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The Demazure product, also called the 0-Hecke product, is an associative operation on Coxeter groups with interesting properties and applications. In (Li et al 2024) it was shown that the Demazure product of two permutations can be described purely combinatorially: using only their one-line notation and not relying on reduced words. In this paper, we extend this to type D Coxeter groups., Comment: 17 pages, 2 figures

We investigate orbifolds of lattice conformal field theories with the goal of constructing theories with large gap. We consider Barnes-Wall lattices, which are a family of lattices with no short vectors, and orbifold by an extraspecial 2-group of lattice automorphisms. To construct the orbifold CFT, we investigate the orbifold vertex operator algebra and its twisted modules. To obtain a holomorphic CFT, a certain anomaly 3-cocycle $\omega$ needs to vanish; based on evidence we provide, we conjecture that it indeed does. Granting this conjecture, we construct a holomorphic CFT of central charge 128 with gap 4., Comment: 27 pages. Ancillary Mathematica and Magma files

It is known from Zhu's results that under modular transformations, correlators of rational $C_2$-cofinite vertex operator algebras transform like Jacobi forms. We investigate the modular transformation properties of VOA correlators that have zero modes inserted. We derive recursion relations for such correlators and use them to establish modular transformation properties. We find that correlators with only zero modes transform like quasi-modular forms, and mixed correlators with both zero modes and vertex operators transform like quasi-Jacobi forms. As an application of our results, we introduce algebras of higher weight fields whose zero mode correlators mimic the properties of those of weight 1 fields. We also give a simplified proof of the weight 1 transformation properties originally proven by Miyamoto.

We prove that the transitive permutation group 17T7, isomorphic to a split extension of $C_2$ by $\mathrm{PSL}_2(\mathbb{F}_{16})$, is a Galois group over the rationals. The group arises from the field of definition of the 2-torsion on an abelian fourfold with real multiplication defined over a real quadratic field. We find such fourfolds using Hilbert modular forms. Finally, building upon work of Demb\'el\'e, we show how to conjecturally reconstruct a period matrix for an abelian variety attached to a Hilbert modular form; we then use this to exhibit an explicit degree 17 polynomial with Galois group 17T7., Comment: 23 pages, comments welcome

Dual-comb ranging has emerged as an effective technology for long-distance metrology, providing absolute distance measurements with high speed, precision, and accuracy. Here, we demonstrate a dual-comb ranging method that utilizes a free-space transceiver unit, enabling dead-zone-free measurements and simultaneous ranging with interchanged comb roles to allow for long-distance measurements even when the target is moving. It includes a GPU-accelerated algorithm for real-time signal processing and a free-running single-cavity solid-state dual-comb laser with a carrier wavelength $\lambda_c \approx$ 1055 nm, a pulse repetition rate of 1 GHz and a repetition rate difference of 5.06 kHz. This combination offers a fast update rate and sufficient signal strength to reach a single-shot time-of-flight precision of around 0.1 $\mu$m (i.e. $< \lambda_c/4$) on a cooperative target placed at a distance of more than 40 m. The free-running laser is sufficiently stable to use the phase information for interferometric distance measurements, which improves the single-shot precision to $<$20 nm. To assess the ranging accuracy, we track the motion of the cooperative target when moved over 40 m and compare it to a reference interferometer. The residuals between the two measurements are below 3 $\mu$m. These results highlight the potential of this approach for accurate and dead-zone-free long-distance ranging, supporting real-time tracking with nm-level precision., Comment: Supplementary Information included

Visualization of multidimensional, categorical data is a common challenge across scientific areas and, in particular, the life sciences. The goal is to create a comprehensive overview of the underlying data which allows to assess multiple variables intuitively. One application where such visualizations are particularly useful is pathway analysis, where we check for dysregulation in known biological regulatory mechanisms and functions across multiple conditions. Here, we propose a new visualization approach that codes such data in a comprehensive and intuitive representation: Dice plots visualize up to four distinct categorical classes in a single view that consist of multiple elements resembling the faces of dice, whereas domino plots add an additional layer of information for binary comparison. The code is available as the diceplot R package, as pydiceplot on pip and at https://github.com/maflot., Comment: 4 pages, 1 figure

Let $E/\mathbf{Q}$ be an elliptic curve and $p\geq 3$ be a prime. We prove the $p$-converse theorems for elliptic curves of potentially good ordinary reduction at Eisenstein primes (i.e., such that the residual representation $E[p]$ is reducible) when the $p$-Selmer rank is $0$ or $1$. The key step is to obtain the anticyclotomic Iwasawa Main Conjectures for an auxiliary imaginary quadratic field $K$ where $E$ does not have CM similar to those in [CGLS22] and descent to $\mathbf{Q}$. As an application we get improved proportions for the number of elliptic curves in quadratic twist families having rank $0$ or $1$., Comment: 34 pages. Comments welcome!

Prime-Cam, one of the primary instruments for the Fred Young Submillimeter Telescope (FYST) developed by the CCAT Collaboration, will house up to seven instrument modules, with the first operating at 280 GHz. Each module will include three arrays of superconducting microwave kinetic inductance detectors (KIDs). The first KID array fabricated for the 280 GHz module uses titanium-nitride (TiN) as the superconducting material and has 3,456 individual detectors, while the other two arrays use aluminum. This paper presents the design and laboratory characterization of the 280 GHz TiN array, which is cooled below its critical temperature to ~0.1 K and read out over six RF feedlines. LED mapping, a technique for matching the measured resonant frequency of a detector to its physical position, was performed on the array so that the results can be used to lithographically trim the KID capacitors and increase the yield of the array by reducing frequency collisions. We present the methods and results of LED mapping the 280 GHz TiN KID array before deployment on FYST., Comment: 4 pages, 4 figures, submitted to IEEE Transactions on Applied Superconductivity (IEEE TAS)

For a finite group $G$, the vertices of the prime graph $\Gamma(G)$ are the primes that divide $|G|$, and two vertices $p$ and $q$ are connected by an edge if there is an element of order $pq$ in $G$. Prime graphs of solvable groups have been classified, and prime graphs of groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group $T$ have been classified in the case where $T$ has order divisible by exactly three or four distinct primes, except for the cases $T = \operatorname{Sz}(8)$, $T = \operatorname{Sz}(32)$, and $T = \operatorname{PSL}(2,q)$, which in some sense are the hardest cases. In this paper, we complete the classification for $T = \operatorname{Sz}(32)$, $T = \operatorname{Sz}(8)$, and $T = \operatorname{PSL}(2,2^5)$, with the latter two being the first cases ever studied where $|\text{Out}(T)|$ has prime factors which do not divide $|T|$. The groups studied in this paper are also the first ones requiring knowledge of their Brauer character tables to complete the classification task., Comment: 32 pages, 4 figures

NLP benchmarks rely on standardized datasets for training and evaluating models and are crucial for advancing the field. Traditionally, expert annotations ensure high-quality labels; however, the cost of expert annotation does not scale well with the growing demand for larger datasets required by modern models. While crowd-sourcing provides a more scalable solution, it often comes at the expense of annotation precision and consistency. Recent advancements in large language models (LLMs) offer new opportunities to enhance the annotation process, particularly for detecting label errors in existing datasets. In this work, we consider the recent approach of LLM-as-a-judge, leveraging an ensemble of LLMs to flag potentially mislabeled examples. Through a case study of four datasets from the TRUE benchmark, covering different tasks and domains, we empirically analyze the labeling quality of existing datasets, and compare expert, crowd-sourced, and our LLM-based annotations in terms of agreement, label quality, and efficiency, demonstrating the strengths and limitations of each annotation method. Our findings reveal a substantial number of label errors, which, when corrected, induce a significant upward shift in reported model performance. This suggests that many of the LLMs so-called mistakes are due to label errors rather than genuine model failures. Additionally, we discuss the implications of mislabeled data and propose methods to mitigate them in training to improve model performance.

The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60 to 80 t capable of probing the remaining WIMP-nucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in $^{136}$Xe using a natural-abundance xenon target. XLZD can reach a 3$\sigma$ discovery potential half-life of 5.7$\times$10$^{27}$ yr (and a 90% CL exclusion of 1.3$\times$10$^{28}$ yr) with 10 years of data taking, corresponding to a Majorana mass range of 7.3-31.3 meV (4.8-20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community., Comment: 29 pages, 7 figures

This report describes the experimental strategy and technologies for a next-generation xenon observatory sensitive to dark matter and neutrino physics. The detector will have an active liquid xenon target mass of 60-80 tonnes and is proposed by the XENON-LUX-ZEPLIN-DARWIN (XLZD) collaboration. The design is based on the mature liquid xenon time projection chamber technology of the current-generation experiments, LZ and XENONnT. A baseline design and opportunities for further optimization of the individual detector components are discussed. The experiment envisaged here has the capability to explore parameter space for Weakly Interacting Massive Particle (WIMP) dark matter down to the neutrino fog, with a 3$\sigma$ evidence potential for the spin-independent WIMP-nucleon cross sections as low as $3\times10^{-49}\rm cm^2$ (at 40 GeV/c$^2$ WIMP mass). The observatory is also projected to have a 3$\sigma$ observation potential of neutrinoless double-beta decay of $^{136}$Xe at a half-life of up to $5.7\times 10^{27}$ years. Additionally, it is sensitive to astrophysical neutrinos from the atmosphere, sun, and galactic supernovae., Comment: 32 pages, 14 figures

The synthesis of binary nanocrystal superlattices (BNSLs) enables the targeted integration of orthogonal physical properties, like photoluminescence and magnetism, into a single superstructure, unlocking a vast design space for multifunctional materials. Yet, the formation mechanism of BNSLs remains poorly understood, restricting the use of simulation to predict the structure and properties of the superlattices. Here, we use a combination of in situ scattering and molecular simulation to elucidate the self-assembly of two common BNSLs through emulsion templating. Our self-assembly experiments reveal that no intermediate structures precede the formation of the final binary phases, indicating that their formation proceeds through classical nucleation. Using simulations, we find that, despite the formation of AlB2 and NaZn13 typically being attributed to entropy, their self-assembly is most consistent with the nanocrystals possessing short-range interparticle attraction, which we find can dramatically accelerate nucleation kinetics in BNSLs. We also find homogenous, classical nucleation in simulation, corroborating our experiments. These results establish a robust correspondence between experiment and theory, paving the way towards a priori prediction of BNSLs.

Ho$_3$ScO$_6$ harbours a frustrated Maple Leaf Lattice (MLL). It crystalizes in the Mg$_3$TeO$_6$-type structure, and has a centrosymmetric trigonal space group (R$\bar{3}$). This system contains stacked layers of magnetic rings along the c-axis consisting of six magnetic Ho$^{3+}$ ions forming Ho hexagons, which are connected into a 2-dimensional network by equilateral and isosceles triangles to form a rare example of a MLL. Long range magnetic order is reached below $T_N=4.1$ K with a 120$^\circ$ spin arrangement on the equilateral triangles resulting in a positive vector chirality ground state configuration.

Accurate characterization of ferroelectric properties in polymer piezoelectrics is critical for optimizing the performance of flexible and wearable ultrasound transducers, such as screen-printed PVDF devices. Standard charge measurement techniques, like the Sawyer-Tower circuit, often fall short when applied to ferroelectric polymers due to low-frequency leakage. In this work, we present PEtra, an open-source and versatile piezoelectric loop tracer. PEtra employs a transimpedance amplifier (LMP7721, TI) to convert picoampere-level currents into measurable voltages, covering a frequency range of 0.1 Hz to 5 Hz for a gain setting of 10^7 V/A, and 0.1 Hz to 200 Hz for gain settings between 10^3 V/A to 10^6 V/A (10-fold increments). We demonstrate through simulations and experimental validations that PEtra achieves a sensitivity down to 2 pA, effectively addressing the limitations of traditional charge measurement methods. Compared to the Sawyer-Tower circuit, PEtra directly amplifies currents without the need for a reference capacitor. As a result, it is less susceptible to leakage and can operate at lower frequencies, improving measurement accuracy and reliability. PEtra's design is fully open source, offering researchers and engineers a versatile tool to drive advancements in flexible PVDF transducer technology.

An eigenvalue problem arising in optimal insulation related to the minimization of the heat decay rate of an insulated body is adapted to enforce a positive lower bound imposed on the distribution of insulating material. We prove the existence of optimal domains among a class of convex shapes and propose a numerical scheme to approximate the eigenvalue. The stability of the shape optimization among convex, bounded domains in $\mathbb{R}^3$ is proven for an approximation with polyhedral domains under a non-conformal convexity constraint. We prove that on the ball, symmetry breaking of the optimal insulation can be expected in general. To observe how the lower bound affects the breaking of symmetry in the optimal insulation and the shape optimization, the eigenvalue and optimal domains are approximated for several values of mass $m$ and lower bounds $\ell_{\min}\ge0$. The numerical experiments suggest, that in general symmetry breaking still arises, unless $m$ is close to a critical value $m_0$, and $\ell_{\min}$ large enough such that almost all of the mass $m$ is fixed through the lower bound. For $\ell_{\min}=0$, the numerical results are consistent with previous numerical experiments on shape optimization restricted to rotationally symmetric, convex domains.

In the rapidly evolving landscape of veterinary healthcare, integrating machine learning (ML) clinical decision-making tools with electronic health records (EHRs) promises to improve diagnostic accuracy and patient care. However, the seamless integration of ML classifiers into existing EHRs in veterinary medicine is frequently hindered by the rigidity of EHR systems or the limited availability of IT resources. To address this shortcoming, we present Anna, a freely-available software solution that provides ML classifier results for EHR laboratory data in real-time.

This paper develops an approach to categorical deformation quantization via factorization homology. We show that a quantization of the local coefficients for factorization homology is equivalent to consistent quantizations of its value on manifolds. To formulate our results we introduce the concepts of shifted almost Poisson and BD categories. Our main example is the character stack of flat principal bundles for a reductive algebraic group $G$, where we show that applying the general framework to the Drinfeld category reproduces deformations previously introduced by Li-Bland and \v{S}evera. As a direct consequence, we can conclude a precise relation between their quantization and those introduced by Alekseev, Grosse, and Schomerus. To arrive at our results we compute factorization homology with values in a ribbon category enriched over complete $\mathbb{C}[[\hbar]]$-modules. More generally, we define enriched skein categories which compute factorization homology for ribbon categories enriched over a general closed symmetric monoidal category $\mathcal{V}$., Comment: 84 pages. First version, comments and suggestions welcome

Characters are at the heart of every story, driving the plot and engaging readers. In this study, we explore the understanding of characters in full-length books, which contain complex narratives and numerous interacting characters. We define two tasks: character description, which generates a brief factual profile, and character analysis, which offers an in-depth interpretation, including character development, personality, and social context. We introduce the BookWorm dataset, pairing books from the Gutenberg Project with human-written descriptions and analyses. Using this dataset, we evaluate state-of-the-art long-context models in zero-shot and fine-tuning settings, utilizing both retrieval-based and hierarchical processing for book-length inputs. Our findings show that retrieval-based approaches outperform hierarchical ones in both tasks. Additionally, fine-tuned models using coreference-based retrieval produce the most factual descriptions, as measured by fact- and entailment-based metrics. We hope our dataset, experiments, and analysis will inspire further research in character-based narrative understanding., Comment: 30 pages, 2 figures, EMNLP 2024 Findings

We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover a single shape (either inverse of normal curves) must dominate in the long-run.

Continuous fields (or bundles) of $C^*$-algebras form an important ingredient for describing emergent phenomena, such as phase transitions and spontaneous symmetry breaking. In this work, we consider the continuous $C^*$-bundle generated by increasing symmetric tensor powers of the complex $\ell\times\ell$ matrices $M_\ell(\mathbb{C})$, which can be interpreted as abstract description of mean-field theories defining the macroscopic limit of infinite quantum systems. Within this framework we discuss the principle of large deviations for the local Gibbs state in the high temperature regime and characterize the limit of the ensuing logarithmic generating function., Comment: 24 pages

There is a vast literature on representation learning based on principles such as coding efficiency, statistical independence, causality, controllability, or symmetry. In this paper we propose to learn representations from sequence data by factorizing the transformations of the latent variables into sparse components. Input data are first encoded as distributions of latent activations and subsequently transformed using a probability flow model, before being decoded to predict a future input state. The flow model is decomposed into a number of rotational (divergence-free) vector fields and a number of potential flow (curl-free) fields. Our sparsity prior encourages only a small number of these fields to be active at any instant and infers the speed with which the probability flows along these fields. Training this model is completely unsupervised using a standard variational objective and results in a new form of disentangled representations where the input is not only represented by a combination of independent factors, but also by a combination of independent transformation primitives given by the learned flow fields. When viewing the transformations as symmetries one may interpret this as learning approximately equivariant representations. Empirically we demonstrate that this model achieves state of the art in terms of both data likelihood and unsupervised approximate equivariance errors on datasets composed of sequence transformations., Comment: submitted to T-PAMI