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In this paper the classical and nonlocal semi-discrete nonlinear Schr\"{o}dinger (sdNLS) equations with nonzero backgrounds are solved by means of the bilinearization-reduction approach. In the first step of this approach, the unreduced sdNLS system with a nonzero background is bilinearized and its solutions are presented in terms of quasi double Casoratians. Then, reduction techniques are implemented to deal with complex and nonlocal reductions, which yields solutions for the four classical and nonlocal sdNLS equations with a plane wave background or a hyperbolic function background. These solutions are expressed with explicit formulae and allow classifications according to canonical forms of certain spectral matrix. In particular, we present explicit formulae for general rogue waves for the classical focusing sdNLS equation. Some obtained solutions are analyzed and illustrated., Comment: 32 pages

Text has become the predominant form of communication on social media, embedding a wealth of emotional nuances. Consequently, the extraction of emotional information from text is of paramount importance. Despite previous research making some progress, existing text sentiment analysis models still face challenges in integrating diverse semantic information and lack interpretability. To address these issues, we propose a quantum-inspired deep learning architecture that combines fundamental principles of quantum mechanics (QM principles) with deep learning models for text sentiment analysis. Specifically, we analyze the commonalities between text representation and QM principles to design a quantum-inspired text representation method and further develop a quantum-inspired text embedding layer. Additionally, we design a feature extraction layer based on long short-term memory (LSTM) networks and self-attention mechanisms (SAMs). Finally, we calculate the text density matrix using the quantum complex numbers principle and apply 2D-convolution neural networks (CNNs) for feature condensation and dimensionality reduction. Through a series of visualization, comparative, and ablation experiments, we demonstrate that our model not only shows significant advantages in accuracy and efficiency compared to previous related models but also achieves a certain level of interpretability by integrating QM principles. Our code is available at QISA.

Multimodal semantic segmentation shows significant potential for enhancing segmentation accuracy in complex scenes. However, current methods often incorporate specialized feature fusion modules tailored to specific modalities, thereby restricting input flexibility and increasing the number of training parameters. To address these challenges, we propose StitchFusion, a straightforward yet effective modal fusion framework that integrates large-scale pre-trained models directly as encoders and feature fusers. This approach facilitates comprehensive multi-modal and multi-scale feature fusion, accommodating any visual modal inputs. Specifically, Our framework achieves modal integration during encoding by sharing multi-modal visual information. To enhance information exchange across modalities, we introduce a multi-directional adapter module (MultiAdapter) to enable cross-modal information transfer during encoding. By leveraging MultiAdapter to propagate multi-scale information across pre-trained encoders during the encoding process, StitchFusion achieves multi-modal visual information integration during encoding. Extensive comparative experiments demonstrate that our model achieves state-of-the-art performance on four multi-modal segmentation datasets with minimal additional parameters. Furthermore, the experimental integration of MultiAdapter with existing Feature Fusion Modules (FFMs) highlights their complementary nature. Our code is available at StitchFusion_repo.

A well-motivated cosmological hybrid inflation scenario based on no-scale SUGRA is considered. It is demonstrated that an extra suppressed $R$-symmetry breaking term $S^n$ with $n\geq 4$ needs to be included in order to realize successful inflation. The resulting potential is found to be similar (but not identical) to the one in the Starobinsky inflation model. A relatively larger tensor-to-scalar ratio $r\sim 10^{-2}$ and a spectral index $n_s\approx 0.965$ are obtained, which are approximately independent of $n$., Comment: 14 pages, 5 figures and 1 table

Last year has witnessed the re-flourishment of tag-aware recommender systems supported by the LLM-enriched tags. Unfortunately, though large efforts have been made, current solutions may fail to describe the diversity and uncertainty inherent in user preferences with only tag-driven profiles. Recently, with the development of geometry-based techniques, e.g., box embedding, diversity of user preferences now could be fully modeled as the range within a box in high dimension space. However, defect still exists as these approaches are incapable of capturing high-order neighbor signals, i.e., semantic-rich multi-hop relations within the user-tag-item tripartite graph, which severely limits the effectiveness of user modeling. To deal with this challenge, in this paper, we propose a novel algorithm, called BoxGNN, to perform the message aggregation via combination of logical operations, thereby incorporating high-order signals. Specifically, we first embed users, items, and tags as hyper-boxes rather than simple points in the representation space, and define two logical operations to facilitate the subsequent process. Next, we perform the message aggregation mechanism via the combination of logical operations, to obtain the corresponding high-order box representations. Finally, we adopt a volume-based learning objective with Gumbel smoothing techniques to refine the representation of boxes. Extensive experiments on two publicly available datasets and one LLM-enhanced e-commerce dataset have validated the superiority of BoxGNN compared with various state-of-the-art baselines. The code is released online

Multimodal semantic segmentation is a pivotal component of computer vision and typically surpasses unimodal methods by utilizing rich information set from various sources.Current models frequently adopt modality-specific frameworks that inherently biases toward certain modalities. Although these biases might be advantageous in specific situations, they generally limit the adaptability of the models across different multimodal contexts, thereby potentially impairing performance. To address this issue, we leverage the inherent capabilities of the model itself to discover the optimal equilibrium in multimodal fusion and introduce U3M: An Unbiased Multiscale Modal Fusion Model for Multimodal Semantic Segmentation. Specifically, this method involves an unbiased integration of multimodal visual data. Additionally, we employ feature fusion at multiple scales to ensure the effective extraction and integration of both global and local features. Experimental results demonstrate that our approach achieves superior performance across multiple datasets, verifing its efficacy in enhancing the robustness and versatility of semantic segmentation in diverse settings. Our code is available at U3M-multimodal-semantic-segmentation.

On-chip integrated metasurface driven by in-plane guided waves is of great interests in various light field manipulation applications such as colorful augmented reality and holographic display. However, it remains a challenge to design colorful multichannel holography by a single on-chip metasurface. Here we present metasurfaces integrated on top of guided-wave photonic slab that achieves multi-channel colorful holographic light display. An end-to-end scheme is used to inverse design the metasurface for projecting off-chip preset multiple patterns. Particular examples are presented for customized patterns that were encoded into the metasurface with a single-cell meta-atom, working simultaneously at RGB color channels and for several different diffractive distance, with polarization dependence. Holographic images are generated at 18 independent channels with such a single-cell metasurface. The proposed design scheme is easy to implement and the resulting device is viable to fabrication, promising a plenty of applications in nanophotonics., Comment: 18 pages and 11 figures

Crowd localization targets on predicting each instance precise location within an image. Current advanced methods propose the pixel-wise binary classification to tackle the congested prediction, in which the pixel-level thresholds binarize the prediction confidence of being the pedestrian head. Since the crowd scenes suffer from extremely varying contents, counts and scales, the confidence-threshold learner is fragile and under-generalized encountering domain knowledge shift. Moreover, at the most time, the target domain is agnostic in training. Hence, it is imperative to exploit how to enhance the generalization of confidence-threshold locator to the latent target domain. In this paper, we propose a Dynamic Proxy Domain (DPD) method to generalize the learner under domain shift. Concretely, based on the theoretical analysis to the generalization error risk upper bound on the latent target domain to a binary classifier, we propose to introduce a generated proxy domain to facilitate generalization. Then, based on the theory, we design a DPD algorithm which is composed by a training paradigm and proxy domain generator to enhance the domain generalization of the confidence-threshold learner. Besides, we conduct our method on five kinds of domain shift scenarios, demonstrating the effectiveness on generalizing the crowd localization. Our code will be available at https://github.com/zhangda1018/DPD.

A crucial yet challenging issue in quantum metrology is to ascertain the ultimate precision achievable in estimation strategies. While there are two paradigms of estimations, local and global, current research is largely confined to local estimations, which are useful once the parameter of interest is approximately known. In this Letter we target a paradigm shift towards global estimations, which can operate reliably even with a few measurement data and no substantial prior knowledge about the parameter. The key innovation here is to develop a technique, dubbed virtual imaginary time evolution, which establishes an equality between the information gained in a global estimation and the quantum Fisher information for a virtual local estimation. This offers an intriguing pathway to surmount challenges in the realm of global estimations by leveraging powerful tools tailored for local estimations. We explore our technique to reveal a strict hierarchy of achievable precision for different global estimation strategies and uncover unexpected results contrary to conventional wisdom in local estimations., Comment: 6+18 pages. Close to the published verion

The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensional matrices as master functions, we are able to investigate evolution relations and recurrence relations of these functions, which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM equation in the Euclidean space and two ultrahyperbolic spaces by reductions to meet the reality conditions and gauge conditions, respectively. Special solutions can be obtained by choosing suitable measures., Comment: 22 pages

Gamma-ray Transient Monitor (GTM) is an all-sky monitor onboard the Distant Retrograde Orbit-A (DRO-A) satellite with the scientific objective of detecting gamma-ray transients ranging from 20 keV to 1 MeV. GTM is equipped with 5 Gamma-ray Transient Probe (GTP) detector modules, utilizing the NaI(Tl) scintillator coupled with a SiPM array. To reduce the SiPM noise, GTP makes use of a dedicated dual-channel coincident readout design. In this work, we firstly studied the impact of different coincidence times on detection efficiency and ultimately selected the 500 ns time coincidence window for offline data processing. To test the performance of GTPs and validate the Monte Carlo simulated energy response, we conducted comprehensive ground calibration tests using Hard X-ray Calibration Facility (HXCF) and radioactive sources, including energy response, detection efficiency, spatial response, bias-voltage response, and temperature dependence. We extensively presented the ground calibration results, and validated the design and mass model of GTP detector. These work paved the road for the in-flight observation and science data analysis., Comment: 15 pages, 25 figures

The intrinsic resolution is the primary limitation on the total energy resolution of LaBr$_3$(Ce) crystal. This intrinsic resolution arises from two effects: fluctuations occurring in the process of energy transfer to luminescent centers within the LaBr$_3$(Ce) crystal and the LaBr$_3$(Ce) crystal's non-proportional luminescence. Presently, experimental measurements regarding the intrinsic resolution of LaBr$_3$(Ce) crystal are scarce, and the underlying physical mechanisms remain incompletely understood. In this paper, we aim to elucidate the concept of intrinsic resolution. We investigated the entire physical process of luminescence following energy deposition in the LaBr$_3$(Ce) crystal, quantifying the various components in the total energy resolution. We conducted a series of experimental measurements and Geant4 simulations, determining the intrinsic resolution of LaBr$_3$(Ce) crystal to 100 keV electrons as 2.12%. The non-proportionality contributes significantly at 1.43%, while fluctuations in the energy transfer process accounted for 0.27%. It is evident that non-proportionality in light output constitutes the primary source of intrinsic resolution. Horizontal and vertical unevenness in light collection contributed 0.25% and 0.07%, respectively. Statistical fluctuations showed the largest impact on the total energy resolution, at 2.86%. The contribution from fluctuations in single-photoelectron events was 0.77%. Furthermore, we reconstructed the photon response using Geant4, and the consistency between the simulated relative light yield and the experimentally measured one confirmed the reliability of the LaBr$_3$(Ce) detector mass model employed in the simulation., Comment: 11 pages, 16 figures

The GECAM series of satellites utilize LaBr3(Ce), LaBr3(Ce,Sr), and NaI(Tl) crystals as sensitive materials for gamma-ray detectors (GRDs). To investigate the non-linearity in the detection of low-energy gamma rays and address errors in the E-C relationship calibration, comprehensive tests and comparative studies of the non-linearity of these three crystals were conducted using Compton electrons, radioactive sources, and mono-energetic X-rays. The non-linearity test results for Compton electrons and X-rays displayed substantial differences, with all three crystals showing higher non-linearity for X-rays and gamma-rays than for Compton electrons. Despite LaBr3(Ce) and LaBr3(Ce,Sr) crystals having higher absolute light yields, they exhibited a noticeable non-linear decrease in light yield, especially at energies below 400 keV. The NaI(Tl) crystal demonstrated excess light output in the 6~200 keV range, reaching a maximum excess of 9.2% at 30 keV in X-ray testing and up to 15.5% at 14 keV during Compton electron testing, indicating a significant advantage in the detection of low-energy gamma rays. Furthermore, this paper explores the underlying causes of the observed non-linearity in these crystals. This study not only elucidates the detector responses of GECAM, but also marks the inaugural comprehensive investigation into the non-linearity of domestically produced lanthanum bromide and sodium iodide crystals., Comment: 12pages, 16 figures

In this paper, we show that all the bilinear Adler-Bobenko-Suris (ABS) equations (except Q2 and Q4) can be obtained from symmetric discrete AKP system by taking proper reductions and continuum limits. Among the bilinear ABS equations, a simpler bilinear form of the ABS H2 equation is given. In addition, an 8-point 3-dimensional lattice equation and an 8-point 4-dimensional lattice equation are obtained as by-products. Both of them can be considered as extensions of the symmetric discrete AKP equation., Comment: 30 pages

Non-Gaussian entangled states play a crucial role in harnessing quantum advantage in continuous-variable quantum information. However, how to fully characterize N-partite (N > 3) non-Gaussian entanglement without quantum state tomography remains elusive, leading to a very limited understanding of the underlying entanglement mechanism. Here, we propose several necessary and sufficient conditions for the positive-partial-transposition separability of multimode nonlinear quantum states resulting from high-order Hamiltonians and successive beam splitting operations. When applied to the initial state, the beam-splitter operations induce the emergence of different types of entanglement mechanisms, including pairwise high-order entanglement, collective high-order entanglement and the crossover between the two. We show numerically that for the four-mode scenario, the threshold for the existence of entanglement for any bipartition does not exceed the entanglement of the original state at fixed high-order moments. These results provide a new perspective for understanding multipartite nonlinear entanglement and will promote their application in quantum information processing., Comment: Comments are welcome

The Higgs boson decay to a massive bottom quark pair provides the dominant contribution to the Higgs boson width. We present an exact result for such a decay induced by the bottom quark Yukawa coupling with next-to-next-to-leading order (NNLO) QCD corrections. We have adopted the canonical differential equations in the calculation and obtained the result in terms of multiple polylogarithms. We also compute the contribution from the decay to four bottom quarks which consists of complete elliptic integrals or their one-fold integrals. The result in the small bottom quark mass limit coincides with the previous calculation using the large momentum expansion. The threshold expansion exhibits power divergent terms in the bottom quark velocity, which has a structure different from that in $e^+e^-\to t\bar{t}$ but can be reproduced by computing the corresponding Coulomb Green function. The NNLO corrections significantly reduce the uncertainties from both the renormalization scale and the renormalization scheme of the bottom quark Yukawa coupling. Our result can be applied to a heavy scalar decay to a top quark pair., Comment: 30 pages, 12 figures

Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein-Podolsky-Rosen (EPR) steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.

As a new member of the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) after GECAM-A and GECAM-B, GECAM-C (originally called HEBS), which was launched on board the SATech-01 satellite on July 27, 2022, aims to monitor and localize X-ray and gamma-ray transients from $\sim$ 6 keV to 6 MeV. GECAM-C utilizes a similar design to GECAM but operates in a more complex orbital environment. In this work, we utilize the secondary particles simultaneously produced by the cosmic-ray events on orbit and recorded by multiple detectors, to calibrate the relative timing accuracy between all detectors of GECAM-C. We find the result is 0.1 $\mu \rm s$, which is the highest time resolution among all GRB detectors ever flown and very helpful in timing analyses such as minimum variable timescale and spectral lags, as well as in time delay localization. Besides, we calibrate the absolute time accuracy using the one-year Crab pulsar data observed by GECAM-C and Fermi/GBM, as well as GECAM-C and GECAM-B. The results are $2.02\pm 2.26\ \mu \rm s$ and $5.82\pm 3.59\ \mu \rm s$, respectively. Finally, we investigate the spectral lag between the different energy bands of Crab pulsar observed by GECAM and GBM, which is $\sim -0.2\ {\rm \mu s\ keV^{-1}}$., Comment: submitted

The Lam\'e function can be used to construct plane wave factors and solutions to the Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) hierarchy. The solutions are usually called elliptic solitons. In this chapter, first, we review recent development in the Hirota bilinear method on elliptic solitons of the KdV equation and KP equation, including bilinear calculations involved with the Lam\'e type plane wave factors, expressions of $\tau$ functions and the generating vertex operators. Then, for the discrete potential KdV and KP equations, we give their bilinear forms, derive $\tau$ functions of elliptic solitons, and show that they share the same vertex operators with the KdV hierarchy and the KP hierarchy, respectively., Comment: 24 pages

Magnetar is a neutron star with an ultrahigh magnetic field ($\sim 10^{14}-10^{15}$ G) which usually manifests as soft gamma-ray repeater (SGR) or anomalous X-ray pulsar (AXP). SGR J1935+2154 is not only one of the most active magnetar detected so far, but also the unique confirmed source of fast radio burst (FRB). Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) are dedicated to monitor gamma-ray transients all over the sky, including SGR bursts. Here we report the GECAM observation of the burst activity of SGR J1935+2154 from January 2021 to December 2022, which results in a unique and valuable data set for this important magnetar. With a targeted search of GECAM data, 164 bursts from SGR J1935+2154 are detected by GECAM-B while 97 bursts by GECAM-C, including the X-ray burst associated with a fast radio burst (FRB 20221014). We find that both the burst duration and the waiting time between two successive bursts follow lognormal distributions. The period of burst activity is $134\pm20$ days, thus the burst activity could be generally divided into 4 active episodes over these two years. Interestingly, the hardness ratio of X-ray bursts tends to be softer and more concentrated over these two years, especially during the active episode with FRBs detected.

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matters due to their exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matters in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions., Comment: 86 pages, 10 figures, submitted

In the recent paper [Stud. App. Math. 147 (2021) 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev-Petviashvili (D$\Delta$mKP) hierarchy converts the D$\Delta$mKP system to the relativistic Toda spectral problem and its hierarchy. In this paper we introduce a new formulation of independent variables in the squared eigenfunction symmetry constraint, under which the D$\Delta$mKP system gives rise to the discrete spectral problem and a hierarchy of the differential-difference derivative nonlinear Schr\"odinger equation of the Chen-Lee-Liu type. In addition, by introducing nonisospectral flows, two sets of symmetries of the D$\Delta$mKP hierarchy and their algebraic structure are obtained. We then present a unified continuum limit scheme, by which we achieve the correspondence of the mKP and the D$\Delta$mKP hierarchies and their integrable structures., Comment: 23 pages