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We investigate dispersive and Strichartz estimates for the Schr\"odinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times.

This paper addresses the modeling and attitude control of jumping quadrupeds in low-gravity environments. First, a convex decomposition procedure is presented to generate high-accuracy and low-cost collision geometries for quadrupeds performing agile maneuvers. A hierarchical control architecture is then investigated, separating torso orientation tracking from the generation of suitable, collision-free, corresponding leg motions. Nonlinear Model Predictive Controllers (NMPCs) are utilized in both layers of the controller. To compute the necessary leg motions, a torque allocation strategy is employed that leverages the symmetries of the system to avoid self-collisions and simplify the respective NMPC. To plan periodic trajectories online, a Finite State Machine (FSM)-based weight switching strategy is also used. The proposed controller is first evaluated in simulation, where 90 degree rotations in roll, pitch, and yaw are stabilized in 6.3, 2.4, and 5.5 seconds, respectively. The performance of the controller is further experimentally demonstrated by stabilizing constant and changing orientation references. Overall, this work provides a framework for the development of advanced model-based attitude controllers for jumping legged systems., Comment: 16 pages, 10 figures, to appear at the International Symposium of Robotics Research (ISRR) 2024. Paper site: https://michalispapadakis.github.io/mpc_olympus/

Macroscopic fundamental diagrams (MFDs) and related network traffic dynamics models have received both theoretical support and empirical validation with the emergence of new data collection technologies. However, the existence of well-defined MFD curves can only be expected for traffic networks with specific topologies and is subject to various disturbances, most importantly hysteresis phenomena. This study aims to improve the understanding of hysteresis in Macroscopic Fundamental Diagrams and Network Exit Functions (NEFs) during rush hour conditions. We apply the LWR theory to a highway corridor featuring a location-dependent downstream bottleneck to identify a figure-eight hysteresis pattern, clockwise on the top and counter-clockwise on the bottom. We discuss why this general pattern is rare in practical scenarios, where a single clockwise loop is more typical. The paper discusses the impact of the road topology and demand parameters on the formation and intensity of hysteresis loops analytically. To substantiate these findings, we employ numerical simulations using the Cell Transmission Model (CTM). Our simulations show that even a slight reduction in the capacity of the homogeneous section can significantly decrease MFD hysteresis while maintaining outflow at the corridor's downstream end. These reductions can be achieved with minimal intervention through standard traffic control measures, such as dynamic speed limits or ramp metering.

Neutrinoless double beta decay is one of the most sensitive probes for new physics beyond the Standard Model of particle physics. One of the isotopes under investigation is $^{136}$Xe, which would double beta decay into $^{136}$Ba. Detecting the single $^{136}$Ba daughter provides a sort of ultimate tool in the discrimination against backgrounds. Previous work demonstrated the ability to perform single atom imaging of Ba atoms in a single-vacancy site of a solid xenon matrix. In this paper, the effort to identify signal from individual barium atoms is extended to Ba atoms in a hexa-vacancy site in the matrix and is achieved despite increased photobleaching in this site. Abrupt fluorescence turn-off of a single Ba atom is also observed. Significant recovery of fluorescence signal lost through photobleaching is demonstrated upon annealing of Ba deposits in the Xe ice. Following annealing, it is observed that Ba atoms in the hexa-vacancy site exhibit antibleaching while Ba atoms in the tetra-vacancy site exhibit bleaching. This may be evidence for a matrix site transfer upon laser excitation. Our findings offer a path of continued research toward tagging of Ba daughters in all significant sites in solid xenon., Comment: 9 pages, 8 figures

Electron-neutrino charged-current interactions with xenon nuclei were modeled in the nEXO neutrinoless double-$\beta$ decay detector (~5 metric ton, 90% ${}^{136}$Xe, 10% ${}^{134}$Xe) to evaluate its sensitivity to supernova neutrinos. Predictions for event rates and detectable signatures were modeled using the Model of Argon Reaction Low Energy Yields (MARLEY) event generator. We find good agreement between MARLEY's predictions and existing theoretical calculations of the inclusive cross sections at supernova neutrino energies. The interactions modeled by MARLEY were simulated within the nEXO simulation framework and were run through an example reconstruction algorithm to determine the detector's efficiency for reconstructing these events. The simulated data, incorporating the detector response, were used to study the ability of nEXO to reconstruct the incident electron-neutrino spectrum and these results were extended to a larger xenon detector of the same isotope enrichment. We estimate that nEXO will be able to observe electron-neutrino interactions with xenon from supernovae as far as 5-8 kpc from Earth, while the ability to reconstruct incident electron-neutrino spectrum parameters from observed interactions in nEXO is limited to closer supernovae., Comment: 17 pages, 16 figures

These proceedings summarize the program and discussions of the ``Workshop on Xenon Detector $0\nu\beta\beta$ Searches: Steps Towards the Kilotonne Scale'' held on October 25-27 2023 at SLAC National Accelerator Laboratory. This workshop brought together experts from the communities of neutrinoless double-beta decay and dark matter detection, to discuss paths forward for the realization of monolithic experiments with xenon approaching the kilotonne scale., Comment: 7 pages, 2 figures. Proceedings

We present a theoretical study on photonic topological crystals whose symmetry is governed by quantum valley-Hall topological insulators and whose propagating edge modes are strongly confined due to bowtie geometries. Dielectric bowtie structures exploit the field discontinuities at boundaries between materials with different refractive indices, and here bowties emerge at the topological interface due to the close proximity of two triangular features in the underlying crystal. The topological bowtie mode features a unit-cell mode volume down to $8\times10^{-4}$ cubic wavelengths at the center of the bowtie bridge of width $10~\text{nm}$, and we show that it is possible to use perturbed versions of the unit cells as building blocks for topological heterostructure bowtie cavities with quality factors exceeding $10^7$. Due to the tightly confined bowtie mode, this implies a strongly enhanced light-matter interaction as quantified by a Purcell factor of $3 \times 10^6$.

Advances in graph machine learning (ML) have been driven by applications in chemistry as graphs have remained the most expressive representations of molecules. While early graph ML methods focused primarily on small organic molecules, recently, the scope of graph ML has expanded to include inorganic materials. Modelling the periodicity and symmetry of inorganic crystalline materials poses unique challenges, which existing graph ML methods are unable to address. Moving to inorganic nanomaterials increases complexity as the scale of number of nodes within each graph can be broad ($10$ to $10^5$). The bulk of existing graph ML focuses on characterising molecules and materials by predicting target properties with graphs as input. However, the most exciting applications of graph ML will be in their generative capabilities, which is currently not at par with other domains such as images or text. We invite the graph ML community to address these open challenges by presenting two new chemically-informed large-scale inorganic (CHILI) nanomaterials datasets: A medium-scale dataset (with overall >6M nodes, >49M edges) of mono-metallic oxide nanomaterials generated from 12 selected crystal types (CHILI-3K) and a large-scale dataset (with overall >183M nodes, >1.2B edges) of nanomaterials generated from experimentally determined crystal structures (CHILI-100K). We define 11 property prediction tasks and 6 structure prediction tasks, which are of special interest for nanomaterial research. We benchmark the performance of a wide array of baseline methods and use these benchmarking results to highlight areas which need future work. To the best of our knowledge, CHILI-3K and CHILI-100K are the first open-source nanomaterial datasets of this scale -- both on the individual graph level and of the dataset as a whole -- and the only nanomaterials datasets with high structural and elemental diversity., Comment: 16 pages, 15 figures, 8 tables. Dataset is available at https://github.com/UlrikFriisJensen/CHILI

This article deals with harmonic analysis on affine buildings. Its main goal is to construct suitable kernels associated to a discrete multitemporal wave equations on the latter spaces, the long-standing motivation being to contribute to progress in arithmetic quantum unique ergodicity (AQUE) on certain Riemannian manifolds.

We study a distinguished random walk on affine buildings of type Ar , which was already considered by Cartwright, Saloff-Coste and Woess. In rank r=2, it is the simple random walk and we obtain optimal global bounds for its transition density (same upper and lower bound, up to multiplicative constants). In the higher rank case, we obtain sharp uniform bounds in fairly large space-time regions which are sufficient for most applications.

This paper introduces the Terrain Recognition And Contact Force Estimation Paw, a compact and sensorized shoe designed for legged robots. The paw end-effector is made of silicon that deforms upon the application of contact forces, while an embedded micro camera is utilized to capture images of the deformed inner surface inside the shoe, and a microphone picks up audio signals. Processed through machine learning techniques, the images are mapped to compute an accurate estimate of the cumulative 3D force vector, while the audio signals are analyzed to identify the terrain class (e.g., gravel, snow). By leveraging its on-edge computation ability, the paw enhances the capabilities of legged robots by providing key information in real-time that can be used to adapt locomotion control strategies. To assess the performance of this novel sensorized paw, we conducted experiments on the data collected through a specially-designed testbed for force estimation, as well as data from recordings of the audio signatures of different terrains interacting with the paw. The results demonstrate the accuracy and effectiveness of the system, highlighting its potential for improving legged robot performance., Comment: 21st International Conference on Advanced Robotics (ICAR 2023)

The potential of Martian lava tubes for resource extraction and habitat sheltering highlights the need for robots capable to undertake the grueling task of their exploration. Driven by this motivation, in this work we introduce a legged robot system optimized for jumping in the low gravity of Mars, designed with leg configurations adaptable to both bipedal and quadrupedal systems. This design utilizes torque-controlled actuators coupled with springs for high-power jumping, robust locomotion, and an energy-efficient resting pose. Key design features include a 5-bar mechanism as leg concept, combined with springs connected by a high-strength cord. The selected 5-bar link lengths and spring stiffness were optimized for maximizing the jump height in Martian gravity and realized as a robot leg. Two such legs combined with a compact body allowed jump testing of a bipedal prototype. The robot is 0.472 m tall and weighs 7.9 kg. Jump testing with significant safety margins resulted in a measured jump height of 1.141 m in Earth's gravity, while a total of 4 jumping experiments are presented. Simulations utilizing the full motor torque and kinematic limits of the design resulted in a maximum possible jump height of 1.52 m in Earth's gravity and 3.63 m in Mars' gravity, highlighting the versatility of jumping as a form of locomotion and overcoming obstacles in lower gravity., Comment: 21st International Conference on Advanced Robotics (ICAR 2023)

In recent years, robotic exploration has become increasingly important in planetary exploration. One area of particular interest for exploration is Martian lava tubes, which have several distinct features of interest. First, it is theorized that they contain more easily accessible resources such as water ice, needed for in-situ utilization on Mars. Second, lava tubes of significant size can provide radiation and impact shelter for possible future human missions to Mars. Third, lava tubes may offer a protected and preserved view into Mars' geological and possible biological past. However, exploration of these lava tubes poses significant challenges due to their sheer size, geometric complexity, uneven terrain, steep slopes, collapsed sections, significant obstacles, and unstable surfaces. Such challenges may hinder traditional wheeled rover exploration. To overcome these challenges, legged robots and particularly jumping systems have been proposed as potential solutions. Jumping legged robots utilize legs to both walk and jump. This allows them to traverse uneven terrain and steep slopes more easily compared to wheeled or tracked systems. In the context of Martian lava tube exploration, jumping legged robots would be particularly useful due to their ability to jump over big boulders, gaps, and obstacles, as well as to descend and climb steep slopes. This would allow them to explore and map such caves, and possibly collect samples from areas that may otherwise be inaccessible. This paper presents the specifications, design, capabilities, and possible mission profiles for state-of-the-art legged robots tailored to space exploration. Additionally, it presents the design, capabilities, and possible mission profiles of a new jumping legged robot for Martian lava tube exploration that is being developed at the Norwegian University of Science and Technology., Comment: 74rd International Astronautical Congress (IAC)

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

The ARIANNA experiment is an Askaryan radio detector designed to measure high-energy neutrino induced cascades within the Antarctic ice. Ultra-high-energy neutrinos above $10^{16}$ eV have an extremely low flux, so experimental data captured at trigger level need to be classified correctly to retain more neutrino signal. We first describe two new physics-based neutrino selection methods, (the updown and dipole cut) that extend the previously published analysis to a specialized ARIANNA station with 8 antenna channels, which is double the number used in the prior analysis. For a standard trigger with a threshold signal to noise ratio at 4.4, the new cuts produce a neutrino efficiency of > 95% per station-year, while rejecting 99.93% of the background (corresponding to 53 remaining experimental background events). When the new cuts are combined with a previously developed cut using neutrino waveform templates, all background is removed at no change of efficiency. In addition, the neutrino efficiency is extrapolated to 1,000 station-years, obtaining 91%. This work then introduces a new selection method (deep learning (DL) cut) to augment the identification of neutrino events by using DL methods and compares the efficiency to the physics-based analysis. The DL cut gives 99% signal efficiency per station-year of operation while rejecting 99.997% of the background (corresponding to 2 remaining experimental background events), which are then removed by the waveform template cut at no significant change in efficiency. The results of the DL cut were verified using measured cosmic rays which shows the simulations do not introduce artifacts with respect to experimental data. The paper demonstrates the background rejection and signal efficiency of near surface antennas meets the requirements of a large scale future array, as considered in baseline design of the radio component of IceCube-Gen2., Comment: 29 pages, 16 figures, 3 tables