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In 1969, Fulton introduced classical Hurwitz spaces parametrizing simple d-sheeted coverings of the projective line in the algebro-geometric setting. He established the irreducibility of these spaces under the assumption that the characteristic of the ground field is greater than d, but the irreducibility problem in smaller characteristics remained open. We resolve this problem in the current paper and prove that the classical Hurwitz spaces are irreducible over any algebraically closed field. On the way, we establish the irreducibility of Severi varieties in arbitrary characteristic for a rich class of toric surfaces, including all classical toric surfaces. Our approach to the irreducibility problems comes from tropical geometry, and the paper contains two more results of independent interest - a lifting result for parametrized tropical curves and a strong connectedness property of the moduli spaces of parametrized tropical curves., Comment: 31 pages, 12 figures. Comments are welcome

We describe group quotients of dg-categories and linear stable $\infty$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with the $\infty$-categorical group quotient., Comment: 19 pages, comments welcome

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the $SU(N)$ group into the space of general complex matrices,$M_N(\mathbb{C})$. Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of $W \in M_N(\mathbb{C})$ as the dynamical variables without group theoretic constraints. The framework enables us to introduce non-separable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC., Comment: 18 pages, 3 figures

We consider the ground state properties of a lattice Bose polaron, a quasiparticle arising from the interaction between an impurity confined to an optical lattice and a surrounding homogeneous Bose-Einstein condensate hosting phononic modes. We present an extension of Wegner's and Wilson's flow equation approach, the operator valued flow equation approach, which allows us to calculate the renormalized dispersion of the polaron and assess the role of two-phonon scattering processes on the dispersion. The results obtained in this way are compared to a variational mean-field approach. We find that in certain impurity phonon interaction regimes the shape of the dispersion is significantly altered by the inclusion of two-phonon scattering events as opposed to only single-phonon scattering events. Moreover, our results predict that a polaronic bound state may emerge, which is not present in Fr\"ohlich-type models that only consider single-phonon scattering events., Comment: 12 pages, 10 figures

As the outputs of generative AI (GenAI) techniques improve in quality, it becomes increasingly challenging to distinguish them from human-created content. Watermarking schemes are a promising approach to address the problem of distinguishing between AI and human-generated content. These schemes embed hidden signals within AI-generated content to enable reliable detection. While watermarking is not a silver bullet for addressing all risks associated with GenAI, it can play a crucial role in enhancing AI safety and trustworthiness by combating misinformation and deception. This paper presents a comprehensive overview of watermarking techniques for GenAI, beginning with the need for watermarking from historical and regulatory perspectives. We formalize the definitions and desired properties of watermarking schemes and examine the key objectives and threat models for existing approaches. Practical evaluation strategies are also explored, providing insights into the development of robust watermarking techniques capable of resisting various attacks. Additionally, we review recent representative works, highlight open challenges, and discuss potential directions for this emerging field. By offering a thorough understanding of watermarking in GenAI, this work aims to guide researchers in advancing watermarking methods and applications, and support policymakers in addressing the broader implications of GenAI.

Cox and Kartsonaki proposed a simple outlier test for a vector of p-values based on the R\'enyi transformation that is fast for large $p$ and numerically stable for very small p-values -- key properties for large data analysis. We propose and implement a generalization of this procedure we call the R\'enyi Outlier Test (ROT). This procedure maintains the key properties of the original but is much more robust to uncertainty in the number of outliers expected a priori among the p-values. The ROT can also account for two types of prior information that are common in modern data analysis. The first is the prior probability that a given p-value may be outlying. The second is an estimate of how far of an outlier a p-value might be, conditional on it being an outlier; in other words, an estimate of effect size. Using a series of pre-calculated spline functions, we provide a fast and numerically stable implementation of the ROT in our R package renyi., Comment: 4 pages

Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced by Christ and Gunn [CRYPTO 2024] for the purpose of watermarking the outputs of randomized algorithms, such as generative AI models. Several constructions of pseudorandom codes have since been proposed, but none of them are robust to error channels that depend on previously seen codewords. This stronger kind of robustness is referred to as adaptive robustness, and it is important for meaningful applications to watermarking. In this work, we show the following. - Adaptive robustness: We show that the pseudorandom codes of Christ and Gunn are adaptively robust, resolving a conjecture posed by Cohen, Hoover, and Schoenbach [S&P 2025]. - Ideal security: We define an ideal pseudorandom code as one which is indistinguishable from the ideal functionality, capturing both the pseudorandomness and robustness properties in one simple definition. We show that any adaptively robust pseudorandom code for single-bit messages can be bootstrapped to build an ideal pseudorandom code with linear information rate, under no additional assumptions. - CCA security: In the setting where the encoding key is made public, we define a CCA-secure pseudorandom code in analogy with CCA-secure encryption. We show that any adaptively robust public-key pseudorandom code for single-bit messages can be used to build a CCA-secure pseudorandom code with linear information rate, in the random oracle model. These results immediately imply stronger robustness guarantees for generative AI watermarking schemes, such as the practical quality-preserving image watermarks of Gunn, Zhao, and Song (2024).

The recent explosion of high-quality language models has necessitated new methods for identifying AI-generated text. Watermarking is a leading solution and could prove to be an essential tool in the age of generative AI. Existing approaches embed watermarks at inference and crucially rely on the large language model (LLM) specification and parameters being secret, which makes them inapplicable to the open-source setting. In this work, we introduce the first watermarking scheme for open-source LLMs. Our scheme works by modifying the parameters of the model, but the watermark can be detected from just the outputs of the model. Perhaps surprisingly, we prove that our watermarks are unremovable under certain assumptions about the adversary's knowledge. To demonstrate the behavior of our construction under concrete parameter instantiations, we present experimental results with OPT-6.7B and OPT-1.3B. We demonstrate robustness to both token substitution and perturbation of the model parameters. We find that the stronger of these attacks, the model-perturbation attack, requires deteriorating the quality score to 0 out of 100 in order to bring the detection rate down to 50%.

Math reasoning is an active area of Large Language Model (LLM) research because it is a hallmark of artificial intelligence and has implications in several domains, including math education. However, few works have explored how math reasoning is encoded within LLM parameters and if it is a skill that can be isolated within models. Doing so could allow targeted intervention to improve math performance without altering non-math behavior and foster understanding of how models encode math reasoning. We introduce Math Neurosurgery (MathNeuro), a computationally efficient method we use to isolate math-specific parameters in LLMs using only forward passes. MathNeuro builds on existing work by using weights and activations to calculate parameter importance, but isolates math-specific parameters by filtering out those important for general language tasks. Through pruning parameters MathNeuro identifies, we delete a LLM's math reasoning ability without significantly impacting its general language ability. Scaling the identified parameters by a small constant improves a pretrained or instruction-tuned LLM's performance by 4-17% on GSM8K and 5-35% on MATH while leaving non-math behavior unaltered. MathNeuro is also data efficient: most of its effectiveness holds when identifying math-specific parameters using a single sample. MathNeuro highlights the potential for future work to intervene on math-specific parameters., Comment: 38 pages, 54 figures

Bubble curtains are widely used to protect marine life from exposure to noise during offshore construction. However, operating a bubble curtain is costly. Therefore optimizing the acoustic effect of the available air is important. An interesting approach is to split the airflow rate into two separate bubble curtains, rather than one single curtain. This concept is tested experimentally and numerically. The experiments and the model show an increase in performance of the compressed air when it is split between two manifolds. An increased insertion loss of up to 11dB is measured. This increase in performance is possibly due to the fact that the reflective properties of the bubble curtains are maintained when halving the airflow rate. In effect, by splitting the airflow a second acoustic barrier is added. Additionally, the variations in the bubble curtain performance between individual measurements are shown to be largely caused by temporal variations in the air distribution. The applicability of equivalent fluid models for bubble curtains is discussed, and it is shown that accounting for a gap in the bubble curtain, close to the manifold where the bubble curtain is not fully developed, results in better agreement between the modelled and the measured insertion loss.

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p-value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling $T^2$ methods based on the conventional $\chi^2$ statistic do not apply, such as for uncorrelated fits. Specifically, we analyze a general alternative to the correlated $\chi^2$ statistic referred to as $q^2$, and show how to use the bootstrap as a data-driven method to determine the expected distribution of $q^2$ for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p-value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p-value of estimating population parameters from a single ensemble of $N$ samples. The overall method is accurate up to a $1/N$ bias which we do not attempt to quantify., Comment: 46 pages, 22 figures

The dawn of Foundation Models has on the one hand revolutionised a wide range of research problems, and, on the other hand, democratised the access and use of AI-based tools by the general public. We even observe an incursion of these models into disciplines related to human psychology, such as the Affective Computing domain, suggesting their affective, emerging capabilities. In this work, we aim to raise awareness of the power of Foundation Models in the field of Affective Computing by synthetically generating and analysing multimodal affective data, focusing on vision, linguistics, and speech (acoustics). We also discuss some fundamental problems, such as ethical issues and regulatory aspects, related to the use of Foundation Models in this research area.

Previous research on the Adiar BDD package has been successful at designing algorithms capable of handling large Binary Decision Diagrams (BDDs) stored in external memory. To do so, it uses consecutive sweeps through the BDDs to resolve computations. Yet, this approach has kept algorithms for multi-variable quantification, the relational product, and variable reordering out of its scope. In this work, we address this by introducing the nested sweeping framework. Here, multiple concurrent sweeps pass information between eachother to compute the result. We have implemented the framework in Adiar and used it to create a new external memory multi-variable quantification algorithm. Compared to conventional depth-first implementations, Adiar with nested sweeping is able to solve more instances of our benchmarks and/or solve them faster., Comment: 27 pages, 14 figures, 2 tables

Quantum technologies extensively use laser light for state preparation, manipulation, and readout. For field applications, these systems must be robust and compact, driving the need for miniaturized and highly stable optical setups and system integration. In this work, we present a micro-integrated crossed-beam optical dipole trap setup, the $\mu$XODT, designed for trapping and cooling $^{87}\text{Rb}$. This fiber-coupled setup operates at $1064\,\text{nm}$ wavelength with up to $2.5\,\text{W}$ optical power and realizes a free-space crossed beam geometry. The $\mu$XODT precisely overlaps two focused beams ($w_0 \approx 33\,\mu\text{m}$) at their waists in a $45^\circ$ crossing angle, achieving a position difference $\leq 3.4\,\mu\text{m}$ and 0.998 power ratio between both beams with long-term stability. We describe the design and assembly process in detail, along with optical and thermal tests with temperatures of up to $65\,^\circ C$. The system's volume of $25\,\text{ml}$ represents a reduction of more than two orders of magnitude compared to typically used macroscopic setups, while demonstrating exceptional mechanical robustness and thermal stability. The $\mu$XODT is integrated with a $^{87}\text{Rb}$ 3D MOT setup, trapping $3 \times 10^5$ atoms from a laser-cooled atomic cloud, and has shown no signs of degradation after two years of operation.

To address the rural broadband challenge and to leverage the unique opportunities that rural regions provide for piloting advanced wireless applications, we design and implement the ARA wireless living lab for research and innovation in rural wireless systems and their applications in precision agriculture, community services, and so on. ARA focuses on the unique community, application, and economic context of rural regions, and it features the first-of-its-kind, real-world deployment of long-distance, high-capacity wireless x-haul and access platforms across a rural area of diameter over 30 km. With both software-defined radios and programmable COTS systems and through effective orchestration of these wireless resources with fiber as well as compute resources embedded end-to-end across user equipment, base stations, edge, and cloud, ARA offers programmability, performance, robustness, and heterogeneity at the same time, thus enabling rural-focused co-evolution of wireless and applications while helping advance the frontiers of wireless systems in domains such as O-RAN, NextG, and agriculture applications. Here we present the design principles and implementation strategies of ARA, characterize its performance and heterogeneity, and highlight example wireless and application experiments uniquely enabled by ARA., Comment: 17 pages, 18 figures

Due to factors such as low population density and expansive geographical distances, network deployment falls behind in rural regions, leading to a broadband divide. Wireless spectrum serves as the blood and flesh of wireless communications. Shared white spaces such as those in the TVWS and CBRS spectrum bands offer opportunities to expand connectivity, innovate, and provide affordable access to high-speed Internet in under-served areas without additional cost to expensive licensed spectrum. However, the current methods to utilize these white spaces are inefficient due to very conservative models and spectrum policies, causing under-utilization of valuable spectrum resources. This hampers the full potential of innovative wireless technologies that could benefit farmers, small Internet Service Providers (ISPs) or Mobile Network Operators (MNOs) operating in rural regions. This study explores the challenges faced by farmers and service providers when using shared spectrum bands to deploy their networks while ensuring maximum system performance and minimizing interference with other users. Additionally, we discuss how spatiotemporal spectrum models, in conjunction with database-driven spectrum-sharing solutions, can enhance the allocation and management of spectrum resources, ultimately improving the efficiency and reliability of wireless networks operating in shared spectrum bands.

Traditional nanophotonic sensing schemes utilize evanescent fields in dielectric or metallic nanoparticles, which confine far-field radiation in dispersive and lossy media. Apart from the lack of a well-defined sensing volume that can be accompanied by moderate sensitivities, these structures suffer from the generally limited access to the modal field, which is key for sensing performance. Recently, a novel strategy for dielectric nanophotonics has been demonstrated, namely, the resonant confinement of light in air. So-called Mie voids created in high-index dielectric host materials support localized resonant modes with exceptional properties. In particular, due to the confinement in air, these structures benefit from the full access to the modal field inside the void. We utilize these Mie voids for refractive index sensing in single voids with volumes down to 100 attoliters and sensitivities on the order of 400 nm per refractive index unit. Taking the signal-to-noise ratio of our measurements into account, we demonstrate detection of refractive index changes as small as 6.9 x 10-4 in a defined volume of just 850 attoliters. The combination of our Mie void sensor platform with appropriate surface functionalization will even enable specificity to biological or other analytes of interest, as the sensing volumes are on the order of cellular signaling chemicals of single vesicles in cellular synapses.

We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calabi--Yau structure. We discovered these algebras through two very distinct routes, one involving perverse schobers whose stalks are cyclic quotients of the derived categories of relative Ginzburg algebras, and another involving deformations of partially wrapped Fukaya categories of surfaces. Applying the results of our previous work arXiv:2303.18249, we describe the spaces of stability conditions on the derived categories of these algebras in terms of spaces of quadratic differentials., Comment: 43 pages. This is the second part split from arXiv:2303.18249

Flattery is an important aspect of human communication that facilitates social bonding, shapes perceptions, and influences behavior through strategic compliments and praise, leveraging the power of speech to build rapport effectively. Its automatic detection can thus enhance the naturalness of human-AI interactions. To meet this need, we present a novel audio textual dataset comprising 20 hours of speech and train machine learning models for automatic flattery detection. In particular, we employ pretrained AST, Wav2Vec2, and Whisper models for the speech modality, and Whisper TTS models combined with a RoBERTa text classifier for the textual modality. Subsequently, we build a multimodal classifier by combining text and audio representations. Evaluation on unseen test data demonstrates promising results, with Unweighted Average Recall scores reaching 82.46% in audio-only experiments, 85.97% in text-only experiments, and 87.16% using a multimodal approach., Comment: Interspeech 2024

The Extreme Universe Space Observatory on a Super Pressure Balloon 2 (EUSO-SPB2) flew on May 13$^{\text{th}}$ and 14$^{\text{th}}$ of 2023. Consisting of two novel optical telescopes, the payload utilized next-generation instrumentation for the observations of extensive air showers from near space. One instrument, the fluorescence telescope (FT) searched for Ultra-High Energy Cosmic Rays (UHECRs) by recording the atmosphere below the balloon in the near-UV with a 1~$\mu$s time resolution using 108 multi-anode photomultiplier tubes with a total of 6,912 channels. Validated by pre-flight measurements during a field campaign, the energy threshold was estimated around 2~EeV with an expected event rate of approximately 1 event per 10 hours of observation. Based on the limited time afloat, the expected number of UHECR observations throughout the flight is between 0 and 2. Consistent with this expectation, no UHECR candidate events have been found. The majority of events appear to be detector artifacts that were not rejected properly due to a shortened commissioning phase. Despite the earlier-than-expected termination of the flight, data were recorded which provide insights into the detectors stability in the near-space environment as well as the diffuse ultraviolet emissivity of the atmosphere, both of which are impactful to future experiments.

The Multimodal Sentiment Analysis Challenge (MuSe) 2024 addresses two contemporary multimodal affect and sentiment analysis problems: In the Social Perception Sub-Challenge (MuSe-Perception), participants will predict 16 different social attributes of individuals such as assertiveness, dominance, likability, and sincerity based on the provided audio-visual data. The Cross-Cultural Humor Detection Sub-Challenge (MuSe-Humor) dataset expands upon the Passau Spontaneous Football Coach Humor (Passau-SFCH) dataset, focusing on the detection of spontaneous humor in a cross-lingual and cross-cultural setting. The main objective of MuSe 2024 is to unite a broad audience from various research domains, including multimodal sentiment analysis, audio-visual affective computing, continuous signal processing, and natural language processing. By fostering collaboration and exchange among experts in these fields, the MuSe 2024 endeavors to advance the understanding and application of sentiment analysis and affective computing across multiple modalities. This baseline paper provides details on each sub-challenge and its corresponding dataset, extracted features from each data modality, and discusses challenge baselines. For our baseline system, we make use of a range of Transformers and expert-designed features and train Gated Recurrent Unit (GRU)-Recurrent Neural Network (RNN) models on them, resulting in a competitive baseline system. On the unseen test datasets of the respective sub-challenges, it achieves a mean Pearson's Correlation Coefficient ($\rho$) of 0.3573 for MuSe-Perception and an Area Under the Curve (AUC) value of 0.8682 for MuSe-Humor.

We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to $K_L\rightarrow\mu^+\mu^-$ decay can be calculated using lattice QCD. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard model prediction for this second-order weak process depends on an accurate result of this two-photon amplitude. A limiting factor of our proposed method comes from low-energy three-particle $\pi\pi\gamma$ states. The contribution from these states will be significantly distorted by the finite volume of our calculation -- a distortion for which there is no available correction. However, a simple estimate of the contribution of these three-particle states suggests their contribution to be at most a few percent allowing their neglect in a lattice calculation with a 10% target accuracy., Comment: 31 pages, 10 figures

In this paper, we introduce the uniform algebraic rank of a divisor class on a finite graph. We show that it lies between Caporaso's algebraic rank and the combinatorial rank of Baker and Norine. We prove the Riemann-Roch theorem for the uniform algebraic rank, and show that both the algebraic and the uniform algebraic rank are realized on effective divisors. As an application, we use the uniform algebraic rank to show that Clifford representatives always exist. We conclude with an explicit description of such Clifford representatives for a large class of graphs., Comment: 20 pages, 3 figures. Comments are welcome!

Telling stories is an integral part of human communication which can evoke emotions and influence the affective states of the audience. Automatically modeling emotional trajectories in stories has thus attracted considerable scholarly interest. However, as most existing works have been limited to unsupervised dictionary-based approaches, there is no benchmark for this task. We address this gap by introducing continuous valence and arousal labels for an existing dataset of children's stories originally annotated with discrete emotion categories. We collect additional annotations for this data and map the categorical labels to the continuous valence and arousal space. For predicting the thus obtained emotionality signals, we fine-tune a DeBERTa model and improve upon this baseline via a weakly supervised learning approach. The best configuration achieves a Concordance Correlation Coefficient (CCC) of $.8221$ for valence and $.7125$ for arousal on the test set, demonstrating the efficacy of our proposed approach. A detailed analysis shows the extent to which the results vary depending on factors such as the author, the individual story, or the section within the story. In addition, we uncover the weaknesses of our approach by investigating examples that prove to be difficult to predict., Comment: Accepted to ACL 2024 Findings. arXiv admin note: text overlap with arXiv:2212.11382

Aligning machine learning systems with human expectations is mostly attempted by training with manually vetted human behavioral samples, typically explicit feedback. This is done on a population level since the context that is capturing the subjective Point-Of-View (POV) of a concrete person in a specific situational context is not retained in the data. However, we argue that alignment on an individual level can boost the subjective predictive performance for the individual user interacting with the system considerably. Since perception differs for each person, the same situation is observed differently. Consequently, the basis for decision making and the subsequent reasoning processes and observable reactions differ. We hypothesize that individual perception patterns can be used for improving the alignment on an individual level. We test this, by integrating perception information into machine learning systems and measuring their predictive performance wrt.~individual subjective assessments. For our empirical study, we collect a novel data set of multimodal stimuli and corresponding eye tracking sequences for the novel task of Perception-Guided Crossmodal Entailment and tackle it with our Perception-Guided Multimodal Transformer. Our findings suggest that exploiting individual perception signals for the machine learning of subjective human assessments provides a valuable cue for individual alignment. It does not only improve the overall predictive performance from the point-of-view of the individual user but might also contribute to steering AI systems towards every person's individual expectations and values.