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While traditional earphones primarily offer private audio spaces, so-called "earables" emerged to offer a variety of sensing capabilities. Pioneering platforms like OpenEarable have introduced novel sensing platforms targeted at the ears, incorporating various sensors. The proximity of the ears to the eyes, brain, and facial muscles has also sparked investigation into sensing biopotentials. However, currently there is no platform available that is targeted at the ears to sense biopotentials. To address this gap, we introduce OpenEarable ExG - an open-source hardware platform designed to measure biopotentials in and around the ears. OpenEarable ExG can be freely configured and has up to 7 sensing channels. We initially validate OpenEarable ExG in a study with a left-right in-ear dual-electrode montage setup with 3 participants. Our results demonstrate the successful detection of smooth pursuit eye movements via Electrooculography (EOG), alpha brain activity via Electroencephalography (EEG), and jaw clenching via Electromyography (EMG). OpenEarable ExG is part of the OpenEarable initiative and is fully open-source under MIT license., Comment: 5 pages, 3 figures

Many socio-economic systems require positive economic growth rates to function properly. Given uncertainty about future growth rates and increasing evidence that economic growth is a driver of social and environmental crises, these growth dependencies pose serious societal challenges. In recent years, more and more researchers have thus tried to identify growth-dependent systems and develop policies to reduce their growth dependence. However, the concept of 'growth dependence' still lacks a consistent definition and operationalization, which impedes more systematic empirical and theoretical research. This article proposes a simple but powerful framework for defining and operationalizing the concept of 'growth dependence' across socio-economic systems. We provide a general definition consisting of four components that can be specified for different empirical cases: (1) the system under investigation, (2) the unit of measurement of growth, (3) the level of growth and (4) the relevant functions or properties of the system under investigation. According to our general definition, a socio-economic system is growth-dependent if it requires a long-term positive growth rate in terms of a unit of economic measurement to maintain all its functions or properties that are relevant within the chosen normative framework. To illustrate the usefulness of our scheme, we apply it to three areas at the heart of the existing literature on growth dependence: employment, social insurance systems and public finance. These case studies demonstrate that whether or not a system is growth-dependent hinges not only on the empirical properties of the system itself but also on the specification of the concept of growth dependence. Our framework enables coherent, robust and effective definitions and research questions, fostering comparability of findings across different cases and disciplines., Comment: 24 pages, 2 figures, 2 tables

The generation of entangled photons from radiative cascades has enabled milestone experiments in quantum information science with several applications in photonic quantum technologies. Significant efforts are being devoted to pushing the performances of near-deterministic entangled-photon sources based on single quantum emitters often embedded in photonic cavities, so to boost the flux of photon pairs. The general postulate is that the emitter generates photons in a nearly maximally entangled state of polarization, ready for application purposes. Here, we demonstrate that this assumption is unjustified. We show that in radiative cascades there exists an interplay between photon polarization and emission wavevector, strongly affecting quantum correlations when emitters are embedded in micro-cavities. We discuss how the polarization entanglement of photon pairs from a biexciton-exciton cascade in quantum dots strongly depends on their propagation wavevector, and it can even vanish for large emission angles. Our experimental results, backed by theoretical modelling, yield a brand-new understanding of cascaded emission for various quantum emitters. In addition, our model provides quantitative guidelines for designing optical microcavities that retain both a high degree of entanglement and collection efficiency, moving the community one step further towards an ideal source of entangled photons for quantum technologies.

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-dimensional ODEs, the influence of such 'ghosts' on the temporal behavior of the system, namely delayed transitions, has been studied previously. We consider spatio-temporal PDEs and characterize the phenomenon of ghosts by defining representative state-space structures, which we term 'ghost states,' as minima of appropriately chosen cost functions. Using recently developed variational methods, we can compute and parametrically continue ghost states of equilibria, periodic orbits, and other invariant solutions. We demonstrate the relevance of ghost states to the observed dynamics in various nonlinear systems including chaotic maps, the Lorenz ODE system, the spatio-temporally chaotic Kuramoto-Sivashinsky PDE, the buckling of an elastic arc, and 3D Rayleigh-B\'enard convection.

Transformer-based Super-Resolution (SR) models have recently advanced image reconstruction quality, yet challenges remain due to computational complexity and an over-reliance on large patch sizes, which constrain fine-grained detail enhancement. In this work, we propose TaylorIR to address these limitations by utilizing a patch size of 1x1, enabling pixel-level processing in any transformer-based SR model. To address the significant computational demands under the traditional self-attention mechanism, we employ the TaylorShift attention mechanism, a memory-efficient alternative based on Taylor series expansion, achieving full token-to-token interactions with linear complexity. Experimental results demonstrate that our approach achieves new state-of-the-art SR performance while reducing memory consumption by up to 60% compared to traditional self-attention-based transformers.

Advancements in computing power have made it possible to numerically simulate large-scale fluid-mechanical and/or particulate systems, many of which are integral to core industrial processes. Among the different numerical methods available, the discrete element method (DEM) provides one of the most accurate representations of a wide range of physical systems involving granular and discontinuous materials. Consequently, DEM has become a widely accepted approach for tackling engineering problems connected to granular flows and powder mechanics. Additionally, DEM can be integrated with grid-based computational fluid dynamics (CFD) methods, enabling the simulation of chemical processes taking place, e.g., in fluidized beds. However, DEM is computationally intensive because of the intrinsic multiscale nature of particulate systems, restricting simulation duration or number of particles. Towards this end, NeuralDEM presents an end-to-end approach to replace slow numerical DEM routines with fast, adaptable deep learning surrogates. NeuralDEM is capable of picturing long-term transport processes across different regimes using macroscopic observables without any reference to microscopic model parameters. First, NeuralDEM treats the Lagrangian discretization of DEM as an underlying continuous field, while simultaneously modeling macroscopic behavior directly as additional auxiliary fields. Second, NeuralDEM introduces multi-branch neural operators scalable to real-time modeling of industrially-sized scenarios - from slow and pseudo-steady to fast and transient. Such scenarios have previously posed insurmountable challenges for deep learning models. Notably, NeuralDEM faithfully models coupled CFD-DEM fluidized bed reactors of 160k CFD cells and 500k DEM particles for trajectories of 28s. NeuralDEM will open many new doors to advanced engineering and much faster process cycles., Comment: Project page: https://nx-ai.github.io/NeuralDEM/

Inherently interpretable machine learning (IML) models provide valuable insights for clinical decision-making but face challenges when features have missing values. Classical solutions like imputation or excluding incomplete records are often unsuitable in applications where values are missing at test time. In this work, we conducted a survey with 71 clinicians from 29 trauma centers across France, including 20 complete responses to study the interaction between medical professionals and IML applied to data with missing values. This provided valuable insights into how missing data is interpreted in clinical machine learning. We used the prediction of hemorrhagic shock as a concrete example to gauge the willingness and readiness of the participants to adopt IML models from three classes of methods. Our findings show that, while clinicians value interpretability and are familiar with common IML methods, classical imputation techniques often misalign with their intuition, and that models that natively handle missing values are preferred. These results emphasize the need to integrate clinical intuition into future IML models for better human-computer interaction., Comment: Findings paper presented at Machine Learning for Health (ML4H) symposium 2024, December 15-16, 2024, Vancouver, Canada, 13 pages

Machine learning is becoming increasingly popular in the context of particle physics. Supervised learning, which uses labeled Monte Carlo (MC) simulations, remains one of the most widely used methods for discriminating signals beyond the Standard Model. However, this paper suggests that supervised models may depend excessively on artifacts and approximations from Monte Carlo simulations, potentially limiting their ability to generalize well to real data. This study aims to enhance the generalization properties of supervised models by reducing the sharpness of local minima. It reviews the application of four distinct white-box adversarial attacks in the context of classifying Higgs boson decay signals. The attacks are divided into weight space attacks, and feature space attacks. To study and quantify the sharpness of different local minima this paper presents two analysis methods: gradient ascent and reduced Hessian eigenvalue analysis. The results show that white-box adversarial attacks significantly improve generalization performance, albeit with increased computational complexity., Comment: 10 pages, 4 figures, 8 tables, 3 algorithms, to be published in Physical Review D (PRD), presented at the ML4Jets 2024 conference

QAOA is a quantum algorithm for solving combinatorial optimization problems. It is capable of searching for the minimizing solution vector $x$ of a QUBO problem $x^TQx$. The number of two-qubit CNOT gates in the QAOA circuit scales linearly in the number of non-zero couplings of $Q$ and the depth of the circuit scales accordingly. Since CNOT operations have high error rates it is crucial to develop algorithms for reducing their number. We, therefore, present the concept of \textit{semi-symmetries} in QUBO matrices and an algorithm for identifying and factoring them out into ancilla qubits. \textit{Semi-symmetries} are prevalent in QUBO matrices of many well-known optimization problems like \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, \textit{Vertex Cover} and \textit{Graph Isomorphism}, among others. We theoretically show that our modified QUBO matrix $Q_{mod}$ describes the same energy spectrum as the original $Q$. Experiments conducted on the five optimization problems mentioned above demonstrate that our algorithm achieved reductions in the number of couplings by up to $49\%$ and in circuit depth by up to $41\%$.

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply connected, topological 4-manifolds can be naturally represented by a Kirby diagram consisting only of 2-handles. This representation is used as input for our algorithm. Along the way, we develop an algorithm to compute the Kirby-Siebenmann invariant of a closed, simply connected, topological 4-manifold from any of its Kirby diagrams and describe an algorithm that decides whether or not two intersection forms are isometric. In a slightly different direction, we discuss the decidability of the stable classification of smooth manifolds with more general fundamental groups. Here we show that there exists an algorithm that takes as input two closed, oriented, smooth 4-manifolds with fundamental groups isomorphic to a finite group with cyclic Sylow 2-subgroup, an infinite cyclic group, or a group of geometric dimension at most 3 (in the latter case we additionally assume that the universal covers of both 4-manifolds are not spin), and decides whether or not these two 4-manifolds are orientation-preserving stably diffeomorphic., Comment: 24 pages, 1 Figure

We investigate the formation of bound states of non-relativistic dark matter particles subject to long-range interactions through radiative capture. The initial scattering and final bound states are described by Coulomb potentials with different strengths, as relevant for non-abelian gauge interactions or theories featuring charged scalars. For bound states with generic quantum numbers $n$ and $\ell$, we provide closed-form expressions for the bound-state formation (BSF) cross sections of monopole, dipole and quadrupole transitions, and of arbitrary multipole order when $\ell=n-1$. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For $\ell=n-1\gg 1$, we show that the BSF cross section for each single bound state violates the perturbative unitarity bound in the vicinity of a certain critical initial velocity, and provide an interpretation in terms of a smooth matching of classical trajectories. When summing the BSF cross section over all possible bound states in the final state, this leads to a unitarity violation below a certain velocity, but within the validity range of the weakly coupled non-relativistic description. We identify an effectively strong interaction as the origin of this unitarity violation, which is caused by an "anomalously" large overlap of scattering and bound-state wave functions in Coulomb potentials of different strength., Comment: 38p

We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often rely on standard metrics to define geometric relationships in data, which may fail to capture the underlying structure of complex data sets. $\texttt{LAMINAR}$ addresses this by using a continuous-normalising-flow and inverse-transform-sampling to define a Riemannian manifold in the data space without the need for the user to specify a metric over the data a-priori. The result is a locally-adaptive-metric that produces structurally-informative density-based distances. We demonstrate the utility of $\texttt{LAMINAR}$ by comparing its output to the Euclidean metric for structured data sets., Comment: Accepted to the NeurIPS 2024 Machine Learning and the Physical Sciences workshop. 6 pages, 6 figures

We propose a quantum error mitigation scheme for single-qubit measurement errors, particularly suited for one-way quantum computation. Contrary to well established error mitigation methods for circuit-based quantum computation, that require to run the circuits several times, our method is capable of mitigating measurement errors in real-time, during the processing measurements of the one-way computation. For that, an ancillary qubit register is entangled with the to-be-measured qubit and additionally measured afterwards. By using a voting protocol on all measurement outcomes, occurring measurement errors can be mitigated in real-time while the one-way computation continues. We provide an analytical expression for the probability to detect a measurement error in dependency of the error rate and the number of ancilla qubits. From this, we derive an estimate of the ancilla register size for a given measurement error rate and a required success probability to detect a measurement error. Additionally, we also consider the CNOT gate error in our mitigation method and investigate how this influences the probability to detect a measurement error. Finally, we show in proof-of-principle simulations, also considering a hardware noise model, that our method is capable of reducing the measurement errors significantly in a one-way quantum computation with only a small number of ancilla qubits., Comment: 11 pages, 10 figures

The standard cosmological model is sufficiently well constrained that precise estimates can be provided for the redshift of various physically defined times in the chronology of the Universe. For example, it is well known that matter-radiation equality, recombination and reionisation happen at redshifts of around 3000, 1000 and 10, respectively, and these can be specified more precisely by fitting to data. What is less well known are the times in years (and their uncertainties) for these and other epochs in the history of the Universe. Here we provide precise time determinations for six epochs in cosmological history within the standard model, using data from the Planck satellite. Our main results are illustrated in a figure., Comment: 11 pages, 2 figures, 2 tables, data available at https://doi.org/10.5281/zenodo.14054334

Squeezed light plays a vital role in quantum information processing. By nature, it is highly sensitive, which presents significant practical challenges, particularly in remote detection, traditionally requiring complex systems such as active phase locking, clock synchronization, and polarization control. Here, we propose and demonstrate an asynchronous detection method for squeezed light that eliminates the need for these complex systems. By employing radio-frequency heterodyne detection with a locally generated local oscillator and applying a series of digital unitary transformations, we successfully reconstruct squeezed states of light. We validate the feasibility of our approach in two key applications: the distribution of squeezed light over a 10 km fiber channel, and secure quantum key distribution between two labs connected via deployed fiber based on continuous variables using squeezed vacuum states without active modulation. This demonstrates a practical digital reconstruction method for squeezed light, opening new avenues for practical distributed quantum sensing networks and high-performance and long-distance quantum communication using squeezed states and standard telecom technology.

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large Hilbert spaces. Hence, finding annealing protocols by variation ultimately appears to be difficult. Similarly, the adiabatic theorem fails on hard problem instances with first-order quantum phase transitions. Here, we show how to use the spin coherent-state path integral to shape the geometry of quantum adiabatic evolution, leading to annealing protocols at polynomial overhead that provide orders-of-magnitude improvements in the probability to measure optimal solutions, relative to linear protocols. These improvements are not obtained on a controllable toy problem but on randomly generated hard instances (Sherrington-Kirkpatrick and Maximum 2-Satisfiability), making them generic and robust. Our method works for large systems and may thus be used to improve the performance of state-of-the-art quantum devices., Comment: 12 pages, 11 figures

Warm dense matter (WDM) plays an important role in astrophysical objects and technological applications, but the rigorous diagnostics of corresponding experiments is notoriously difficult. In this work, we present a model-free analysis of x-ray Thomson scattering (XRTS) measurements at multiple scattering angles. Specifically, we analyze scattering data that have been collected for isochorically heated graphite at the Linac Coherent Light Source (LCLS). Overall, we find good consistency in the extracted temperature between small and large scattering angles, whereas possible signatures of non-equilibrium may be hidden by the source function, and by the available dynamic spectral range. The present proof-of-principle study directly points to improved experimental set-ups for equation-of-state measurements and for the model-free study of relaxation times.

Higher-point functions in N = 4 super Yang-Mills theory can be constructed using integrability by triangulating the surfaces on which Feynman graphs would be drawn. It remains hard to analytically compute the necessary re-gluing of the tiles by virtual particles. We propose a new approach to study a series of residues encountered in the two-particle gluing of the planar one-loop five-point function of stress tensor multiplets. After exposing the twisted period nature of the integral functions, we employ intersection theory to derive canonical differential equations and present a solution., Comment: 11 pages, 1 figure, LaTeX

A common challenge in continual learning (CL) is catastrophic forgetting, where the performance on old tasks drops after new, additional tasks are learned. In this paper, we propose a novel framework called ReCL to slow down forgetting in CL. Our framework exploits an implicit bias of gradient-based neural networks due to which these converge to margin maximization points. Such convergence points allow us to reconstruct old data from previous tasks, which we then combine with the current training data. Our framework is flexible and can be applied on top of existing, state-of-the-art CL methods to slow down forgetting. We further demonstrate the performance gain from our framework across a large series of experiments, including different CL scenarios (class incremental, domain incremental, task incremental learning) different datasets (MNIST, CIFAR10), and different network architectures. Across all experiments, we find large performance gains through ReCL. To the best of our knowledge, our framework is the first to address catastrophic forgetting by leveraging models in CL as their own memory buffers.

We introduce a nonstabilizerness monotone which we name basis-minimised stabilizerness asymmetry (BMSA). It is based on the notion of $G$-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group $G$. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures known in the literature. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones., Comment: 19 pages, 3 figures

Developing robust drone detection systems is often constrained by the limited availability of large-scale annotated training data and the high costs associated with real-world data collection. However, leveraging synthetic data generated via game engine-based simulations provides a promising and cost-effective solution to overcome this issue. Therefore, we present SynDroneVision, a synthetic dataset specifically designed for RGB-based drone detection in surveillance applications. Featuring diverse backgrounds, lighting conditions, and drone models, SynDroneVision offers a comprehensive training foundation for deep learning algorithms. To evaluate the dataset's effectiveness, we perform a comparative analysis across a selection of recent YOLO detection models. Our findings demonstrate that SynDroneVision is a valuable resource for real-world data enrichment, achieving notable enhancements in model performance and robustness, while significantly reducing the time and costs of real-world data acquisition. SynDroneVision will be publicly released upon paper acceptance., Comment: Accepted at the 2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)

Nearly fifty years ago, Roberts (1978) postulated that Earth's magnetic field, which is generated by turbulent motions of liquid metal in its outer core, likely results from a subcritical dynamo instability characterised by a dominant balance between Coriolis, pressure and Lorentz forces. Here we numerically explore the generation of subcritical geomagnetic fields using techniques from optimal control and dynamical systems theory to uncover the nonlinear dynamical landscape underlying dynamo action. Through nonlinear optimisation, via direct-adjoint looping, we identify the minimal seed - the smallest magnetic field that attracts to a nonlinear dynamo solution. Additionally, using the Newton-hookstep algorithm, we converge stable and unstable travelling wave solutions to the governing equations. By combining these two techniques, complex nonlinear pathways between attracting states are revealed, providing insight into a potential subcritical origin of the geodynamo. This paper showcases these methods on the widely studied benchmark of Christensen et al. (2001), laying the foundations for future studies in more extreme and realistic parameter regimes. We show that the minimal seed reaches a nonlinear dynamo solution by first attracting to an unstable travelling wave solution, which acts as an edge state separating a hydrodynamic solution from a magnetohydrodynamic one. Furthermore, by carefully examining the choice of cost functional, we establish a robust optimisation procedure that can systematically locate dynamo solutions on short time horizons with no prior knowledge of its structure., Comment: 21 pages, 8 figures

The joint implementation of Federated learning (FL) and Explainable artificial intelligence (XAI) will allow training models from distributed data and explaining their inner workings while preserving important aspects of privacy. Towards establishing the benefits and tensions associated with their interplay, this scoping review maps those publications that jointly deal with FL and XAI, focusing on publications where an interplay between FL and model interpretability or post-hoc explanations was found. In total, 37 studies met our criteria, with more papers focusing on explanation methods (mainly feature relevance) than on interpretability (mainly algorithmic transparency). Most works used simulated horizontal FL setups involving 10 or fewer data centers. Only one study explicitly and quantitatively analyzed the influence of FL on model explanations, revealing a significant research gap. Aggregation of interpretability metrics across FL nodes created generalized global insights at the expense of node-specific patterns being diluted. 8 papers addressed the benefits of incorporating explanation methods as a component of the FL algorithm. Studies using established FL libraries or following reporting guidelines are a minority. More quantitative research and structured, transparent practices are needed to fully understand their mutual impact and under which conditions it happens., Comment: 16 pages, 11 figures, submitted in IEEE Trans. Knowledge and Data Engineering

Neural fields or implicit neural representations (INRs) have attracted significant attention in machine learning and signal processing due to their efficient continuous representation of images and 3D volumes. In this work, we build on INRs and introduce a coordinate-based local processing framework for solving imaging inverse problems, termed LoFi (Local Field). Unlike conventional methods for image reconstruction, LoFi processes local information at each coordinate \textit{separately} by multi-layer perceptrons (MLPs), recovering the object at that specific coordinate. Similar to INRs, LoFi can recover images at any continuous coordinate, enabling image reconstruction at multiple resolutions. With comparable or better performance than standard CNNs for image reconstruction, LoFi achieves excellent generalization to out-of-distribution data and memory usage almost independent of image resolution. Remarkably, training on $1024 \times 1024$ images requires just 3GB of memory -- over 20 times less than the memory typically needed by standard CNNs. Additionally, LoFi's local design allows it to train on extremely small datasets with less than 10 samples, without overfitting or the need for regularization or early stopping. Finally, we use LoFi as a denoising prior in a plug-and-play framework for solving general inverse problems to benefit from its continuous image representation and strong generalization. Although trained on low-resolution images, LoFi can be used as a low-dimensional prior to solve inverse problems at any resolution. We validate our framework across a variety of imaging modalities, from low-dose computed tomography to radio interferometric imaging.

The Jordan-Schwinger map is widely employed to switch between bosonic or fermionic mode operators and spin observables, with numerous applications ranging from quantum field theories of magnetism and ultracold quantum gases to quantum optics. While the construction of observables obeying the algebra of spin operators across multiple modes is straightforward, a mapping between bosonic or fermionic Fock states and spin states has remained elusive beyond the two-mode case. Here, we generalize the Jordan-Schwinger map by algorithmically constructing complete sets of spin states over several bosonic or fermionic modes, allowing one to describe arbitrary multi-mode systems faithfully in terms of spins. As a byproduct, we uncover a deep link between the degeneracy of multi-mode spin states in the bosonic case and Gaussian polynomials. We demonstrate the feasibility of our approach by deriving explicit relations between arbitrary three-mode Fock and spin states, which provide novel interpretations of the genuinely tripartite entangled GHZ and W state classes., Comment: 14 + 3 pages; comments welcome!

The recently derived Fourier--Matsubara expansion of imaginary--time correlation functions comprises an exact result of linear response theory for finite-temperature quantum many-body systems. In its density--density version, the expansion facilitates systematic comparisons between quasi-exact \emph{ab initio} path integral Monte Carlo simulations and approximate dielectric formalism schemes at the level of the imaginary--time (density--density) correlation functions and the dynamic Matsubara local field corrections. On this theoretical basis, the dynamic properties of the quantum version of the Singwi--Tosi--Land--Sj\"olander scheme are analyzed for the paramagnetic warm dense uniform electron gas. The marginal improvement compared to the semi-classical version of the Singwi--Tosi--Land--Sj\"olander scheme is attributed to the weak Matsubara order dependence of the approximate dynamic Matsubara local field correction. The evaluation of the ideal density response function at the non-interacting occupation numbers is identified to constitute a general deficiency of the dielectric formalism, which calls for a reformulation in future works., Comment: 26 pages, 4 figures

Let $s \in (0, 1]$ and $N > 2s$. It is known that positive solutions to the (fractional) fast diffusion equation $\partial_t u + (-\Delta)^s (u^\frac{N-2s}{N+2s}) = 0$ on $(0, \infty) \times \mathbb R^N$ with regular enough initial datum extinguish after some finite time $T_* > 0$. More precisely, one has $\frac{u(t,\cdot)}{U_{T_*, z, \lambda}(t,\cdot)} - 1 =o(1)$ as $t \to T_*^-$ for a certain extinction profile $U_{T_*, z, \lambda}$, uniformly on $\mathbb R^N$. In this paper, we prove the quantitative bound $ \frac{u(t,\cdot)}{U_{T_*, z, \lambda}(t,\cdot)} - 1 = \mathcal O( (T_*-t)^\frac{N+2s}{N-2s+2})$, in a natural weighted energy norm. The main point here is that the exponent $\frac{N+2s}{N-2s+2}$ is sharp. This is the analogue of a recent result by Bonforte and Figalli (CPAM, 2021) valid for $s = 1$ and bounded domains $\Omega \subset \mathbb R^N$. Our result is new also in the local case $s = 1$. The main obstacle we overcome is the degeneracy of an associated linearized operator, which generically does not occur in the bounded domain setting. For a smooth bounded domain $\Omega \subset \mathbb R^N$, we prove similar results for positive solutions to $\partial_t u + (-\Delta)^s (u^m) = 0$ on $(0, \infty) \times \Omega$ with Dirichlet boundary conditions when $s \in (0,1)$ and $m \in (\frac{N-2s}{N+2s}, 1)$, under a non-degeneracy assumption on the stationary solution. An important step here is to prove the convergence of the relative error, which is new for this case., Comment: 33 pages, comments welcome!

Earphones can give access to sensitive information via voice assistants which demands security methods that prevent unauthorized use. Therefore, we developed EarCapAuth, an authentication mechanism using 48 capacitive electrodes embedded into the soft silicone eartips of two earables. For evaluation, we gathered capactive ear canal measurements from 20 participants in 20 wearing sessions (12 at rest, 8 while walking). A per user classifier trained for authentication achieves an EER of 7.62% and can be tuned to a FAR (False Acceptance Rate) of 1% at FRR (False Rejection Rate) of 16.14%. For identification, EarCapAuth achieves 89.95%. This outperforms some earable biometric principles from related work. Performance under motion slightly decreased to 9.76% EER for authentication and 86.40% accuracy for identification. Enrollment can be performed rapidly with multiple short earpiece insertions and a biometric decision is made every 0.33s. In the future, EarCapAuth could be integrated into high-resolution brain sensing electrode tips.

We live in a world full of networks where our economy, our communication, and even our social life crucially depends on them. These networks typically emerge from the interaction of many entities, which is why researchers study agent-based models of network formation. While traditionally static networks with a fixed set of links were considered, a recent stream of works focuses on networks whose behavior may change over time. In particular, Bil\`o et al. (IJCAI 2023) recently introduced a game-theoretic network formation model that embeds temporal aspects in networks. More precisely, a network is formed by selfish agents corresponding to nodes in a given host network with edges having labels denoting their availability over time. Each agent strategically selects local, i.e., incident, edges to ensure temporal reachability towards everyone at low cost. In this work we set out to explore the impact of two novel conceptual features: agents are no longer restricted to creating incident edges, called the global setting, and agents might only want to ensure that they can reach a subset of the other nodes, called the terminal model. For both, we study the existence, structure, and quality of equilibrium networks. For the terminal model, we prove that many core properties crucially depend on the number of terminals. We also develop a novel tool that allows translating equilibrium constructions from the non-terminal model to the terminal model. For the global setting, we show the surprising result that equilibria in the global and the local model are incomparable and we establish a high lower bound on the Price of Anarchy of the global setting that matches the upper bound of the local model. This shows the counter-intuitive fact that allowing agents more flexibility in edge creation does not improve the quality of equilibrium networks.

We demonstrate how the composition of two unsupervised clustering algorithms, $\texttt{AstroLink}$ and $\texttt{FuzzyCat}$, makes for a powerful tool when studying galaxy formation and evolution. $\texttt{AstroLink}$ is a general-purpose astrophysical clustering algorithm built for extracting meaningful hierarchical structure from point-cloud data defined over any feature space, while $\texttt{FuzzyCat}$ is a generalised soft-clustering algorithm that propagates the dynamical effects of underlying data processes into a fuzzy hierarchy of stable fuzzy clusters. Their composition, $\texttt{FuzzyCat}$ $\circ$ $\texttt{AstroLink}$, can therefore identify a fuzzy hierarchy of astrophysically- and statistically-significant fuzzy clusters within any point-based data set whose representation is subject to changes caused by some underlying process. Furthermore, the pipeline achieves this without relying upon strong assumptions about the data, the change process, the number/importance of specific structure types, or much user input -- thereby making itself applicable to a wide range of fields in the physical sciences. We find that for the task of structurally decomposing simulated galaxies into their constituents, our context-agnostic approach has a substantial impact on the diversity and completeness of the structures extracted as well as on their relationship within the broader galactic structural hierarchy -- revealing dwarf galaxies, infalling groups, stellar streams (and their progenitors), stellar shells, galactic bulges, and star-forming regions., Comment: Accepted to the NeurIPS 2024 Machine Learning and the Physical Sciences workshop. 9 pages, 2 figures

We present an outline of the first large language model (LLM) based chatbot application in the context of patient-reported outcome measures (PROMs) for diabetic retinopathy. By utilizing the capabilities of current LLMs, we enable patients to provide feedback about their quality of life and treatment progress via an interactive application. The proposed framework offers significant advantages over the current approach, which encompasses only qualitative collection of survey data or a static survey with limited answer options. Using the PROBot LLM-PROM application, patients will be asked tailored questions about their individual challenges, and can give more detailed feedback on the progress of their treatment. Based on this input, we will use machine learning to infer conventional PROM scores, which can be used by clinicians to evaluate the treatment status. The goal of the application is to improve adherence to the healthcare system and treatments, and thus ultimately reduce cases of subsequent vision impairment. The approach needs to be further validated using a survey and a clinical study.

The Traveling Salesman Problem (TSP) in the two-dimensional Euclidean plane is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial time approximation schemes. The running time of their approximation schemes was improved by Rao and Smith [STOC 1998] to $(1/\varepsilon)^{O(1/\varepsilon)} n \log n$. Bartal and Gottlieb [FOCS 2013] gave an approximation scheme of running time $2^{(1/\varepsilon)^{O(1)}} n$, which is optimal in $n$. Recently, Kisfaludi-Bak, Nederlof, and W\k{e}grzycki [FOCS 2021] gave a $2^{O(1/\varepsilon)} n \log n$ time approximation scheme, achieving the optimal running time in $\varepsilon$ under the Gap-ETH conjecture. In our work, we give a $2^{O(1/\varepsilon)} n$ time approximation scheme, achieving the optimal running time both in $n$ and in $\varepsilon$ under the Gap-ETH conjecture.

Bak, Tang, and Wiesenfeld introduced self-organized criticality with the example of a growing sandpile that reaches then sustains a critical density. They presented the abelian sandpile as a potential model. About a decade later, Dickman, Mu\~noz, Vespignani, and Zapperi claimed that self-organizing sandpile models share their critical densities with parametrized model versions that have conventional phase transitions. Fey, Levine, and Wilson subsequently demonstrated that this fails to occur with the abelian sandpile model. However, the primary subject of Dickman et al.'s work was stochastic sandpile models, and it was widely speculated that their paradigm might still hold in that setting. To this end, we confirm a conjecture of Levine and Silvestri by providing the first rigorous proof that activated random walk in dimension one is driven directly to a critical density corresponding to a parametrized phase transition and then remains there., Comment: 12 pages

Galaxies obey a set of strict dynamical laws, which imply a close coupling between the visible matter (stars and gas) and the observed dynamics (set by dark matter in the standard cosmological context). Here we review recent results from weak gravitational lensing, which allows studying the empirical laws of galaxy dynamics out to exceedingly large radii in both late-type galaxies (LTGs) and early-type galaxies (ETGs). We focus on three laws: (1) the circular velocity curves of both LTGs and ETGs remain indefinitely flat out to several hundreds of kpc; (2) the same baryonic Tully-Fisher relation is followed by LTGs and ETGs; (3) the same radial acceleration relation (RAR) is followed by LTGs and ETGs. Combining galaxy data with Solar System data, the RAR covers about 16 orders of magnitude in the Newtonian baryonic acceleration. Remarkably, these empirical facts were predicted a priori by MOND., Comment: Invited review for the IAU General Assembly 2024, Focus Meeting 9 (6 pages, 3 figures)

Recent advances in artificial intelligence (AI) have produced systems capable of increasingly sophisticated performance on cognitive tasks. However, AI systems still struggle in critical ways: unpredictable and novel environments (robustness), lack of transparency in their reasoning (explainability), challenges in communication and commitment (cooperation), and risks due to potential harmful actions (safety). We argue that these shortcomings stem from one overarching failure: AI systems lack wisdom. Drawing from cognitive and social sciences, we define wisdom as the ability to navigate intractable problems - those that are ambiguous, radically uncertain, novel, chaotic, or computationally explosive - through effective task-level and metacognitive strategies. While AI research has focused on task-level strategies, metacognition - the ability to reflect on and regulate one's thought processes - is underdeveloped in AI systems. In humans, metacognitive strategies such as recognizing the limits of one's knowledge, considering diverse perspectives, and adapting to context are essential for wise decision-making. We propose that integrating metacognitive capabilities into AI systems is crucial for enhancing their robustness, explainability, cooperation, and safety. By focusing on developing wise AI, we suggest an alternative to aligning AI with specific human values - a task fraught with conceptual and practical difficulties. Instead, wise AI systems can thoughtfully navigate complex situations, account for diverse human values, and avoid harmful actions. We discuss potential approaches to building wise AI, including benchmarking metacognitive abilities and training AI systems to employ wise reasoning. Prioritizing metacognition in AI research will lead to systems that act not only intelligently but also wisely in complex, real-world situations., Comment: 26 pages, 1 figure, 2 tables

As tools for designing and manufacturing hardware become more accessible, smaller producers can develop and distribute novel hardware. However, there aren't established tools to support end-user hardware troubleshooting or routine maintenance. As a result, technical support for hardware remains ad-hoc and challenging to scale. Inspired by software troubleshooting workflows like StackOverflow, we propose a workflow for asynchronous hardware troubleshooting: SplatOverflow. SplatOverflow creates a novel boundary object, the SplatOverflow scene, that users reference to communicate about hardware. The scene comprises a 3D Gaussian Splat of the user's hardware registered onto the hardware's CAD model. The splat captures the current state of the hardware, and the registered CAD model acts as a referential anchor for troubleshooting instructions. With SplatOverflow, maintainers can directly address issues and author instructions in the user's workspace. The instructions define workflows that can easily be shared between users and recontextualized in new environments. In this paper, we describe the design of SplatOverflow, detail the workflows it enables, and illustrate its utility to different kinds of users. We also validate that non-experts can use SplatOverflow to troubleshoot common problems with a 3D printer in a user study., Comment: Our accompanying video figure is available at: https://youtu.be/m4TKeBDuZkU

Virtual fixtures assist human operators in teleoperation settings by constraining their actions. This extended abstract introduces a novel virtual fixture formulation \emph{on surfaces} for tactile robotics tasks. Unlike existing methods, our approach constrains the behavior based on the position on the surface and generalizes it over the surface by considering the distance (metric) on the surface. Our method works directly on possibly noisy and partial point clouds collected via a camera. Given a set of regions on the surface together with their desired behaviors, our method diffuses the behaviors across the entire surface by taking into account the surface geometry. We demonstrate our method's ability in two simulated experiments (i) to regulate contact force magnitude or tangential speed based on surface position and (ii) to guide the robot to targets while avoiding restricted regions defined on the surface. All source codes, experimental data, and videos are available as open access at https://sites.google.com/view/diffusion-virtual-fixtures, Comment: Presented at ICRA@40

As the landscape of large language models expands, efficiently finetuning for specific tasks becomes increasingly crucial. At the same time, the landscape of parameter-efficient finetuning methods rapidly expands. Consequently, practitioners face a multitude of complex choices when searching for an optimal finetuning pipeline for large language models. To reduce the complexity for practitioners, we investigate transfer learning for finetuning large language models and aim to transfer knowledge about configurations from related finetuning tasks to a new task. In this work, we transfer learn finetuning by meta-learning performance and cost surrogate models for grey-box meta-optimization from a new meta-dataset. Counter-intuitively, we propose to rely only on transfer learning for new datasets. Thus, we do not use task-specific Bayesian optimization but prioritize knowledge transferred from related tasks over task-specific feedback. We evaluate our method on eight synthetic question-answer datasets and a meta-dataset consisting of 1,800 runs of finetuning Microsoft's Phi-3. Our transfer learning is superior to zero-shot, default finetuning, and meta-optimization baselines. Our results demonstrate the transferability of finetuning to adapt large language models more effectively., Comment: Accepted at NeurIPS 2024 Workshop on Adaptive Foundation Models

This paper introduces a new approach to enhance the robustness of humanoid walking under strong perturbations, such as substantial pushes. Effective recovery from external disturbances requires bipedal robots to dynamically adjust their stepping strategies, including footstep positions and timing. Unlike most advanced walking controllers that restrict footstep locations to a predefined convex region, substantially limiting recoverable disturbances, our method leverages reinforcement learning to dynamically adjust the permissible footstep region, expanding it to a larger, effectively non-convex area and allowing cross-over stepping, which is crucial for counteracting large lateral pushes. Additionally, our method adapts footstep timing in real time to further extend the range of recoverable disturbances. Based on these adjustments, feasible footstep positions and DCM trajectory are planned by solving a QP. Finally, we employ a DCM controller and an inverse dynamics whole-body control framework to ensure the robot effectively follows the trajectory.

Statistical model checking estimates probabilities and expectations of interest in probabilistic system models by using random simulations. Its results come with statistical guarantees. However, many tools use unsound statistical methods that produce incorrect results more often than they claim. In this paper, we provide a comprehensive overview of tools and their correctness, as well as of sound methods available for estimating probabilities from the literature. For expected rewards, we investigate how to bound the path reward distribution to apply sound statistical methods for bounded distributions, of which we recommend the Dvoretzky-Kiefer-Wolfowitz inequality that has not been used in SMC so far. We prove that even reachability rewards can be bounded in theory, and formalise the concept of limit-PAC procedures for a practical solution. The 'modes' SMC tool implements our methods and recommendations, which we use to experimentally confirm our results.

We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many favorable properties of the original proposal such as mitigation of the effects of barren plateaus and avoidance of NP-hard parameter optimization. By collecting the entire classical feasibility structure in a single constraint, we enlarge QCP's scope to arbitrary hard-constrained problems. Yet, we prove that the additional restriction is mild enough to still allow for an efficient parameter optimization via the formulation of a generalized eigenvalue problem (GEP) of adaptable dimension. Our rigorous proof further fills some apparent gaps in prior derivations of GEPs from parameter optimization problems. We further detail a measurement protocol for formulating the classical parameter optimization that does not require us to implement any (time evolution with a) problem-specific objective Hamiltonian or a quantum feasibility oracle. Lastly, we prove that, even under the influence of noise, QCP's parameterized ansatz class always captures the optimum attainable within its generated subcone. All of our results hold true for arbitrarily-constrained combinatorial optimization problems., Comment: 14 pages, submitted to QIP 2025

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair Discrete Variable Representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed Helium, is naturally well-suited for systems interacting with a pair-wise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Therefore, our approach relies on using the pair factorization approach in conjunction with a discretized Path Integral Ground State (PIGS) paradigm to study a chain of planar rotors interacting with a pair-wise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behaviour of the pair-DVR method near criticality. Density Matrix Renormalization Group results are used for benchmarking throughout.

Understanding the nature of dark matter in the Universe is an important goal of modern cosmology. A key method for probing this distribution is via weak gravitational lensing mass-mapping - a challenging ill-posed inverse problem where one infers the convergence field from observed shear measurements. Upcoming stage IV surveys, such as those made by the Vera C. Rubin Observatory and Euclid satellite, will provide a greater quantity and precision of data for lensing analyses, necessitating high-fidelity mass-mapping methods that are computationally efficient and that also provide uncertainties for integration into downstream cosmological analyses. In this work we introduce MMGAN, a novel mass-mapping method based on a regularised conditional generative adversarial network (GAN) framework, which generates approximate posterior samples of the convergence field given shear data. We adopt Wasserstein GANs to improve training stability and apply regularisation techniques to overcome mode collapse, issues that otherwise are particularly acute for conditional GANs. We train and validate our model on a mock COSMOS-style dataset before applying it to true COSMOS survey data. Our approach significantly outperforms the Kaiser-Squires technique and achieves similar reconstruction fidelity as alternative state-of-the-art deep learning approaches. Notably, while alternative approaches for generating samples from a learned posterior are slow (e.g. requiring $\sim$10 GPU minutes per posterior sample), MMGAN can produce a high-quality convergence sample in less than a second.

In this paper, we present an innovative iterative approach to rule learning specifically designed for (but not limited to) text-based data. Our method focuses on progressively expanding the vocabulary utilized in each iteration resulting in a significant reduction of memory consumption. Moreover, we introduce a Value of Confidence as an indicator of the reliability of the generated rules. By leveraging the Value of Confidence, our approach ensures that only the most robust and trustworthy rules are retained, thereby improving the overall quality of the rule learning process. We demonstrate the effectiveness of our method through extensive experiments on various textual as well as non-textual datasets including a use case of significant interest to insurance industries, showcasing its potential for real-world applications., Comment: 29 pages, 8 figures

The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate image reconstruction algorithms to solve the ill-posed radio interferometric imaging problem. Most state-of-the-art reconstruction methods lack trustworthy and scalable uncertainty quantification, which is critical for the rigorous scientific interpretation of radio observations. We propose an unsupervised technique based on a conformalized version of a radio-augmented equivariant bootstrapping method, which allows us to quantify uncertainties for fast reconstruction methods. Noticeably, we rely on reconstructions from ultra-fast unrolled algorithms. The proposed method brings more reliable uncertainty estimations to our problem than existing alternatives., Comment: 13 pages, 7 figures. Accepted at the Machine Learning and the Physical Sciences Workshop, NeurIPS 2024

We derive an implicit description of the image of a semialgebraic set under a birational map, provided that the denominators of the map are positive on the set. For statistical models which are globally rationally identifiable, this yields model-defining constraints which facilitate model membership testing, representation learning, and model equivalence tests. Many examples illustrate the applicability of our results. The implicit equations recover well-known Markov properties of classical graphical models, as well as other well-studied equations such as the Verma constraint. They also provide Markov properties for generalizations of these frameworks, such as colored or interventional graphical models, staged trees, and the recently introduced Lyapunov models. Under a further mild assumption, we show that our implicit equations generate the vanishing ideal of the model up to a saturation, generalizing previous results of Geiger, Meek and Sturmfels, Duarte and G\"orgen, Sullivant, and others., Comment: 25 pages, 10 figures

We present jf1uids, a one-dimensional fluid solver that can, by virtue of a geometric formulation of the Euler equations, model radially symmetric fluid problems in a conservative manner, i.e., without losing mass or energy. For spherical problems, such as ideal supernova explosions or stellar wind-blown bubble expansions, simulating only along a radial dimension drastically reduces compute and memory demands compared to a full three-dimensional method. This simplification also alleviates constraints on backpropagation through the solver. Written in JAX, jf1uids is a GPU-compatible and fully differentiable simulator. We demonstrate the advantages of this differentiable physics simulator by retrieving the wind's parameters for an adiabatic stellar wind expansion from the final fluid state using gradient descent. As part of a larger "stellar winds, cosmic rays and machine learning" research track, jf1uids serves as a solid foundation to be extended with additional physics modules, foremost cosmic rays and a neural-net powered gas-cooling surrogate and improved by higher order and more accurate numerical schemes. All code is available under https://github.com/leo1200/jf1uids/., Comment: 8 pages, 4 figures, accepted for the Machine Learning and the Physical Sciences workshop at NeurIPS 2024

The density-density correlations of the non-interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic structure factor, thermal structure factor and imaginary time correlation function. Applications of these expressions in the classical mapping approach, self-consistent dielectric formalism and equation-of-state construction are analyzed in depth., Comment: 18 pages, no figures

The FAIR data principles advocate for making scientific and research datasets 'Findable' and 'Accessible'. Yet, the sheer volume and diversity of these datasets present significant challenges. Despite advancements in data search technologies, techniques for representing search results are still traditional and inadequate, often returning extraneous results. To address these issues, we developed a knowledge graph based visual search application designed to enhance data search for Earth System Scientists. This application utilizes various chart widgets and a knowledge graph at the backend, connecting two disparate data repositories.

We study a quantum particle coupled to a scalar quantized field, such as the regularized Nelson model. We show that there are situations where the Hamiltonian of the particle alone does not have a bound state, while the particle--field Hamiltonian has a ground state. This complements results for other models such as the Pauli--Fierz model, where such results have been shown. When the uncoupled quantum particle already has a bound state, we show that this bound state persists when coupling the particle to the field, for any coupling strength. This was known previously only for small enough coupling. Our results use the functional integral representation and rely on a recent method using the Gaussian correlation inequality., Comment: 24 pages