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This paper shows that the basic properties of Sobolev, Besov, and Bessel potential spaces are valid on Riemannian manifolds with boundary, which either have bounded geometry or posses singularities. In the latter case the appropriate setting is that of Kondratiev-type weighted spaces. The importance and usefulness of our results are indicated by a demonstration of a maximal regularity result for a linear parabolic initial value problem on singular manifolds. more...

Higher rank graphs, also known as $k$-graphs, are a $k$-dimensional generalization of directed graphs and a rich source of examples of $C^*$-algebras. In the present paper, we contribute to the geometric classification program for $k$-graph $C^*$-algebras by introducing a new move on $k$-graphs, called LiMaR-split, which is a generalization of outsplit for directed graphs. We show, under one additional assumption, that LiMaR-split preserves the $k$-graph $C^*$-algebras up to Morita equivalence. more...

We report on the observation and study of the magneto-ratchet effect in a graphene-based two-dimensional metamaterial formed by a graphite gate that is placed below a graphene monolayer and patterned with an array of triangular antidots. We demonstrate that terahertz/gigahertz excitation of the metamaterial leads to sign-alternating magneto-oscillations with an amplitude that exceeds the ratchet current at zero magnetic field by orders of magnitude. The oscillations are shown to be related to the Shubnikov-de Haas effect. In addition to the giant ratchet current oscillations we detect resonant ratchet currents caused by the cyclotron and electron spin resonances. The results are well described by the developed theory considering the magneto-ratchet effect caused by the interplay of the near-field radiation and the nonuniform periodic electrostatic potential of the metamaterial controlled by the gate voltages., Comment: 10 pages, 6 figures more...

Speech disfluency commonly occurs in conversational and spontaneous speech. However, standard Automatic Speech Recognition (ASR) models struggle to accurately recognize these disfluencies because they are typically trained on fluent transcripts. Current research mainly focuses on detecting disfluencies within transcripts, overlooking their exact location and duration in the speech. Additionally, previous work often requires model fine-tuning and addresses limited types of disfluencies. In this work, we present an inference-only approach to augment any ASR model with the ability to detect open-set disfluencies. We first demonstrate that ASR models have difficulty transcribing speech disfluencies. Next, this work proposes a modified Connectionist Temporal Classification(CTC)-based forced alignment algorithm from \cite{kurzinger2020ctc} to predict word-level timestamps while effectively capturing disfluent speech. Additionally, we develop a model to classify alignment gaps between timestamps as either containing disfluent speech or silence. This model achieves an accuracy of 81.62% and an F1-score of 80.07%. We test the augmentation pipeline of alignment gap detection and classification on a disfluent dataset. Our results show that we captured 74.13% of the words that were initially missed by the transcription, demonstrating the potential of this pipeline for downstream tasks., Comment: Accepted by SLT2024 more...

Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our numerical observations reveal the emergence of synchronization cluster bursting, characterized by periodic transitions between cluster synchronization and global synchronization. By investigating a reduced model, the mechanisms underlying synchronization cluster bursting are clarified. We show that a minimal model exhibiting this phenomenon can be reduced to a phase oscillator with complex-valued adaptation. Furthermore, the adaptivity of the system leads to the appearance of additional symmetries and thus to the coexistence of stable bursting solutions with very different Kuramoto order parameters. more...

The concept of multifunctionality has enabled reservoir computers (RCs), a type of dynamical system that is typically realised as an artificial neural network, to reconstruct multiple attractors simultaneously using the same set of trained weights. However there are many additional phenomena that arise when training a RC to reconstruct more than one attractor. Previous studies have found that, in certain cases, if the RC fails to reconstruct a coexistence of attractors then it exhibits a form of metastability whereby, without any external input, the state of the RC switches between different modes of behaviour that resemble properties of the attractors it failed to reconstruct. In this paper we explore the origins of these switching dynamics in a paradigmatic setting via the `seeing double' problem., Comment: Preprint submitted to Frontiers in Network Physiology more...

Collective perception has received considerable attention as a promising approach to overcome occlusions and limited sensing ranges of vehicle-local perception in autonomous driving. In order to develop and test novel collective perception technologies, appropriate datasets are required. These datasets must include not only different environmental conditions, as they strongly influence the perception capabilities, but also a wide range of scenarios with different road users as well as realistic sensor models. Therefore, we propose the Synthetic COllective PErception (SCOPE) dataset. SCOPE is the first synthetic multi-modal dataset that incorporates realistic camera and LiDAR models as well as parameterized and physically accurate weather simulations for both sensor types. The dataset contains 17,600 frames from over 40 diverse scenarios with up to 24 collaborative agents, infrastructure sensors, and passive traffic, including cyclists and pedestrians. In addition, recordings from two novel digital-twin maps from Karlsruhe and T\"ubingen are included. The dataset is available at https://ekut-es.github.io/scope more...

Comprehensive perception of the vehicle's environment and correct interpretation of the environment are crucial for the safe operation of autonomous vehicles. The perception of surrounding objects is the main component for further tasks such as trajectory planning. However, safe trajectory planning requires not only object detection, but also the detection of drivable areas and lane corridors. While first approaches consider an advanced safety evaluation of object detection, the evaluation of lane detection still lacks sufficient safety metrics. Similar to the safety metrics for object detection, additional factors such as the semantics of the scene with road type and road width, the detection range as well as the potential causes of missing detections, incorporated by vehicle speed, should be considered for the evaluation of lane detection. Therefore, we propose the Lane Safety Metric (LSM), which takes these factors into account and allows to evaluate the safety of lane detection systems by determining an easily interpretable safety score. We evaluate our offline safety metric on various virtual scenarios using different lane detection approaches and compare it with state-of-the-art performance metrics. more...

We report on the observation of the circular ratchet effect excited by terahertz laser radiation in a specially designed two-dimensional metamaterial consisting of a graphene monolayer deposited on a graphite gate patterned with an array of triangular antidots. We show that a periodically driven Dirac fermion system with spatial asymmetry converts the a.c. power into a d.c. current, whose direction reverses when the radiation helicity is switched. The circular ratchet effect is demonstrated for room temperature and a radiation frequency of 2.54 THz. It is shown that the ratchet current magnitude can be controllably tuned by the patterned and uniform back gate voltages. The results are analyzed in the light of the developed microscopic theory considering electronic and plasmonic mechanisms of the ratchet current formation., Comment: 10 pages, 8 figures, 2 tables more...

Variations with oxygen concentration of titanium lattice parameters are obtained by means of ab initio calculations, considering the impact of oxygen ordering. The quasiharmonic approximation is used to take into account the thermal expansion at finite temperature. Results show that lattice parameters depend mainly on oxygen concentration and, to a lesser extent, on the ordering state. Knowing these theoretical variations, one can get insights into the composition of ordered compounds existing in Ti-O binary alloys from their lattice mismatch measured experimentally by x-ray diffraction. The approach is used in a binary alloy containing 6000 ppm in weight of oxygen. It is concluded that the ordered compounds, which are observed after a recrystallization heat treatment, do not have the expected Ti6O stoichiometry but have a composition close to the nominal concentration. Oxygen ordering proceeds, therefore, before oxygen partitioning in titanium. more...

We report the observation of the terahertz-induced ratchet effect in graphene-based two-dimensional (2D) metamaterials. The metamaterial consists of a graphite gate patterned with an array of triangular antidots placed under a graphene monolayer. We show that the ratchet current appears due to the noncentrosymmetry of the periodic structure unit cell. The ratchet current is generated owing to the combined action of a spatially periodic in-plane electrostatic potential and a periodically modulated radiation electric field caused by near-field diffraction. The magnitude and direction of the ratchet current are shown to be controlled by voltages applied to both back and patterned gates, which change the lateral asymmetry, carrier type and density. The phenomenological and microscopic theories of ratchet effects in graphene-based 2D metamaterials are developed. The experimental data are discussed in the light of the theory based on the solution of the Boltzmann kinetic equation and the calculated electrostatic potential profile. The theory describes well all the experimental results and shows that the observed ratchet current consists of the Seebeck thermoratchet contribution as well as the linear contribution, which is sensitive to the orientation of the radiation electric field vector with respect to the triangles., Comment: 14 pages, 13 figures more...

The aim of the present work is to construct prediction intervals via the Jackknife and the Jackknife+ whose coverage probability conditional on the training data is close to its nominal level in finite samples and can be asymptotically valid in high-dimensions. The main innovation is twofold: Firstly, we generalize the results of Steinberger and Leeb (2023) for the Jackknife to a non-continuous response distribution and to the case of non-linear models. Secondly, we show that under a stability assumption the prediction intervals via a Jackknife+-approach are closely related to their Jackknife analogues and therefore share a similar conditional coverage probability. More specifically, this work is split into four parts: in the first part we introduce the $\varepsilon$-variational divergence in order to link the prediction interval's coverage probability to the accuracy of estimating the distribution of the prediction error. In the second part, we define an approach based on the Jackknife for the estimation of the prediction error's distribution conditional on the training data. We show that the prediction error's distribution can be estimated consistently if two conditions are fulfilled: the prediction error should be bounded in probability and the prediction algorithm should satisfy a stability condition. In particular, we show that under these two conditions the prediction intervals based on the Jackknife are asymptotically valid. In the fourth part we draw a connection between the Jackknife and the Jackknife+ and show that corresponding prediction intervals are closely related to each other given the stability condition. In the last part we show that under mild assumptions the conditions for asymptotically valid prediction intervals based on the Jackknife or the Jackknife+ are fulfilled for several predictors., Comment: 107 pages, 0 figures more...

We report on the realization of a large-scale quantum-processing architecture surpassing the tier of 1000 atomic qubits. By tiling multiple microlens-generated tweezer arrays, each operated by an independent laser source, we can eliminate laser-power limitations in the number of allocatable qubits. Already with two separate arrays, we implement combined 2D configurations of 3000 qubit sites with a mean number of 1167(46) single-atom quantum systems. The transfer of atoms between the two arrays is achieved with high efficiency. Thus, supercharging one array designated as quantum processing unit with atoms from the secondary array significantly increases the number of qubits and the initial filling fraction. This drastically enlarges attainable qubit cluster sizes and success probabilities allowing us to demonstrate the defect-free assembly of clusters of up to 441 qubits with persistent stabilization at near-unity filling fraction over tens of detection cycles. The presented method substantiates neutral atom quantum information science by facilitating configurable geometries of highly scalable quantum registers with immediate application in Rydberg-state mediated quantum simulation, fault-tolerant universal quantum computation, quantum sensing, and quantum metrology. more...

A wideband vibration energy harvester with multiple nonlinear forces is investigated. The nonlinearities are due to repulsive magnets and hardening springs, which gives rise to multistabilities between a number of energy branches. Not all branches are accessible by a simple up or down sweep of the driving frequency and in particular the highest energy branch is often hidden, requiring a suitable frequency schedule to be accessed. Detailed theoretical understanding of the energy branch structure along with robust experimental methods are essential for characterizing each of the energy branches to enhance the energy output from such vibration energy harvesting system. We introduce a graphical representation in the form of eye diagrams based on time-resolved measurements of acceleration and output voltage to study the dynamical features of the different branches. This generic approach allows us to optimize the design, which results in 1.3mW of power generated at 1g over 44Hz frequency bandwidth while maintaining a small footprint of $1.23 cm^3$. The energy conversion ratio of the energy harvester at 120Hz drive frequency is 0.52 for the high energy branch. more...