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It is widely established that a lower bound on the dark matter particle mass, $m$, can be obtained by demanding that the de Broglie wavelength in a given galaxy must be smaller than the virial radius of the galaxy, leading to $m\gtrsim 10^{-22}\text{ eV}$ when applied to typical dwarf galaxies. This lower limit has never been derived precisely or rigorously. We use stellar kinematical data for the Milky Way satellite galaxy Leo II to self-consistently reconstruct a statistical ensemble of dark matter wavefunctions and corresponding density profiles. By comparison to a data-driven, model-independent reconstruction, and using a variant of the maximum mean discrepancy as a statistical measure, we determine that a self-consistent description of dark matter in the local Universe requires $m>2.2 \times 10^{-21}\,\mathrm{eV}\;\mathrm{(CL>95\%)}$. This lower limit is free of any assumptions pertaining to cosmology, microphysics (including spin), or dynamics of dark matter, and only assumes that it is predominantly composed of a single bosonic particle species., Comment: 5 pages, 3 figures. The jaxsp library is available at https://github.com/timzimm/jaxsp. v2: significantly expanded appendix containing jaxsp numerical checks and more details on statistical approach

The increasing number of vehicles highlights the need for efficient parking space management. Predicting real-time Parking Availability (PA) can help mitigate traffic congestion and the corresponding social problems, which is a pressing issue in densely populated cities like Singapore. In this study, we aim to collectively predict future PA across Singapore with complex factors from various domains. The contributions in this paper are listed as follows: (1) A New Dataset: We introduce the \texttt{SINPA} dataset, containing a year's worth of PA data from 1,687 parking lots in Singapore, enriched with various spatial and temporal factors. (2) A Data-Driven Approach: We present DeepPA, a novel deep-learning framework, to collectively and efficiently predict future PA across thousands of parking lots. (3) Extensive Experiments and Deployment: DeepPA demonstrates a 9.2% reduction in prediction error for up to 3-hour forecasts compared to existing advanced models. Furthermore, we implement DeepPA in a practical web-based platform to provide real-time PA predictions to aid drivers and inform urban planning for the governors in Singapore. We release the dataset and source code at https://github.com/yoshall/SINPA., Comment: Accepted by IJCAI 2024 (Multi-Year Track On AI And Social Good with ~20% acceptance rate)

We present the model we developed to reconstruct the CUORE radioactive background based on the analysis of an experimental exposure of 1038.4 kg yr. The data reconstruction relies on a simultaneous Bayesian fit applied to energy spectra over a broad energy range. The high granularity of the CUORE detector, together with the large exposure and extended stable operations, allow for an in-depth exploration of both spatial and time dependence of backgrounds. We achieve high sensitivity to both bulk and surface activities of the materials of the setup, detecting levels as low as 10 nBq kg$^{-1}$ and 0.1 nBq cm$^{-2}$, respectively. We compare the contamination levels we extract from the background model with prior radio-assay data, which informs future background risk mitigation strategies. The results of this background model play a crucial role in constructing the background budget for the CUPID experiment as it will exploit the same CUORE infrastructure.

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr\"ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fr\"ohlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties., Comment: 14 pages, 9 figures

Accurate mid-term (weeks to one year) hourly electricity load forecasts are essential for strategic decision-making in power plant operation, ensuring supply security and grid stability, and energy trading. While numerous models effectively predict short-term (hours to a few days) hourly load, mid-term forecasting solutions remain scarce. In mid-term load forecasting, besides daily, weekly, and annual seasonal and autoregressive effects, capturing weather and holiday effects, as well as socio-economic non-stationarities in the data, poses significant modeling challenges. To address these challenges, we propose a novel forecasting method using Generalized Additive Models (GAMs) built from interpretable P-splines and enhanced with autoregressive post-processing. This model uses smoothed temperatures, Error-Trend-Seasonal (ETS) modeled non-stationary states, a nuanced representation of holiday effects with weekday variations, and seasonal information as input. The proposed model is evaluated on load data from 24 European countries. This analysis demonstrates that the model not only has significantly enhanced forecasting accuracy compared to state-of-the-art methods but also offers valuable insights into the influence of individual components on predicted load, given its full interpretability. Achieving performance akin to day-ahead TSO forecasts in fast computation times of a few seconds for several years of hourly data underscores the model's potential for practical application in the power system industry.

In our increasingly interconnected world, where intelligent devices continually amass copious personalized multi-modal data, a pressing need arises to deliver high-quality, personalized device-aware services. However, this endeavor presents a multifaceted challenge to prevailing artificial intelligence (AI) systems primarily rooted in the cloud. As these systems grapple with shifting data distributions between the cloud and devices, the traditional approach of fine-tuning-based adaptation (FTA) exists the following issues: the costly and time-consuming data annotation required by FTA and the looming risk of model overfitting. To surmount these challenges, we introduce a Universal On-Device Multi-modal Model Adaptation Framework, revolutionizing on-device model adaptation by striking a balance between efficiency and effectiveness. The framework features the Fast Domain Adaptor (FDA) hosted in the cloud, providing tailored parameters for the Lightweight Multi-modal Model on devices. To enhance adaptability across multi-modal tasks, the AnchorFrame Distribution Reasoner (ADR) minimizes communication costs. Our contributions, encapsulated in the Cloud-Device Collaboration Multi-modal Parameter Generation (CDC-MMPG) framework, represent a pioneering solution for on-Device Multi-modal Model Adaptation (DMMA). Extensive experiments validate the efficiency and effectiveness of our method, particularly in video question answering and retrieval tasks, driving forward the integration of intelligent devices into our daily lives.

This paper studies how a large increase in the price level is transmitted to the real economy through firm balance sheets. Using newly digitized macro- and micro-level data from the German inflation of 1919-1923, we show that inflation led to a large reduction in real debt burdens and bankruptcies. Firms with higher nominal liabilities at the onset of inflation experienced a larger decline in interest expenses, a relative increase in their equity values, and higher employment during the inflation. The results are consistent with real effects of a debt-inflation channel that operates even when prices and wages are flexible.

Spatio-temporal graph neural networks have proven efficacy in capturing complex dependencies for urban computing tasks such as forecasting and kriging. Yet, their performance is constrained by the reliance on extensive data for training on a specific task, thereby limiting their adaptability to new urban domains with varied task demands. Although transfer learning has been proposed to remedy this problem by leveraging knowledge across domains, the cross-task generalization still remains under-explored in spatio-temporal graph transfer learning due to the lack of a unified framework. To bridge the gap, we propose Spatio-Temporal Graph Prompting (STGP), a prompt-based framework capable of adapting to multi-diverse tasks in a data-scarce domain. Specifically, we first unify different tasks into a single template and introduce a task-agnostic network architecture that aligns with this template. This approach enables capturing dependencies shared across tasks. Furthermore, we employ learnable prompts to achieve domain and task transfer in a two-stage prompting pipeline, facilitating the prompts to effectively capture domain knowledge and task-specific properties. Our extensive experiments demonstrate that STGP outperforms state-of-the-art baselines in three tasks-forecasting, kriging, and extrapolation-achieving an improvement of up to 10.7%.

Foundation models in computational pathology promise to unlock the development of new clinical decision support systems and models for precision medicine. However, there is a mismatch between most clinical analysis, which is defined at the level of one or more whole slide images, and foundation models to date, which process the thousands of image tiles contained in a whole slide image separately. The requirement to train a network to aggregate information across a large number of tiles in multiple whole slide images limits these models' impact. In this work, we present a slide-level foundation model for H&E-stained histopathology, PRISM, that builds on Virchow tile embeddings and leverages clinical report text for pre-training. Using the tile embeddings, PRISM produces slide-level embeddings with the ability to generate clinical reports, resulting in several modes of use. Using text prompts, PRISM achieves zero-shot cancer detection and sub-typing performance approaching and surpassing that of a supervised aggregator model. Using the slide embeddings with linear classifiers, PRISM surpasses supervised aggregator models. Furthermore, we demonstrate that fine-tuning of the PRISM slide encoder yields label-efficient training for biomarker prediction, a task that typically suffers from low availability of training data; an aggregator initialized with PRISM and trained on as little as 10% of the training data can outperform a supervised baseline that uses all of the data.

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the $x$ dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term lattice cross section. In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a $n_f = 2+1$ gauge ensemble with lattice spacing $a = 0.0856~\mathrm{fm}$ and pseudoscalar masses $m_\pi = 355~\mathrm{MeV}$ and $m_K = 441~\mathrm{MeV}$. The four-point functions have been evaluated in a previous project. The lattice data is converted to the $\overline{\mathrm{MS}}$ scheme at a scale $\mu=2~\mathrm{GeV}$ and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs., Comment: 11 pages, 6 figures

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales., Comment: Converged 1D solutions of Schr\"odinger-Poisson model including spatial expansion, comparison between various methods and optimisation of integrators

The injectivity radius of a manifold is an important quantity, both from a theoretical point of view and in terms of numerical applications. It is the largest possible radius within which all geodesics are unique and length-minimizing. In consequence, it is the largest possible radius within which calculations in Riemannian normal coordinates are well-defined. A matrix manifold that arises frequently in a wide range of practical applications is the compact Stiefel manifold of orthogonal $p$-frames in $\mathbb{R}^n$. We observe that geodesics on this manifold are space curves of constant Frenet curvatures. Using this fact, we prove that the injectivity radius on the Stiefel manifold under the Euclidean metric is $\pi$., Comment: 10 pages

Self-supervised learning (SSL) has emerged as a key technique for training networks that can generalize well to diverse tasks without task-specific supervision. This property makes SSL desirable for computational pathology, the study of digitized images of tissues, as there are many target applications and often limited labeled training samples. However, SSL algorithms and models have been primarily developed in the field of natural images and whether their performance can be improved by adaptation to particular domains remains an open question. In this work, we present an investigation of modifications to SSL for pathology data, specifically focusing on the DINOv2 algorithm. We propose alternative augmentations, regularization functions, and position encodings motivated by the characteristics of pathology images. We evaluate the impact of these changes on several benchmarks to demonstrate the value of tailored approaches., Comment: Presented at DCA in MI Workshop, CVPR 2024

This study evaluates the impact of students' usage of generative artificial intelligence (GenAI) tools such as ChatGPT on their exam performance. We analyse student essays using GenAI detection systems to identify GenAI users among the cohort. Employing multivariate regression analysis, we find that students using GenAI tools score on average 6.71 (out of 100) points lower than non-users. While GenAI may offer benefits for learning and engagement, the way students actually use it correlates with diminished exam outcomes. Exploring the underlying mechanism, additional analyses show that the effect is particularly detrimental to students with high learning potential, suggesting an effect whereby GenAI tool usage hinders learning. Our findings provide important empirical evidence for the ongoing debate on the integration of GenAI in higher education and underscores the necessity for educators, institutions, and policymakers to carefully consider its implications for student performance., Comment: This version: November 2024

Timed B\"uchi automata provide a very expressive formalism for expressing requirements of real-time systems. Online monitoring of embedded real-time systems can then be achieved by symbolic execution of such automata on the trace observed from the system. This direct construction however only is faithful if observation of the trace is immediate in the sense that the monitor can assign exact time stamps to the actions it observes, which is rarely true in practice due to the substantial and fluctuating parametric delays introduced by the circuitry connecting the observed system to its monitoring device. We present a purely zone-based online monitoring algorithm, which handles such parametric delays exactly without recurrence to costly verification procedures for parametric timed automata. We have implemented our monitoring algorithm on top of the real-time model checking tool UPPAAL, and report on encouraging initial results.

HyperLTL model-checking enables the automated verification of information-flow properties for security-critical systems. However, it only provides a binary answer. Here, we introduce two paradigms to compute counterexamples and explanations for HyperLTL model-checking, thereby considerably increasing its usefulness. Both paradigms are based on the maxim ``counterexamples/explanations are Skolem functions for the existentially quantified trace variables''. Our first paradigm is complete (everything can be explained), but restricted to ultimately periodic system traces. The second paradigm works with (Turing machine) computable Skolem functions and is therefore much more general, but also shown incomplete (not everything can computably be explained). Finally, we prove that it is decidable whether a given finite transition system and a formula have computable Skolem functions witnessing that the system satisfies the formula. Our algorithm also computes transducers implementing computable Skolem functions, if they exist.

Photographing optoelectronic displays often introduces unwanted moir\'e patterns due to analog signal interference between the pixel grids of the display and the camera sensor arrays. This work identifies two problems that are largely ignored by existing image demoir\'eing approaches: 1) moir\'e patterns vary across different channels (RGB); 2) repetitive patterns are constantly observed. However, employing conventional convolutional (CNN) layers cannot address these problems. Instead, this paper presents the use of our recently proposed Shape concept. It was originally employed to model consistent features from fragmented regions, particularly when identical or similar objects coexist in an RGB-D image. Interestingly, we find that the Shape information effectively captures the moir\'e patterns in artifact images. Motivated by this discovery, we propose a ShapeMoir\'e method to aid in image demoir\'eing. Beyond modeling shape features at the patch-level, we further extend this to the global image-level and design a novel Shape-Architecture. Consequently, our proposed method, equipped with both ShapeConv and Shape-Architecture, can be seamlessly integrated into existing approaches without introducing additional parameters or computation overhead during inference. We conduct extensive experiments on four widely used datasets, and the results demonstrate that our ShapeMoir\'e achieves state-of-the-art performance, particularly in terms of the PSNR metric. We then apply our method across four popular architectures to showcase its generalization capabilities. Moreover, our ShapeMoir\'e is robust and viable under real-world demoir\'eing scenarios involving smartphone photographs., Comment: 12 pages

Spectacular quantum phenomena such as superconductivity often emerge in flat-band systems where Coulomb interactions overpower electron kinetics. Engineering strategies for flat-band physics is therefore of great importance. Here, using high-energy grazing-incidence x-ray diffraction, we demonstrate how in-situ temperature annealing of the infinite-layer nickelate PrNiO$_2$ induces a giant superlattice structure. The annealing effect has a maximum well above room temperature. By covering a large scattering volume, we show a rare period-six in-plane (bi-axial) symmetry and a period-four symmetry in the out-of-plane direction. This giant unit-cell superstructure likely stems from ordering of diffusive oxygen. The stability of this superlattice structure suggests a connection to an energetically favorable electronic state of matter. As such, our study provides a new pathway - different from Moir\'e structures - to ultra-small Brillouin zone electronics., Comment: Main: 7 pages, 4 figures. Supplementary: 2 pages, 3 figures

Climate risk assessments must account for a wide range of possible futures, so scientists often use simulations made by numerous global climate models to explore potential changes in regional climates and their impacts. Some of the latest-generation models have high effective climate sensitivities or EffCS. It has been argued these so-called hot models are unrealistic and should therefore be excluded from analyses of climate change impacts. Whether this would improve regional impact assessments, or make them worse, is unclear. Here we show there is no universal relationship between EffCS and projected changes in a number of important climatic drivers of regional impacts. Analysing heavy rainfall events, meteorological drought, and fire weather in different regions, we find little or no significant correlation with EffCS for most regions and climatic drivers. Even when a correlation is found, internal variability and processes unrelated to EffCS have similar effects on projected changes in the climatic drivers as EffCS. Model selection based solely on EffCS appears to be unjustified and may neglect realistic impacts, leading to an underestimation of climate risks., Comment: Preprint, 30 pages, 4 figures and 2 tables

Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified by special matrix structures, such as orthogonality or definiteness. Following this line of research, we investigate tools for Riemannian optimization on the symplectic Stiefel manifold. We complement the existing set of numerical optimization algorithms with a Riemannian trust region method tailored to the symplectic Stiefel manifold. To this end, we derive a matrix formula for the Riemannian Hessian under a right-invariant metric. Moreover, we propose a novel retraction for approximating the Riemannian geodesics. Finally, we conduct a comparative study in which we juxtapose the performance of the Riemannian variants of the steepest descent, conjugate gradients, and trust region methods on selected matrix optimization problems that feature symplectic constraints., Comment: 24 pages, 2 figures

We study the problem of self-supervised 3D scene flow estimation from real large-scale raw point cloud sequences, which is crucial to various tasks like trajectory prediction or instance segmentation. In the absence of ground truth scene flow labels, contemporary approaches concentrate on deducing optimizing flow across sequential pairs of point clouds by incorporating structure based regularization on flow and object rigidity. The rigid objects are estimated by a variety of 3D spatial clustering methods. While state-of-the-art methods successfully capture overall scene motion using the Neural Prior structure, they encounter challenges in discerning multi-object motions. We identified the structural constraints and the use of large and strict rigid clusters as the main pitfall of the current approaches and we propose a novel clustering approach that allows for combination of overlapping soft clusters as well as non-overlapping rigid clusters representation. Flow is then jointly estimated with progressively growing non-overlapping rigid clusters together with fixed size overlapping soft clusters. We evaluate our method on multiple datasets with LiDAR point clouds, demonstrating the superior performance over the self-supervised baselines reaching new state of the art results. Our method especially excels in resolving flow in complicated dynamic scenes with multiple independently moving objects close to each other which includes pedestrians, cyclists and other vulnerable road users. Our codes are publicly available on https://github.com/ctu-vras/let-it-flow.

In this contribution, we provide convergence rates for a finite volume scheme of the stochastic heat equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions (SHE). More precisely, we give an error estimate for the $L^2$-norm of the space-time discretization of SHE by a semi-implicit Euler scheme with respect to time and a TPFA scheme with respect to space and the variational solution of SHE. The only regularity assumptions additionally needed is spatial regularity of the initial datum and smoothness of the diffusive term., Comment: 28 pages

The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta ($0\nu \beta\beta$) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta\beta$ decay of $^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for $0\nu \beta\beta$ decay and place a lower limit on the half-life of T$_{1/2}$ $>$ 3.8 $\times$ 10$^{25}$ years (90% C.I.) with over 2 tonne$\cdot$year TeO$_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for $0\nu \beta\beta$ decay across multiple isotopes.

Privacy engineering is gaining momentum in industry and academia alike. So far, manifold low-level primitives and higher-level methods and strategies have successfully been established. Still, fostering adoption in real-world information systems calls for additional aspects to be consciously considered in research and practice.

We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields of characteristic p>0. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, generalising work of Iskovskikh. As an application, we discuss rationality problems for regular surfaces and the structure of the plane Cremona group., Comment: 71 pages. Expanded the section on existence of Sarkisov links, added theorem that over separably closed fields of characteristic distinct from two, the plane Cremona group is generated by involutions

Product bundling has been a prevailing marketing strategy that is beneficial in the online shopping scenario. Effective product bundling methods depend on high-quality item representations, which need to capture both the individual items' semantics and cross-item relations. However, previous item representation learning methods, either feature fusion or graph learning, suffer from inadequate cross-modal alignment and struggle to capture the cross-item relations for cold-start items. Multimodal pre-train models could be the potential solutions given their promising performance on various multimodal downstream tasks. However, the cross-item relations have been under-explored in the current multimodal pre-train models. To bridge this gap, we propose a novel and simple framework Cross-Item Relational Pre-training (CIRP) for item representation learning in product bundling. Specifically, we employ a multimodal encoder to generate image and text representations. Then we leverage both the cross-item contrastive loss (CIC) and individual item's image-text contrastive loss (ITC) as the pre-train objectives. Our method seeks to integrate cross-item relation modeling capability into the multimodal encoder, while preserving the in-depth aligned multimodal semantics. Therefore, even for cold-start items that have no relations, their representations are still relation-aware. Furthermore, to eliminate the potential noise and reduce the computational cost, we harness a relation pruning module to remove the noisy and redundant relations. We apply the item representations extracted by CIRP to the product bundling model ItemKNN, and experiments on three e-commerce datasets demonstrate that CIRP outperforms various leading representation learning methods., Comment: arXiv preprint, 10 pages, 4 figures, 6 tables

Next-generation low-cost semiconductors such as halide perovskites exhibit optoelectronic properties dominated by nanoscale variations in their structure, composition and photophysics. While microscopy provides a proxy for ultimate device function, past works have focused on neat thin-films on insulating substrates, missing crucial information about charge extraction losses and recombination losses introduced by transport layers. Here we use a multimodal operando microscopy toolkit to measure nanoscale current-voltage curves, recombination losses and chemical composition in an array of state-of-the-art perovskite solar cells before and after extended operational stress. We apply this toolkit to the same scan areas before and after extended operation to reveal that devices with the highest performance have the lowest initial performance spatial heterogeneity - a crucial link that is missed in conventional microscopy. We find that subtle compositional engineering of the perovskite has surprising effects on local disorder and resilience to operational stress. Minimising variations in local efficiency, rather than compositional disorder, is predictive of improved performance and stability. Modulating the interfaces with different contact layers or passivation treatments can increase initial performance but can also lead to dramatic nanoscale, interface-dominated degradation even in the presence of local performance homogeneity, inducing spatially varying transport, recombination, and electrical losses. These operando measurements of full devices act as screenable diagnostic tools, uniquely unveiling the microscopic mechanistic origins of device performance losses and degradation in an array of halide perovskite devices and treatments. This information in turn reveals guidelines for future improvements to both performance and stability., Comment: Main text and supplementary information. Main text 26 pages, 4 figures. Supplementary information 79 pages, 76 figures. Kyle Frohna and Cullen Chosy contributed equally

We study non-linear Schr\"odinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear setting. We provide characterizations for this property in terms of a semi-linear Liouville theorem. It is employed to establish a non-linear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds., Comment: 23 pages

We determine the rational real forms of the complex Mori fiber spaces for which the identity component of the automorphism group is a maximal connected algebraic subgroup of $\mathrm{Bir}(\mathbb{P}_{\mathbb{C}}^{3})$. This yields a list of maximal connected algebraic subgroup of $\mathrm{Bir}(\mathbb{P}_{\mathbb{R}}^{3})$. We furthermore determine the equivariant Sarkisov links starting from these rational real forms. This article is the first step towards classifying all the maximal connected algebraic subgroups of $\mathrm{Bir}(\mathbb{P}_{\mathbb{R}}^{3})$., Comment: 48 pages, comments are welcome

Nanoscale superconducting quantum interference devices (SQUIDs) are fabricated in-situ from a single Bi$_{0.26}$Sb$_{1.74}$Te$_{3}$ nanoribbon that is defined using selective-area growth and contacted with superconducting Nb electrodes via a shadow mask technique. We present $h/(2e)$ magnetic flux periodic interference in both, fully and non-fully proximitized nanoribbons. The pronounced oscillations are explained by interference effects of coherent transport through topological surface states surrounding the cross-section of the nanoribbon., Comment: 7 pages, 4 figures, supplementary material

We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions and random initial data $u_0\in L^2(\Omega;L^2(D))$. The main novelty is the presence of a merely H\"older continuous multiplicative noise term. In order to show the well-posedness, we simultaneously regularize the H\"older noise term by inf-convolution and add a perturbation by a higher order operator to the equation. Using a stochastic compactness argument we may pass to the limit and we obtain first a martingale solution. Then by a pathwise uniqueness argument we get existence of a probabilistically strong solution.

Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In 2021, H\"uper et al. proposed a one-parameter family of Riemannian metrics on the Stiefel manifold, subsuming the well-known Euclidean and canonical metrics. Since then, several methods have been proposed to obtain a candidate for the Riemannian logarithm given any metric from the family. Most of these methods are based on the shooting method or rely on optimization approaches. For the canonical metric, Zimmermann proposed in 2017 a particularly efficient method based on a pure matrix-algebraic approach. In this paper, we derive a generalization of this algorithm that works for the one-parameter family of Riemannian metrics. The algorithm is proposed in two versions, termed backward and forward, for which we prove that it conserves the local linear convergence previously exhibited in Zimmermann's algorithm for the canonical metric., Comment: 21 pages, 7 figures, 3 tables

We present variational inference with sequential sample-average approximation (VISA), a method for approximate inference in computationally intensive models, such as those based on numerical simulations. VISA extends importance-weighted forward-KL variational inference by employing a sequence of sample-average approximations, which are considered valid inside a trust region. This makes it possible to reuse model evaluations across multiple gradient steps, thereby reducing computational cost. We perform experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and a Pickover attractor, which demonstrate that VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more for conservatively chosen learning rates.

We consider the problem of when a closed hyperbolic surface admits a totally geodesic embedding into a closed hyperbolic 3-manifold, and in particular equivariant versions of such embeddings. In a previous paper we considered orientation-preserving actions on orientable surfaces; in the present paper, we consider large orientation-reversing actions on orientable surfaces, and also large actions on nonorientable surfaces.

Arguably, geodesics are the most important geometric objects on a differentiable manifold. They describe candidates for shortest paths and are guaranteed to be unique shortest paths when the starting velocity stays within the so-called injectivity radius of the manifold. In this work, we investigate the injectivity radius of the Stiefel manifold under the canonical metric. The Stiefel manifold $St(n,p)$ is the set of rectangular matrices of dimension $n$-by-$p$ with orthogonal columns, sometimes also called the space of orthogonal $p$-frames in $\mathbb{R}^n$. Using a standard curvature argument, Rentmeesters has shown in 2013 that the injectivity radius of the Stiefel manifold is bounded by $\sqrt{\frac{4}{5}}\pi$. It is an open question, whether this bound is sharp. With the definition of the injectivity radius via cut points of geodesics, we gain access to the information of the injectivity radius by investigating geodesics. More precisely, we consider the behavior of special variations of geodesics, called Jacobi fields. By doing so, we are able to present an explicit example of a cut point. In addition, since the theoretical analysis of geodesics for cut points and especially conjugate points as a type of cut points is difficult, we investigate the question of the sharpness of the bound by means of numerical experiments.

We present SpaceHopper, a three-legged, small-scale robot designed for future mobile exploration of asteroids and moons. The robot weighs 5.2kg and has a body size of 245mm while using space-qualifiable components. Furthermore, SpaceHopper's design and controls make it well-adapted for investigating dynamic locomotion modes with extended flight-phases. Instead of gyroscopes or fly-wheels, the system uses its three legs to reorient the body during flight in preparation for landing. We control the leg motion for reorientation using Deep Reinforcement Learning policies. In a simulation of Ceres' gravity (0.029g), the robot can reliably jump to commanded positions up to 6m away. Our real-world experiments show that SpaceHopper can successfully reorient to a safe landing orientation within 9.7 degree inside a rotational gimbal and jump in a counterweight setup in Earth's gravity. Overall, we consider SpaceHopper an important step towards controlled jumping locomotion in low-gravity environments., Comment: To be published in the 2024 IEEE International Conference on Robotics and Automation

Methods and algorithms that work with data on nonlinear manifolds are collectively summarized under the term `Riemannian computing'. In practice, curvature can be a key limiting factor for the performance of Riemannian computing methods. Yet, curvature can also be a powerful tool in the theoretical analysis of Riemannian algorithms. In this work, we investigate the sectional curvature of the Stiefel and Grassmann manifold. On the Grassmannian, tight curvature bounds are known since the late 1960ies. On the Stiefel manifold under the canonical metric, it was believed that the sectional curvature does not exceed 5/4. Under the Euclidean metric, the maximum was conjectured to be at 1. For both manifolds, the sectional curvature is given by the Frobenius norm of certain structured commutator brackets of skew-symmetric matrices. We provide refined inequalities for such terms and pay special attention to the maximizers of the curvature bounds. In this way, we prove for the Stiefel manifold that the global bounds of 5/4 (canonical metric) and 1 (Euclidean metric) hold indeed. With this addition, a complete account of the curvature bounds in all admissible dimensions is obtained. We observe that `high curvature means low-rank', more precisely, for the Stiefel and Grassmann manifolds under the canonical metric, the global curvature maximum is attained at tangent plane sections that are spanned by rank-two matrices, while the extreme curvature cases of the Euclidean Stiefel manifold occur for rank-one matrices. Numerical examples are included for illustration purposes., Comment: 29 pages, 5 figures