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This article develops the hydrostatic Lagrangian approach to the compressible primitive equations. A fundamental aspect in the analysis is the investigation of the compressible hydrostatic Lam\'{e} and Stokes operators. Local strong well-posedness for large data and global strong well-posedness for small data are established under various assumptions on the pressure law, both in the presence and absence of gravity., Comment: Accepted in Mathematische Annalen

This paper proposes a minimalist three-layer model for artificial consciousness, focusing on the emergence of self-awareness. The model comprises a Cognitive Integration Layer, a Pattern Prediction Layer, and an Instinctive Response Layer, interacting with Access-Oriented and Pattern-Integrated Memory systems. Unlike brain-replication approaches, we aim to achieve minimal self-awareness through essential elements only. Self-awareness emerges from layer interactions and dynamic self-modeling, without initial explicit self-programming. We detail each component's structure, function, and implementation strategies, addressing technical feasibility. This research offers new perspectives on consciousness emergence in artificial systems, with potential implications for human consciousness understanding and adaptable AI development. We conclude by discussing ethical considerations and future research directions., Comment: 46 pages

We show that Iida--Taniguchi's $\mathbb{Z}$-valued slice-torus invariant $q_M$ cannot be realized as a linear combination of Rasmussen's $s$-invariant, Ozsv\'ath--Szab\'o's $\tau$-invariant, all of the $\mathfrak{sl}_N$-concordance invariants ($N \geq 2$), Baldwin--Sivek's instanton $\tau$-invariant, Daemi--Imori--Sato--Scaduto--Taniguchi's instanton $\tilde{s}$-invariant and Sano--Sato's Rasmussen type invariants $\tilde{ss}_c$., Comment: 14 pages, 3 figures

We investigate the phase structure and the equation of state (EoS) for dense two-color QCD at low temperatures, $T = 40$ MeV ($32^4$ lattice) and $T = 80$ MeV ($16^4$ lattice). A rich phase structure below the pseudo-critical temperature $T_c$ as a function of quark chemical potential $\mu$ has been revealed. By performing $T = 40$ MeV simulations, essentially similar results to the previous ones at $T = 80$ MeV are obtained, but several finer understandings are achieved. Breaking of the conformal bound is also confirmed thanks to smaller statistical errors. This talk is mainly based on Refs.~\cite{Iida:2022hyy, Iida:2024irv}. It also includes related studies and subsequent developments that were not mentioned in the original papers., Comment: 1+7+3pages; The 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August 2024, Liverpool, UK

This paper introduces the Comprehensive AI-assisted Translation Edit Ratio (CATER), a novel and fully prompt-driven framework for evaluating machine translation (MT) quality. Leveraging large language models (LLMs) via a carefully designed prompt-based protocol, CATER expands beyond traditional reference-bound metrics, offering a multidimensional, reference-independent evaluation that addresses linguistic accuracy, semantic fidelity, contextual coherence, stylistic appropriateness, and information completeness. CATER's unique advantage lies in its immediate implementability: by providing the source and target texts along with a standardized prompt, an LLM can rapidly identify errors, quantify edit effort, and produce category-level and overall scores. This approach eliminates the need for pre-computed references or domain-specific resources, enabling instant adaptation to diverse languages, genres, and user priorities through adjustable weights and prompt modifications. CATER's LLM-enabled strategy supports more nuanced assessments, capturing phenomena such as subtle omissions, hallucinations, and discourse-level shifts that increasingly challenge contemporary MT systems. By uniting the conceptual rigor of frameworks like MQM and DQF with the scalability and flexibility of LLM-based evaluation, CATER emerges as a valuable tool for researchers, developers, and professional translators worldwide. The framework and example prompts are openly available, encouraging community-driven refinement and further empirical validation., Comment: 17pages,1sample prompt

A crossover involving three-fermion clusters is relevant to the hadron-quark crossover, which, if occurring in a neutron star, could naturally reproduce the dense-matter equation of state recently deduced from simultaneous observations of neutron-star masses and radii. To understand the crossover mechanism, we examine the role of tripling fluctuations induced by the formation of three-fermion clusters. The phase-shift representation of fluctuations manifests an interplay of bound and scattering states, leading to non-monotonic momentum distributions of baryon-like clusters and peaked sound speed at finite densities. We demonstrate them by applying our approach to a nonrelativistic system of one-dimensional three-color fermions analogous to the hadron-quark matter., Comment: 7 pages, 5 figures

Neutrinoless double beta decay (0v2b) has been investigated as a physical process that can provide evidence for the Majorana nature of neutrinos. The theoretical predictions of the 0v2b rate are subject to significant uncertainty, primarily due to nuclear matrix elements (NME). To reduce this uncertainty, experimental measurements of the half-lives of two-neutrino double beta decay (2v2b) in various nuclei are essential as a benchmark for NME calculations. The PIKACHU (Pure Inorganic scintillator experiment in KAmioka for CHallenging Underground sciences) project searches for the previously unobserved 2v2b decay of 160Gd, employing Ce-doped Gd3Ga3Al2O12 (GAGG) single crystals. In the Phase 1 experiment, we aim to improve the current lower limit on the 2v2b half-life of 160Gd by a prior study using a Ce-doped Gd2SiO5 (GSO) crystal. Ultimately, in Phase 2, the project seeks to achieve a sensitivity surpassing the theoretical prediction of 7.4 x 10^20 years, enabling the potential discovery of the 160Gd 2v2b decay. In this paper, we describe the development of background models based on GEANT4 simulations. The modeled backgrounds are contributions from uranium and thorium decay chains, 40K present in GAGG, and 40K gamma-rays from outside of GAGG. Additionally, we developed models for both 2v2b and 0v2b decay by implementing the theoretical kinematics of two-electron emission in double beta decay in the GEANT4 simulation. As a result, our background models successfully reproduced the measured background spectrum through fitting. By generating pseudo background spectra expected in Phase 1 and analyzing them with the combined background and 2v2b models, we evaluated the 2v2b sensitivity of Phase 1 to be 2.78 x 10^19 years (90% C.L.). This paper presents the development of these simulation models and the expected sensitivities for both Phase 1 and Phase 2 based on the pseudo data analyses., Comment: 18 pages, 12 figures

The complex structure and extensive details of solar spectral data, combined with a recent surge in volume, present significant processing challenges. To address this, we propose a deep learning-based compression technique using deep autoencoder (DAE) and 1D-convolutional autoencoder (CAE) models developed with Hinode SOT/SP data. We focused on compressing Stokes I and V polarization spectra from the quiet Sun, as well as from active regions, providing a novel insight into comprehensive spectral analysis by incorporating spectra from extreme magnetic fields. The results indicate that the CAE model outperforms the DAE model in reconstructing Stokes profiles, demonstrating greater robustness and achieving reconstruction errors around the observational noise level. The proposed method has proven effective in compressing Stokes I and V spectra from both the quiet Sun and active regions, highlighting its potential for impactful applications in solar spectral analysis, such as detection of unusual spectral signals.

In multiplayer cooperative video games, players traditionally use individual controllers, inferring others' actions through on-screen visuals and their own movements. This indirect understanding limits truly collaborative gameplay. Research in Joint Action shows that when manipulating a single object, motor performance improves when two people operate together while sensing each other's movements. Building on this, we developed a controller allowing multiple players to operate simultaneously while sharing haptic sensations. We showcased our system at exhibitions, gathering feedback from over 150 participants on how shared sensory input affects their gaming experience. This approach could transform player interaction, enhance cooperation, and redefine multiplayer gaming experiences., Comment: Part of proceedings of 6th International Conference AsiaHaptics 2024

A human-shaped robotic hand offers unparalleled versatility and fine motor skills, enabling it to perform a broad spectrum of tasks with precision, power and robustness. Across the paleontological record and animal kingdom we see a wide range of alternative hand and actuation designs. Understanding the morphological design space and the resulting emergent behaviors can not only aid our understanding of dexterous manipulation and its evolution, but also assist design optimization, achieving, and eventually surpassing human capabilities. Exploration of hand embodiment has to date been limited by inaccessibility of customizable hands in the real-world, and by the reality gap in simulation of complex interactions. We introduce an open parametric design which integrates techniques for simplified customization, fabrication, and control with design features to maximize behavioral diversity. Non-linear rolling joints, anatomical tendon routing, and a low degree-of-freedom, modulating, actuation system, enable rapid production of single-piece 3D printable hands without compromising dexterous behaviors. To demonstrate this, we evaluated the design's low-level behavior range and stability, showing variable stiffness over two orders of magnitude. Additionally, we fabricated three hand designs: human, mirrored human with two thumbs, and aye-aye hands. Manipulation tests evaluate the variation in each hand's proficiency at handling diverse objects, and demonstrate emergent behaviors unique to each design. Overall, we shed light on new possible designs for robotic hands, provide a design space to compare and contrast different hand morphologies and structures, and share a practical and open-source design for exploring embodied manipulation., Comment: 44 pages, 11 figures

Multi-Q magnetic structures on triangular lattices, with their two-dimensional topological spin texture, have attracted significant interest. However, unambiguously confirming their formation by excluding the presence of three equally-populated single-Q domains remains challenging. In the metallic triangular lattice antiferromagnet Co1/3TaS2, two magnetic ground states have been suggested at different temperature ranges, with the low-temperature phase being a triple-Q structure corresponding to the highest-density Skyrmion lattice. Using inelastic neutron scattering (INS) and advanced spin dynamics simulations, we demonstrate a clear distinction in the excitation spectra between the single-Q and triple-Q phases of Co1/3TaS2 and, more generally, a triangular lattice. First, we refined the spin Hamiltonian by fitting the excitation spectra measured in its paramagnetic phase, allowing us to develop an unbiased model independent of magnetic ordering. Second, we observed that the two magnetically ordered phases in Co1/3TaS2 exhibit markedly different behaviors in their long-wavelength Goldstone modes. Our spin model, derived from the paramagnetic phase, confirms that these behaviors originate from the single-Q and triple-Q nature of the respective ordered phases, providing unequivocal evidence of the single-Q to triple-Q phase transition in Co1/3TaS2. Importantly, we propose that the observed contrast in the long-wavelength spin dynamics between the single-Q and triple-Q orderings is universal, offering a potentially unique way to distinguish a generic triple-Q ordering on a triangular lattice from its multi-domain single-Q counterparts. We describe its applicability with examples of similar hexagonal systems forming potential triple-Q orderings. (For the full abstract, please refer to the manuscript), Comment: 14 pages, 6 figures excluding Appendices

Understanding the nature of grain boundaries is a prerequisite for fabricating high-performance superconducting bulks and wires. For iron-based superconductors [e.g. Ba(Fe,Co)$_2$As$_2$, Fe(Se,Te), and NdFeAs(O,F)], the dependence of the critical current density $J_\mathrm{c}$ on misorientation angle ($\theta_\mathrm{GB}$) has been explored on [001]-tilt grain boundaries, but no data for other types of orientations have been reported. Here, we report on the structural and transport properties of Fe(Se,Te) grown on CeO$_2$-buffered symmetric [010]-tilt roof-type SrTiO$_3$ bicrystal substrates by pulsed laser deposition. X-ray diffraction and transmission electron microscopy revealed that $\theta_\mathrm{GB}$ of Fe(Se,Te) was smaller whereas $\theta_\mathrm{GB}$ of CeO$_2$ was larger than that of the substrate. The difference in $\theta_\mathrm{GB}$ between the CeO$_2$ buffer layer and the substrate is getting larger with increasing $\theta_\mathrm{GB}$. For $\theta_\mathrm{GB}\geq24^\circ$ of the substrates, $\theta_\mathrm{GB}$ of Fe(Se,Te) was zero, whereas $\theta_\mathrm{GB}$ of CeO$_2$ was continuously increasing. The inclined growth of CeO$_2$ can be explained by the geometrical coherency model. The $c$-axis growth of Fe(Se,Te) for $\theta_\mathrm{GB}\geq24^\circ$ of the substrates is due to the domain matching epitaxy on (221) planes of CeO$_2$. Electrical transport measurements confirmed no reduction of inter-grain $J_\mathrm{c}$ for $\theta_\mathrm{GB}\leq9^\circ$, indicative of strong coupling between the grains., Comment: 6 figures, with Supplementary Information

Recent advances in machine learning have paved the way for the development of musical and entertainment robots. However, human-robot cooperative instrument playing remains a challenge, particularly due to the intricate motor coordination and temporal synchronization. In this paper, we propose a theoretical framework for human-robot cooperative piano playing based on non-verbal cues. First, we present a music improvisation model that employs a recurrent neural network (RNN) to predict appropriate chord progressions based on the human's melodic input. Second, we propose a behavior-adaptive controller to facilitate seamless temporal synchronization, allowing the cobot to generate harmonious acoustics. The collaboration takes into account the bidirectional information flow between the human and robot. We have developed an entropy-based system to assess the quality of cooperation by analyzing the impact of different communication modalities during human-robot collaboration. Experiments demonstrate that our RNN-based improvisation can achieve a 93\% accuracy rate. Meanwhile, with the MPC adaptive controller, the robot could respond to the human teammate in homophony performances with real-time accompaniment. Our designed framework has been validated to be effective in allowing humans and robots to work collaboratively in the artistic piano-playing task., Comment: 20 pages

We present the first measurement of the missing energy due to nuclear effects in monoenergetic, muon neutrino charged-current interactions on carbon, originating from $K^+ \rightarrow \mu^+ \nu_\mu$ decay-at-rest ($E_{\nu_\mu}=235.5$ MeV), performed with the JSNS$^2$ liquid scintillator based experiment. Towards characterizing the neutrino interaction, ostensibly $\nu_\mu n \rightarrow \mu^- p$ or $\nu_\mu$$^{12}\mathrm{C}$ $\rightarrow \mu^-$$^{12}\mathrm{N}$, and in analogy to similar electron scattering based measurements, we define the missing energy as the energy transferred to the nucleus ($\omega$) minus the kinetic energy of the outgoing proton(s), $E_{m} \equiv \omega-\sum T_p$, and relate this to visible energy in the detector, $E_{m}=E_{\nu_\mu}~(235.5~\mathrm{MeV})-m_\mu~(105.7~\mathrm{MeV}) - E_{vis}$. The missing energy, which is naively expected to be zero in the absence of nuclear effects (e.g. nucleon separation energy, Fermi momenta, and final-state interactions), is uniquely sensitive to many aspects of the interaction, and has previously been inaccessible with neutrinos. The shape-only, differential cross section measurement reported, based on a $(77\pm3)$% pure double-coincidence KDAR signal (621 total events), provides an important benchmark for models and event generators at 100s-of-MeV neutrino energies, characterized by the difficult-to-model transition region between neutrino-nucleus and neutrino-nucleon scattering, and relevant for applications in nuclear physics, neutrino oscillation measurements, and Type-II supernova studies.

We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant $p$-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the $p$-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Moreover, two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of $^1S_0$ neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result would be useful for understanding many-body physics in astrophysical environments as well as the formation of multi-nucleon clusters in neutron-halo nuclei., Comment: 12 pages, 6 figures. Published version

The transparent formulation of explanation methods is essential for elucidating the predictions of neural networks, which are typically black-box models. Layer-wise Relevance Propagation (LRP) is a well-established method that transparently traces the flow of a model's prediction backward through its architecture by backpropagating relevance scores. However, the conventional LRP does not fully consider the existence of skip connections, and thus its application to the widely used ResNet architecture has not been thoroughly explored. In this study, we extend LRP to ResNet models by introducing Relevance Splitting at points where the output from a skip connection converges with that from a residual block. Our formulation guarantees the conservation property throughout the process, thereby preserving the integrity of the generated explanations. To evaluate the effectiveness of our approach, we conduct experiments on ImageNet and the Caltech-UCSD Birds-200-2011 dataset. Our method achieves superior performance to that of baseline methods on standard evaluation metrics such as the Insertion-Deletion score while maintaining its conservation property. We will release our code for further research at https://5ei74r0.github.io/lrp-for-resnet.page/, Comment: Accepted for presentation at ECCV2024

Soft robotics has emerged as the standard solution for grasping deformable objects, and has proven invaluable for mobile robotic exploration in extreme environments. However, despite this growth, there are no widely adopted computational design tools that produce quality, manufacturable designs. To advance beyond the diminishing returns of heuristic bio-inspiration, the field needs efficient tools to explore the complex, non-linear design spaces present in soft robotics, and find novel high-performing designs. In this work, we investigate a hierarchical design optimization methodology which combines the strengths of topology optimization and quality diversity optimization to generate diverse and high-performance soft robots by evolving the design domain. The method embeds variably sized void regions within the design domain and evolves their size and position, to facilitating a richer exploration of the design space and find a diverse set of high-performing soft robots. We demonstrate its efficacy on both benchmark topology optimization problems and soft robotic design problems, and show the method enhances grasp performance when applied to soft grippers. Our method provides a new framework to design parts in complex design domains, both soft and rigid.

FeSe$_{1-x}$S$_{x}$ superconductors are commonly considered layered van der Waals materials with negligible inter-layer coupling. Here, using inelastic neutron scattering to study spin excitations in single-crystal samples, we reveal that the magnetic coupling between adjacent Fe layers is not only significant, as it affects excitations up to \textcolor{black}{15} meV, but also ferromagnetic in nature, making the system different from most unconventional superconductors including iron pnictides. Our observation provides a new standpoint to understand the absence of magnetic order in FeSe$_{1-x}$S$_{x}$. Since intercalating between the Fe layers is known to enhance superconductivity and suppress the inter-layer coupling, superconductivity appears to be a more robust phenomenon in the two-dimensional limit than antiferromagnetic order.

This study introduces a groundbreaking approach to simultaneous interpretation by directly leveraging the predictive capabilities of Large Language Models (LLMs). We present a novel algorithm that generates real-time translations by predicting speaker utterances and expanding multiple possibilities in a tree-like structure. This method demonstrates unprecedented flexibility and adaptability, potentially overcoming the structural differences between languages more effectively than existing systems. Our theoretical analysis, supported by illustrative examples, suggests that this approach could lead to more natural and fluent translations with minimal latency. The primary purpose of this paper is to share this innovative concept with the academic community, stimulating further research and development in this field. We discuss the theoretical foundations, potential advantages, and implementation challenges of this technique, positioning it as a significant step towards democratizing multilingual communication., Comment: 7 pages