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In this article we classify all $L_9$-free finite groups.

Van der Waals atomic solids of noble gases on metals at cryogenic temperatures were the first experimental examples of two-dimensional systems. Recently such structures have also been created on surfaces under encapsulation by graphene, allowing studies at elevated temperatures through scanning tunneling microscopy. However, for this technique, the encapsulation layer often obscures the actual arrangement of the noble gas atoms. Here, we create Kr and Xe clusters in between two suspended graphene layers, and uncover their atomic structure through direct imaging with transmission electron microscopy. We show that small crystals (N<9) arrange as expected based on the simple non-directional van der Waals interaction. Crystals larger than this show some deviations for the outermost atoms, possibly enabled by deformations in the encapsulating graphene lattice. We further discuss the dynamics of the clusters within the graphene sandwich, and show that while all Xe clusters with up to N~100 remain solid, Kr clusters with already N~16 turn occasionally fluid under our experimental conditions with an estimated pressure of ca. 0.3 GPa. This study opens a way for the so-far unexplored frontier of encapsulated two-dimensional van der Waals solids with exciting possibilities for fundamental condensed matter physics research and possible applications in quantum information technology., Comment: 31 pages, 14 figures, including the supplement

Let $(\mathfrak{g}, \mathfrak{k})$ be a complex quaternionic symmetric pair with $\mathfrak{k}$ having an ideal $\mathfrak{sl}(2, \mathbb{C})$, $\mathfrak{k}=\mathfrak{sl}(2, \mathbb{C})+\mathfrak{m}_c$. Consider the representation $S^m(\mathbb{C}^2)=\mathbb{C}^{m+1}$ of $\mathfrak{k}$ via the projection onto the ideal $\mathfrak{k}\to \mathfrak{sl}(2, \mathbb{C})$. We study the finite dimensional irreducible representations $V(\lambda)$ of $\mathfrak{g}$ which contain $S^m(\mathbb{C}^2)$ under $\mathfrak{k}\subseteq \mathfrak{g}$. We give a characterization of all such representations $V(\lambda)$ and find the corresponding multiplicity $m(\lambda,m)=\dim \operatorname{Hom} (V(\lambda)|_\mathfrak{k},S^m(\mathbb{C}^2)).$ We consider also the branching problem of $V(\lambda)$ under $\mathfrak{l}=\mathfrak{u}(1)_{\mathbb{C}} + \mathfrak{m}_c\subseteq \mathfrak{k}$ and find the multiplicities. Geometrically the Lie subalgebra $\mathfrak{l}\subseteq \mathfrak{k}$ defines a twistor space over the compact symmetric space of the compact real form $G_c$ of $G_{\mathbb{C}}$, $\text{Lie}(G_{\mathbb{C}})=\mathfrak{g}$, and our results give the decomposition for the $L^2$-spaces of sections of certain vector bundles over the symmetric space and line bundles over the twistor space. This generalizes Cartan--Helgason's theorem for symmetric spaces $(\mathfrak{g}, \mathfrak{k})$ and Schlichtkrull's theorem for Hermitian symmetric spaces where one-dimensional representations of $\mathfrak{k}$ are considered., Comment: updated version, correcting some inaccurate arguments in the proof of Proposition A1 in the earlier version

The analysis of survey data is a frequently arising issue in clinical trials, particularly when capturing quantities which are difficult to measure. Typical examples are questionnaires about patient's well-being, pain, or consent to an intervention. In these, data is captured on a discrete scale containing only a limited number of possible answers, from which the respondent has to pick the answer which fits best his/her personal opinion. This data is generally located on an ordinal scale as answers can usually be arranged in an ascending order, e.g., "bad", "neutral", "good" for well-being. Since responses are usually stored numerically for data processing purposes, analysis of survey data using ordinary linear regression models are commonly applied. However, assumptions of these models are often not met as linear regression requires a constant variability of the response variable and can yield predictions out of the range of response categories. By using linear models, one only gains insights about the mean response which may affect representativeness. In contrast, ordinal regression models can provide probability estimates for all response categories and yield information about the full response scale beyond the mean. In this work, we provide a concise overview of the fundamentals of latent variable based ordinal models, applications to a real data set, and outline the use of state-of-the-art-software for this purpose. Moreover, we discuss strengths, limitations and typical pitfalls. This is a companion work to a current vignette-based structured interview study in paediatric anaesthesia.

Task and Motion Planning (TAMP) approaches are effective at planning long-horizon autonomous robot manipulation. However, it can be difficult to apply them to domains where the environment and its dynamics are not fully known. We propose to overcome these limitations by leveraging deep generative modeling, specifically diffusion models, to learn constraints and samplers that capture these difficult-to-engineer aspects of the planning model. These learned samplers are composed and combined within a TAMP solver in order to find action parameter values jointly that satisfy the constraints along a plan. To tractably make predictions for unseen objects in the environment, we define these samplers on low-dimensional learned latent embeddings of changing object state. We evaluate our approach in an articulated object manipulation domain and show how the combination of classical TAMP, generative learning, and latent embeddings enables long-horizon constraint-based reasoning. We also apply the learned sampler in the real world. More details are available at https://sites.google.com/view/dimsam-tamp

Plasma-based CO2 conversion is a promising pathway towards greenhouse gas recycling. In the corresponding research field, various types of plasma reactors are applied for carbon dioxide dissociation. So far, spatial inhomogeneities of the specific energy (SEI) distribution in plasma generators, e.g., induced by non-uniform heating or an inhomogeneous mass distribution, are not the focus of the investigations. In this work, the spatial inhomogeneity of mass-specific enthalpy in the plasma jet of the inductive plasma generator IPG4 at the Institute of Space Systems (IRS) is examined. For this, the mean mass-specific enthalpy as well as the radial distribution of the local enthalpy are measured using plasma probes. Moreover, the influence of the determined specific enthalpy inhomogeneity on the CO2 splitting performance is quantified. It is shown that an inhomogeneous radial distribution of the specific energy can significantly lower the carbon dioxide conversion, compared to a homogeneous case. With regards to IPG4, the performance reduction is 16 %., Comment: 30 pages, 12 figures

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that those processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a master equation approach in combination with the full counting statistics of multiple Andreev reflection., Comment: Manuscript only, supplement available upon request

The assessment of source code in university education is a central and important task for lecturers of programming courses. In doing so, educators are confronted with growing numbers of students having increasingly diverse prerequisites, a shortage of tutors, and highly dynamic learning objectives. To support lecturers in meeting these challenges, the use of automated programming assessment systems (APASs), facilitating formative assessments by providing timely, objective feedback, is a promising solution. Measuring the effectiveness and success of these platforms is crucial to understanding how such platforms should be designed, implemented, and used. However, research and practice lack a common understanding of aspects influencing the success of APASs. To address these issues, we have devised a success model for APASs based on established models from information systems as well as blended learning research and conducted an online survey with 414 students using the same APAS. In addition, we examined the role of mediators intervening between technology-, system- or self-related factors, respectively, and the users' satisfaction with APASs. Ultimately, our research has yielded a model of success comprising seven constructs influencing user satisfaction with an APAS.

Efficiently serving neural network models with low latency is becoming more challenging due to increasing model complexity and parameter count. Model quantization offers a solution which simultaneously reduces memory footprint and compute requirements. However, aggressive quantization may lead to an unacceptable loss in model accuracy owing to differences in sensitivity to numerical imperfection across different layers in the model. To address this challenge, we propose a mixed-precision post training quantization (PTQ) approach that assigns different numerical precisions to tensors in a network based on their specific needs, for a reduced memory footprint and improved latency while preserving model accuracy. Previous works rely on layer-wise Hessian information to determine numerical precision, but as we demonstrate, Hessian estimation is typically insufficient in determining an effective ordering of layer sensitivities. We address this by augmenting the estimated Hessian with additional information to capture inter-layer dependencies. We demonstrate that this consistently improves PTQ performance along the accuracy-latency Pareto frontier across multiple models. Our method combines second-order information and inter-layer dependencies to guide a bisection search, finding quantization configurations within a user-configurable model accuracy degradation range. We evaluate the effectiveness of our method on the ResNet50, MobileNetV2, and BERT models. Our experiments demonstrate latency reductions compared to a 16-bit baseline of $25.48\%$, $21.69\%$, and $33.28\%$ respectively, while maintaining model accuracy to within $99.99\%$ of the baseline model.

The use of high energy transients such as Gamma Ray Bursts (GRBs) as probes of the distant universe relies on the close collaboration between space and ground facilities. In this context, the Sino-French mission SVOM has been designed to combine a space and a ground segment and to make the most of their synergy. On the ground, the 1.3 meter robotic telescope COLIBRI, jointly developed by France and Mexico, will quickly point the sources detected by the space hard X-ray imager ECLAIRs, in order to detect and localise their visible/NIR counterpart and alert large telescopes in minutes. COLIBRI is equipped with two visible cameras, called DDRAGO-blue and DDRAGO-red, and an infrared camera, called CAGIRE, designed for the study of high redshift GRBs candidates. Being a low-noise NIR camera mounted at the focus of an alt-azimutal robotic telescope imposes specific requirements on CAGIRE. We describe here the main characteristics of the camera: its optical, mechanical and electronics architecture, the ALFA detector, and the operation of the camera on the telescope. The instrument description is completed by three sections presenting the calibration strategy, an image simulator incorporating known detector effects, and the automatic reduction software for the ramps acquired by the detector. This paper aims at providing an overview of the instrument before its installation on the telescope., Comment: Accepted by Experimental Astronomy

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings.

Non-functional properties, such as energy, time, and security (ETS) are becoming increasingly important in Cyber-Physical Systems (CPS) programming. This article describes TeamPlay, a research project funded under the EU Horizon 2020 programme between January 2018 and June 2021. TeamPlay aimed to provide the system designer with a toolchain for developing embedded applications where ETS properties are first-class citizens, allowing the developer to reflect directly on energy, time and security properties at the source code level. In this paper we give an overview of the TeamPlay methodology, introduce the challenges and solutions of our approach and summarise the results achieved. Overall, applying our TeamPlay methodology led to an improvement of up to 18% performance and 52% energy usage over traditional approaches.

The Go programming language offers strong protection from memory corruption. As an escape hatch of these protections, it provides the unsafe package. Previous studies identified that this unsafe package is frequently used in real-world code for several purposes, e.g., serialization or casting types. Due to the variety of these reasons, it may be possible to refactor specific usages to avoid potential vulnerabilities. However, the classification of unsafe usages is challenging and requires the context of the call and the program's structure. In this paper, we present the first automated classifier for unsafe usages in Go, UNGOML, to identify what is done with the unsafe package and why it is used. For UNGOML, we built four custom deep learning classifiers trained on a manually labeled data set. We represent Go code as enriched control-flow graphs (CFGs) and solve the label prediction task with one single-vertex and three context-aware classifiers. All three context-aware classifiers achieve a top-1 accuracy of more than 86% for both dimensions, WHAT and WHY. Furthermore, in a set-valued conformal prediction setting, we achieve accuracies of more than 93% with mean label set sizes of 2 for both dimensions. Thus, UNGOML can be used to efficiently filter unsafe usages for use cases such as refactoring or a security audit. UNGOML: https://github.com/stg-tud/ungoml Artifact: https://dx.doi.org/10.6084/m9.figshare.22293052, Comment: 13 pages, accepted at the 2023 IEEE/ACM 20th International Conference on Mining Software Repositories (MSR 2023)

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier-Stokes-Cahn-Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche's method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor-Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only impossibility results are known so far. Countering this, we show that all multiobjective optimization problems can, in principle, be approximated equally well by scalarizations. In this context, we introduce a transformation theory for scalarizations that establishes the following: Suppose there exists a scalarization that yields an approximation of a certain quality for arbitrary instances of multiobjective optimization problems with a given decomposition specifying which objective functions are to be minimized / maximized. Then, for each other decomposition, our transformation yields another scalarization that yields the same approximation quality for arbitrary instances of problems with this other decomposition. In this sense, the existing results about the approximation via scalarizations for minimization problems carry over to any other objective decomposition -- in particular, to maximization problems -- when suitably adapting the employed scalarization. We further provide necessary and sufficient conditions on a scalarization such that its optimal solutions achieve a constant approximation quality. We give an upper bound on the best achievable approximation quality that applies to general scalarizations and is tight for the majority of norm-based scalarizations applied in the context of multiobjective optimization. As a consequence, none of these norm-based scalarizations can induce approximation sets for optimization problems with maximization objectives, which unifies and generalizes the existing impossibility results concerning the approximation of maximization problems.

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem.

It is well known that, under very weak assumptions, multiobjective optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the size of the instance and in $\frac{1}{\varepsilon}$). While an approximation guarantee of $1+\varepsilon$ for any $\varepsilon>0$ is the best one can expect for singleobjective problems (apart from solving the problem to optimality), even better approximation guarantees than $(1+\varepsilon,\dots,1+\varepsilon)$ can be considered in the multiobjective case since the approximation might be exact in some of the objectives. Hence, in this paper, we consider partially exact approximation sets that require to approximate each feasible solution exactly, i.e., with an approximation guarantee of $1$, in some of the objectives while still obtaining a guarantee of $1+\varepsilon$ in all others. We characterize the types of polynomial-cardinality, partially exact approximation sets that are guaranteed to exist for general multiobjective optimization problems. Moreover, we study minimum-cardinality partially exact approximation sets concerning (weak) efficiency of the contained solutions and relate their cardinalities to the minimum cardinality of a $(1+\varepsilon,\dots,1+\varepsilon)$-approximation set.

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias or exponential sample complexity when the wave function contains some (possibly approximate) zeros, an important case for fermionic systems and quantum information protocols; (ii) show that a different scheme based on the solution of an optimization problem at each time step is free from such problems; (iii) improve the sample complexity of this latter approach by several orders of magnitude with respect to previous proofs of concept. Finally, we apply our advancements to study the high-entanglement phase in a protocol of non-Clifford unitary dynamics with local random measurements in 2D, first benchmarking on small spin lattices and then extending to large systems., Comment: 8+6 pages, 6 figures

We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we present our new SageMath package operator_gb, which offers functionality for automatising such computations. We aim to provide a practical understanding of our approach and the software through examples, while also explaining the completeness of the method in the sense that it allows to find algebraic proofs for every true first-order operator statement. We illustrate the capability of the framework in combination with our software by a case study on statements about the Moore-Penrose inverse, including classical facts and recent results, presented in an online notebook., Comment: 22 pages, plus 8 additional pages appendix

The protection number of a vertex $v$ in a tree is the length of the shortest path from $v$ to any leaf contained in the maximal subtree where $v$ is the root. In this paper, we determine the distribution of the maximum protection number of a vertex in simply generated trees, thereby refining a recent result of Devroye, Goh and Zhao. Two different cases can be observed: if the given family of trees allows vertices of outdegree $1$, then the maximum protection number is on average logarithmic in the tree size, with a discrete double-exponential limiting distribution. If no such vertices are allowed, the maximum protection number is doubly logarithmic in the tree size and concentrated on at most two values. These results are obtained by studying the singular behaviour of the generating functions of trees with bounded protection number. While a general distributional result by Prodinger and Wagner can be used in the first case, we prove a variant of that result in the second case.

Boolean functions and their representation through logics, circuits, machine learning classifiers, or binary decision diagrams (BDDs) play a central role in the design and analysis of computing systems. Quantifying the relative impact of variables on the truth value by means of importance values can provide useful insights to steer system design and debugging. In this paper, we introduce a uniform framework for reasoning about such values, relying on a generic notion of importance value functions (IVFs). The class of IVFs is defined by axioms motivated from several notions of importance values introduced in the literature, including Ben-Or and Linial's influence and Chockler, Halpern, and Kupferman's notion of responsibility and blame. We establish a connection between IVFs and game-theoretic concepts such as Shapley and Banzhaf values, both of which measure the impact of players on outcomes in cooperative games. Exploiting BDD-based symbolic methods and projected model counting, we devise and evaluate practical computation schemes for IVFs., Comment: This is a preprint of the paper accepted at the 32nd International Joint Conferences on Artificial Intelligence (IJCAI'23). It includes proofs and other additional material in the appendix. An implementation of the computing schemes for IVFs can be found at https://github.com/graps1/impmeas

In an offline reinforcement learning setting, the safe policy improvement (SPI) problem aims to improve the performance of a behavior policy according to which sample data has been generated. State-of-the-art approaches to SPI require a high number of samples to provide practical probabilistic guarantees on the improved policy's performance. We present a novel approach to the SPI problem that provides the means to require less data for such guarantees. Specifically, to prove the correctness of these guarantees, we devise implicit transformations on the data set and the underlying environment model that serve as theoretical foundations to derive tighter improvement bounds for SPI. Our empirical evaluation, using the well-established SPI with baseline bootstrapping (SPIBB) algorithm, on standard benchmarks shows that our method indeed significantly reduces the sample complexity of the SPIBB algorithm., Comment: Accecpted at IJCAI 2023

The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions converges if and only if it is eventually constant at every argument. We develop new techniques to prove there is no other Polish topology turning this semigroup into a topological one, and show that previous techniques are insufficient for this matter., Comment: 43 pages, 7 figures

Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments., Comment: 12 pages, 10 figures

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the Isogeometric Analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4,700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders.

With the precision now afforded by modern space-based photometric observations from the retired K2 and current TESS missions, the effects of general relativity (GR) may be detectable in the light curves of pulsating white dwarfs (WDs). Almost all WD models are calculated using a Newtonian description of gravity and hydrodynamics. To determine if inclusion of GR leads to observable effects, we used idealized models of compact stars and made side-by-side comparison of mode periods computed using a (i) Newtonian and (ii) GR description of the equilibrium structure and nonradial pulsations. For application to white dwarfs, it is only necessary to include the first post-Newtonian (1PN) approximation to GR. The mathematical nature of the linear nonradial pulsation problem is then qualitatively unchanged and the GR corrections can be written as extensions of the classic Dziembowski equations. As such, GR effects might easily be included in existing asteroseismology codes. The idealized stellar models are (i) \pn1 relativistic polytropes and (ii) stars with cold degenerate-electron equation of state featuring a near-surface chemical transition from $\mu_e = 2$ to $\mu_e = 1$, simulating a surface hydrogen layer. Comparison of Newtonian and 1PN normal mode periods reveals fractional differences on the order of the surface gravitational redshift $z$. For a typical WD, this fractional difference is $\sim 10^{-4}$ and is greater than the period uncertainty $\sigma_{\Pi}/\Pi$ of many white dwarf pulsation modes observed by TESS. A consistent theoretical modeling of periods observed in these stars should in principle include GR effects to 1PN order.

Three polynomials are defined for given sets $S$ of $n$ points in general position in the plane: The Voronoi polynomial with coefficients the numbers of vertices of the order-$k$ Voronoi diagrams of $S$, the circle polynomial with coefficients the numbers of circles through three points of $S$ enclosing $k$ points of $S$, and the $E_{\leq k}$ polynomial with coefficients the numbers of (at most $k$)-edges of $S$. We present several formulas for the rectilinear crossing number of $S$ in terms of these polynomials and their roots. We also prove that the roots of the Voronoi polynomial lie on the unit circle if, and only if, $S$ is in convex position. Further, we present bounds on the location of the roots of these polynomials., Comment: 18 pages, 3 figures, published in Discrete Mathematics and Theoretical Computer Science

The multiterminal Josephson effect aroused considerable interest recently, in connection with theoretical and experimental evidence for correlations among Cooper pairs, that is, the so-called Cooper quartets. It was further predicted that the spectrum of Andreev bound states in such devices could host Weyl-point singularities. However, the relative phase between the Cooper pair and quartet supercurrents has not yet been addressed experimentally. Here, we propose an experiment involving four-terminal Josephson junctions with two independent orthogonal supercurrents, and calculate the critical current contours (CCCs) from a multiterminal Josephson junction circuit theory. We predict a generically $\pi$-shifted contribution of both the local or nonlocal second-order Josephson harmonics. Furthermore, we show that these lead to marked nonconvex shapes for the CCCs in zero magnetic field, where the dissipative state reenters into the superconducting one. Eventually, we discuss distinctive features of the non-local Josephson processes in the CCCs. The experimental observation of the latter could allow providing firm evidence of the $\pi$-shifted Cooper quartet current-phase relation., Comment: Third revision: manuscript in final form

Data-driven machine learning is playing a crucial role in the advancements of Industry 4.0, specifically in enhancing predictive maintenance and quality inspection. Federated learning (FL) enables multiple participants to develop a machine learning model without compromising the privacy and confidentiality of their data. In this paper, we evaluate the performance of different FL aggregation methods and compare them to central and local training approaches. Our study is based on four datasets with varying data distributions. The results indicate that the performance of FL is highly dependent on the data and its distribution among clients. In some scenarios, FL can be an effective alternative to traditional central or local training methods. Additionally, we introduce a new federated learning dataset from a real-world quality inspection setting.

We address the important problem of generalizing robotic rearrangement to clutter without any explicit object models. We first generate over 650K cluttered scenes - orders of magnitude more than prior work - in diverse everyday environments, such as cabinets and shelves. We render synthetic partial point clouds from this data and use it to train our CabiNet model architecture. CabiNet is a collision model that accepts object and scene point clouds, captured from a single-view depth observation, and predicts collisions for SE(3) object poses in the scene. Our representation has a fast inference speed of 7 microseconds per query with nearly 20% higher performance than baseline approaches in challenging environments. We use this collision model in conjunction with a Model Predictive Path Integral (MPPI) planner to generate collision-free trajectories for picking and placing in clutter. CabiNet also predicts waypoints, computed from the scene's signed distance field (SDF), that allows the robot to navigate tight spaces during rearrangement. This improves rearrangement performance by nearly 35% compared to baselines. We systematically evaluate our approach, procedurally generate simulated experiments, and demonstrate that our approach directly transfers to the real world, despite training exclusively in simulation. Robot experiment demos in completely unknown scenes and objects can be found at this http https://cabinet-object-rearrangement.github.io

We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network estimating the regularization parameter-map from the input data while the second one unrolling T iterations of the Primal-Dual Three-Operator Splitting (PD3O) algorithm. The latter approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is then trained end-to-end in a supervised learning fashion using pairs of clean-corrupted data but crucially without the need of having access to labels for the optimal regularization parameter-maps., Comment: arXiv admin note: substantial text overlap with arXiv:2301.05888

We present Nb thin films deposited in-situ on GaAs by combining molecular beam epitaxy and magnetron sputtering within an ultra-high vacuum cluster. Nb films deposited at varying power, and a reference film from a commercial system, are compared. The results show clear variation between the in-situ and ex-situ deposition which we relate to differences in magnetron sputtering conditions and chamber geometry. The Nb films have critical temperatures of around $9 \textrm{K}$. and critical perpendicular magnetic fields of up to $B_{c2} = 1.4 \textrm{T}$ at $4.2 \textrm{K}$. From STEM images of the GaAs-Nb interface we find the formation of an amorphous interlayer between the GaAs and the Nb for both the ex-situ and in-situ deposited material., Comment: 12 pages paper, 9 pages supplementary, 6 figures paper, 7 figures supplementary

Every simple Hermitian Lie group has a unique family of spherical representations induced from a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. For most Hermitian groups, this family contains a complementary series, and at its endpoint sits a proper unitarizable subrepresentation. We show that this subrepresentation is next-to-minimal in the sense that its associated variety is a next-to-minimal nilpotent coadjoint orbit. Moreover, for the Hermitian groups $\operatorname{SO}_0(2,n)$ and $E_{6(-14)}$ we study some branching problems of these next-to-minimal representations., Comment: 21 pages

We show that finite (i.e. locally finite and decomposition-finite) objects of a connected Grothendieck topos span a Boolean pretopos with an essentially unique Galois point. The automorphism group of this point carries a profinite topology whose classifying topos is equivalent to the given Grothendieck topos if the latter is finitely generated. This leads to an intrinsic definition of the fundamental group of any connected Grothendieck topos., Comment: 24 pages. Changes in v5: Introduction, Section 3 and Section 4 expanded. Galois points defined and their essential uniqueness proved. Bibliography extended

Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it difficult to accurately measure technological advancements, compare performance with conventional methods, and identify promising future research directions. Prior neuromorphic computing benchmark efforts have not seen widespread adoption due to a lack of inclusive, actionable, and iterative benchmark design and guidelines. To address these shortcomings, we present NeuroBench: a benchmark framework for neuromorphic computing algorithms and systems. NeuroBench is a collaboratively-designed effort from an open community of nearly 100 co-authors across over 50 institutions in industry and academia, aiming to provide a representative structure for standardizing the evaluation of neuromorphic approaches. The NeuroBench framework introduces a common set of tools and systematic methodology for inclusive benchmark measurement, delivering an objective reference framework for quantifying neuromorphic approaches in both hardware-independent (algorithm track) and hardware-dependent (system track) settings. In this article, we present initial performance baselines across various model architectures on the algorithm track and outline the system track benchmark tasks and guidelines. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community., Comment: Updated from whitepaper to full perspective article preprint

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error $\varepsilon$, provided that a sample set (of size $N$) of the states can be efficiently prepared and measured. In a recent work [Huang et al., Science 377, eabk3333 (2022)], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, $N=m^{{\cal{O}}\left(\frac{1}{\varepsilon}\right)}$, was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large while the scaling with the accuracy is not an urgent factor. In this work, we consider an alternative scenario where $m$ is a finite, not necessarily large constant while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the uniform prediction error $\varepsilon$ and the number of qubits $n$. Moreover, if restricted to learning local quantum-state properties, the number of samples with respect to $n$ can be further reduced exponentially. Our results provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications not restricted to ground states of gapped Hamiltonians., Comment: Published on Physical Review Research 6, 033035 (2024)