks. Results demonstrate that our approach consistently outperforms baseline models, particularly in scenarios with distributional shifts, adversarial perturbations, and noise., Comment: Accepted at Transactions on Machine Learning Research (TMLR) 2025

We expand \v{C}ech cohomology of a topological space $X$ with values in a presheaf on $X$ to \v{C}ech cohomology of a commutative ring with unity $R$ with values in a presheaf on $R$. The strategy is to observe that both the set of open subsets of $X$ and the set of ideals of $R$ provide examples of a (semicartesian) quantale. We study a particular pair of (adjoint) functors $(\theta, \tau)$ between the quantale of open subsets of $X$ and the quantale of ideals of $C(X)$, the ring of real-valued continuous functions on $X$. This leads to the main result of this paper: the $q$th \v{C}ech cohomology groups of $X$ with values on the constant sheaf $F$ on $X$ is isomorphic to the $q$th \v{C}ech cohomology groups of the ring $C(X)$ with values on a sheaf $F \circ \tau$ on $C(X)$., Comment: 20 pages. We have removed one of the examples and the notion of a "basis" for a quantale; we will discuss them elsewhere with more details

We demonstrate efficient sub-thermal cooling of the modified cyclotron mode of a single trapped antiproton and reach particle temperatures $T_+=E_+/k_\text{B}$ below $200\,$mK in preparation times shorter than $500\,$s. This corresponds to the fastest resistive single-particle cyclotron cooling to sub-thermal temperatures ever demonstrated. By cooling trapped particles to such low energies, we demonstrate the detection of antiproton spin transitions with an error-rate $<0.000025$, more than three orders of magnitude better than in previous best experiments. This method will have enormous impact on multi-Penning-trap experiments that measure magnetic moments with single nuclear spins for tests of matter/antimatter symmetry, high-precision mass-spectrometry, and measurements of electron $g$-factors bound to highly-charged ions that test quantum electrodynamics.

We present a comprehensive computational study of the under-investigated phenomenon of personal name compounds (PNCs) in German such as Willkommens-Merkel ('Welcome-Merkel'). Prevalent in news, social media, and political discourse, PNCs are hypothesized to exhibit an evaluative function that is reflected in a more positive or negative perception as compared to the respective personal full name (such as Angela Merkel). We model 321 PNCs and their corresponding full names at discourse level, and show that PNCs bear an evaluative nature that can be captured through a variety of computational methods. Specifically, we assess through valence information whether a PNC is more positively or negatively evaluative than the person's name, by applying and comparing two approaches using (i) valence norms and (ii) pretrained language models (PLMs). We further enrich our data with personal, domain-specific, and extra-linguistic information and perform a range of regression analyses revealing that factors including compound and modifier valence, domain, and political party membership influence how a PNC is evaluated., Comment: Accepted at LREC-COLING 2024