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We propose an optimized optical vector network analyzer with automatic polarization control to stabilize the reference arm polarization throughout the sweep range. We demonstrate this technique, successfully removing the polarization-induced fading and measurement distortions in insertion loss by characterizing a 10 km multi-core fiber., Comment: Oral presentation at ECOC 2024 (Tu4A.4)- version with correction on the last sentence of paragraph 3 in the introduction

We study the evolution of populations of binary stars within massive cluster-forming regions. We simulate the formation of young massive star clusters within giant molecular clouds with masses ranging from 2 x 10$^{4}$ to 3.2 x 10$^{5}$ M$_{\odot}$. We use Torch, which couples stellar dynamics, magnetohydrodynamics, star and binary formation, stellar evolution, and stellar feedback through the AMUSE framework. We find that the binary fraction decreases during cluster formation at all molecular cloud masses. The binaries' orbital properties also change, with stronger and quicker changes in denser, more massive clouds. Most of the changes we see can be attributed to the disruption of binaries wider than 100 au, although the close binary fraction also decreases in the densest cluster-forming region. The binary fraction for O stars remains above 90%, but exchanges and dynamical hardening are ubiquitous, indicating that O stars undergo frequent few-body interactions early during the cluster formation process. Changes to the populations of binaries are a by-product of hierarchical cluster assembly: most changes to the binary population take place when the star formation rate is high and there are frequent mergers between sub-clusters in the cluster-forming region. A universal primordial binary distribution based on observed inner companions in the Galactic field is consistent with the binary populations of young clusters with resolved stellar populations, and the scatter between clusters of similar masses could be explained by differences in their formation history., Comment: 15 pages, 8 figures, 3 tables. Submitted to ApJ

The patent domain is gaining attention in natural language processing research, offering practical applications in streamlining the patenting process and providing challenging benchmarks for large language models (LLMs). However, the generation of the description sections of patents, which constitute more than 90% of the patent document, has not been studied to date. We address this gap by introducing the task of outline-guided paper-to-patent generation, where an academic paper provides the technical specification of the invention and an outline conveys the desired patent structure. We present PAP2PAT, a new challenging benchmark of 1.8k patent-paper pairs with document outlines, collected using heuristics that reflect typical research lab practices. Our experiments with current open-weight LLMs and outline-guided chunk-based generation show that they can effectively use information from the paper but struggle with repetitions, likely due to the inherent repetitiveness of patent language. We release our data and code.

Multi-view consistency remains a challenge for image diffusion models. Even within the Text-to-Texture problem, where perfect geometric correspondences are known a priori, many methods fail to yield aligned predictions across views, necessitating non-trivial fusion methods to incorporate the results onto the original mesh. We explore this issue for a Collaborative Control workflow specifically in PBR Text-to-Texture. Collaborative Control directly models PBR image probability distributions, including normal bump maps; to our knowledge, the only diffusion model to directly output full PBR stacks. We discuss the design decisions involved in making this model multi-view consistent, and demonstrate the effectiveness of our approach in ablation studies, as well as practical applications., Comment: 19 pages, 13 figures

AI Safety has become a vital front-line concern of many scientists within and outside the AI community. There are many immediate and long term anticipated risks that range from existential risk to human existence to deep fakes and bias in machine learning systems [1-5]. In this paper, we reduce the full scope and immense complexity of AI safety concerns to a trilogy of three important but tractable opportunities for advances that have the short-term potential to improve AI safety and reliability without reducing AI innovation in critical domains. In this perspective, we discuss this vision based on several case studies that already produced proofs of concept in critical ML applications in biomedical science.

Cookie paywalls allow visitors to access the content of a website only after making a choice between paying a fee (paying option) or accepting tracking (cookie option). The practice has been studied in previous research in regard to its prevalence and legal standing, but the effects of the clients' device and geographic location remain unexplored. To address these questions, this study explores the effects of three factors: 1) the clients' browser, 2) the device type (desktop or mobile), and 3) the geographic location on the presence and behavior of cookie paywalls and the handling of users' data. Using an automatic crawler on our dataset composed of 804 websites that present a cookie paywall, we observed that the presence of a cookie paywall was most affected by the geographic location of the user. We further showed that both the behavior of a cookie paywall and the processing of user data are impacted by all three factors, but no patterns of significance could be found. Finally, an additional type of paywall was discovered to be used on approximately 11% of the studied websites, coined the "double paywall", which consists of a cookie paywall complemented by another paywall once tracking is accepted., Comment: Submitted to ICISSP 2025

We consider the space of $n$-tuples of pairwise commuting elements in the Lie algebra of $U(m)$. We relate its one-point compactification to the subquotients of certain rank filtrations of connective complex $K$-theory. We also describe the variant for connective real $K$-theory., Comment: 15 pages

Recently, language models like Llama 3.1 Instruct have become increasingly capable of agentic behavior, enabling them to perform tasks requiring short-term planning and tool use. In this study, we apply refusal-vector ablation to Llama 3.1 70B and implement a simple agent scaffolding to create an unrestricted agent. Our findings imply that these refusal-vector ablated models can successfully complete harmful tasks, such as bribing officials or crafting phishing attacks, revealing significant vulnerabilities in current safety mechanisms. To further explore this, we introduce a small Safe Agent Benchmark, designed to test both harmful and benign tasks in agentic scenarios. Our results imply that safety fine-tuning in chat models does not generalize well to agentic behavior, as we find that Llama 3.1 Instruct models are willing to perform most harmful tasks without modifications. At the same time, these models will refuse to give advice on how to perform the same tasks when asked for a chat completion. This highlights the growing risk of misuse as models become more capable, underscoring the need for improved safety frameworks for language model agents.

In this note we analyze the performance of a simple root-finding algorithm in uniform attachment trees. The leaf-stripping algorithm recursively removes all leaves of the tree for a carefully chosen number of rounds. We show that, with probability $1 - \epsilon$, the set of remaining vertices contains the root and has a size only depending on $\epsilon$ but not on the size of the tree., Comment: 9 pages, 5 figures

Recent advancements in prompt engineering strategies, such as Chain-of-Thought (CoT) and Self-Discover, have demonstrated significant potential in improving the reasoning abilities of Large Language Models (LLMs). However, these state-of-the-art (SOTA) prompting strategies rely on single or fixed set of static seed reasoning modules like "think step by step" or "break down this problem" intended to simulate human approach to problem-solving. This constraint limits the flexibility of models in tackling diverse problems effectively. In this paper, we introduce Auto-Evolve, a novel framework that enables LLMs to self-create dynamic reasoning modules and downstream action plan, resulting in significant improvements over current SOTA methods. We evaluate Auto-Evolve on the challenging BigBench-Hard (BBH) dataset with Claude 2.0, Claude 3 Sonnet, Mistral Large, and GPT 4, where it consistently outperforms the SOTA prompt strategies. Auto-Evolve outperforms CoT by up to 10.4% and on an average by 7% across these four models. Our framework introduces two innovations: a) Auto-Evolve dynamically generates reasoning modules for each task while aligning with human reasoning paradigm, thus eliminating the need for predefined templates. b) We introduce an iterative refinement component, that incrementally refines instruction guidance for LLMs and helps boost performance by average 2.8% compared to doing it in a single step., Comment: Accepted at EMNLP 2024

Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard PSF subtraction methods use techniques based on a low-rank approximation to separate the rotating planet signal from the quasi-static speckles, and rely on signal-to-noise ratio maps to detect the planet. These steps do not interact or feed each other, leading to potential limitations in the accuracy and efficiency of exoplanet detection. We aim to develop a novel approach that iteratively finds the flux of the planet and the low-rank approximation of quasi-static signals, in an attempt to improve upon current PSF subtraction techniques. In this study, we extend the standard L2 norm minimization paradigm to an L1 norm minimization framework to better account for noise statistics in the high contrast images. Then, we propose a new method, referred to as Alternating Minimization Algorithm with Trajectory, that makes a more advanced use of estimating the low-rank approximation of the speckle field and the planet flux by alternating between them and utilizing both L1 and L2 norms. For the L1 norm minimization, we propose using L1 norm low-rank approximation, a low-rank approximation computed using an exact block-cyclic coordinate descent method, while we use randomized singular value decomposition for the L2 norm minimization. Additionally, we enhance the visibility of the planet signal using a likelihood ratio as a postprocessing step. Numerical experiments performed on a VLT/SPHERE-IRDIS dataset show the potential of AMAT to improve upon the existing approaches in terms of higher S/N, sensitivity limits, and ROC curves. Moreover, for a systematic comparison, we used datasets from the exoplanet data challenge to compare our algorithm to other algorithms in the challenge, and AMAT with likelihood ratio map performs better than most algorithms tested on the exoplanet data challenge., Comment: Submitted to A&A, 20 pages, 20 figures

Massive stars are predominantly born in stellar associations or clusters. Their radiation fields, stellar winds, and supernovae strongly impact their local environment. In the first few million years of a cluster's life, massive stars are dynamically ejected running away from the cluster at high speed. However, the production rate of dynamically ejected runaways is poorly constrained. Here we report on a sample of 55 massive runaway stars ejected from the young cluster R136 in the Large Magellanic Cloud. Astrometric analysis with Gaia reveals two channels of dynamically ejected runaways. The first channel ejects massive stars in all directions and is consistent with dynamical interactions during and after the birth of R136. The second channel launches stars in a preferred direction and may be related to a cluster interaction. We find that 23-33% of the most luminous stars initially born in R136 are runaways. Model predictions have significantly underestimated the dynamical escape fraction of massive stars. Consequently, their role in shaping and heating the interstellar and galactic medium, along with their role in driving galactic outflows, is far more important than previously thought., Comment: Published in Nature on 2024 October 09. 39 pages, 17 figures

High redshift observations of 10$^9$ M$_\odot$ supermassive black holes (SMBHs) at $z \sim7$ and `Little Red Dots' that may host overmassive black holes at $z>4$ suggests the existence of so-called heavy seeds (>1000 M$_\odot$) in the early Universe. Recent work has suggested that the rapid assembly of halos may be the key to forming heavy seeds early enough in the Universe to match such observations without the need for extreme radiation fields or dark matter streaming velocities. We perform simulations of BH seed formation in 4 distinct idealised halo collapse scenarios; an isolated 10$^6$ M$_\odot$ minihalo, an isolated 10$^7$ M$_\odot$ atomic halo, the direct collision of two 10$^7$ M$_\odot$ halos and a fly-by collision of two 10$^7$ M$_\odot$ halos. We have shown that halo collisions create a central environment of enhanced density, inside which BH seeds can accrete at enhanced rates. For direct collisions, the gas density peaks are disrupted by the interaction, as the collisionless DM peaks pass through each other while the colliding gas is left in the center, removing the sink particle from its accretion source. When the central density peaks instead experience a fly-by interaction, the sink particle remains embedded in the dense gas and maintains enhanced accretion rates throughout the simulated period when compared to the isolated halo cases. Here the final mass of the sink particle achieved a factor of 2 greater in mass than in the isolated atomic halo case, and a factor of 3 greater than the minihalo case, reaching 10$^4$ M$_\odot$ via its 0.03 pc accretion radius. As the maximum halo mass before collapse is determined by the atomic cooling limit of a few times 10$^7$ M$_{\odot}$, the ability of halo-halo mergers to further boost accretion rates onto the central object may play a crucial role in growing SMBH seeds., Comment: Submitted to A&A

We give an exact application of a recently developed, operator-based theory of wave propagation in dispersive, time-varying media. Using this theory we find that the usual symmetry of complex conjugation plus changing the sign of the frequency, required for real valued fields, implies that the allowed propagation constants in the medium are either real valued or come in conjugate pairs. The real valued wave numbers are only present in time-varying media, implying that time variation leads to modes that are free from dissipation, even in a lossy medium. Moreover, these symmetry-unbroken waves lack a defined propagation direction. This can lead to a divergent transmission coefficient when waves are incident onto a finite, time-varying slab. The techniques used in this work present a route towards further analytic applications of this operator formalism., Comment: 23 page, 6 figures

Transformer-based large language models (LLMs) have demonstrated surprisingly robust performance across a wide range of language-related tasks, including programming language understanding and generation. In this paper, we take the first steps towards a formal investigation of using transformers as compilers from an expressive power perspective. To this end, we introduce a representative programming language, Mini-Husky, which encapsulates key features of modern C-like languages. We show that if the input code sequence has a bounded depth in both the Abstract Syntax Tree (AST) and type inference (reasonable assumptions based on the clean code principle), then the number of parameters required by transformers depends only on the logarithm of the input sequence length to handle compilation tasks, such as AST construction, symbol resolution, and type analysis. A significant technical challenge stems from the fact that transformers operate at a low level, where each layer processes the input sequence as raw vectors without explicitly associating them with predefined structure or meaning. In contrast, high-level compiler tasks necessitate managing intricate relationships and structured program information. Our primary technical contribution is the development of a domain-specific language, Cybertron, which generates formal proofs of the transformer's expressive power, scaling to address compiler tasks. We further establish that recurrent neural networks (RNNs) require at least a linear number of parameters relative to the input sequence, leading to an exponential separation between transformers and RNNs. Finally, we empirically validate our theoretical results by comparing transformers and RNNs on compiler tasks within Mini-Husky., Comment: 65 pages

ECG-gated cine imaging in breath-hold enables high-quality diagnostics in most patients, arrhythmia and inability to hold breath, however, can severely corrupt outcomes. Real-time cardiac MRI in free-breathing leverages robust and faster investigations regardless of these confounding factors. With the need for sufficient acceleration, adequate reconstruction methods, which transfer data into high quality images, are required. Undersampled spiral real-time acquisitions in free-breathing were conducted in a study with 16 healthy volunteers and 5 patients. Image reconstructions were performed using a novel score-based diffusion model, as well as a variational network and different compressed sensing approaches. The techniques were compared by means of an expert reader study, by calculating scalar metrics and difference images with respect to a segmented reference, and by a Bland-Altman analysis of cardiac functional parameters. In participants with irregular RR-cycles, spiral real-time acquisitions showed superior image quality with respect to the clinical reference standard. Reconstructions using the diffusion model, the variational network and l1-wavelets offered an overall comparable image quality, however sharpness was slightly increased by the diffusion approach. While slightly larger ejection fractions for the real-time acquisitions were exhibited with a bias of 1.6% for healthy subjects, differences in the data acquisition procedure resulted in uncertainties of 7.4%. The proposed real-time technique enables free-breathing acquisitions of spatio-temporal images with high-quality, covering the entire heart in less than one minute. Evaluation of the ejection fractions using the segmented reference can be significantly corrupted due to arrhythmias and averaging effects. Prolonged inference times of the diffusion model represent the main obstacle to overcome for clinical translation., Comment: 29 pages, 8 figures

Gaia astrometry of nearby stars is precise enough to detect the tiny displacements induced by substellar companions, but radial velocity data are needed for definitive confirmation. Here we present radial velocity follow-up observations of 28 M and K stars with candidate astrometric substellar companions, which led to the confirmation of two systems, Gaia-4b and Gaia-5b, and the refutation of 21 systems as stellar binaries. Gaia-4b is a massive planet ($M = 11.8 \pm 0.7 \:\mathrm{M_J}$) in a $P = 571.3 \pm 1.4\:\mathrm{day}$ orbit with a projected semi-major axis $a_0=0.312 \pm 0.040\:\mathrm{mas}$ orbiting a $0.644 \pm 0.02 \:\mathrm{M_\odot}$ star. Gaia-5b is a brown dwarf ($M = 20.9 \pm 0.5\:\mathrm{M_J}$) in a $P = 358.58 \pm 0.19\:\mathrm{days}$ eccentric $e=0.6412 \pm 0.0027$ orbit with a projected angular semi-major axis of $a_0 = 0.947 \pm 0.038\:\mathrm{mas}$ around a $0.34 \pm 0.03 \mathrm{M_\odot}$ star. Gaia-4b is one of the first exoplanets discovered via the astrometric technique, and is one of the most massive planets known to orbit a low-mass star., Comment: Submitted to AAS journals. 26 pages, 12 figures, 4 tables

We measure the non-linear magnetic susceptibility $\chi^{(3)}$ of the disordered quantum Ising magnet, \lihofour, and demonstrate four-wave mixing due to coherent (anti-)Stokes Raman scattering at $\sim$ 100 Hz (p$e$V) energy scales. The temperature dependence of $\chi^{(3)}$ approximately follows a $\frac{1}{T}$ form, with a high-$T$ cutoff that can be linked to dissipation in the coherent spin clusters. $\chi^{(3)}$ also decreases monotonically with a transverse field, approaching a constant offset above a few kOe, suggesting the presence of both coherent, and spontaneous Raman scattering.

We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplaciancs in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin-Li-Yau and Kr\"oger, valid for Riesz exponents $\gamma\geq 1$, extend to certain values $\gamma<1$, provided the underlying domain is convex. We also characterize the implications of a possible failure of P\'olya's conjecture for convex sets in terms of Riesz means. These findings allow us to describe the asymptotic behavior of solutions of a spectral shape optimization problem for convex sets.

When the physics is wrong, physics-informed machine learning becomes physics-misinformed machine learning. A powerful black-box model should not be able to conceal misconceived physics. We propose two criteria that can be used to assert integrity that a hybrid (physics plus black-box) model: 0) the black-box model should be unable to replicate the physical model, and 1) any best-fit hybrid model has the same physical parameter as a best-fit standalone physics model. We demonstrate them for a sample nonlinear mechanical system approximated by its small-signal linearization.

Linear high-pass phenomena matter in signal processing, circuits, and control. In nonlinear systems, however, there is no working definition of high-pass behavior. Any definition would have to agree with the existing theory on linear systems and offer concrete benefits for nonlinear systems above and beyond existing nonlinear theory. To satisfy these two requirements, we propose to define: a nonlinear input-output system is high-pass if its output is stable with respect to the derivative of the input. We first show that definition generalizes high-pass resistor-capacitor circuit analysis to accommodate nonlinear resistors. We then show that this definition generalizes the steady-state disturbance rejection property of integral feedback controllers for linear systems. The theoretical payoff is that low-frequency disturbance rejection is captured by a quantitative, non-asymptotic output cost bound. Finally, we raise theoretical questions about compositionality and noncommutativity of nonlinear operators., Comment: preprint submitted to ACC 2025

The first generation of stars (PopIII) are too dim to be observed directly and probably too short-lived to have survived for local observations. Hence, we rely on simulations and indirect observations to constrain the nature of the first stars. In this study, we calibrate the semi-analytical model A-SLOTH (Ancient Stars and Local Observables by Tracing Halos), designed for simulating star formation in the early Universe, using a likelihood function based on nine independent observables. These observables span Milky Way-specific and cosmologically representative variables, ensuring a comprehensive calibration process. This calibration methodology ensures that A-SLOTH provides a robust representation of the early Universe's star formation processes, aligning simulated values with observed benchmarks across a diverse set of parameters. The outcome of this calibration process is best-fit values and their uncertainties for 11 important parameters that describe star formation in the early Universe, such as the shape of the initial mass function (IMF) of PopIII stars or escape fractions of ionizing photons. Our best-fitting model has a PopIII IMF with a steeper slope, d$N$/d$M \propto M^{-1.77}$, than the log-flat models often proposed in the literature, and also relatively high minimum and maximum masses, $M_{\rm min} = 13.6$Msun and $M_{\rm max} = 197$Msun. However, we emphasize that the IMF-generating parameters are poorly constrained and, e.g., the IMF slope could vary from log-flat to Salpeter. We also provide data products, such as delay time distribution, bubble size distributions for ionizing and metal-enriched bubbles at high redshift, and correlation plots between all 11 input parameters. Our study contributes to understanding the formation of early stars through A-SLOTH and provides valuable insights into the intricate processes involved in the early Universe's star formation., Comment: Accepted in MNRAS, source code can be found under https://gitlab.com/thartwig/asloth

In this paper we study the solvability of the magnetohydrostatic equations with Grad-Rubin boundary conditions in general domains. Earlier results for this problem were obtained in the recent years by D. Alonso-Or\'an and J. L. L. Vel\'azquez, where particularly simple geometries were considered. In this article we develop a theory that allows to solve these boundary value problems for a larger class of domains. We will give precise applications to more physically relevant situations, like the case of the space between two circumferences or spheres and domains close to them., Comment: 60 pages, 1 figure

In the realm of dermatological diagnoses, where the analysis of dermatoscopic and microscopic skin lesion images is pivotal for the accurate and early detection of various medical conditions, the costs associated with creating diverse and high-quality annotated datasets have hampered the accuracy and generalizability of machine learning models. We propose an innovative unsupervised augmentation solution that harnesses Generative Adversarial Network (GAN) based models and associated techniques over their latent space to generate controlled semiautomatically-discovered semantic variations in dermatoscopic images. We created synthetic images to incorporate the semantic variations and augmented the training data with these images. With this approach, we were able to increase the performance of machine learning models and set a new benchmark amongst non-ensemble based models in skin lesion classification on the HAM10000 dataset; and used the observed analytics and generated models for detailed studies on model explainability, affirming the effectiveness of our solution., Comment: This preprint has been submitted to the Workshop on Synthetic Data for Computer Vision (SyntheticData4CV 2024 is a side event on 18th European Conference on Computer Vision 2024). This preprint has not undergone peer review or any post-submission improvements or corrections

The anticipation of human behavior is a crucial capability for robots to interact with humans safely and efficiently. We employ a smart edge sensor network to provide global observations along with future predictions and goal information to integrate anticipatory behavior for the control of a mobile manipulation robot. We present approaches to anticipate human behavior in the context of safe navigation and a collaborative mobile manipulation task. First, we anticipate human motion by employing projections of human trajectories from smart edge sensor network observations into the planning map of a mobile robot. Second, we anticipate human intentions in a collaborative furniture-carrying task to achieve a given goal. Our experiments indicate that anticipating human behavior allows for safer navigation and more efficient collaboration. Finally, we showcase an integrated system that anticipates human behavior and collaborates with a human to achieve a target room layout, including the placement of tables and chairs.

Stock markets are impacted by a large variety of factors including news and discussions among investors about investment opportunities. With the emergence of social media, new opportunities for having financial discussions arose. The market frenzy surrounding GameStop (GME) on the Reddit subreddit Wallstreetbets, caused financial discussion forums to receive widespread attention and it was established that Wallstreetbets played a leading role in the stock market movements of GME. Here, we present a new data set for exploring the effect of social media discussion forums on the stock market. The dataset consists of posts published on various Reddit subreddits concerning the popular meme stocks GameStop (GME), American Multi-Cinema Entertainment Holdings (AMC), and BlackBerry (BB). We document the data collection and processing steps and show that the posts and comments about these meme stocks are related to their market movements.

We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional model the problem of testing $k$-star-freeness, and more generally $k$-source-subgraph-freeness, is almost maximally hard for large $k$. We prove that this problem has almost quadratic advantage in the quantum setting. Moreover, we prove that this advantage is nearly tight, by showing a quantum lower bound using the method of dual polynomials on an intermediate problem for a new, property testing version of the $k$-collision problem that was not studied before. To illustrate that not all problems in graph property testing admit such a quantum speedup, we consider the problem of $3$-colorability in the related undirected bounded-degree model, when graphs are now undirected. This problem is maximally hard to test classically, and we show that also quantumly it requires a linear number of queries.

Interactions between emitters within an ensemble can give rise to cooperative processes that significantly alter the properties of the emitted light. One such process is superfluorescence (SF), where excited electric dipoles spontaneously couple coherently and effectively radiate as one macroscopic emitter. It requires low energetic disorder, high temporal coherence and oscillator strength, and sub-wavelength volumes of material can be sufficient. Conversely, amplified spontaneous emission (ASE) originates from an avalanche-like stimulated amplification of initially spontaneously emitted photons and does not necessitate temporally coherent interactions among the emitters, but rather requires spatially long enough light propagation within the material to harvest the optical gain. Cesium lead halide perovskite nanocrystals (NCs) are one of the very few materials where both ASE (in disordered films) and SF (in ordered assemblies) were observed, however leaving unclear whether and how these regimes could be connected. Here, we demonstrate that temperature and excitation density can drive the transition between both regimes in a thin film of giant CsPbBr3 perovskite NCs. At temperatures below 45 K, excitonic SF was observed, whereas above a transition range between 45 K and 100 K, ASE prevails, but requires increased optical excitation and emitter density. Our results work out the different collective effects present in lead halide perovskites, providing fundamental insights into cooperative phenomena and important guidance for the development of compact and bright (quantum) light sources.

Wettability of a surface depends on both surface chemistry and topography. To move a three-phase contact line, a de-pinning force needs to be applied, which is of practical importance in various applications. However, a unified understanding and description of the de-pinning force on both flat and superhydrophobic surfaces is still lacking. This study aims to bridge the existing gap in our understanding of the three-phase contact line pinning on flat and microstructured superhydrophobic surfaces. The findings indicate that a general model, based on two different pinning mechanisms, can describe the pinning force on both flat and microstructured surfaces. We compare the general model against experimental data from literature, as well as our experiments on flat and microstructured surfaces coated with a liquid-like layer of grafted polymer chains. While this theoretical framework can be useful for designing micro-engineered surfaces on which the contact line behaviour is important, it also provides a potential experimental strategy to distinguish the contribution of defects from that of molecular re-orientation to contact line pinning on a given solid material.

We consider neural networks (NNs) where the final layer is down-scaled by a fixed hyperparameter $\gamma$. Recent work has identified $\gamma$ as controlling the strength of feature learning. As $\gamma$ increases, network evolution changes from "lazy" kernel dynamics to "rich" feature-learning dynamics, with a host of associated benefits including improved performance on common tasks. In this work, we conduct a thorough empirical investigation of the effect of scaling $\gamma$ across a variety of models and datasets in the online training setting. We first examine the interaction of $\gamma$ with the learning rate $\eta$, identifying several scaling regimes in the $\gamma$-$\eta$ plane which we explain theoretically using a simple model. We find that the optimal learning rate $\eta^*$ scales non-trivially with $\gamma$. In particular, $\eta^* \propto \gamma^2$ when $\gamma \ll 1$ and $\eta^* \propto \gamma^{2/L}$ when $\gamma \gg 1$ for a feed-forward network of depth $L$. Using this optimal learning rate scaling, we proceed with an empirical study of the under-explored "ultra-rich" $\gamma \gg 1$ regime. We find that networks in this regime display characteristic loss curves, starting with a long plateau followed by a drop-off, sometimes followed by one or more additional staircase steps. We find networks of different large $\gamma$ values optimize along similar trajectories up to a reparameterization of time. We further find that optimal online performance is often found at large $\gamma$ and could be missed if this hyperparameter is not tuned. Our findings indicate that analytical study of the large-$\gamma$ limit may yield useful insights into the dynamics of representation learning in performant models., Comment: 33 Pages, 38 figures, preprint text corrected

Text-to-image (T2I) models are increasingly used in impactful real-life applications. As such, there is a growing need to audit these models to ensure that they generate desirable, task-appropriate images. However, systematically inspecting the associations between prompts and generated content in a human-understandable way remains challenging. To address this, we propose \emph{Concept2Concept}, a framework where we characterize conditional distributions of vision language models using interpretable concepts and metrics that can be defined in terms of these concepts. This characterization allows us to use our framework to audit models and prompt-datasets. To demonstrate, we investigate several case studies of conditional distributions of prompts, such as user defined distributions or empirical, real world distributions. Lastly, we implement Concept2Concept as an open-source interactive visualization tool facilitating use by non-technical end-users. Warning: This paper contains discussions of harmful content, including CSAM and NSFW material, which may be disturbing to some readers.

Direct Preference Optimization (DPO) has been widely adopted for preference alignment of Large Language Models (LLMs) due to its simplicity and effectiveness. However, DPO is derived as a bandit problem in which the whole response is treated as a single arm, ignoring the importance differences between tokens, which may affect optimization efficiency and make it difficult to achieve optimal results. In this work, we propose that the optimal data for DPO has equal expected rewards for each token in winning and losing responses, as there is no difference in token importance. However, since the optimal dataset is unavailable in practice, we propose using the original dataset for importance sampling to achieve unbiased optimization. Accordingly, we propose a token-level importance sampling DPO objective named TIS-DPO that assigns importance weights to each token based on its reward. Inspired by previous works, we estimate the token importance weights using the difference in prediction probabilities from a pair of contrastive LLMs. We explore three methods to construct these contrastive LLMs: (1) guiding the original LLM with contrastive prompts, (2) training two separate LLMs using winning and losing responses, and (3) performing forward and reverse DPO training with winning and losing responses. Experiments show that TIS-DPO significantly outperforms various baseline methods on harmlessness and helpfulness alignment and summarization tasks. We also visualize the estimated weights, demonstrating their ability to identify key token positions., Comment: 27 pages, 7 figures, 2 tables

Debate is the process of exchanging viewpoints or convincing others on a particular issue. Recent research has provided empirical evidence that the persuasiveness of an argument is determined not only by language usage but also by communicator characteristics. Researchers have paid much attention to aspects of languages, such as linguistic features and discourse structures, but combining argument persuasiveness and impact with the social personae of the audience has not been explored due to the difficulty and complexity. We have observed the impressive simulation and personification capability of ChatGPT, indicating a giant pre-trained language model may function as an individual to provide personae and exert unique influences based on diverse background knowledge. Therefore, we propose a persona knowledge-aligned framework for argument quality assessment tasks from the audience side. This is the first work that leverages the emergence of ChatGPT and injects such audience personae knowledge into smaller language models via prompt tuning. The performance of our pipeline demonstrates significant and consistent improvement compared to competitive architectures., Comment: Accepted to ECAI 2024

This work studies the problems of channel estimation and beamforming for active reconfigurable intelligent surface~(RIS)-assisted communication, incorporating the mutual coupling~(MC) effect through an electromagnetically consistent model based on scattering parameters. We first demonstrate that MC can be incorporated into a compressed sensing~(CS) estimation formulation, albeit with an increase in the dimensionality of the sensing matrix. To overcome this increased complexity, we propose a two-stage strategy. Initially, a low-complexity MC-unaware CS estimation is performed to obtain a coarse channel estimate, which is then used to implement a dictionary reduction (DR) technique, effectively reducing the dimensionality of the sensing matrices. This method achieves low complexity comparable to the conventional MC-unaware approach while providing estimation accuracy close to that of the direct MC-aware CS method. We then consider the joint optimization of RIS configuration and base station (BS) combining in an uplink single-input multiple-output system. We employ an alternating optimization strategy where the BS combiner is derived in closed form for a given RIS configuration. The primary challenge lies in optimizing the RIS configuration, as the MC effect renders the problem non-convex and intractable. To address this, we propose a novel algorithm based on the successive convex approximation (SCA) and the Neumann series. Within the SCA framework, we propose a surrogate function that rigorously satisfies both convexity and equal-gradient conditions to update the iteration direction. Numerical results validate our proposal, demonstrating that the proposed channel estimation and beamforming methods effectively manage the MC in RIS, achieving higher spectral efficiency compared to state-of-the-art approaches.

The planar Thirring model is thought to have a strongly coupled critical point for a single flavour of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterisation via an equation of state. Since the computation is numerically challenging we investigate improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte Carlo scheme, and calculations of the bilinear condensate, an equation of state, and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered., Comment: 25 pages, 10 figures

In this paper, we aim to tackle the limitation of the Adversarial Inverse Reinforcement Learning (AIRL) method in stochastic environments where theoretical results cannot hold and performance is degraded. To address this issue, we propose a novel method which infuses the dynamics information into the reward shaping with the theoretical guarantee for the induced optimal policy in the stochastic environments. Incorporating our novel model-enhanced rewards, we present a novel Model-Enhanced AIRL framework, which integrates transition model estimation directly into reward shaping. Furthermore, we provide a comprehensive theoretical analysis of the reward error bound and performance difference bound for our method. The experimental results in MuJoCo benchmarks show that our method can achieve superior performance in stochastic environments and competitive performance in deterministic environments, with significant improvement in sample efficiency, compared to existing baselines.

As climate change intensifies, the shift to cleaner energy sources becomes increasingly urgent. With wind energy production set to accelerate, reliable wind probabilistic forecasts are essential to ensure its efficient use. However, since numerical weather prediction models are computationally expensive, probabilistic forecasts are produced at resolutions too coarse to capture all mesoscale wind behaviors. Statistical downscaling, typically applied to enchance the resolution of climate model simulations, presents a viable solution with lower computational costs by learning a mapping from low-resolution (LR) variables to high-resolution (HR) meteorological variables. Leveraging deep learning, we evaluate a downscaling model based on a state-of-the-art U-Net architecture, applied to an ensemble member from a coarse-scale probabilistic forecast of wind velocity. The architecture is modified to incorporate (1) a learned grid alignment strategy to resolve LR-HR grid mismatches and (2) a processing module for multi-level atmospheric predictors. To extend the downscaling model's applicability from fixed spatial domains to the entire Canadian region, we assess a transfer learning approach. Our results show that the learned grid alignment strategy performs as well as conventional pre-processing interpolation steps and that LR wind speed at multiple levels is sufficient as a predictor, enabling a more compact architecture. Additionally, they suggest that extending to new spatial domains using transfer learning is promising, and that downscaled wind velocities demonstrate potential in improving the detection of wind power ramps, a critical phenomenon for wind energy.

We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations.

The induced conservative tidal response of self-gravitating objects in general relativity is parametrized in terms of a set of coefficients, which are commonly referred to as Love numbers. For asymptotically-flat black holes in four spacetime dimensions, the Love numbers are notoriously zero in the static regime. In this work, we show that this result continues to hold upon inclusion of nonlinearities in the theory for Schwarzschild black holes. We first solve the quadratic Einstein equations in the static limit to all orders in the multipolar expansion, including both even and odd perturbations. We show that the second-order solutions take simple analytic expressions, generically expressible in the form of finite polynomials. We then define the quadratic Love numbers at the level of the point-particle effective field theory. By performing the matching with the full solution in general relativity, we show that quadratic Love number coefficients are zero to all orders in the derivative expansion, like the linear ones., Comment: 55 pages, 3 figures

This paper provides a detailed analysis of the NeuroPiano dataset, which comprise 104 audio recordings of student piano performances accompanied with 2255 textual feedback and ratings given by professional pianists. We offer a statistical overview of the dataset, focusing on the standardization of annotations and inter-annotator agreement across 12 evaluative questions concerning performance quality. We also explore the predictive relationship between audio features and teacher ratings via machine learning, as well as annotations provided for text analysis of the responses.

The Visual Monitoring Camera (VMC) is a small imaging instrument onboard Mars Express with a field of view of ~40x30 degrees. The camera was initially intended to provide visual confirmation of the separation of the Beagle 2 lander and has similar technical specifications to a typical webcam of the 2000s. In 2007, a few years after the end of its original mission, VMC was turned on again to obtain full-disk images of Mars to be used for outreach purposes. As VMC obtained more images, the scientific potential of the camera became evident, and in 2018 the camera was given an upgraded status of a new scientific instrument, with science goals in the field of Martian atmosphere meteorology. The wide Field of View of the camera combined with the orbit of Mars Express enable the acquisition of full-disk images of the planet showing different local times, which for a long time has been rare among orbital missions around Mars. The small data volume of images also allows videos that show the atmospheric dynamics of dust and cloud systems to be obtained. This paper is intended to be the new reference paper for VMC as a scientific instrument, and thus provides an overview of the updated procedures to plan, command and execute science observations of the Martian atmosphere. These observations produce valuable science data that is calibrated and distributed to the community for scientific use.

The structure and chemistry of the dusty interstellar medium (ISM) are shaped by complex processes that depend on the local radiation field, gas composition, and dust grain properties. Of particular importance are Polycyclic Aromatic Hydrocarbons (PAHs), which emit strong vibrational bands in the mid-infrared, and play a key role in the ISM energy balance. We recently identified global correlations between PAH band and optical line ratios across three nearby galaxies, suggesting a connection between PAH heating and gas ionization throughout the ISM. In this work, we perform a census of the PAH heating -- gas ionization connection using $\sim$700,000 independent pixels that probe scales of 40--150 pc in nineteen nearby star-forming galaxies from the PHANGS survey. We find a universal relation between $\log$PAH(11.3 \mic/7.7 \mic) and $\log$([SII]/H$\alpha$) with a slope of $\sim$0.2 and a scatter of $\sim$0.025 dex. The only exception is a group of anomalous pixels that show unusually high (11.3 \mic/7.7 \mic) PAH ratios in regions with old stellar populations and high starlight-to-dust emission ratios. Their mid-infrared spectra resemble those of elliptical galaxies. AGN hosts show modestly steeper slopes, with a $\sim$10\% increase in PAH(11.3 \mic/7.7 \mic) in the diffuse gas on kpc scales. This universal relation implies an emerging simplicity in the complex ISM, with a sequence that is driven by a single varying property: the spectral shape of the interstellar radiation field. This suggests that other properties, such as gas-phase abundances, gas ionization parameter, and grain charge distribution, are relatively uniform in all but specific cases., Comment: resubmitted to ApJ after addressing referee report; Figure 12 summarizes the results

Protoplanetary disks surrounding young stars are the birth places of planets. Among them, transition disks with inner dust cavities of tens of au are sometimes suggested to host massive companions. Yet, such companions are often not detected. Some transition disks exhibit a large amount of gas inside the dust cavity and relatively high stellar accretion rates, which contradicts typical models of gas-giant-hosting systems. Therefore, we investigate whether a sequence of low-mass planets can produce cavities in the dust disk. We evolve the disks with low-mass accreting embryos in combination with 1D dust transport and 3D pebble accretion, to investigate the reduction of the pebble flux at the embryos' orbits. We vary the planet and disk properties. We find that multiple pebble-accreting planets can efficiently decrease the dust surface density, resulting in dust cavities consistent with transition disks. The number of low-mass planets necessary to sweep up all pebbles decreases with decreasing turbulent strength and is preferred when the dust Stokes number is $10^{-2}-10^{-4}$. Compared to dust rings caused by pressure bumps, those by efficient pebble accretion exhibit more extended outer edges. We also highlight the observational reflections: the transition disks with rings featuring extended outer edges tend to have a large gas content in the dust cavities and rather high stellar accretion rates. We propose that planet-hosting transition disks consist of two groups. In Group A disks, planets have evolved into gas giants, opening deep gaps in the gas disk. Pebbles concentrate in pressure maxima, forming dust rings. In Group B, multiple Neptunes (unable to open deep gas gaps) accrete incoming pebbles, causing the appearance of inner dust cavities. The morphological discrepancy of these rings may aid in distinguishing between the two groups using high-resolution ALMA observations., Comment: 12 pages, 9 figures. Accepted for publication in A&A

A central result of Marx [ToC '10] proves that there are $k$-vertex graphs $H$ of maximum degree $3$ such that $n^{o(k /\log k)}$ time algorithms for detecting colorful $H$-subgraphs would refute the Exponential-Time Hypothesis (ETH). This result is widely used to obtain almost-tight conditional lower bounds for parameterized problems under ETH. Our first contribution is a new and fully self-contained proof of this result that further simplifies a recent work by Karthik et al. [SOSA 2024]. Towards this end, we introduce a novel graph parameter, the linkage capacity $\gamma(H)$, and show with an elementary proof that detecting colorful $H$-subgraphs in time $n^{o(\gamma(H))}$ refutes ETH. Then, we use a simple construction of communication networks credited to Bene\v{s} to obtain $k$-vertex graphs of maximum degree $3$ and linkage capacity $\Omega(k / \log k)$, avoiding the use of expander graphs. We also show that every graph $H$ of treewidth $t$ has linkage capacity $\Omega(t / \log t)$, thus recovering the stronger result of Marx [ToC '10] with a simplified proof. Additionally, we obtain new tight lower bounds for certain types of patterns by analyzing their linkage capacity. For example, we prove that almost all $k$-vertex graphs of polynomial average degree $\Omega(k^{\beta})$ for some $\beta > 0$ have linkage capacity $\Theta(k)$, which implies tight lower bounds for such patterns $H$. As an application of these results, we also obtain tight lower bounds for counting small induced subgraphs having a certain property $\Phi$, improving bounds from [Roth et al., FOCS 2020].

Consider a Bellman--Harris-type branching process, in which individuals evolve independently of one another, giving birth after a random time $T$ to a random number $L$ of children. In this article, we study the asymptotic behaviour of the length of the longest branches of this branching process at time $t$, both pendant branches (corresponding to individuals still alive at time $t$) and interior branches (corresponding to individuals dead before time $t$)., Comment: 13 pages, correction of an error in the previous version of that article

Starting from the well-known relationship $|{{\mathrm{e}}}^z| = {{\mathrm{e}}}^{{\mathrm Re}(z)}$, we consider the question whether $|E_{\alpha,\beta}(z)|$ and $E_{\alpha,\beta}({\mathrm Re}(z))$ are comparable, as functions of the complex variable $z$, where $E_{\alpha,\beta}$ denotes the two-parameter Mittag-Leffler function, a generalization of the exponential function. For some ranges of the parameters $\alpha$ and $\beta$ we prove inequalities between $|E_{\alpha,\beta}(z)|$ and $E_{\alpha,\beta}({\mathrm Re}(z))$ holding globally for all $z\in \mathbb{C}$. In some other ranges of $\alpha$ and $\beta$ the same inequalities are proved to hold asymptotically, i.e. for sufficiently small or large $z$. There are moreover some values of $\alpha$ and $\beta$ for which the situation is less clear, and some conjectures, motivated by numerical observations, are proposed.

As the field of multi-agent reinforcement learning (MARL) progresses towards larger and more complex environments, achieving strong performance while maintaining memory efficiency and scalability to many agents becomes increasingly important. Although recent research has led to several advanced algorithms, to date, none fully address all of these key properties simultaneously. In this work, we introduce Sable, a novel and theoretically sound algorithm that adapts the retention mechanism from Retentive Networks to MARL. Sable's retention-based sequence modelling architecture allows for computationally efficient scaling to a large number of agents, as well as maintaining a long temporal context, making it well-suited for large-scale partially observable environments. Through extensive evaluations across six diverse environments, we demonstrate how Sable is able to significantly outperform existing state-of-the-art methods in the majority of tasks (34 out of 45, roughly 75\%). Furthermore, Sable demonstrates stable performance as we scale the number of agents, handling environments with more than a thousand agents while exhibiting a linear increase in memory usage. Finally, we conduct ablation studies to isolate the source of Sable's performance gains and confirm its efficient computational memory usage. Our results highlight Sable's performance and efficiency, positioning it as a leading approach to MARL at scale.

Given a connected reductive group G over the finite field of order p and a cocharacter of G over the algebraic closure of the finite field, we can define G-Zips. The collection of these G-Zips form an algebraic stack which is a stack quotient of G. In this paper we study the K-theory rings of this quotient stack, focusing on the Grothendieck group. Under the additional assumption that the derived group is simply connected, the Grothendieck group is described as a quotient of the representation ring of the Levi subgroup centralising the cocharacter.

We investigate the sensitivity of the 21cm power spectrum from cosmic dawn and the epoch of reionization to models of free-streaming dark radiation (parameterized through $N_{\rm eff}$) and interacting dark radiation-dark matter models (DM-DR). The latter models have gained attention for their potential in addressing recent cosmological tensions and structure formation challenges. We perform a Fisher matrix analysis under different assumptions regarding the astrophysical modeling, and forecast the sensitivity of HERA observations, combined with CMB data from Planck and the Simons Observatory (SO), to $N_{\rm eff}$ and DM-DR interaction modeled using the ETHOS framework assuming a constant scattering rate between the two components. Most importantly, we find that 21cm observations can improve the sensitivity to the DM-DR interaction rate by up to four order of magnitude compared to Planck and SO. Conversely, in the limit of low interaction rate (which asymptotically matches $N_{\rm eff}$), CMB data dominates the constraining power, but the inclusion of HERA data can provide a $\sim 20\%$ improvement in sensitivity over CMB data alone. Moreover, we find that HERA observations will be able to probe a region of the DM-DR interaction parameter space which is promising to explain the weak lensing amplitude `$S_8$' tension. Our results demonstrate the complementarity of 21cm and CMB data in exploring dark sector interactions., Comment: 25+13pages, 11 figures. Comments welcome!

Black holes in Lorentz violating gravity enjoy a double horizon structure which resembles that of the Kerr solution in General Relativity. Moreover, when a scalar field with a modified dispersion relation is coupled to these backgrounds, an on-shell mode with negative energy becomes possible in the region in between the horizons. Both properties together call for the possibility of extracting energy from the black hole by scattering of waves, even if the space-time is stationary. Here, we perform such scattering explicitly in the frequency domain, showing that indeed, a superradiant effect, leading to energy extraction, can be observed for modes with $l>0$ in spherical symmetry. In particular, we show that the mode $l=1$ can display a reflectivity exceeding 700% for certain values of the Lorentz violating scale. This leads us to conjecture the instability of these space-times against such perturbations, although astrophysical size objects should have long life-times. Our results are not unique to Lorentz violating gravity and can be extended to any setting where modified dispersion relations are present, such as analogue gravity., Comment: 19 pages, 8 figures