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Topology profoundly influences diverse fields of science, providing a powerful framework for classifying phases of matter and predicting nontrivial excitations, such as solitons, vortices, and skyrmions. These topological defects are typically characterized by integer numbers, called topological charges, representing the winding number in their order parameter field. The classification and prediction of topological defects, however, become challenging when singularities are included within the integration domain for calculating the topological charge. While such exotic nonlinear excitations have been proposed in the superfluid $^3$He-A phase and spinor Bose-Einstein condensate of atomic gases, experimental observation of these structures and studies of their stability have long been elusive. Here we report the observation of a singular skyrmion that goes beyond the framework of topology in a ferromagnetic superfluid. The exotic skyrmions are sustained by undergoing anomalous symmetry breaking associated with the eccentric spin singularity and carry half of the elementary charge, distinctive from conventional skyrmions or merons. By successfully realizing the universal regime of the quantum Kelvin-Helmholtz instability, we identified the eccentric fractional skyrmions, produced by emission from a magnetic domain wall and a spontaneous splitting of an integer skyrmion with spin singularities. The singular skyrmions are stable and can be observed after 2~s of hold time. Our results confirm the universality between classical and quantum Kelvin-Helmholtz instabilities and broaden our understanding on complex nonlinear dynamics of nontrivial texture beyond skyrmion in topological quantum systems., Comment: 13 pages, 5 main figures and 7 supplemental figures

In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operators whose symbols depend only on time and spatial frequencies. The main focus of this paper is to relax the conditions on the symbols of pseudo-differential operators and data while still ensuring that the stochastic partial differential equations remain well-posed in a weak sense. Specifically, we allow symbols to be random and remove all regularity and ellipticity conditions on them. As a result, our main operators include many interesting rough operators that cannot generate any regularity gain or integrability improvement from the equations. In addition, our data do not need to be regular or possess finite stochastic moments., Comment: 91 pages

In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to infinity under the effect of surface tension. We assume that the two fluids are immiscible and incompressible and that there is no interfacial jump in the fluid velocity. For this PDE system, a circular fluid bubble is a steady-state solution. Given an initial contour for the fluid bubble which is sufficiently close to a circle, we show that there exists a unique, global-in-time solution. This unique solution decays to a circle exponentially fast, which means that circular fluid bubbles are stable steady-state solutions. We also obtain a result concerning the regularity of the unique solution, that although the initial perturbation around a circular contour is assumed to be of low regularity, any later perturbation becomes real analytic, hence smooth., Comment: 53 pages, 0 figures

The NEON experiment, situated at the Hanbit Nuclear Power Plant, is designed to observe coherent neutrinonucleus scattering (CE{\nu}NS) and search for dark sector particle such as axion-like particles (ALPs). Using six NaI(Tl) detector modules, data were collected during both reactor-on and reactor-off periods between April 2022 and June 2023, providing a total exposure of 1596 kg{\cdot}days and 1467 kg{\cdot}days, respectively. The search for ALPs leverages the difference between reactor-on and reactor-off datasets. A thorough understanding of time-dependent backgrounds, including cosmogenic activation and seasonal variations of radon contamination, is essential to the analysis. This paper presents detailed modeling of these backgrounds, identifying their contributions across different energy ranges and detector modules. Systematic uncertainties arising from energy resolution, background shape, and rate variations are considered in the final analysis. The results provide insights into the future potential of ALP searches in short-baseline reactor experiments and demonstrate the efficacy of background reduction techniques in the NEON experiment., Comment: We have included information on the time-dependent background model for the NEON experiment in this manuscript. The manuscript will be updated later with the corrected results from the ALP search

This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and variable-order nonlocal operators in mixed norm $L_q(L_p)$-spaces. We introduce a new condition (strongly reinforced Dalang's condition) on colored noise, which facilitates a deeper understanding of the complicated relation between nonlinearities and stochastic forces. Additionally, we establish the space-time H\"older type regularity of solutions., Comment: 47 pages

As recent advances in mobile camera technology have enabled the capability to capture high-resolution images, such as 4K images, the demand for an efficient deblurring model handling large motion has increased. In this paper, we discover that the image residual errors, i.e., blur-sharp pixel differences, can be grouped into some categories according to their motion blur type and how complex their neighboring pixels are. Inspired by this, we decompose the deblurring (regression) task into blur pixel discretization (pixel-level blur classification) and discrete-to-continuous conversion (regression with blur class map) tasks. Specifically, we generate the discretized image residual errors by identifying the blur pixels and then transform them to a continuous form, which is computationally more efficient than naively solving the original regression problem with continuous values. Here, we found that the discretization result, i.e., blur segmentation map, remarkably exhibits visual similarity with the image residual errors. As a result, our efficient model shows comparable performance to state-of-the-art methods in realistic benchmarks, while our method is up to 10 times computationally more efficient., Comment: CVPR2024 Camera-Ready

We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This formulation is applicable to evolution equations involving pseudo-differential operators, even when the signs of their symbols may vary over time. Notably, our main operator includes the logarithmic Laplacian operator $\log (-\Delta)$ and a second-order differential operator whose leading coefficients are not positive semi-definite., Comment: 49 pages

Large language models (LLMs) have recently received considerable attention as alternative solutions for task planning. However, comparing the performance of language-oriented task planners becomes difficult, and there exists a dearth of detailed exploration regarding the effects of various factors such as pre-trained model selection and prompt construction. To address this, we propose a benchmark system for automatically quantifying performance of task planning for home-service embodied agents. Task planners are tested on two pairs of datasets and simulators: 1) ALFRED and AI2-THOR, 2) an extension of Watch-And-Help and VirtualHome. Using the proposed benchmark system, we perform extensive experiments with LLMs and prompts, and explore several enhancements of the baseline planner. We expect that the proposed benchmark tool would accelerate the development of language-oriented task planners., Comment: ICLR 2024. Code: https://github.com/lbaa2022/LLMTaskPlanning

This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and continuity of solutions., Comment: 19 pages; The paper has been accepted for publication in "Potential Analysis"