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The integration of superconducting niobium and tantalum into superconducting quantum devices has been increasingly explored over the past few years. Recent developments have shown that two-level-systems (TLS) in the surface oxides of these superconducting films are a leading source of decoherence in quantum circuits, and understanding the surface oxidation kinetics of these materials is key to enabling scalability of these technologies. We analyze the nature of atmospheric oxidation of both niobium and a-tantalum surfaces at time scales relevant to fabrication, from sub-minute to two-week atmospheric exposure, employing a combination of x-ray photoelectron spectroscopy and transmission electron microscopy to monitor the growth of the surface oxides. The oxidation kinetics are modeled according to the Cabrera-Mott model of surface oxidation, and the model growth parameters are reported for both films. Our results indicate that niobium surface oxidation follows a consistent regime of inverse logarithmic growth for the entire time scale of the study, whereas a-Ta surface oxidation shows a clear transition between two inverse logarithmic growth regimes at time t = 1 hour, associated with the re-coordination of the surface oxide as determined by x-ray photoelectron spectroscopy analysis. Our findings provide a more complete understanding of the differences in atmospheric surface oxidation between Nb and a-Ta, particularly at short time scales, paving the way for the development of more robust fabrication control for quantum computing architectures., Comment: 15 pages, 5 figures, 4 embedded tables

We propose a $O(\log k \log n)$-competitive randomized algorithm for online node-weighted Steiner forest. This is essentially optimal and significantly improves over the previous bound of $O(\log^2 k \log n)$ by Hajiaghayi et al. [2017]. In fact, our result extends to the more general prize-collecting setting, improving over previous works by a poly-logarithmic factor. Our key technical contribution is a randomized online algorithm for set cover and non-metric facility location in a new adversarial model which we call semi-adaptive adversaries. As a by-product of our techniques, we obtain the first deterministic $O(\log |C| \log |F|)$-competitive algorithm for non-metric facility location., Comment: to appear in SODA 2025

We prove rigidity properties for von Neumann algebraic graph products. We introduce the notion of rigid graphs and define a class of II$_1$-factors named $\mathcal{C}_{\rm Rigid}$. For von Neumann algebras in this class we show a unique rigid graph product decomposition. In particular, we obtain unique prime factorization results and unique free product decomposition results for new classes of von Neumann algebras. Furthermore, we show that for many graph products of II$_1$-factors, including the hyperfinite II$_1$-factor, we can, up to a constant 2, retrieve the radius of the graph from the graph product. We also prove several technical results concerning relative amenability and embeddings of (quasi)-normalizers in graph products. Furthermore, we give sufficient conditions for a graph product to be nuclear and characterize strong solidity, primeness and free-indecomposability for graph products., Comment: Added a new result (Theorem F) and shortened section 5.1

The aging population poses numerous challenges to healthcare, including the increase in chronic wounds in the elderly. The current approach to wound assessment by therapists based on photographic documentation is subjective, highlighting the need for computer-aided wound recognition from smartphone photos. This offers objective and convenient therapy monitoring, while being accessible to patients from their home at any time. However, despite research in mobile image segmentation, there is a lack of focus on mobile wound segmentation. To address this gap, we conduct initial research on three lightweight architectures to investigate their suitability for smartphone-based wound segmentation. Using public datasets and UNet as a baseline, our results are promising, with both ENet and TopFormer, as well as the larger UNeXt variant, showing comparable performance to UNet. Furthermore, we deploy the models into a smartphone app for visual assessment of live segmentation, where results demonstrate the effectiveness of TopFormer in distinguishing wounds from wound-coloured objects. While our study highlights the potential of transformer models for mobile wound segmentation, future work should aim to further improve the mask contours., Comment: Extended version of our paper that was published in the "47th German Conference on Artificial Intelligence (KI 2024)"

Time series analysis remains a major challenge due to its sparse characteristics, high dimensionality, and inconsistent data quality. Recent advancements in transformer-based techniques have enhanced capabilities in forecasting and imputation; however, these methods are still resource-heavy, lack adaptability, and face difficulties in integrating both local and global attributes of time series. To tackle these challenges, we propose a new architectural concept for time series analysis based on introspection. Central to this concept is the self-supervised pretraining of Time Series Representation Models (TSRMs), which once learned can be easily tailored and fine-tuned for specific tasks, such as forecasting and imputation, in an automated and resource-efficient manner. Our architecture is equipped with a flexible and hierarchical representation learning process, which is robust against missing data and outliers. It can capture and learn both local and global features of the structure, semantics, and crucial patterns of a given time series category, such as heart rate data. Our learned time series representation models can be efficiently adapted to a specific task, such as forecasting or imputation, without manual intervention. Furthermore, our architecture's design supports explainability by highlighting the significance of each input value for the task at hand. Our empirical study using four benchmark datasets shows that, compared to investigated state-of-the-art baseline methods, our architecture improves imputation and forecasting errors by up to 90.34% and 71.54%, respectively, while reducing the required trainable parameters by up to 92.43%. The source code is available at https://github.com/RobertLeppich/TSRM.

We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that interconnects dispatchers with compatible servers. Each dispatcher receives tasks over time and sends every task to a compatible server with the least number of tasks, or to a server with the least number of tasks among $d$ compatible servers selected uniformly at random. We focus on networks where the neighborhood of at least one server is skewed in a limiting regime. This means that a diverging number of dispatchers are in the neighborhood which are each compatible with a uniformly bounded number of servers; thus, the degree of the central server approaches infinity while the degrees of many neighboring dispatchers remain bounded. We prove that each server with a skewed neighborhood saturates, in the sense that the mean number of tasks queueing in front of it in steady state approaches infinity. Paradoxically, this pathological behavior can even arise in random networks where nearly all the servers have at most one task in the limit., Comment: 48 pages, 5 figures, accepted at SIGMETRICS 2024

Renewable hydrogen storage in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. Such operational conditions raise concerns about the mechanical stability of salt caverns. Choosing an appropriate constitutive model for salt mechanics is an important step in investigating this issue, and many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and which parameter set represent the given rock, based on stress-strain data, remains an unsolved challenge. For the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation datasets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is achieved by framing the calibration process as an optimization problem, for which the global PSO algorithm is employed. Dynamic data integration is achieved by a multi-step calibration strategy for a situation where experiments are included one at a time, as they become available. Additionally, our calibration strategy is made flexible to account for mild heterogeneity between rock samples, resulting in a single set of parameters that is representative of the deformation datasets. As a rigorous mathematical analysis and the lack of relevant experimental datasets, we consider a wide range of synthetic experimental data, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust and accuracy is improved as more experiments are included for calibration., Comment: 27 pages, 23 figures

This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while sacrificing as little computational performance as possible in comparison to a pure floating-point implementation. The study also addresses the adaptation of certification techniques for correctness verification. Computational studies demonstrate the effectiveness of these techniques, showcasing a 23% performance improvement on the MIPLIB 2017 benchmark test set.

The online matching problem was introduced by Karp, Vazirani and Vazirani (STOC 1990) on bipartite graphs with vertex arrivals. It is well-known that the optimal competitive ratio is $1-1/e$ for both integral and fractional versions of the problem. Since then, there has been considerable effort to find optimal competitive ratios for other related settings. In this work, we go beyond the graph case and study the online matching problem on $k$-uniform hypergraphs. For $k=3$, we provide an optimal primal-dual fractional algorithm, which achieves a competitive ratio of $(e-1)/(e+1)\approx 0.4621$. As our main technical contribution, we present a carefully constructed adversarial instance, which shows that this ratio is in fact optimal. It combines ideas from known hard instances for bipartite graphs under the edge-arrival and vertex-arrival models. For $k\geq 3$, we give a simple integral algorithm which performs better than greedy when the online nodes have bounded degree. As a corollary, it achieves the optimal competitive ratio of 1/2 on 3-uniform hypergraphs when every online node has degree at most 2. This is because the special case where every online node has degree 1 is equivalent to the edge-arrival model on graphs, for which an upper bound of 1/2 is known.

The present paper establishes an explicit multi-dimensional state space collapse (SSC) for parallel-processing systems with arbitrary compatibility constraints between servers and job types. This breaks major new ground beyond the SSC results and queue length asymptotics in the literature which are largely restricted to complete resource pooling (CRP) scenarios where the steady-state queue length vector concentrates around a line in heavy traffic. The multi-dimensional SSC that we establish reveals heavy-traffic behavior which is also far more tractable than the pre-limit queue length distribution, yet exhibits a fundamentally more intricate structure than in the one-dimensional case, providing useful insight into the system dynamics. In particular, we prove that the limiting queue length vector lives in a $K$-dimensional cone of which the set of spanning vectors is random in general, capturing the delicate interplay between the various job types and servers. For a broad class of systems we provide a further simplification which shows that the collection of random cones constitutes a fixed $K$-dimensional cone, resulting in a $K$-dimensional SSC. The dimension $K$ represents the number of critically loaded subsystems, or equivalently, capacity bottlenecks in heavy-traffic, with $K=1$ corresponding to conventional CRP scenarios. Our approach leverages probability generating function (PGF) expressions for Markovian systems operating under redundancy policies.

Artificial Intelligence (AI) has witnessed remarkable growth, particularly through the proliferation of Deep Neural Networks (DNNs). These powerful models drive technological advancements across various domains. However, to harness their potential in real-world applications, specialized hardware accelerators are essential. This demand has sparked a market for parameterizable AI hardware accelerators offered by different vendors. Manufacturers of AI-integrated products face a critical challenge: selecting an accelerator that aligns with their product's performance requirements. The decision involves choosing the right hardware and configuring a suitable set of parameters. However, comparing different accelerator design alternatives remains a complex task. Often, engineers rely on data sheets, spreadsheet calculations, or slow black-box simulators, which only offer a coarse understanding of the performance characteristics. The Abstract Computer Architecture Description Language (ACADL) is a concise formalization of computer architecture block diagrams, which helps to communicate computer architecture on different abstraction levels and allows for inferring performance characteristics. In this paper, we demonstrate how to use the ACADL to model AI hardware accelerators, use their ACADL description to map DNNs onto them, and explain the timing simulation semantics to gather performance results., Comment: Accepted Version for: MBMV'24

The anticipated launch of fully autonomous vehicles presents an opportunity to develop and implement novel traffic management systems. Intersections are one of the bottlenecks for urban traffic, and thus offer tremendous potential for performance improvements of traffic flow if managed efficiently. Platoon-forming algorithms, in which vehicles are grouped together with short inter-vehicular distances just before arriving at an intersection at high speed, seem particularly promising in this aspect. In this work, we present an intersection access control system based on platoon-forming for heterogeneous autonomous traffic. The heterogeneity of traffic arises from vehicles with different acceleration capabilities and safety constraints. We focus on obtaining computationally fast and interpretable closed-form expressions for safe and efficient vehicle trajectories that lead to platoon formation, and show that these trajectories are solutions to certain classes of optimisation problems. Additionally, we conduct a numerical study to obtain approximations for intersection capacity as a result of such platoon formation., Comment: 42 pages, 16 figures. 3D Animations included as ancillary files

Let $W$ be a finitely generated right-angled Coxeter group with group von Neumann algebra $\mathcal{L}(W)$. We prove the following dichotomy: either $\mathcal{L}(W)$ is strongly solid or $W$ contains $\mathbb{Z} \times \mathbb{F}_2$ as a subgroup. This proves in particular strong solidity of $\mathcal{L}(W)$ for all non-hyperbolic Coxeter groups that do not contain $\mathbb{Z} \times \mathbb{F}_2$.

Superconductors are materials with zero electrical resistivity and the ability to expel magnetic fields known as the Meissner effect. Their dissipationless diamagnetic response is central to magnetic levitation and circuits such as quantum interference devices. Here, we use superconducting diamagnetism to shape the magnetic environment governing the transport of spin waves - collective spin excitations in magnets that are promising on-chip signal carriers - in a thin-film magnet. Using diamond-based magnetic imaging, we observe hybridized spin-wave-Meissner-current transport modes with strongly altered, temperature-tunable wavelengths. We extract the temperature-dependent London penetration depth from the wavelength shifts and realize local control of spin-wave refraction using a focused laser. Our results demonstrate the versatility of superconductor-manipulated spin-wave transport and have potential applications in spin-wave gratings, filters, crystals and cavities., Comment: main: 8 pages, 5 figures, supp: 15 pages, 6 figures

Magnetic imaging using nitrogen-vacancy (NV) spins in diamonds is a powerful technique for acquiring quantitative information about sub-micron scale magnetic order. A major challenge for its application in the research on two-dimensional (2D) magnets is the positioning of the NV centers at a well-defined, nanoscale distance to the target material required for detecting the small magnetic fields generated by magnetic monolayers. Here, we develop a diamond 'dry-transfer' technique, akin to the state-of-the-art 2D-materials assembly methods, and use it to place a diamond micro-membrane in direct contact with the 2D interlayer antiferromagnet CrSBr. We harness the resulting NV-sample proximity to spatially resolve the magnetic stray fields generated by the CrSBr, present only where the CrSBr thickness changes by an odd number of layers. From the magnetic stray field of a single uncompensated ferromagnetic layer in the CrSBr, we extract a monolayer magnetization of $M_\mathrm{CSB}$ = 0.46(2) T, without the need for exfoliation of monolayer crystals or applying large external magnetic fields. The ability to deterministically place NV-ensemble sensors into contact with target materials and detect ferromagnetic monolayer magnetizations paves the way for quantitative analysis of a wide range of 2D magnets assembled on arbitrary target substrates.

Consider a network of $n$ single-server queues where tasks arrive independently at each of the servers at rate $\lambda_n$. The servers are interconnected by a graph that is resampled at rate $\mu_n$ in a way that is symmetric with respect to the servers, and each task is dispatched to the shortest queue in the graph neighborhood where it appears. The so-called occupancy process describes the empirical distribution of the number of tasks across the servers. This stochastic process evolves on the underlying dynamic graph, and its dynamics depend on the the number of tasks at each individual server and the neighborhood structure of the graph. We prove that this dependency disappears in the limit as $n \to \infty$ when $\lambda_n / n \to \lambda$ and $\mu_n \to \infty$, and establish that the limit of the occupancy process is given by a system of differential equations that depends solely on $\lambda$ and the limiting degree distribution of the graph. We further show that the stationary distribution of the occupancy process converges to an equilibrium point of the differential equations, and derive properties of this equilibrium that reflect the impact of the degree distribution. Our focus is on truly sparse graphs where the maximum degree is uniformly bounded across $n$, making neighboring servers strongly correlated., Comment: 60 pages, 4 figures

This paper evaluates the viability of using fixed language models for training text classification networks on low-end hardware. We combine language models with a CNN architecture and put together a comprehensive benchmark with 8 datasets covering single-label and multi-label classification of topic, sentiment, and genre. Our observations are distilled into a list of trade-offs, concluding that there are scenarios, where not fine-tuning a language model yields competitive effectiveness at faster training, requiring only a quarter of the memory compared to fine-tuning., Comment: 5+4 pages, 6 tables; fixed affiliation

For a normal measurable operator $a$ affiliated with a von Neumann factor $\mathcal{M}$ we show: If $\mathcal{M}$ is infinite, then there is $\lambda_0\in \mathbb{C}$ so that for $\varepsilon>0$ there are $u_{\varepsilon}=u_{\varepsilon}^*$, $v_{\varepsilon}\in \mathcal{U}(\mathcal{M})$ with $$v_\varepsilon|[a,u_\varepsilon]|v_\varepsilon^*\geq(1-\varepsilon)(|a-\lambda_0\textbf{1}|+u_\varepsilon|a-\lambda_0\textbf{1}|u_\varepsilon).$$ If $\mathcal{M}$ is finite, then there is $\lambda_0\in\mathbb{C}$ and $u,v\in\mathcal{U}(\mathcal{M})$ so that $$v|[a,u]|v^*\geq \frac{\sqrt{3}}{2}(|a-\lambda_0\textbf{1}|+u|a-\lambda_0\textbf{1}|u^*).$$ These bounds are optimal for infinite factors, II$_1$-factors and some I$_n$-factors. Furthermore, for finite factors applying $\|\cdot\|_{1}$-norms to the inequality provides estimates on the norm of the inner derivation $\delta_{a}:\mathcal{M}\to L_1(\mathcal{M},\tau)$ associated to $a$. While by [3,Theorem 1.1] it is known for finite factors and self-adjoint $a\in L_1(\mathcal{M},\tau)$ that $\|\delta_{a}\|_{\mathcal{M}\to L_1(\mathcal{M},\tau)} = 2\min_{z\in \mathbb{C}}\|a-z\|_{1}$, we present concrete examples of finite factors $\mathcal{M}$ and normal operators $a\in \mathcal{M}$ for which this fails.

The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reduced-load equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit.