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This is the 12th edition of EdChoice's Schooling in America survey. The purpose of this annual survey is to gauge public opinion on a range of issues in K-12 education, including school choice policies and parents' schooling experiences. From April 9 to April 30, 2024, we surveyed 2,319 current school parents and 1,502 members of the general population. We report polling results based on a nationally representative sample of both groups. Nearly 4,000 interviews were conducted online and over the phone. In this year's survey, we also asked new questions related to recent issues in education pertaining to transparency, accountability, technology, and artificial intelligence. The survey yielded many findings including: (1) School safety is now the top reason to choose a school for charter (37%), private (36%) and homeschool (53%) parents; (2) Most Americans (70%) and nearly two-thirds of parents (64%) say K-12 education is on the wrong track; (3) The majority of school parents think standardized tests are an important accountability measure, especially for teachers (67%), schools (65%), and school districts (65%); and (4) Two-thirds of parents (66%) say that schools should teach students how to use artificial intelligence responsibly.

The study of matroid products traces back to the 1970s, when Lov\'asz and Mason studied the existence of various types of matroid products with different strengths. Among these, the tensor product is arguably the most important, which can be considered as an extension of the tensor product from linear algebra. However, Las Vergnas showed that the tensor product of two matroids does not always exist. Over the following four decades, matroid products remained surprisingly underexplored, regaining attention only in recent years due to applications in tropical geometry and the limit theory of matroids. In this paper, inspired by the concept of coupling in probability theory, we introduce the notion of coupling for matroids -- or, more generally, for submodular set functions. This operation can be viewed as a relaxation of the tensor product. Unlike the tensor product, however, we prove that a coupling always exists for any two submodular functions and can be chosen to be increasing if the original functions are increasing. As a corollary, we show that two matroids always admit a matroid coupling, leading to a novel operation on matroids. Our construction is algorithmic, providing an oracle for the coupling matroid through a polynomial number of oracle calls to the original matroids. We apply this construction to derive new necessary conditions for matroid representability and establish connection between tensor products and Ingleton's inequality. Additionally, we verify the existence of set functions that are universal with respect to a given property, meaning any set function over a finite domain with that property can be obtained as a quotient., Comment: 24 pages

There is a long list of open questions rooted in the same underlying problem: understanding the structure of bases or common bases of matroids. These conjectures suggest that matroids may possess much stronger structural properties than are currently known. One example is related to cyclic orderings of matroids. A rank-$r$ matroid is called cyclically orderable if its ground set admits a cyclic ordering such that any interval of $r$ consecutive elements forms a basis. In this paper, we show that if the ground set of a split matroid decomposes into pairwise disjoint bases, then it is cyclically orderable. This result answers a conjecture of Kajitani, Ueno, and Miyano in a special case, and also strengthens Gabow's conjecture for this class of matroids. Our proof is algorithmic, hence it provides a procedure for determining a cyclic ordering in question using a polynomial number of independence oracle calls., Comment: 11 pages

Quantization reduces the model's hardware costs, such as data movement, storage, and operations like multiply and addition. It also affects the model's behavior by degrading the output quality. Therefore, there is a need for methods that preserve the model's behavior when quantizing model parameters. More exotic numerical encodings, such as block-scaled number formats, have shown advantages for utilizing a fixed bit budget to encode model parameters. This paper presents error diffusion (ED), a hyperparameter-free method for post-training quantization with support for block-scaled data formats. Our approach does not rely on backpropagation or Hessian information. We describe how to improve the quantization process by viewing the neural model as a composite function and diffusing the quantization error in every layer. In addition, we introduce TensorCast, an open-source library based on PyTorch to emulate a variety of number formats, including the block-scaled ones, to aid the research in neural model quantization. We demonstrate the efficacy of our algorithm through rigorous testing on various architectures, including vision and large language models (LLMs), where it consistently delivers competitive results. Our experiments confirm that block-scaled data formats provide a robust choice for post-training quantization and could be used effectively to enhance the practical deployment of advanced neural networks.

The first FASER search for a light, long-lived particle decaying into a pair of photons is reported. The search uses LHC proton-proton collision data at $\sqrt{s}=13.6~\text{TeV}$ collected in 2022 and 2023, corresponding to an integrated luminosity of $57.7\text{fb}^{-1}$. A model with axion-like particles (ALPs) dominantly coupled to weak gauge bosons is the primary target. Signal events are characterised by high-energy deposits in the electromagnetic calorimeter and no signal in the veto scintillators. One event is observed, compared to a background expectation of $0.44 \pm 0.39$ events, which is entirely dominated by neutrino interactions. World-leading constraints on ALPs are obtained for masses up to $300~\text{MeV}$ and couplings to the Standard Model W gauge boson, $g_{aWW}$, around $10^{-4}$ GeV$^{-1}$, testing a previously unexplored region of parameter space. Other new particle models that lead to the same experimental signature, including ALPs coupled to gluons or photons, U(1)$_B$ gauge bosons, up-philic scalars, and a Type-I two-Higgs doublet model, are also considered for interpretation, and new constraints on previously viable parameter space are presented in this paper., Comment: 37 pages, 22 figures

Social robots have emerged as valuable contributors to individuals' well-being coaching. Notably, their integration into long-term human coaching trials shows particular promise, emphasizing a complementary role alongside human coaches rather than outright replacement. In this context, robots serve as supportive entities during coaching sessions, offering insights based on their knowledge about users' well-being and activity. Traditionally, such insights have been gathered through methods like written self-reports or wearable data visualizations. However, the disclosure of people's information by a robot raises concerns regarding privacy, appropriateness, and trust. To address this, we conducted an initial study with [n = 22] participants to quantify their perceptions of privacy regarding disclosures made by a robot coaching assistant. The study was conducted online, presenting participants with six prerecorded scenarios illustrating various types of information disclosure and the robot's role, ranging from active on-demand to proactive communication conditions., Comment: IEEE ICRA 2024 Workshop on Robot Trust for Symbiotic Societies (RTSS)

Learning from demonstration is a promising way of teaching robots new skills. However, a central problem when executing acquired skills is to recognize risks and failures. This is essential since the demonstrations usually cover only a few mostly successful cases. Inevitable errors during execution require specific reactions that were not apparent in the demonstrations. In this paper, we focus on teaching the robot situational awareness from an initial skill demonstration via kinesthetic teaching and sparse labeling of autonomous skill executions as safe or risky. At runtime, our system, called ILeSiA, detects risks based on the perceived camera images by encoding the images into a low-dimensional latent space representation and training a classifier based on the encoding and the provided labels. In this way, ILeSiA boosts the confidence and safety with which robotic skills can be executed. Our experiments demonstrate that classifiers, trained with only a small amount of user-provided data, can successfully detect numerous risks. The system is flexible because the risk cases are defined by labeling data. This also means that labels can be added as soon as risks are identified by a human supervisor. We provide all code and data required to reproduce our experiments at imitrob.ciirc.cvut.cz/publications/ilesia., Comment: 7 pages, 8 figures

Many users are confronted multiple times daily with the choice of whether to take the stairs or the elevator. Whereas taking the stairs could be beneficial for cardiovascular health and wellness, taking the elevator might be more convenient but it also consumes energy. By precisely tracking and boosting users' stairs and elevator usage through their wearable, users might gain health insights and motivation, encouraging a healthy lifestyle and lowering the risk of sedentary-related health problems. This research describes a new exploratory dataset, to examine the patterns and behaviors related to using stairs and lifts. We collected data from 20 participants while climbing and descending stairs and taking a lift in a variety of scenarios. The aim is to provide insights and demonstrate the practicality of using wearable sensor data for such a scenario. Our collected dataset was used to train and test a Random Forest machine learning model, and the results show that our method is highly accurate at classifying stair and lift operations with an accuracy of 87.61% and a multi-class weighted F1-score of 87.56% over 8-second time windows. Furthermore, we investigate the effect of various types of sensors and data attributes on the model's performance. Our findings show that combining inertial and pressure sensors yields a viable solution for real-time activity detection., Comment: submitted to iWOAR 2024

This paper presents the Equimetrics data capture system. The primary objective is to apply HAR principles to enhance the understanding and optimization of equestrian performance. By integrating data from strategically placed sensors on the rider's body and the horse's limbs, the system provides a comprehensive view of their interactions. Preliminary data collection has demonstrated the system's ability to accurately classify various equestrian activities, such as walking, trotting, cantering, and jumping, while also detecting subtle changes in rider posture and horse movement. The system leverages open-source hardware and software to offer a cost-effective alternative to traditional motion capture technologies, making it accessible for researchers and trainers. The Equimetrics system represents a significant advancement in equestrian performance analysis, providing objective, data-driven insights that can be used to enhance training and competition outcomes., Comment: 5 pages, 6 figures, Additional materials can be found at: https://zenodo.org/records/13367775

Hand washing is a crucial part of personal hygiene. Hand washing detection is a relevant topic for wearable sensing with applications in the medical and professional fields. Hand washing detection can be used to aid workers in complying with hygiene rules. Hand washing detection using body-worn IMU-based sensor systems has been shown to be a feasible approach, although, for some reported results, the specificity of the detection was low, leading to a high rate of false positives. In this work, we present a novel, open-source prototype device that additionally includes a humidity, temperature, and barometric sensor. We contribute a benchmark dataset of 10 participants and 43 hand-washing events and perform an evaluation of the sensors' benefits. Added to that, we outline the usefulness of the additional sensor in both the annotation pipeline and the machine learning models. By visual inspection, we show that especially the humidity sensor registers a strong increase in the relative humidity during a hand-washing activity. A machine learning analysis of our data shows that distinct features benefiting from such relative humidity patterns remain to be identified., Comment: iWOAR2024

We study positively closed and strongly positively closed $\mathcal{C}\to Sh(B)$ models, where $\mathcal{C}$ is a $(\kappa ,\kappa )$-coherent category and $B$ is a $(\kappa ,\kappa )$-coherent Boolean-algebra for some weakly compact $\kappa $. We prove that if $\mathcal{C}$ is coherent and $X$ is a Stone-space then positively closed, not strongly positively closed $\mathcal{C}\to Sh(X)$ models may exist.

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper we aim to address a gap in the literature, namely, to examine how gradual improvement of power grid models affect the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying level of heterogeneity through the coupling strength, the nodal powers and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. The most heterogeneous models showed very low synchronization and thus suggest a limitation of the second-order Kuramoto equation. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior., Comment: 7 pages, 7 figures

This paper summarises the Competition on Presentation Attack Detection on ID Cards (PAD-IDCard) held at the 2024 International Joint Conference on Biometrics (IJCB2024). The competition attracted a total of ten registered teams, both from academia and industry. In the end, the participating teams submitted five valid submissions, with eight models to be evaluated by the organisers. The competition presented an independent assessment of current state-of-the-art algorithms. Today, no independent evaluation on cross-dataset is available; therefore, this work determined the state-of-the-art on ID cards. To reach this goal, a sequestered test set and baseline algorithms were used to evaluate and compare all the proposals. The sequestered test dataset contains ID cards from four different countries. In summary, a team that chose to be "Anonymous" reached the best average ranking results of 74.80%, followed very closely by the "IDVC" team with 77.65%.

Phonocardiography has recently gained popularity in low-cost and remote monitoring, including passive fetal heart monitoring. Development for methods which analyse phonocardiographical data try to capitalize on this opportunity, and in recent years a multitude of such algorithms and models have been published. Although there is little to no standardization in these published algorithms and multiple parts of these models have to be reimplemented on a case-by-case basis. Datasets containing heart sound recordings also lack standardization in both data storage and labeling, especially in fetal phonocardiography. We are presenting a toolbox that can serve as a basis for a future standard framework for heart sound analysis. This toolbox contains some of the most widely used processing steps, and with these, complex analysis processes can be created. These functions can be individually tested. Due to the interdependence of the steps, we validated the current segmentation stage using a manually labeled fetal phonocardiogram dataset comprising 50 one-minute abdominal PCG recordings, which include 6,758 S1 and 6,729 S2 labels. Our results were compared to other common and available segmentation methods, peak detection with the Neurokit2 library, and the Hidden Semi-Markov Model by Springer et al. With a 30 ms tolerance our best model achieved a 97.1% F1 score and 10.8 +/- 7.9 ms mean absolute error for S1 detection. This detection accuracy outperformed all tested methods. With this a more accurate S2 detection method can be created as a multi-step process. After an accurate segmentation the extracted features should be representative of the selected segments, which allows for more accurate statistics or classification models. The toolbox contains functions for both feature extraction and statistics creation which are compatible with the previous steps., Comment: 25 pages, 11 figures, submitted to Open Source and Validated Computational Tools for Physiological Time Series Analysis, for associated program documentation, see https://pypcg-toolbox.readthedocs.io/en/latest/

As wearable-based data annotation remains, to date, a tedious, time-consuming task requiring researchers to dedicate substantial time, benchmark datasets within the field of Human Activity Recognition in lack richness and size compared to datasets available within related fields. Recently, vision foundation models such as CLIP have gained significant attention, helping the vision community advance in finding robust, generalizable feature representations. With the majority of researchers within the wearable community relying on vision modalities to overcome the limited expressiveness of wearable data and accurately label their to-be-released benchmark datasets offline, we propose a novel, clustering-based annotation pipeline to significantly reduce the amount of data that needs to be annotated by a human annotator. We show that using our approach, the annotation of centroid clips suffices to achieve average labelling accuracies close to 90% across three publicly available HAR benchmark datasets. Using the weakly annotated datasets, we further demonstrate that we can match the accuracy scores of fully-supervised deep learning classifiers across all three benchmark datasets. Code as well as supplementary figures and results are publicly downloadable via github.com/mariusbock/weak_har., Comment: 8 pages, 3 figures, accepted at ISWC'24: International Symposium on Wearable Computers, Oct, 2024

Global optimization of crystal compositions is a significant yet computationally intensive method to identify stable structures within chemical space. The specific physical properties linked to a three-dimensional atomic arrangement make this an essential task in the development of new materials. We present a method that efficiently uses active learning of neural network force fields for structure relaxation, minimizing the required number of steps in the process. This is achieved by neural network force fields equipped with uncertainty estimation, which iteratively guide a pool of randomly generated candidates towards their respective local minima. Using this approach, we are able to effectively identify the most promising candidates for further evaluation using density functional theory (DFT). Our method not only reliably reduces computational costs by up to two orders of magnitude across the benchmark systems Si16 , Na8Cl8 , Ga8As8 and Al4O6 , but also excels in finding the most stable minimum for the unseen, more complex systems Si46 and Al16O24 . Moreover, we demonstrate at the example of Si16 that our method can find multiple relevant local minima while only adding minor computational effort.

We prove that $i)$ if $\mathcal{A}$ is $\lambda $-accessible and it is axiomatizable in (finitary) coherent logic then $\lambda $-pure maps are strict monomorphisms and $ii)$ if there is a proper class of strongly compact cardinals and $\mathcal{A}$ is $\lambda $-accessible then for some $\mu \vartriangleright \lambda $ every $\mu $-pure map is a strict monomorphism.

Building on Whitney's classical method of triangulating smooth manifolds, we show that every compact $d$-dimensional smooth manifold admits a triangulation with dual graph of twin-width at most $d^{O(d)}$. In particular, it follows that every compact 3-manifold has a triangulation with dual graph of bounded twin-width. This is in sharp contrast to the case of treewidth, where for any natural number $n$ there exists a closed 3-manifold such that every triangulation thereof has dual graph with treewidth at least $n$. To establish this result, we bound the twin-width of the incidence graph of the $d$-skeleton of the second barycentric subdivision of the $2d$-dimensional hypercubic honeycomb. We also show that every compact, piecewise-linear (hence smooth) $d$-dimensional manifold has triangulations where the dual graph has an arbitrarily large twin-width., Comment: 18 pages, 8 figures

Testing and validating Cyber-Physical Systems (CPSs) in the aerospace domain, such as field testing of drone rescue missions, poses challenges due to volatile mission environments, such as weather conditions. While testing processes and methodologies are well established, structured guidance and execution support for field tests are still weak. This paper identifies requirements for field testing of drone missions, and introduces the Field Testing Scenario Management (FiTS) approach for adaptive field testing guidance. FiTS aims to provide sufficient guidance for field testers as a foundation for efficient data collection to facilitate quality assurance and iterative improvement of field tests and CPSs. FiTS shall leverage concepts from scenario-based requirements engineering and Behavior-Driven Development to define structured and reusable test scenarios, with dedicated tasks and responsibilities for role-specific guidance. We evaluate FiTS by (i) applying it to three use cases for a search-and-rescue drone application to demonstrate feasibility and (ii) interviews with experienced drone developers to assess its usefulness and collect further requirements. The study results indicate FiTS to be feasible and useful to facilitate drone field testing and data analysis, Comment: Accepted for publication at the 50th Euromicro Conference on Software Engineering and Advanced Applications (SEAA)

In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} $T_1,\ldots,T_q$. In this setting, one is allowed to choose these representatives so that the minimum-weight cut separating these sets \emph{via their representatives} is as small as possible. We distinguish different cases depending on (A) whether the representative of a candidate set has to be separated from the other candidate sets completely or only from the representatives, and (B) whether there is a single representative for each candidate set or the choice of representative is independent for each pair of candidate sets. For fixed $q$, we give approximation algorithms for each of these problems that match the best known approximation guarantee for multiway cut. Our technical contribution is a new extension of the CKR relaxation that preserves approximation guarantees. For general $q$, we show $o(\log q)$-inapproximability for all cases where the choice of representatives may depend on the pair of candidate sets, as well as for the case where the goal is to separate a fixed node from a single representative from each candidate set. As a positive result, we give a $2$-approximation algorithm for the case where we need to choose a single representative from each candidate set. This is a generalization of the $(2-2/k)$-approximation for k-cut, and we can solve it by relating the tree case to optimization over a gammoid.

Besides standard Lagrange interpolation, i.e., interpolation of target functions from scattered point evaluations, positive definite kernel functions are well-suited for the solution of more general reconstruction problems. This is due to the intrinsic structure of the underlying reproducing kernel Hilbert space (RKHS). In fact, kernel-based interpolation has been applied to the reconstruction of bivariate functions from scattered Radon samples in computerized tomography (cf. Iske, 2018) and, moreover, to the numerical solution of elliptic PDEs (cf. Wenzel et al., 2022). As shown in various previous contributions, numerical algorithms and theoretical results from kernel-based Lagrange interpolation can be transferred to more general interpolation problems. In particular, greedy point selection methods were studied in (Wenzel et al., 2022), for the special case of Sobolev kernels. In this paper, we aim to develop and analyze more general kernel-based interpolation methods, for less restrictive settings. To this end, we first provide convergence results for generalized interpolation under minimalistic assumptions on both the selected kernel and the target function. Finally, we prove convergence of popular greedy data selection algorithms for totally bounded sets of functionals. Supporting numerical results are provided for illustration.

In this paper, we consider the tractability of the matroid intersection problem under the minimum rank oracle. In this model, we are given an oracle that takes as its input a set of elements, and returns as its output the minimum of the ranks of the given set in the two matroids. For the unweighted matroid intersection problem, we show how to construct a necessary part of the exchangeability graph, which enables us to emulate the standard augmenting path algorithm. Furthermore, we reformulate Edmonds' min-max theorem only using the minimum rank function, providing a new perspective on this result. For the weighted problem, the tractability is open in general. Nevertheless, we describe several special cases where tractability can be achieved, and we discuss potential approaches and the challenges encountered. In particular, we present a solution for the case where no circuit of one matroid is contained within a circuit of the other. Additionally, we propose a fixed-parameter tractable algorithm, parameterized by the maximum circuit size. We also show that a lexicographically maximal common independent set can be found by the same approach, which leads to at least $1/2$-approximation for finding a maximum-weight common independent set., Comment: 21 pages, 4 figures

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight spanning tree among those containing a perfect matching. On the positive side, we design a simple greedy algorithm for the case when the graph is complete (or complete bipartite) and the edge weights take at most two values. On the negative side, the problem is NP-hard even when the graph is complete (or complete bipartite) and the edge weights take at most three values, or when the graph is cubic, planar, and bipartite and the edge weights take at most two values. We also consider an interesting variant. We call a tree strongly balanced if on one side of the bipartition of the vertex set with respect to the tree, all but one of the vertices have degree $2$ and the remaining one is a leaf. This property is a sufficient condition for a tree to have a perfect matching, which enjoys an additional property. When the underlying graph is bipartite, strongly balanced spanning trees can be written as matroid intersection, and this fact was recently utilized to design an approximation algorithm for some kind of connectivity augmentation problem. The natural question is its tractability in nonbipartite graphs. As a negative answer, it turns out NP-hard to test whether a given graph has a strongly balanced spanning tree or not even when the graph is subcubic and planar., Comment: 14 pages, 5 figures

Interconnect resistance and reliability have emerged as critical factors limiting the performance of advanced CMOS circuits. With the slowdown of transistor scaling, interconnect scaling has become the primary driver of continued circuit miniaturization. The associated scaling challenges for interconnects are expected to further intensify in future CMOS technology nodes. As interconnect dimensions approach the 10 nm scale, the limitations of conventional Cu dual-damascene metallization are becoming increasingly difficult to overcome, spurring over a decade of focused research into alternative metallization schemes. The selection of alternative metals is a highly complex process, requiring consideration of multiple criteria, including resistivity at reduced dimensions, reliability, thermal performance, process technology readiness, and sustainability. This tutorial introduces the fundamental criteria for benchmarking and selecting alternative metals and reviews the current state of the art in this field. It covers materials nearing adoption in high-volume manufacturing, materials currently under active research, and potential future directions for fundamental study. While early alternatives to Cu metallization have recently been introduced in commercial CMOS devices, the search for the optimal interconnect metal remains ongoing., Comment: 74 pages, 27 figures, 5 Tables

A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from an analytic point of view and introduced the cycle matroid of a graphing. Motivated by the limit theory of graphs, the authors introduced a form of right-convergence, called quotient-convergence, for a sequence of submodular setfunctions, leading to a notion of convergence for matroids through their rank functions. In this paper, we study the connection between local-global convergence of graphs and quotient-convergence of their cycle matroids. We characterize the exposed points of associated convex sets, forming an analytic counterpart of matroid independence- and base-polytopes. Finally, we consider dual planar graphings and show that the cycle matroid of one is the cocycle matroid of its dual if and only if the underlying graphings are hyperfinite., Comment: 19 pages

We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of bounded degree graphs, which analyzes graph sequences via neighborhood sampling, we address the challenge posed by the absence of a neighborhood concept in matroids. We show that any bounded set function can be approximated by a sequence of finite set functions that quotient-converges to it. In addition, we explicitly construct such sequences for increasing, submodular, and upper continuous set functions, and prove the completeness of the space under quotient-convergence., Comment: 12 pages

Inverse and bilevel optimization problems play a central role in both theory and applications. These two classes are known to be closely related due to the pioneering work of Dempe and Lohse (2006), and thus have often been discussed together ever since. In this paper, we consider inverse problems for multi-unit assignment valuations. Multi-unit assignment valuations form a subclass of strong-substitutes valuations that can be represented by edge-weighted complete bipartite graphs. These valuations play a key role in auction theory as the strong substitutes condition implies the existence of a Walrasian equilibrium. A recent line of research concentrated on the problem of deciding whether a bivariate valuation function is an assignment valuation or not. In this paper, we consider an \emph{inverse} variant of the problem: we are given a bivariate function $g$, and our goal is to find a bivariate multi-unit assignment valuation function $f$ that is as close to $g$ as possible. The difference between $f$ and $g$ can be measured either in $\ell_1$- or $\ell_\infty$-norm. Using tools from discrete convex analysis, we show that the problem is strongly NP-hard. On the other hand, we derive linear programming formulations that solve relaxed versions of the problem.

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they found applications in the theory of finitely additive measures, nonlinear integrals, and electric capacities. Recently, a number of connections between these two branches have been established, and the aim of this paper is to generalize further results on submodular set functions on finite sets to the analytic setting. We first extend the notion of duality of matroids to submodular set functions, and characterize the uniquely determined decomposition of a submodular set function into the sum of a nonnegaive charge and an increasing submodular set function in which the charge is maximal. Then, we describe basic properties of infinite-alternating set functions, a subclass of submodular set functions that serves as an analytic counterpart of coverage functions. By relaxing the monotonicity assumption in the definition, we introduce a new class of submodular functions with distinguished structural properties that includes, among others, weighted cut functions of graphs. We prove that, unlike general submodular set functions over an infinite domain, any infinite-alternating set function can be written as the sum of an increasing and a decreasing submodular function or as the difference of two increasing submodular functions, thus giving extension of results on monotonic decompositions in the finite case. Finally, motivated by its connections to graph parameters such as the maximum size of a cut and the maximum size of a fractional triangle packing, we study the structure of such decompositions for weighted cut functions of undirected graphs., Comment: 26 pages

Analysis of Markov Decision Processes (MDP) is often hindered by state space explosion. Abstraction is a well-established technique in model checking to mitigate this issue. This paper presents a novel lazy abstraction method for MDP analysis based on adaptive simulation graphs. Refinement is performed only when new parts of the state space are explored, which makes partial exploration techniques like Bounded Real-Time Dynamic Programming (BRTDP) retain more merged states. Therefore, we propose a combination of lazy abstraction and BRTDP. To evaluate the performance of our algorithm, we conduct initial experiments using the Quantitative Verification Benchmark Set.

Recent results in the literature indicate that artificial neural networks (ANNs) can outperform the dynamic factor model (DFM) in terms of the accuracy of GDP nowcasts. Compared to the DFM, the performance advantage of these highly flexible, nonlinear estimators is particularly evident in periods of recessions and structural breaks. From the perspective of policy-makers, however, nowcasts are the most useful when they are conveyed with uncertainty attached to them. While the DFM and other classical time series approaches analytically derive the predictive (conditional) distribution for GDP growth, ANNs can only produce point nowcasts based on their default training procedure (backpropagation). To fill this gap, first in the literature, we adapt two different deep learning algorithms that enable ANNs to generate density nowcasts for U.S. GDP growth: Bayes by Backprop and Monte Carlo dropout. The accuracy of point nowcasts, defined as the mean of the empirical predictive distribution, is evaluated relative to a naive constant growth model for GDP and a benchmark DFM specification. Using a 1D CNN as the underlying ANN architecture, both algorithms outperform those benchmarks during the evaluation period (2012:Q1 -- 2022:Q4). Furthermore, both algorithms are able to dynamically adjust the location (mean), scale (variance), and shape (skew) of the empirical predictive distribution. The results indicate that both Bayes by Backprop and Monte Carlo dropout can effectively augment the scope and functionality of ANNs, rendering them a fully compatible and competitive alternative for classical time series approaches.

The generation of ligands that both are tailored to a given protein pocket and exhibit a range of desired chemical properties is a major challenge in structure-based drug design. Here, we propose an in-silico approach for the $\textit{de novo}$ generation of 3D ligand structures using the equivariant diffusion model PILOT, combining pocket conditioning with a large-scale pre-training and property guidance. Its multi-objective trajectory-based importance sampling strategy is designed to direct the model towards molecules that not only exhibit desired characteristics such as increased binding affinity for a given protein pocket but also maintains high synthetic accessibility. This ensures the practicality of sampled molecules, thus maximizing their potential for the drug discovery pipeline. PILOT significantly outperforms existing methods across various metrics on the common benchmark dataset CrossDocked2020. Moreover, we employ PILOT to generate novel ligands for unseen protein pockets from the Kinodata-3D dataset, which encompasses a substantial portion of the human kinome. The generated structures exhibit predicted $IC_{50}$ values indicative of potent biological activity, which highlights the potential of PILOT as a powerful tool for structure-based drug design.

This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic scattering by a perfectly conducting body. The governing operator is shown to be coercive by means of the electric field integral operator with a purely imaginary wave number. Consequently, the continuous variational problem is uniquely solvable, given that the wave number does not belong to the spectrum of the interior Maxwell's problem. A Petrov-Galerkin discretization scheme is then introduced, employing Raviart-Thomas boundary elements for the solution space and Buffa-Christiansen boundary elements for the test space. Under a mild assumption depending only on the geometrical domain, the corresponding discrete inf-sup condition is proven, implying the unique solvability of the discrete problem. An asymptotically quasi-optimal error estimate for numerical solutions is established, and the convergence rate of the numerical scheme is examined. In addition, the resulting matrix system is shown to be well-conditioned regardless of the mesh refinement. Some numerical results are presented to support the theoretical analysis., Comment: 21 pages, 5 figures

Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake Predictability (CSEP, Schorlemmer et al., 2018) with new statistical methods supported by mathematical theory. To demonstrate their applicability, we evaluate three short-term forecasting models that were submitted to the CSEP Italy experiment, and two ensemble models thereof. The models produce weekly overlapping forecasts for the expected number of M4+ earthquakes in a collection of grid cells. We compare the models' forecasts using consistent scoring functions for means or expectations, which are widely used and theoretically principled tools for forecast evaluation. We further discuss and demonstrate their connection to CSEP-style earthquake likelihood model testing. Then, using tools from isotonic regression, we investigate forecast reliability and apply score decompositions in terms of calibration and discrimination. Our results show where and how models outperform their competitors and reveal a substantial lack of calibration for various models. The proposed methods also apply to full-distribution (e.g., catalog-based) forecasts, without requiring Poisson distributions or making any other type of parametric assumption.

Graph convolutional neural networks (GCNs) are powerful tools for learning graph-based knowledge representations from training data. However, they are vulnerable to small perturbations in the input graph, which makes them susceptible to input faults or adversarial attacks. This poses a significant problem for GCNs intended to be used in critical applications, which need to provide certifiably robust services even in the presence of adversarial perturbations. We propose an improved GCN robustness certification technique for node classification in the presence of node feature perturbations. We introduce a novel polyhedra-based abstract interpretation approach to tackle specific challenges of graph data and provide tight upper and lower bounds for the robustness of the GCN. Experiments show that our approach simultaneously improves the tightness of robustness bounds as well as the runtime performance of certification. Moreover, our method can be used during training to further improve the robustness of GCNs.

In this paper, we propose an innovative method for determining the fill level of containers, such as trash cans, addressing a critical aspect of waste management. The method combines spatial impulse response analysis with machine learning (ML) techniques, offering a unique and effective approach for sound-based classification that can be extended to various domains beyond waste management. By employing a buzzer-generated sine sweep signal, we create a distinctive signature specific to the fill level of the waste container. This signature, once accurately decoded, is then interpreted by a specially developed ensemble learning algorithm. Our approach achieves a classification accuracy of over 90% when implemented locally on a development board, optimizing operational efficiencies and eliminating the need to delegate complex classification tasks to external entities. Using low-cost and energy-efficient hardware components, our method offers a cost-effective approach that contributes to sustainable and efficient waste management practices, providing a reliable and locally deployable solution.

The tight relationship between infrared luminosity (L$_\mathrm{TIR}$) and 1.4 GHz radio continuum luminosity (L$_\mathrm{1.4GHz}$) has proven useful for understanding star formation free from dust obscuration. Infrared emission in star-forming galaxies typically arises from recently formed, dust-enshrouded stars, whereas radio synchrotron emission is expected from subsequent supernovae. By leveraging the wealth of ancillary far-ultraviolet - far-infrared photometry from the Deep Extragalactic VIsible Legacy Survey (DEVILS) and Galaxy and Mass Assembly (GAMA) surveys, combined with 1.4 GHz observations from the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey and Deep Investigation of Neutral Gas Origins (DINGO) projects, we investigate the impact of timescale differences between far-ultraviolet - far-infrared and radio-derived star formation rate (SFR) tracers. We examine how the SED-derived star formation histories (SFH) of galaxies can be used to explain discrepancies in these SFR tracers, which are sensitive to different timescales. Galaxies exhibiting an increasing SFH have systematically higher L$_\mathrm{TIR}$ and SED-derived SFRs than predicted from their 1.4 GHz radio luminosity. This indicates that insufficient time has passed for subsequent supernovae-driven radio emission to accumulate. We show that backtracking the SFR(t) of galaxies along their SED-derived SFHs to a time several hundred megayears prior to their observed epoch will both linearise the SFR-L$_\mathrm{1.4GHz}$ relation and reduce the overall scatter. The minimum scatter in the SFR(t)-L$_\mathrm{1.4GHz}$ is reached at 200 - 300 Myr prior, consistent with theoretical predictions for the timescales required to disperse the cosmic ray electrons responsible for the synchrotron emission., Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in MNRAS

Heterostructures of magnetic topological insulators (MTIs) and superconductors (SCs) in two-dimensional (2D) slab and one-dimensional (1D) nanoribbon geometries have been predicted to host, respectively, chiral Majorana edge states (CMESs) and Majorana bound states (MBSs). We study the topological properties of such MTI/SC heterostructures upon variation of the geometry from wide slabs to quasi-1D nanoribbon systems and as a function of the chemical potential, the magnetic doping, and the induced superconducting pairing potential. To do so, we construct effective symmetry-constrained low-energy Hamiltonians accounting for the real-space confinement. For a nanoribbon geometry with finite width and length, we observe different phases characterized by CMESs, MBSs, as well as coexisting CMESs and MBSs, as the chemical potential, the magnetic doping and/or the width are varied.

Embodied reasoning systems integrate robotic hardware and cognitive processes to perform complex tasks typically in response to a natural language query about a specific physical environment. This usually involves changing the belief about the scene or physically interacting and changing the scene (e.g. 'Sort the objects from lightest to heaviest'). In order to facilitate the development of such systems we introduce a new simulating environment that makes use of MuJoCo physics engine and high-quality renderer Blender to provide realistic visual observations that are also accurate to the physical state of the scene. Together with the simulator we propose a new benchmark composed of 10 classes of multi-step reasoning scenarios that require simultaneous visual and physical measurements. Finally, we develop a new modular Closed Loop Interactive Reasoning (CLIER) approach that takes into account the measurements of non-visual object properties, changes in the scene caused by external disturbances as well as uncertain outcomes of robotic actions. We extensively evaluate our reasoning approach in simulation and in the real world manipulation tasks with a success rate above 76% and 64%, respectively.

We develop an accurate nanoelectronic modeling approach for realistic three-dimensional topological insulator nanostructures and investigate their low-energy surface-state spectrum. Starting from the commonly considered four-band $\boldsymbol{\mathrm{k\cdot p}}$ bulk model Hamiltonian for the Bi$_2$Se$_3$ family of topological insulators, we derive new parameter sets for Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$. We consider a fitting strategy applied to \emph{ab initio} band structures around the $\Gamma$ point that ensures a quantitatively accurate description of the low-energy bulk and surface states, while avoiding the appearance of unphysical low-energy states at higher momenta, something that is not guaranteed by the commonly considered perturbative approach. We analyze the effects that arise in the low-energy spectrum of topological surface states due to band anisotropy and electron-hole asymmetry, yielding Dirac surface states that naturally localize on different side facets. In the thin-film limit, when surface states hybridize through the bulk, we resort to a thin-film model and derive thickness-dependent model parameters from \emph{ab initio} calculations that show good agreement with experimentally resolved band structures, unlike the bulk model that neglects relevant many-body effects in this regime. Our versatile modeling approach offers a reliable starting point for accurate simulations of realistic topological material-based nanoelectronic devices.

This work presents a framework for automatically extracting physical object properties, such as material composition, mass, volume, and stiffness, through robot manipulation and a database of object measurements. The framework involves exploratory action selection to maximize learning about objects on a table. A Bayesian network models conditional dependencies between object properties, incorporating prior probability distributions and uncertainty associated with measurement actions. The algorithm selects optimal exploratory actions based on expected information gain and updates object properties through Bayesian inference. Experimental evaluation demonstrates effective action selection compared to a baseline and correct termination of the experiments if there is nothing more to be learned. The algorithm proved to behave intelligently when presented with trick objects with material properties in conflict with their appearance. The robot pipeline integrates with a logging module and an online database of objects, containing over 24,000 measurements of 63 objects with different grippers. All code and data are publicly available, facilitating automatic digitization of objects and their physical properties through exploratory manipulations., Comment: 8 pages, 8 figures

Assembly processes involving humans and robots are challenging scenarios because the individual activities and access to shared workspace have to be coordinated. Fixed robot programs leave no room to diverge from a fixed protocol. Working on such a process can be stressful for the user and lead to ineffective behavior or failure. We propose a novel approach of online constraint-based scheduling in a reactive execution control framework facilitating behavior trees called CoBOS. This allows the robot to adapt to uncertain events such as delayed activity completions and activity selection (by the human). The user will experience less stress as the robotic coworkers adapt their behavior to best complement the human-selected activities to complete the common task. In addition to the improved working conditions, our algorithm leads to increased efficiency, even in highly uncertain scenarios. We evaluate our algorithm using a probabilistic simulation study with 56000 experiments. We outperform all baselines by a margin of 4-10%. Initial real robot experiments using a Franka Emika Panda robot and human tracking based on HTC Vive VR gloves look promising., Comment: 7 pages, 8 figures

This paper presents the first results of the study of high-energy electron and muon neutrino charged-current interactions in the FASER$\nu$ emulsion/tungsten detector of the FASER experiment at the LHC. A subset of the FASER$\nu$ volume, which corresponds to a target mass of 128.6~kg, was exposed to neutrinos from the LHC $pp$ collisions with a centre-of-mass energy of 13.6~TeV and an integrated luminosity of 9.5 fb$^{-1}$. Applying stringent selections requiring electrons with reconstructed energy above 200~GeV, four electron neutrino interaction candidate events are observed with an expected background of $0.025^{+0.015}_{-0.010}$, leading to a statistical significance of 5.2$\sigma$. This is the first direct observation of electron neutrino interactions at a particle collider. Eight muon neutrino interaction candidate events are also detected, with an expected background of $0.22^{+0.09}_{-0.07}$, leading to a statistical significance of 5.7$\sigma$. The signal events include neutrinos with energies in the TeV range, the highest-energy electron and muon neutrinos ever detected from an artificial source. The energy-independent part of the interaction cross section per nucleon is measured over an energy range of 560--1740 GeV (520--1760 GeV) for $\nu_e$ ($\nu_{\mu}$) to be $(1.2_{-0.7}^{+0.8}) \times 10^{-38}~\mathrm{cm}^{2}\,\mathrm{GeV}^{-1}$ ($(0.5\pm0.2) \times 10^{-38}~\mathrm{cm}^{2}\,\mathrm{GeV}^{-1}$), consistent with Standard Model predictions. These are the first measurements of neutrino interaction cross sections in those energy ranges.