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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"

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are other norms arising in the theory of partial differential equations such as Sobolev-Slobodeckij spaces. It is known that two norms are equivalent when one considers constant regularity function spaces without weights. We show that the equivalence still holds for variable smoothness and weights, which is accomplished by making use of shifted maximal functions, Peetre's maximal functions, and the reverse H\"older inequality. Moreover, we obtain a weighted regularity estimate for time-fractional evolution equations and a generalized Sobolev embedding theorem without weights., Comment: 36 pages

In recent years, patch-based image restoration approaches have demonstrated superior performance compared to conventional variational methods. This paper delves into the mathematical foundations underlying patch-based image restoration methods, with a specific focus on establishing restoration guarantees for patch-based image inpainting, leveraging the assumption of self-similarity among patches. To accomplish this, we present a reformulation of the image inpainting problem as structured low-rank matrix completion, accomplished by grouping image patches with potential overlaps. By making certain incoherence assumptions, we establish a restoration guarantee, given that the number of samples exceeds the order of $rlog^2(N)$, where $N\times N$ denotes the size of the image and $r > 0$ represents the sum of ranks for each group of image patches. Through our rigorous mathematical analysis, we provide valuable insights into the theoretical foundations of patch-based image restoration methods, shedding light on their efficacy and offering guidelines for practical implementation.

This paper considers traces at the initial time for solutions of evolution equations with local or non-local derivatives in vector-valued $L_p$ spaces with $A_p$ weight. To achieve this, we begin by introducing a generalized real interpolation method. Within the framework of generalized interpolation theory, we make use of stochastic process theory and two-weight Hardy's inequality to derive our trace and extension theorems. Our results encompass findings applicable to time-fractional equations with broad temporal weight functions., Comment: few glitches corrected, Appendix B for finite time case added

Quantitative organ assessment is an essential step in automated abdominal disease diagnosis and treatment planning. Artificial intelligence (AI) has shown great potential to automatize this process. However, most existing AI algorithms rely on many expert annotations and lack a comprehensive evaluation of accuracy and efficiency in real-world multinational settings. To overcome these limitations, we organized the FLARE 2022 Challenge, the largest abdominal organ analysis challenge to date, to benchmark fast, low-resource, accurate, annotation-efficient, and generalized AI algorithms. We constructed an intercontinental and multinational dataset from more than 50 medical groups, including Computed Tomography (CT) scans with different races, diseases, phases, and manufacturers. We independently validated that a set of AI algorithms achieved a median Dice Similarity Coefficient (DSC) of 90.0\% by using 50 labeled scans and 2000 unlabeled scans, which can significantly reduce annotation requirements. The best-performing algorithms successfully generalized to holdout external validation sets, achieving a median DSC of 89.5\%, 90.9\%, and 88.3\% on North American, European, and Asian cohorts, respectively. They also enabled automatic extraction of key organ biology features, which was labor-intensive with traditional manual measurements. This opens the potential to use unlabeled data to boost performance and alleviate annotation shortages for modern AI models., Comment: MICCAI FLARE22: https://flare22.grand-challenge.org/

In this paper, we present an $L_q(L_p)$-regularity theory for parabolic equations of the form: $$ \partial_t u(t,x)=\mathcal{L}^{\vec{a},\vec{b}}(t)u(t,x)+f(t,x),\quad u(0,x)=0. $$ Here, $\mathcal{L}^{\vec{a},\vec{b}}(t)$ represents anisotropic non-local operators encompassing the singular anisotropic fractional Laplacian with measurable coefficients: $$ \mathcal{L}^{\vec{a},\vec{0}}(t)u(x)=\sum_{i=1}^{d} \int_{\mathbb{R}}\left( u(x^{1},\dots,x^{i-1},x^{i}+y^{i},x^{i+1},\dots,x^{d}) - u(x) \right) \frac{a_{i}(t,y^{i})}{|y^{i}|^{1+\alpha_{i}}} \mathrm{d}y^{i} . $$ To address the anisotropy of the operator, we employ a probabilistic representation of the solution and Calder\'on-Zygmund theory. As applications of our results, we demonstrate the solvability of elliptic equations with anisotropic non-local operators and parabolic equations with isotropic non-local operators.

Underwater communication signals typically suffer from distortion due to motion-induced Doppler. Especially in shallow water environments, recovering the signal is challenging due to the time-varying Doppler effects distorting each path differently. However, conventional Doppler estimation algorithms typically model uniform Doppler across all paths and often fail to provide robust Doppler tracking in multipath environments. In this paper, we propose a dynamic programming-inspired method, called online segmented recursive least-squares (OSRLS) to sequentially estimate the time-varying non-uniform Doppler across different multipath arrivals. By approximating the non-linear time distortion as a piece-wise-linear Markov model, we formulate the problem in a dynamic programming framework known as segmented least-squares (SLS). In order to circumvent an ill-conditioned formulation, perturbations are added to the Doppler model during the linearization process. The successful operation of the algorithm is demonstrated in a simulation on a synthetic channel with time-varying non-uniform Doppler.

Exotic quantum many-body states, such as Haldane and spin liquid phases, can exhibit remarkable features like fractional excitations and non-abelian statistics and offer new understandings of quantum entanglement in many-body quantum systems. These phases are classified by non-local correlators that can be directly measured in atomic analog quantum simulating platforms, such as optical lattices and Rydberg atom arrays. However, characterizing these phases in large systems is experimentally challenging because they are sensitive to local errors like atom loss, which suppress its signals exponentially. Additionally, protocols for systematically identifying and mitigating uncorrelated errors in analog quantum simulators are lacking. Here, we address these challenges by developing an error correction method for large-scale neutral atom quantum simulators using optical lattices. Our error correction method can distinguish correlated particle-hole pairs from uncorrelated holes in the Mott insulator. After removing the uncorrelated errors, we observe a dramatic improvement in the non-local parity correlator and find the perimeter scaling law. Furthermore, the error model provides a statistical estimation of fluctuations in site occupation, from which we measure the generalized brane correlator and confirm that it can be an order parameter for Mott insulators in two dimensions. Our work provides a promising avenue for investigating and characterizing exotic phases of matters in large-scale quantum simulators., Comment: 7 pages, 4 figures, and supplemental materials

Scale invariance and self-similarity in physics provide a unified framework to classify phases of matter and dynamical properties of near-equilibrium systems. However, extending this framework to far-from-equilibrium quantum many-body systems and categorizing their dynamics have remained a major challenge in physics. Here, we report on the first classification of universal coarsening dynamics in a quenched two-dimensional ferromagnetic spinor Bose gas. We observe spatiotemporal scaling of spin correlation functions with distinguishable scaling exponents, $1/z=0.58(2)$ and $1/z=0.43(2)$, characteristic, respectively, of binary and diffusive fluids. We find the universality class of the coarsening dynamics are determined by the symmetry of the order parameters and the annihilation dynamics of the topological defects. These observations are in excellent agreement with many-body simulations. Our results represent a paradigmatic example of categorizing far-from-equilibrium dynamics in quantum many-body systems., Comment: 7 pages, 5 figures, and supplemental materials

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt's class, and the initial data is in weighted Besov spaces with variable order., Comment: 47 pages

The COSINE-100 experiment has been operating with 106 kg of low-background NaI(Tl) detectors to test the results from the DAMA/LIBRA experiment, which claims to have observed dark matter. However, since the background of the NaI(Tl) crystals used in the COSINE-100 experiment is 2-3 times higher than that in the DAMA detectors, no conclusion regarding the claimed observation from the DAMA/LIBRA experiment could be reached. Therefore, we plan to upgrade the current COSINE-100 experiment to the next phase, COSINE-200, by using ultra-low background NaI(Tl) detectors. The basic principle was already proved with the commercially available Astro-grade NaI powder from Sigma-Aldrich company. However, we have developed a mass production process of ultra-pure NaI powder at the Center for Underground Physics (CUP) of the Institute for Basic Science (IBS), Korea, using the direct purification of the raw NaI powder. We plan to produce more than 1,000 kg of ultra-pure powder for the COSINE200 experiment. With our crystal grower installed at CUP, we have successfully grown a low-background crystal using our purification technique for the NaI powder. We have assembled a low-background NaI(Tl) detector. In this article, we report the performance of this ultra-pure NaI(Tl) crystal detector produced at IBS, Korea.

As technology advances, it is possible to process a lot of data, and as various elements in the city become diverse and complex, cities are becoming smart cities. One of the core systems of smart cities is Cooperative-Intelligent Transport Systems (C-ITS). C-ITS is a system that provides drivers with real-time accident risk information such as surrounding traffic conditions, sudden stops, and falling objects while a vehicle is driving, and consists of road infrastructure, C-ITS center, and vehicle terminals. Meanwhile, smart cities can have cybersecurity problems because many elements of the city are networked and electronically controlled. If cybersecurity problems occur in C-ITS, there is a high risk of safety problems. The purpose of this technical document is to describe C-ITS environment modeling and C-ITS attack scenarios for C-ITS security. After describing the concept of C-ITS and MITRE ATT&CK, we describe the C-ITS environment model and the attack scenario model that we define., Comment: in Korean language

For more clinical applications of deep learning models for medical image segmentation, high demands on labeled data and computational resources must be addressed. This study proposes a coarse-to-fine framework with two teacher models and a student model that combines knowledge distillation and cross teaching, a consistency regularization based on pseudo-labels, for efficient semi-supervised learning. The proposed method is demonstrated on the abdominal multi-organ segmentation task in CT images under the MICCAI FLARE 2022 challenge, with mean Dice scores of 0.8429 and 0.8520 in the validation and test sets, respectively.

In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which has the minimal $\ell_1$-norm of the canonical wavelet frame coefficients among all possible solutions. Then we further connect the error estimate for the discrete model to the approximation to the underlying function from which the underlying image comes., Comment: arXiv admin note: text overlap with arXiv:2207.07473

The finite-rate-of-innovation (FRI) framework which corresponds a signal/image to a structured low-rank matrix is emerging as an alternative to the traditional sparse regularization. This is because such an off-the-grid approach is able to alleviate the basis mismatch between the true support in the continuous domain and the discrete grid. In this paper, we propose a two-stage off-the-grid regularization model for the image restoration. Given that the discontinuities/edges of the image lie in the zero level set of a band-limited periodic function, we can derive that the Fourier samples of the gradient of the image satisfy an annihilation relation, resulting in a low-rank two-fold Hankel matrix. In addition, since the singular value decomposition of a low-rank Hankel matrix corresponds to an adaptive tight frame system which can represent the image with sparse canonical coefficients, our approach consists of the following two stages. The first stage learns the tight wavelet frame system from a given measurement, and the second stage restores the image via the analysis approach based sparse regularization. The numerical results are presented to demonstrate that the proposed approach is compared favorably against several popular discrete regularization approaches and structured low-rank matrix approaches., Comment: arXiv admin note: text overlap with arXiv:2012.06827

The performances of commonly used electrocardiogram (ECG) diagnosis models have recently improved with the introduction of deep learning (DL). However, the impact of various combinations of multiple DL components and/or the role of data augmentation techniques on the diagnosis have not been sufficiently investigated. This study proposes an ensemble-based multi-view learning approach with an ECG augmentation technique to achieve a higher performance than traditional automatic 12-lead ECG diagnosis methods. The data analysis results show that the proposed model reports an F1 score of 0.840, which outperforms existing state-ofthe-art methods in the literature., Comment: 9 pages, 3 figures, and 5 tables

Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in the framework of compressed sensing, there are few works on the restoration guarantee of the restoration from partial observations. This paper is to analyze the error of TV based restoration from random entrywise samples. In particular, we estimate the error between the underlying original data and the approximate solution that interpolates (or approximates with an error bound depending on the noise level) the given data that has the minimal TV seminorm among all possible solutions. Finally, we further connect the error estimate for the discrete model to the sparse gradient restoration problem and to the approximation to the underlying function from which the underlying true data comes.

We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem \begin{equation}\label{ab eqn} \begin{cases} \partial_t u(t,x)=\psi(t,-i\nabla)u(t,x)+f(t,x),\quad &(t,x)\in(0,T)\times\mathbb{R}^d,\\ u(0,x)=0,\quad & x\in\mathbb{R}^d \end{cases} \end{equation} in (Muckenhoupt) weighted $L_p$-spaces with time-measurable pseudo-differential operators \begin{equation} \label{ab op} \psi(t,-i\nabla)u(t,x):=\mathcal{F}^{-1}\left[\psi(t,\cdot)\mathcal{F}[u](t,\cdot)\right](x). \end{equation} More precisely, we find sufficient conditions of the symbol $\psi(t,\xi)$ (especially depending on the smoothness of the symbol with respect to $\xi$) to guarantee that equation is well-posed in (Muckenhoupt) weighted $L_p$-spaces. Here the symbol $\psi(t,\xi)$ is merely measurable with respect to $t$, and the sufficient smoothness of $\psi(t,\xi)$ with respect to $\xi$ is characterized by a property of each weight. In particular, we prove the existence of a positive constant $N$ such that for any solution $u$ to the equation, \begin{equation} \label{ab est} \int_0^T \int_{\mathbb{R}^d} |(-\Delta)^{\gamma/2} u(t,x) |^p (t^2 + |x|^2)^{\alpha/2} \mathrm{d}x\mathrm{d}t \leq N\int_0^T \int_{\mathbb{R}^d} |f(t,x)|^p (t^2 + |x|^2)^{\alpha/2} \mathrm{d}x\mathrm{d}t \end{equation} and \begin{equation} \label{ab est 2} \int_0^T \left(\int_{\mathbb{R}^d} |(-\Delta)^{\gamma/2} u(t,x) |^p |x|^{\alpha_2} \mathrm{d}x \right)^{q/p} t^{\alpha_1}\mathrm{d}t \leq N\int_0^T \left(\int_{\mathbb{R}^d} |f(t,x) |^p |x|^{\alpha_2} \mathrm{d}x \right)^{q/p} t^{\alpha_1}\mathrm{d}t, \end{equation} where $p,q\in(1,\infty)$, $-d-1<\alpha < (d+1)(p-1)$, $-1 < \alpha_1 < q-1$, $-d <\alpha_2< d(p-1)$, and $\gamma$ is the order of the operator $\psi(t,-i\nabla)$., Comment: 41 pages, We corrected some typos

We study the zero exterior problem for the elliptic equation $$ \Delta^{\alpha/2}u-\lambda u=f, \quad x\in D\,; \quad u|_{D^c}=0 $$ as well as for the parabolic equation $$ u_t=\Delta^{\alpha/2}u+f, \quad t>0,\, x\in D \,; \quad u(0,\cdot)|_D=u_0, \,u|_{[0,T]\times D^c}=0. $$ Here, $\alpha\in (0,2)$, $\lambda \geq 0$ and $D$ is a $C^{1,1}$ open set. We prove uniqueness and existence of solutions in weighted Sobolev spaces, and obtain global Sobolev and H\"older estimates of solutions and their arbitrary order derivatives. We measure the Sobolev and H\"older regularities of solutions and their arbitrary derivatives using a system of weights consisting of appropriate powers of the distance to the boundary. The range of admissible powers of the distance to the boundary is sharp., Comment: 42 pages; Title changed; The paper has been accepted for publication in "Discrete and Continuous Dynamical Systems (DCDS)"

Cavities play a fundamental role in optical physics by providing spatio-temporal confinement of energy that facilitates light-matter interactions. They are routinely utilized in a variety of settings, ranging from lasers to spectral filters, to nonlinear wave mixers, and modulators. While their resonant properties make them suitable for sensing, in many applications, like in lasers, it is desired to alleviate their sensitivity in order to make a device more resilient to perturbations. Along these lines there have been several recent reports of using concepts from topological physics in order to design laser arrays that are inherently more robust. Here, we present a new class of topological cavities based on Majorana bound states that provide unique scaling features as well as non-degenerate single-mode behaviors. These cavities may lead to a new family of lasers and laser arrays that are robust to defects, fabrication imperfections, and external perturbations.

Domain Adaptation (DA) has recently raised strong interests in the medical imaging community. While a large variety of DA techniques has been proposed for image segmentation, most of these techniques have been validated either on private datasets or on small publicly available datasets. Moreover, these datasets mostly addressed single-class problems. To tackle these limitations, the Cross-Modality Domain Adaptation (crossMoDA) challenge was organised in conjunction with the 24th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2021). CrossMoDA is the first large and multi-class benchmark for unsupervised cross-modality DA. The challenge's goal is to segment two key brain structures involved in the follow-up and treatment planning of vestibular schwannoma (VS): the VS and the cochleas. Currently, the diagnosis and surveillance in patients with VS are performed using contrast-enhanced T1 (ceT1) MRI. However, there is growing interest in using non-contrast sequences such as high-resolution T2 (hrT2) MRI. Therefore, we created an unsupervised cross-modality segmentation benchmark. The training set provides annotated ceT1 (N=105) and unpaired non-annotated hrT2 (N=105). The aim was to automatically perform unilateral VS and bilateral cochlea segmentation on hrT2 as provided in the testing set (N=137). A total of 16 teams submitted their algorithm for the evaluation phase. The level of performance reached by the top-performing teams is strikingly high (best median Dice - VS:88.4%; Cochleas:85.7%) and close to full supervision (median Dice - VS:92.5%; Cochleas:87.7%). All top-performing methods made use of an image-to-image translation approach to transform the source-domain images into pseudo-target-domain images. A segmentation network was then trained using these generated images and the manual annotations provided for the source image., Comment: In Medical Image Analysis

We demonstrate a single-site and single-atom-resolved fluorescence imaging of a bosonic Mott insulator of $^7$Li atoms in an optical lattice. The fluorescence images are obtained by implementing Raman sideband cooling on a deep two-dimensional square lattice, where we collect scattered photons with a high numerical aperture objective lens. The square lattice is created by a folded retro-reflected beam configuration that can reach 2.5~mK lattice depth from a single laser source. The lattice beam is elliptically focused to have a large area with deep potential. On average 4,000 photons are collected per atom during 1~s of the Raman sideband cooling, and the imaging fidelity is over 95$\%$ in the central 80$\times$80 lattice sites. As a first step to study correlated quantum phases, we present the site-resolved imaging of a Mott insulator. Tuning the magnetic field near the Feshbach resonance, the scattering length can be increased to 680$a_B$, and we are able to produce a large-sized unity filling Mott insulator with 2,000 atoms at low temperature. Our work provides a stepping stone to further in-depth investigations of intriguing quantum many-body phases in optical lattices., Comment: 9 pages, 5 figures

The purpose of this study is to apply and evaluate out-of-the-box deep learning frameworks for the crossMoDA challenge. We use the CUT model, a model for unpaired image-to-image translation based on patchwise contrastive learning and adversarial learning, for domain adaptation from contrast-enhanced T1 MR to high-resolution T2 MR. As data augmentation, we generate additional images with vestibular schwannomas with lower signal intensity. For the segmentation task, we use the nnU-Net framework. Our final submission achieved mean Dice scores of 0.8299 in the validation phase and 0.8253 in the test phase. Our method ranked 3rd in the crossMoDA challenge., Comment: 9 pages, 3 figures, MICCAI 2021 Cross-Modality Domain Adaptation for Medical Image Segmentation Challenge; extended manuscript and modified results

The use of wireless implanted medical devices (IMDs) is growing because they facilitate continuous monitoring of patients during normal activities, simplify medical procedures required for data retrieval and reduce the likelihood of infection associated with trailing wires. However, most of the state-of-the-art IMDs are passive and offline devices. One of the key obstacles to an active and online IMD is the infeasibility of real-time, high-quality video broadcast from the IMD. Such broadcast would help develop innovative devices such as a video-streaming capsule endoscopy (CE) pill with therapeutic intervention capabilities. State-of-the-art IMDs employ radio-frequency electromagnetic waves for information transmission. However, high attenuation of RF-EM waves in tissues and federal restrictions on the transmit power and operable bandwidth lead to fundamental performance constraints for IMDs employing RF links, and prevent achieving high data rates that could accomodate video broadcast. In this work, ultrasonic waves were used for video transmission and broadcast through biological tissues. The proposed proof-of-concept system was tested on a porcine intestine ex vivo and a rabbit in vivo. It was demonstrated that using a millimeter-sized, implanted biocompatible transducer operating at 1.1-1.2 MHz, it was possible to transmit endoscopic video with high resolution (1280 pixels by 720 pixels) through porcine intestine wrapped with bacon, and to broadcast standard definition (640 pixels by 480 pixels) video near real-time through rabbit abdomen in vivo. A media repository that includes experimental demonstrations and media files accompanies this paper. The accompanying media repository can be found at this link: https://bit.ly/3wuc7tk., Comment: arXiv admin note: text overlap with arXiv:1909.13172

Matching and recommending products is beneficial for both customers and companies. With the rapid increase in home goods e-commerce, there is an increasing demand for quantitative methods for providing such recommendations for millions of products. This approach is facilitated largely by online stores such as Amazon and Wayfair, in which the goal is to maximize overall sales. Instead of focusing on overall sales, we take a product design perspective, by employing big-data analysis for determining the design qualities of a highly recommended product. Specifically, we focus on the visual style compatibility of such products. We build off previous work which implemented a style-based similarity metric for thousands of furniture products. Using analysis and visualization, we extract attributes of furniture products that are highly compatible style-wise. We propose a designer in-the-loop workflow that mirrors methods of displaying similar products to consumers browsing e-commerce websites. Our findings are useful when designing new products, since they provide insight regarding what furniture will be strongly compatible across multiple styles, and hence, more likely to be recommended., Comment: 15 pages, 9 figures, interdisciplinary book chapter on using computer vision and style similarity for industrial design

Topological insulator lasers (TILs) are a recently introduced family of lasing arrays in which phase locking is achieved through synthetic gauge fields. These single frequency light source arrays operate in the spatially extended edge modes of topologically non-trivial optical lattices. Because of the inherent robustness of topological modes against perturbations and defects, such topological insulator lasers tend to demonstrate higher slope efficiencies as compared to their topologically trivial counterparts. So far, magnetic and non-magnetic optically pumped topological laser arrays as well as electrically pumped TILs that are operating at cryogenic temperatures have been demonstrated. Here we present the first room temperature and electrically pumped topological insulator laser. This laser array, using a structure that mimics the quantum spin Hall effect for photons, generates light at telecom wavelengths and exhibits single frequency emission. Our work is expected to lead to further developments in laser science and technology, while opening up new possibilities in topological photonics.

The purpose of this paper is to provide a more general Cameron-Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process $\mathcal Z_k$ on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions $a(t)$ and $b(t)$ on $[0,T]$. As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley-Wiener-Zygmund stochastic integrals.

In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is a function space which is induced by the generalized Brownian motion process associated with continuous functions $a$ and $b$. The structure of the analytic operator-valued generalized Feynman integral is suggested and the existence of the analytic operator-valued generalized Feynman integral is investigated as an operator from $L^1(\mathbb R, \nu_{\delta,a})$ to $L^{\infty}(\mathbb R)$ where $\nu_{\delta,a}$ is a $\sigma$-finite measure on $\mathbb R$ given by \[ d\nu_{\delta,a}=\exp\{\delta \mathrm{Var}(a)u^2\} du, \] where $\delta>0$ and $\mathrm{Var}(a)$ denotes the total variation of the mean function $a$ of the generalized Brownian motion process. It turns out in this paper that the analytic operator-valued generalized Feynman integrals of functionals defined by the stochastic Fourier--Stieltjes transform of complex measures on the infinite dimensional Hilbert space $C_{a,b}'[0,T]$ are elements of the linear space \[ \bigcap_{\delta>0} \mathcal L( L^1(\mathbb R,\nu_{\delta,a}),L^{\infty}(\mathbb R)). \], Comment: 24pages

We study nonlinear response of a dimer composed of two identical Mie-resonant dielectric nanoparticles illuminated normally by a circularly polarized light. We develop a general theory describing hybridization of multipolar modes of the coupled nanoparticles, and reveal nonvanishing nonlinear circular dichroism (CD) in the second-harmonic generation (SHG) signal enhanced by the multipolar resonances in the dimer provided its axis is oriented under an angle to the crystalline lattice of the dielectric material. We present experimental results for this SHG-CD effect obtained for the AlGaAs dimers placed on an engineered substrate which confirm the basic prediction of our general multipolar hybridization theory.

We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of $^7$Li atoms. Directional atomic beams with $|{F=1,m_F=1}\rangle$ and $|{F=1,m_F=-1}\rangle$ spin states are generated from $|{F=1,m_F=0}\rangle$ state condensates, or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states ($|{F=1,m_F=\pm1}\rangle$) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter-spin and intra-spin momentum correlation peaks display a high contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level and can identify its entanglement after 100~ms of a long time-of-flight., Comment: 13 pages(6 main text, 7 supplemental material), 12 figures

The collective response of a system is profoundly shaped by the interaction dynamics between its constituent elements. In physics, tailoring these interactions can enable the observation of unusual phenomena that are otherwise inaccessible in standard settings, ranging from the possibility of a Kramer's degeneracy even in the absence of spin to the breakdown of the bulkboundary correspondence. Here, we show how such tailored asymmetric coupling terms can be realized in photonic integrated platforms by exploiting non-Hermitian concepts. In this regard, we introduce a generalized photonic molecule composed of a pair of microring resonators with internal S-bends connected via two directional couplers and a link waveguide. By judiciously designing the parameters of this system, namely the length of the links and the power division ratio of the directional couplers, we experimentally show the emergence of Hermitian and non-Hermitian type exchange interactions. The ramifications of such coupling dynamics are then studied in 1D chain and ring-type active lattices. Our findings establish the proposed structure as a promising building block for the realization of a variety of phenomena, especially those associated with phase locking in laser arrays and non-Hermitian topological lattices.

Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the continuous domain and the discrete grid. In this paper, we introduce a novel structured low rank matrix framework to restore piecewise smooth functions. Inspired by the total generalized variation to use sparse higher order derivatives, we derive that the Fourier samples of higher order derivatives satisfy an annihilation relation, resulting in a low rank multi-fold Hankel matrix. We further observe that the SVD of a low rank Hankel matrix corresponds to a tight wavelet frame system which can represent the image with sparse coefficients. Based on this observation, we also propose a wavelet frame analysis approach based continuous domain regularization model for the piecewise smooth image restoration. Finally, numerical results on image restoration tasks are presented as a proof-of-concept study to demonstrate that the proposed approach is compared favorably against several popular discrete regularization approaches and structured low rank matrix approaches.

Creating realistic styled spaces is a complex task, which involves design know-how for what furniture pieces go well together. Interior style follows abstract rules involving color, geometry and other visual elements. Following such rules, users manually select similar-style items from large repositories of 3D furniture models, a process which is both laborious and time-consuming. We propose a method for fast-tracking style-similarity tasks, by learning a furniture's style-compatibility from interior scene images. Such images contain more style information than images depicting single furniture. To understand style, we train a deep learning network on a classification task. Based on image embeddings extracted from our network, we measure stylistic compatibility of furniture. We demonstrate our method with several 3D model style-compatibility results, and with an interactive system for modeling style-consistent scenes., Comment: Accepted to Pacific Graphics 2020

Let $Z=(Z_t)_{t\geq0}$ be an additive process with a bounded triplet $(0,0,\Lambda_t)_{t\geq0}$. Suppose that for any Schwartz function $\varphi$ on $\mathbb{R}^d$ whose Fourier transform is in $C_c^{\infty}(B_{c_s} \setminus B_{c_s^{-1}} )$, there exist positive constants $N_0$, $N_1$, and $N_2$ such that \begin{equation*} \int_{\mathbb{R}^d}|\mathbb{E}[\varphi(x+r^{-1}Z_t)]|dx\leq N_0 e^{- \frac{N_1 t}{s(r)}},\quad \forall (r,t)\in(0,1)\times[0,T], \end{equation*} and $$ \|\psi^{\mu}(r^{-1}D)\varphi\|_{L_1(\mathbb{R}^d)}\leq \frac{N_2}{s(r)},\quad \forall r\in(0,1). $$ where $s$ is a scaling function (Definition 2.4), $c_s$ is a positive constant related to $s$, $\mu$ is a symmetric L\'evy measure on $\mathbb{R}^d$, $\psi^{\mu}(r^{-1}D)\varphi(x)= \mathcal{F}^{-1} \left[ \psi^{\mu}(r^{-1}\xi) \mathcal{F}[\varphi]\right](x)$ and $$\psi^{\mu}(\xi):=\int_{\mathbb{R}^d}(e^{iy\cdot\xi}-1-iy\cdot\xi 1_{|y|\leq 1})\mu(dy).$$ In this paper, we establish the $L_p$-solvability to the initial value problem \begin{equation} \frac{\partial u}{\partial t}(t,x)=\mathcal{A}_Z(t)u(t,x),\quad u(0,\cdot)=u_0,\quad (t,x)\in(0,T)\times\mathbb{R}^d, \end{equation} In other words, there exists a unique solution $u$ to equation satisfying $$ \|u\|_{L_q((0,T);H_p^{\mu;\gamma}(\mathbb{R}^d))}\leq N\|u_0\|_{B_{p,q}^{s;\gamma-\frac{2}{q}}(\mathbb{R}^d)}, $$ where $N$ is independent of $u$ and $u_0$, and the spaces $B_{p,q}^{s;\gamma-\frac{2}{q}}(\mathbb{R}^d)$ and $H_p^{\mu;\gamma}(\mathbb{R}^d)$ are scaled Besov spaces (see Definition 2.8) and generalized Bessel potential spaces (see Definition 2.3), respectively., Comment: 47 pages

We report the observation of strongly ferromagnetic $F=1$ spinor Bose-Einstein condensates of $^7$Li atoms. The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom. Studying the non-equilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the $s$-wave scattering length difference among total spin $f$ channels to be $a_{f=2}-a_{f=0} =-18(3)$ Bohr radius. This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition. We were able to excite a radial monopole mode after a spin-flip transition between the $|m_F=0\rangle$ and $|m_F=1\rangle$ spin states. From the experiments, we estimated the scattering length ratio $a_{f=2}/a_{f=0}=0.27(6)$, and determined $a_{f=2}$ = 7(2) and $a_{f=0}$ = 25(5) Bohr radii, respectively. The results indicate the spin-dependent interaction energy of our system is as large as 46$\%$ of the condensate chemical potential.

Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad (t,x)\in(0,\infty)\times\mathbb{R}^d, $$ where $\lambda \geq 0$ and the coefficients depend on $(\omega,t,x)$. The strategy of handling nonlinearity of the diffusion coefficient is to find a sharp estimation for a general Lipschitz case, and apply it to the super-linear case. Moreover, investigation for the estimate provides a range of $\lambda$, a sufficient condition for the unique solvability, where the range depends on the spatial covariance of $F$ and the spatial dimension $d$., Comment: 27 pages

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space $C_{a,b}^2[0,T]$. The function space $C_{a,b}[0,T]$ can be induced by the generalized Brownian motion process associated with continuous functions $a$ and $b$. To do this we first introduce the class $\mathcal F_{A_1,A_2}^{\,\,a,b}$ of functionals on $C_{a,b}^2[0,T]$ which is a generalization of the Kallianpur and Bromley Fresnel class $\mathcal F_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick type theorem on the product function space $C_{a,b}^2[0,T]$. Finally we use our Cameron--Storvick type theorem to obtain several meaningful results and examples.

In this paper we study an analytic Yeh--Feynman integral and an analytic Yeh--Fourier--Feynman transform associated with Gaussian processes. Fubini theorems involving the generalized analytic Yeh--Feynman integrals are established. The Fubini theorems investigated in this paper are to express the iterated generalized Yeh--Feynman integrals associated with Gaussian processes as a single generalized Yeh--Feynman integral. Using our Fubini theorems, we next examined fundamental relationships (with extended versions) between generalized Yeh--Fourier--Feynman transforms and convolution products (with respect to Gaussian processes) of functionals on Yeh--Wiener space.

Recently, the finite-rate-of-innovation (FRI) based continuous domain regularization is emerging as an alternative to the conventional on-the-grid sparse regularization for the compressed sensing (CS) due to its ability to alleviate the basis mismatch between the true support of the shape in the continuous domain and the discrete grid. In this paper, we propose a new off-the-grid regularization for the CS-MRI reconstruction. Following the recent works on two dimensional FRI, we assume that the discontinuities/edges of the image are localized in the zero level set of a band-limited periodic function. This assumption induces the linear dependencies among the Fourier samples of the gradient of the image, which leads to a low rank two-fold Hankel matrix. We further observe that the singular value decomposition of a low rank Hankel matrix corresponds to an adaptive tight frame system which can represent the image with sparse canonical coefficients. Based on this observation, we propose a data driven tight frame based off-the-grid regularization model for the CS-MRI reconstruction. To solve the nonconvex and nonsmooth model, a proximal alternating minimization algorithm with a guaranteed global convergence is adopted. Finally, the numerical experiments show that our proposed data driven tight frame based approach outperforms the existing approaches.

Bound states in the continuum (BICs) represent localized modes with energies embedded in the continuous spectrum of radiating waves. BICs were discovered initially as a mathematical curiosity in quantum mechanics, and more recently were employed in photonics. Pure mathematical bound states have infinitely-large quality factors (Q factors) and zero resonant linewidth. In optics, BICs are physically limited by a finite size, material absorption, structural disorder, and surface scattering, and they manifest themselves as the resonant states with large Q factors, also known as supercavity modes or quasi-BICs. Optical BIC resonances have been demonstrated only in extended 2D and 1D systems and have been employed for distinct applications including lasing and sensing. Optical quasi-BIC modes in individual nanoresonators have been discovered recently but they were never observed in experiment. Here, we demonstrate experimentally an isolated subwavelength nanoresonator hosting a quasi-BIC resonance. We fabricate the resonator from AlGaAs material on an engineered substrate, and couple to the quasi-BIC mode using structured light. We employ the resonator as a nonlinear nanoantenna and demonstrate record-high efficiency of second-harmonic generation. Our study brings a novel platform to resonant subwavelength photonics.

The purpose of this article is to present the second type fundamental relationship between the generalized Fourier--Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions (to the case on an infinite dimensional Banach space) of the structure which exists between the Fourier transform and the convolution of functions on Euclidean spaces.

Machine learning-based analysis of medical images often faces several hurdles, such as the lack of training data, the curse of dimensionality problem, and the generalization issues. One of the main difficulties is that there exists computational cost problem in dealing with input data of large size matrices which represent medical images. The purpose of this paper is to introduce a framelet-pooling aided deep learning method for mitigating computational bundle, caused by large dimensionality. By transforming high dimensional data into low dimensional components by filter banks with preserving detailed information, the proposed method aims to reduce the complexity of the neural network and computational costs significantly during the learning process. Various experiments show that our method is comparable to the standard unreduced learning method, while reducing computational burdens by decomposing large-sized learning tasks into several small-scale learning tasks.