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Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional assumptions on the solution of the state equation, the differentiability of the value function with respect to the time variable. In our proof, we rely on local growth assumptions commonly associated with the study of second-order sufficient conditions. These assumptions are generally applicable to a wide range of problems, including, for instance, certain tracking-type problems. Finally, we discuss the differentiability of the value function in a neighborhood of the optimal trajectory when a growth condition for optimal controls is used.

Quantum correlations in the form of entanglement, quantum steering or Bell nonlocality are resources for various information-processing tasks, but their detailed quantification and characterization remains complicated. One counter-intuitive effect is the phenomenon of superactivation, meaning that two copies of a quantum state may exhibit forms of correlations which are absent on the single-copy level. We develop a systematic approach towards a full understanding of this phenomenon using the paradigm of genuine multipartite entanglement. We introduce systematic methods for studying superactivation of entanglement based on symmetries and generalized notions of multipartite distillability. With this, we present novel criteria for superactivation as well as a quantitative theory of it. Moreover, we present evidence for incompressible entanglement on multi-copy systems, which cannot be reduced to the single-copy level., Comment: 20 pages, 7 figures

In this paper we derive new types of KZ equations for conformal blocks with one irregular singularity at infinity. To this end, we construct irregular representations of Kac-Moody algebras where we restrict ourselves to the $sl(2,\mathbb{C})$ case. We show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra. By connecting to 2d Liouville theory, we show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres-Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve., Comment: 38 pages, 1 figure

We introduce the Velocity Jumps approach, denoted as JUMP, a new class of Molecular dynamics integrators, replacing the Langevin dynamics by a hybrid model combining a classical Langevin diffusion and a piecewise deterministic Markov process, where the expensive computation of long-range pairwise interactions is replaced by a resampling of the velocities at random times. This framework allows for an acceleration in the simulation speed while preserving sampling and dynamical properties such as the diffusion constant. It can also be integrated in classical multi-timestep methods, pushing further the computational speedup, while avoiding some of the resonance issues of the latter thanks to the random nature of jumps. The JUMP, JUMP-RESPA and JUMP-RESPA1 integrators have been implemented in the GPU-accelerated version of the Tinker-HP package and are shown to provide significantly enhanced performances compared to their BAOAB, BAOAB-RESPA and BAOAB-RESPA1 counterparts respectively.

We generalize the seminal polynomial partitioning theorems of Guth and Katz to a set of semi-Pfaffian sets. Specifically, given a set $\Gamma \subseteq \mathbb{R}^n$ of $k$-dimensional semi-Pfaffian sets, where each $\gamma \in \Gamma$ is defined by a fixed number of Pfaffian functions, and each Pfaffian function is in turn defined with respect to a Pfaffian chain $\vec{q}$ of length $r$, for any $D \ge 1$, we prove the existence of a polynomial $P \in \mathbb{R}[X_1, \ldots, X_n]$ of degree at most $D$ such that each connected component of $\mathbb{R}^n \setminus Z(P)$ intersects at most $\sim \frac{|\Gamma|}{D^{n - k - r}}$ elements of $\Gamma$. Also, under some mild conditions on $\vec{q}$, for any $D \ge 1$, we prove the existence of a Pfaffian function $P'$ of degree at most $D$ defined with respect to $\vec{q}$, such that each connected component of $\mathbb{R}^n \setminus Z(P')$ intersects at most $\sim \frac{|\Gamma|}{D^{n-k}}$ elements of $\Gamma$. To do so, given a $k$-dimensional semi-Pfaffian set $\mathcal{X} \subseteq \mathbb{R}^n$, and a polynomial $P \in \mathbb{R}[X_1, \ldots, X_n]$ of degree at most $D$, we establish a uniform bound on the number of connected components of $\mathbb{R}^n \setminus Z(P)$ that $\mathcal{X}$ intersects; that is, we prove that the number of connected components of $(\mathbb{R}^n \setminus Z(P)) \cap \mathcal{X}$ is at most $\sim D^{k+r}$. Finally as applications, we derive Pfaffian versions of Szemer\'edi-Trotter type theorems, and also prove bounds on the number of joints between Pfaffian curves., Comment: 29 pages, 0 figures Added hypothesis of algebraic independence of Pfaffian chain to avoid obtaining a zero Pfaffian partitioning function

Fuel-lean hydrogen combustion systems hold significant potential for low pollutant emissions, but are also susceptible to intrinsic combustion instabilities. While most research on these instabilities has focused on flames without wall confinement, practical combustors are typically enclosed by walls that strongly influence the combustion dynamics. In part I of this work, the flame-wall interaction of intrinsically unstable hydrogen/air flames has been studied for a single operating condition through detailed numerical simulations in a two-dimensional head-on quenching configuration. This study extends the previous investigation to a wide range of gas turbine and engine-relevant operating conditions, including variations in equivalence ratio (0.4 - 1.0), unburnt gas temperature (298 K - 700 K), and pressure (1.01325 bar - 20 bar). These parametric variations allow for a detailed analysis and establish a baseline for modeling the effects of varying instability intensities on the quenching process, as the relative influence of thermodiffusive and hydrodynamic instabilities depends on the operating conditions. While the quenching characteristics remain largely unaffected by hydrodynamic instabilities, the presence of thermodiffusive instabilities significantly increases the mean wall-heat flux and reduces the mean quenching distance. Furthermore, the impact of thermodiffusive instabilities on the quenching process intensifies as their intensity increases, driven by an increase in pressures and a decrease in equivalence ratio and unburnt gas temperature., Comment: submitted to Combustion and Flame

We propose a new approach to studying hyperbolic Kac-Moody algebras, focussing on the rank-3 algebra $\mathfrak{F}$ first investigated by Feingold and Frenkel. Our approach is based on the concrete realization of this Lie algebra in terms of a Hilbert space of transverse and longitudinal physical string states, which are expressed in a basis using DDF operators. When decomposed under its affine subalgebra $A_1^{(1)}$, the algebra $\mathfrak{F}$ decomposes into an infinite sum of affine representation spaces of $A_1^{(1)}$ for all levels $\ell\in\mathbb{Z}$. For $|\ell| >1$ there appear in addition coset Virasoro representations for all minimal models of central charge $c<1$, but the different level-$\ell$ sectors of $\mathfrak{F}$ do not form proper representations of these because they are incompletely realized in $\mathfrak{F}$. To get around this problem we propose to nevertheless exploit the coset Virasoro algebra for each level by identifying for each level a (for $|\ell|\geq 3$ infinite) set of `Virasoro ground states' that are not necessarily elements of $\mathfrak{F}$ (in which case we refer to them as `virtual'), but from which the level-$\ell$ sectors of $\mathfrak{F}$ can be fully generated by the joint action of affine and coset Virasoro raising operators. We conjecture (and present partial evidence) that the Virasoro ground states for $|\ell|\geq 3$ in turn can be generated from a finite set of `maximal ground states' by the additional action of the `spectator' coset Virasoro raising operators present for all levels $|\ell| > 2$. Our results hint at an intriguing but so far elusive secret behind Einstein's theory of gravity, with possibly important implications for quantum cosmology., Comment: 48 pages

Hydrogen combustion systems operated under fuel-lean conditions offer great potential for low emissions. However, these operating conditions are also susceptible to intrinsic thermodiffusive combustion instabilities. Even though technical combustors are enclosed by walls that significantly influence the combustion process, intrinsic flame instabilities have mostly been investigated in canonical freely-propagating flame configurations unconfined by walls. This study aims to close this gap by investigating the flame-wall interaction of thermodiffusive unstable hydrogen/air flame through detailed numerical simulations in a two-dimensional head-on quenching configuration. It presents an in-depth qualitative and quantitative analysis of the quenching process, revealing the major impact factors of the instabilities on the quenching characteristics. The thermodiffusive instabilities result in lower quenching distances and increased wall heat fluxes compared to one-dimensional head-on quenching flames under similar operation conditions. The change in quenching characteristics seems not to be driven by kinematic effects. Instead, the increased wall heat fluxes are caused by the enhanced flame reactivity of the unstable flame approaching the wall, which results from mixture variations associated with the instabilities. Overall, the study highlights the importance of studying flame-wall interaction in more complex domains than simple one-dimensional configurations, where such instabilities are inherently suppressed. Further, it emphasizes the need to incorporate local mixture variations induced by intrinsic combustion instabilities in combustion models for flame-wall interactions. In part II of this study, the scope is expanded to gas turbine and internal combustion engine relevant conditions through a parametric study, varying the equivalence ratio, pressure, and unburnt temperature., Comment: submitted to Combustion and Flame

Modern reconstruction techniques can effectively model complex 3D scenes from sparse 2D views. However, automatically assessing the quality of novel views and identifying artifacts is challenging due to the lack of ground truth images and the limitations of no-reference image metrics in predicting detailed artifact maps. The absence of such quality metrics hinders accurate predictions of the quality of generated views and limits the adoption of post-processing techniques, such as inpainting, to enhance reconstruction quality. In this work, we propose a new no-reference metric, Puzzle Similarity, which is designed to localize artifacts in novel views. Our approach utilizes image patch statistics from the input views to establish a scene-specific distribution that is later used to identify poorly reconstructed regions in the novel views. We test and evaluate our method in the context of 3D reconstruction; to this end, we collected a novel dataset of human quality assessment in unseen reconstructed views. Through this dataset, we demonstrate that our method can not only successfully localize artifacts in novel views, correlating with human assessment, but do so without direct references. Surprisingly, our metric outperforms both no-reference metrics and popular full-reference image metrics. We can leverage our new metric to enhance applications like automatic image restoration, guided acquisition, or 3D reconstruction from sparse inputs.

We extend the graphical calculus developed in the first part of this paper to the parametrising spaces of quantum vertex operators. This involves a graphical implementation of the dynamical twist functor, which is a strict monoidal functor that describes how a morphism acting on the spin space of a quantum vertex operator $\Phi$ is transported to a morphism on the parametrising space of $\Phi$. The monoidal structure of the underlying nonstrict monoidal functor, considered before by Etingof and Varchenko in 1999, is given in terms of dynamical fusion operators, which are operators that describe the fusion of quantum vertex operators on the level of parametrising spaces. In the second part of the paper we use the extended graphical calculus to give intuitive, graphical derivations of various systems of difference equations for universal multipoint weighted trace functions. This includes the dual $q$-Knizhnik-Zamolodchikov-Bernard (KZB) and the dual Macdonald-Ruijsenaars (MR) equations, earlier obtained by Etingof and Varchenko in 2000, as well as an extension of the dual MR equations called dual coordinate MR equations. We use a known symmetry property of the universal weighted trace function, involving the exchange of its geometric and spectral parameter, to derive non-dual versions of these equations., Comment: 89 pages

Driving the nuclear fusion reaction p+11B -> 3 alpha + 8.7 MeV in laboratory conditions, by interaction between high-power laser pulses and matter, has become a popular field of research, due to numerous applications that it can potentially allow: an alternative to deuterium-tritium (DT) for fusion energy production, astrophysics studies and alpha-particle generation for medical treatments. A possible scheme for laser-driven p-11B reactions is to direct a beam of laser-accelerated protons onto a boron sample (the so-called 'pitcher-catcher' scheme). This technique was successfully implemented on large, energetic lasers, yielding hundreds of joules per shot at low repetition. We present here a complementary approach, exploiting the high-repetition rate of the VEGA III petawatt laser at CLPU (Spain), aiming at accumulating results from many interactions at much lower energy, for better controlling the parameters and the statistics of the measurements. Despite a moderate energy per pulse, our experiment allowed exploring the laser-driven fusion process with tens (up to hundreds) of laser shots. The experiment provided a clear signature of the produced reactions and of the fusion products, accumulated over many shots, leading to an improved optimization of the diagnostic for these experimental campaigns In this paper we discuss the effectiveness of the laser-driven p-11B fusion in the pitcher-catcher scheme, at high-repetition rate, addressing the challenges of this experimental scheme and highlighting its critical aspects. Our proposed methodologies allow evaluating the performance of this scheme for laser-driven alpha particle production and can be adapted to high-repetition rate laser facilities with higher energy and intensity.

The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simu-lations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jumpprocesses have gained interest over the last decade. One interest of the latter is the possibility to split forces(at the continuous-time level), reducing the numerical cost for sampling the trajectory. Motivated by this, anumerical scheme based on hybrid dynamics combining velocity jumps and Langevin diffusion, numericallymore efficient than their classical Langevin counterparts, has been introduced for computational chemistry in [42]. The present work is devoted to the numerical analysis of this scheme. Our main results are, first, theexponential ergodicity of the continuous-time velocity jump Langevin process, second, a Talay-Tubaro expan-sion of the invariant measure of the numerical scheme, showing in particular that the scheme is of weak order2 in the step-size and, third, a bound on the quadratic risk of the corresponding practical MCMC estimator(possibly with Richardson extrapolation). With respect to previous works on the Langevin diffusion, newdifficulties arise from the jump operator, which is non-local.

In this paper we study the question of how to reconstruct the state of a power system using Phasor Measurement Units (PMUs). In our previous research we proved that this question has an affirmative answer imposing some rather strict structural assumptions: namely, neglecting the generator rotors saliency and assuming that the stator resistance of the synchronous generator is zero. It was shown in simulations that the performance of the proposed observer was sensitive to these assumptions, observing a transient quality degradation for realistic simulations not imposing these assumptions. Moreover, it was assumed in our previous work that the mechanical power and the field voltage are available for measurement, a scenario that it is not always realistic. In this paper we accomplish two ambitious objectives. First, we propose a new observer that does not impose the simplifying assumptions on the generator model. Secondly, we consider the more realistic scenario where only mechanical power is available for measurement. That is, we solve a problem of state reconstruction of a nonlinear system with partially known input measurements -- that is well-known to be a very challenging task. The design of the first observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the Dynamic Regressor Extension and Mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. On the other hand, the observer for the partial input measurement scenario relies on the clever exploitation of the systems model. Simulation results illustrates the good performance of the proposed observers.

This is mainly a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (so-called optimality mappings) of optimization problems in infinite dimensional spaces. The focus is on the optimality mappings associated with optimal control problems for ODE systems or PDEs. We especially emphasize an extension of the concepts of SMR and SMsR which involves two metrics either in the domain or in the image spaces. The paper shows the relevance of this extension in optimal control.

Trajectories can be regarded as time-series of coordinates, typically arising from motile objects. Methods for trajectory classification are particularly important to detect different movement patterns, while methods for regression to compute motility metrics and forecasting. Recent advances in computer vision have facilitated the processing of trajectories rendered as images via artificial neural networks with 2d convolutional layers (CNNs). This approach leverages the capability of CNNs to learn spatial hierarchies of features from images, necessary to recognize complex shapes. Moreover, it overcomes the limitation of other machine learning methods that require input trajectories with a fixed number of points. However, rendering trajectories as images can introduce poorly investigated artifacts such as information loss due to the plotting of coordinates on a discrete grid, and spectral changes due to line thickness and aliasing. In this study, we investigate the effectiveness of CNNs for solving classification and regression problems from synthetic trajectories that have been rendered as images using different modalities. The parameters considered in this study include line thickness, image resolution, usage of motion history (color-coding of the temporal component) and anti-aliasing. Results highlight the importance of choosing an appropriate image resolution according to model depth and motion history in applications where movement direction is critical., Comment: 13 pages, 5 figures

This contribution gives a panoramic overview of the development of N=8 supergravity and its relation to other maximally supersymmetric theories over the past 40 years. It also provides a personal perspective on the future role of this theory in attempts at unification., Comment: Invited contribution to the book "Half a century of supergravity", eds. A. Ceresole and G. Dall'Agata, 22 pages. V2: minor corrections, references added

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations in $L_{p}$-setting with singular lower order coefficients.

There is increased interest in using generative AI to create 3D spaces for Virtual Reality (VR) applications. However, today's models produce artificial environments, falling short of supporting collaborative tasks that benefit from incorporating the user's physical context. To generate environments that support VR telepresence, we introduce SpaceBlender, a novel pipeline that utilizes generative AI techniques to blend users' physical surroundings into unified virtual spaces. This pipeline transforms user-provided 2D images into context-rich 3D environments through an iterative process consisting of depth estimation, mesh alignment, and diffusion-based space completion guided by geometric priors and adaptive text prompts. In a preliminary within-subjects study, where 20 participants performed a collaborative VR affinity diagramming task in pairs, we compared SpaceBlender with a generic virtual environment and a state-of-the-art scene generation framework, evaluating its ability to create virtual spaces suitable for collaboration. Participants appreciated the enhanced familiarity and context provided by SpaceBlender but also noted complexities in the generative environments that could detract from task focus. Drawing on participant feedback, we propose directions for improving the pipeline and discuss the value and design of blended spaces for different scenarios.

Reinforcement learning from human feedback (RLHF) has become a key method for aligning large language models (LLMs) with human preferences through the use of reward models. However, traditional reward models typically generate point estimates, which oversimplify the diversity and complexity of human values and preferences. In this paper, we introduce Quantile Reward Models (QRMs), a novel approach to reward modeling that learns a distribution over rewards instead of a single scalar value. Our method uses quantile regression to estimate a full, potentially multimodal distribution over preferences, providing a more powerful and nuanced representation of preferences. This distributional approach can better capture the diversity of human values, addresses label noise, and accommodates conflicting preferences by modeling them as distinct modes in the distribution. Our experimental results show that QRM outperforms comparable traditional point-estimate models on RewardBench. Furthermore, we demonstrate that the additional information provided by the distributional estimates can be utilized in downstream applications, such as risk-aware reinforcement learning, resulting in LLM policies that generate fewer extremely negative responses. Our code and model are released at https://github.com/Nicolinho/QRM.

{The paper studies classical, type-free theories of truth and determinateness. Recently, Volker Halbach and Kentaro Fujimoto proposed a novel approach to classical determinate truth, in which determinateness is axiomatized by a primitive predicate. In the paper we propose a different strategy to develop theories of classical determinate truth in Halbach and Fujimoto's sense featuring a \emph{defined} determinateness predicate. This puts our theories of classical determinate truth in continuity with a standard approach to determinateness by authors such as Feferman and Reinhardt. The theories entail all principles of Fujimoto and Halbach's theories, and are proof-theoretically equivalent to Halbach and Fujimoto's CD+. They will be shown to be logically equivalent to a class of natural theories of truth, the \emph{classical closures of Kripke-Feferman truth}. The analysis of the proposed theories will also provide new insights on Fujimoto and Halbach's theories: we show that the latter cannot prove most of the axioms of the classical closures of Kripke-Feferman truth. This entails that, unlike what happens in our theories of truth and determinateness, Fujimoto and Halbach's \emph{inner theories} -- the sentences living under two layers of truth -- cannot be closed under standard logical rules of inference.}

In this work, we analyze the cosmological model in which the expansion is driven by a classical, free Klein-Gordon field on a flat, four-dimensional Friedmann-Lema\^itre-Robertson-Walker spacetime. The model allows for arbitrary mass, non-zero cosmological constant and coupling to curvature. We find that there are strong restrictions to the parameter space, due to the requirement for the reality of the field values. At early cosmological times, we observe Big Bang singularities, solutions where the scale factor asymptotically approaches zero, and Small Bangs. The latter are solutions for which the Hubble parameter diverges at a finite value of the scale factor. They appear generically in our model for certain curvature couplings. An early inflationary era is observed for a specific value of the curvature coupling without further assumptions (unlike in many other inflationary models). A late-time Dark Energy period is present for all solutions with positive cosmological constant, numerically suggesting that a "cosmic no-hair" theorem holds under more general assumptions than the original Wald version which relies on classical energy conditions. The classical fields in consideration can be viewed as resembling one-point functions of a semiclassical model, in which the cosmological expansion is driven by a quantum field., Comment: 48 pages, 13 figures

Work-related transportation incidents significantly impact urban mobility and productivity. These incidents include traffic crashes, collisions between vehicles, and falls that occurred during commuting or work-related transportation (e.g., falling while getting off a bus during the morning commute or while riding a bicycle for work). This study analyzes a decade of work-related transportation incident data (2012--2021) in Santiago, Chile, using records from a major worker's insurance company. Using negative binomial regression, we assess the impact of a 2018 urban speed limit reduction law on incident injury severity. We also explore broader temporal, spatial, and demographic patterns in these incidents in urban and rural areas. The urban speed limit reduction is associated with a decrease of 4.26 days in prescribed medical leave for incidents in urban areas, suggesting that lower speed limits contribute to reduced injury severity. Our broader analysis reveals distinct incident patterns across different groups. Workers traveling by motorcycle and bicycle experience more severe injuries when involved in traffic incidents, with marginal effects of 26.94 and 13.06 additional days of medical leave, respectively, compared to motorized vehicles. Women workers tend to have less severe injuries, with an average of 7.57 fewer days of medical leave. Age is also a significant factor, with older workers experiencing more severe injuries -- each additional year of age is associated with 0.57 more days of medical leave. Our results provide insights for urban planning, transportation policy, and workplace safety initiatives., Comment: 18 pages, 9 figures. Second version after reviews

In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space $X$ of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact $X$., Comment: 47 pages, 23 figures

High-dimensional encoding of quantum information holds the potential to greatly increase the computational power of existing devices by enlarging the accessible state space for fixed register size and by reducing the number of required entangling gates. However, qudit-based quantum computation remains far less developed than conventional qubit-based approaches, in particular for photons, which represent natural multi-level information carriers that play a crucial role in the development of quantum networks. A major obstacle for realizing quantum gates between two individual photons is the restriction of direct interaction between photons in linear media. In particular, essential logic components for quantum operations such as native qudit-qudit entangling gates are still missing for optical quantum information processing. Here we address this challenge by presenting a protocol for realizing an entangling gate -- the controlled phase-flip (CPF) gate -- for two photonic qudits in arbitrary dimension. We experimentally demonstrate this protocol by realizing a four-dimensional qudit-qudit CPF gate, whose decomposition would require at least 13 two-qubit entangling gates. Our photonic qudits are encoded in orbital angular momentum (OAM) and we have developed a new active high-precision phase-locking technology to construct a high-dimensional OAM beam splitter that increases the stability of the CPF gate, resulting in a process fidelity within a range of $ [0.64 \pm 0.01, 0.82 \pm 0.01]$. Our experiment represents a significant advance for high-dimensional optical quantum information processing and has the potential for wider applications beyond optical system., Comment: 14 pages, 7 figures

In a previous work [K.A. Meissner and H. Nicolai, Eur. Phys. J. C {\bf 84}, 269 (2024)], two of the present authors have suggested possible experimental ways to search for stable supermassive particles with electric charges of $\cO(1)$ in upcoming underground experiments, in particular the new Jiangmen Underground Neutrino Observatory (JUNO) experiment. In the current paper, we present a detailed analysis of the specific signature of such gravitino-induced events for the JUNO detector and for upcoming liquid argon detectors like DUNE (Deep Underground Neutrino Experiment). The proposed method of detection relies on the ``glow'' produced by photons during the passage of such particles through the detector liquid, which would last for about a few to a few hundred microseconds depending on its velocity and the track. The cross sections for electronic excitation of the main component of the scintillator liquid, namely linear alkylbenzene (LAB), by the passing gravitino are evaluated using quantum-chemical methods. The results show that, if such particles exist, the resulting signals would lead to a unique and unmistakable signature, for which we present event simulations as they would be seen by the JUNO or DUNE photomultipliers. Our analysis brings together two very different research areas, namely fundamental particles physics and the search for a fundamental theory on the one hand, and methods of advanced quantum chemistry on the other.

In this paper, we address the data scarcity problem in automatic data-driven glossing for low-resource languages by coordinating multiple sources of linguistic expertise. We supplement models with translations at both the token and sentence level as well as leverage the extensive linguistic capability of modern LLMs. Our enhancements lead to an average absolute improvement of 5%-points in word-level accuracy over the previous state of the art on a typologically diverse dataset spanning six low-resource languages. The improvements are particularly noticeable for the lowest-resourced language Gitksan, where we achieve a 10%-point improvement. Furthermore, in a simulated ultra-low resource setting for the same six languages, training on fewer than 100 glossed sentences, we establish an average 10%-point improvement in word-level accuracy over the previous state-of-the-art system., Comment: arXiv admin note: text overlap with arXiv:2403.08189

Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key feature distinguishing entanglement from classical correlations is the occurrence of correlations for complementary measurement bases. In particular, mutually unbiased bases (MUBs) are a paradigmatic example that is well-understood and routinely employed for entanglement certification. However, implementing unbiased measurements exactly is challenging and not generically possible for all physical platforms. Here, we extend the entanglement-certification toolbox from correlations in MUBs to arbitrary bases, even without requiring aligned reference frames. This represents a practically significant simplification that paves the way for the efficient characterization of high-dimensional entanglement in a wide range of physical systems., Comment: 21 pages, 8 figures, 1 table

In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well known, obstacle problems can be formulated as a complementarity system and consequently the associated solution operator is not Gateaux differentiable. As a consequence, we utilize a regularization approach to obtain optimality conditions as the limit of optimality conditions of a family of regularized problems. Due to the coupling of the controlled coefficient with the gradients of the solution to the obstacle problem, weak convergence arguments can not be applied and we need to argue by $H$-convergence. We show, that, based on initial $H$-convergence, a bootstrapping argument can be utilized to prove strong $L^p$-convergence of the control and thus enable the passage to the limit in the optimality conditions.

This paper introduces holographic cross-device interaction, a new class of remote cross-device interactions between local physical devices and holographically rendered remote devices. Cross-device interactions have enabled a rich set of interactions with device ecologies. Most existing research focuses on co-located settings (meaning when users and devices are in the same physical space) to achieve these rich interactions and affordances. In contrast, holographic cross-device interaction allows remote interactions between devices at distant locations by providing a rich visual affordance through real-time holographic rendering of the device's motion, content, and interactions on mixed reality head-mounted displays. This maintains the advantages of having a physical device, such as precise input through touch and pen interaction. Through holographic rendering, not only can remote devices interact as if they are co-located, but they can also be virtually augmented to further enrich interactions, going beyond what is possible with existing cross-device systems. To demonstrate this concept, we developed HoloDevice, a prototype system for holographic cross-device interaction using the Microsoft Hololens 2 augmented reality headset. Our contribution is threefold. First, we introduce the concept of holographic cross-device interaction. Second, we present a design space containing three unique benefits, which include: (1) spatial visualization of interaction and motion, (2) rich visual affordances for intermediate transition, and (3) dynamic and fluid configuration. Last we discuss a set of implementation demonstrations and use-case scenarios that further explore the space.

In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then we look at the semiclassical limit of the quantum spin Calogero--Moser system. The result is a hybrid integrable system driven by usual classical Calogero--Moser (CM) dynamics. This system at the fixed point of the multi-time classical dynamics CM system gives commuting spin Hamiltonians of Haldane--Shastry model., Comment: 31 pages

The precise point cloud ground segmentation is a crucial prerequisite of virtually all perception tasks for LiDAR sensors in autonomous vehicles. Especially the clustering and extraction of objects from a point cloud usually relies on an accurate removal of ground points. The correct estimation of the surrounding terrain is important for aspects of the drivability of a surface, path planning, and obstacle prediction. In this article, we propose our system GroundGrid which relies on 2D elevation maps to solve the terrain estimation and point cloud ground segmentation problems. We evaluate the ground segmentation and terrain estimation performance of GroundGrid and compare it to other state-of-the-art methods using the SemanticKITTI dataset and a novel evaluation method relying on airborne LiDAR scanning. The results show that GroundGrid is capable of outperforming other state-of-the-art systems with an average IoU of 94.78% while maintaining a high run-time performance of 171Hz. The source code is available at https://github.com/dcmlr/groundgrid, Comment: This letter has been accepted for publication in IEEE Robotics and Automation Letters

The new generation of observatories and instruments (VLT/ERIS, JWST, ELT) motivate the development of robust methods to detect and characterise faint and close-in exoplanets. Molecular mapping and cross-correlation for spectroscopy use molecular templates to isolate a planet's spectrum from its host star. However, reliance on signal-to-noise ratio (S/N) metrics can lead to missed discoveries, due to strong assumptions of Gaussian independent and identically distributed noise. We introduce machine learning for cross-correlation spectroscopy (MLCCS); the method aims to leverage weak assumptions on exoplanet characterisation, such as the presence of specific molecules in atmospheres, to improve detection sensitivity for exoplanets. MLCCS methods, including a perceptron and unidimensional convolutional neural networks, operate in the cross-correlated spectral dimension, in which patterns from molecules can be identified. We test on mock datasets of synthetic planets inserted into real noise from SINFONI at K-band. The results from MLCCS show outstanding improvements. The outcome on a grid of faint synthetic gas giants shows that for a false discovery rate up to 5%, a perceptron can detect about 26 times the amount of planets compared to an S/N metric. This factor increases up to 77 times with convolutional neural networks, with a statistical sensitivity shift from 0.7% to 55.5%. In addition, MLCCS methods show a drastic improvement in detection confidence and conspicuity on imaging spectroscopy. Once trained, MLCCS methods offer sensitive and rapid detection of exoplanets and their molecular species in the spectral dimension. They handle systematic noise and challenging seeing conditions, can adapt to many spectroscopic instruments and modes, and are versatile regarding atmospheric characteristics, which can enable identification of various planets in archival and future data., Comment: 27 pages, 24 figures. Submitted for publication in A&A January 2, 2024. After first iteration with the referee, resubmitted May 17, 2024

Fuzzing has proven to be a highly effective approach to uncover software bugs over the past decade. After AFL popularized the groundbreaking concept of lightweight coverage feedback, the field of fuzzing has seen a vast amount of scientific work proposing new techniques, improving methodological aspects of existing strategies, or porting existing methods to new domains. All such work must demonstrate its merit by showing its applicability to a problem, measuring its performance, and often showing its superiority over existing works in a thorough, empirical evaluation. Yet, fuzzing is highly sensitive to its target, environment, and circumstances, e.g., randomness in the testing process. After all, relying on randomness is one of the core principles of fuzzing, governing many aspects of a fuzzer's behavior. Combined with the often highly difficult to control environment, the reproducibility of experiments is a crucial concern and requires a prudent evaluation setup. To address these threats to validity, several works, most notably Evaluating Fuzz Testing by Klees et al., have outlined how a carefully designed evaluation setup should be implemented, but it remains unknown to what extent their recommendations have been adopted in practice. In this work, we systematically analyze the evaluation of 150 fuzzing papers published at the top venues between 2018 and 2023. We study how existing guidelines are implemented and observe potential shortcomings and pitfalls. We find a surprising disregard of the existing guidelines regarding statistical tests and systematic errors in fuzzing evaluations. For example, when investigating reported bugs, ...

Objective: Federated Learning (FL) enables collaborative model training while keeping data locally. Currently, most FL studies in radiology are conducted in simulated environments due to numerous hurdles impeding its translation into practice. The few existing real-world FL initiatives rarely communicate specific measures taken to overcome these hurdles, leaving behind a significant knowledge gap. Minding efforts to implement real-world FL, there is a notable lack of comprehensive assessment comparing FL to less complex alternatives. Materials & Methods: We extensively reviewed FL literature, categorizing insights along with our findings according to their nature and phase while establishing a FL initiative, summarized to a comprehensive guide. We developed our own FL infrastructure within the German Radiological Cooperative Network (RACOON) and demonstrated its functionality by training FL models on lung pathology segmentation tasks across six university hospitals. We extensively evaluated FL against less complex alternatives in three distinct evaluation scenarios. Results: The proposed guide outlines essential steps, identified hurdles, and proposed solutions for establishing successful FL initiatives conducting real-world experiments. Our experimental results show that FL outperforms less complex alternatives in all evaluation scenarios, justifying the effort required to translate FL into real-world applications. Discussion & Conclusion: Our proposed guide aims to aid future FL researchers in circumventing pitfalls and accelerating translation of FL into radiological applications. Our results underscore the value of efforts needed to translate FL into real-world applications by demonstrating advantageous performance over alternatives, and emphasize the importance of strategic organization, robust management of distributed data and infrastructure in real-world settings.

This paper explores the potential of large language models (LLMs) to make the Aeronautical Regulations of Colombia (RAC) more accessible. Given the complexity and extensive technicality of the RAC, this study introduces a novel approach to simplifying these regulations for broader understanding. By developing the first-ever RAC database, which contains 24,478 expertly labeled question-and-answer pairs, and fine-tuning LLMs specifically for RAC applications, the paper outlines the methodology for dataset assembly, expert-led annotation, and model training. Utilizing the Gemma1.1 2b model along with advanced techniques like Unsloth for efficient VRAM usage and flash attention mechanisms, the research aims to expedite training processes. This initiative establishes a foundation to enhance the comprehensibility and accessibility of RAC, potentially benefiting novices and reducing dependence on expert consultations for navigating the aviation industry's regulatory landscape. You can visit the dataset (https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1) and the model (https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.