In this work, we investigate the long-time asymptotic behavior of the Wadati-Konno-Ichikawa equation with initial data belonging to Schwartz space at infinity by using the nonlinear steepest descent method of Deift and Zhou for the oscillatory Rieman
n-Hilbert problem. Based on the initial value condition, the original Riemann-Hilbert problem is constructed to express the solution of the Wadati-Konno-Ichikawa equation. Through a series of deformations, the original RH problem is transformed into a model RH problem, from which the long-time asymptotic solution of the equation is obtained explicitly.
Meta-learning has achieved great success in leveraging the historical learned knowledge to facilitate the learning process of the new task. However, merely learning the knowledge from the historical tasks, adopted by current meta-learning algorithms,
may not generalize well to testing tasks when they are not well-supported by training tasks. This paper studies a low-resource text classification problem and bridges the gap between meta-training and meta-testing tasks by leveraging the external knowledge bases. Specifically, we propose KGML to introduce additional representation for each sentence learned from the extracted sentence-specific knowledge graph. The extensive experiments on three datasets demonstrate the effectiveness of KGML under both supervised adaptation and unsupervised adaptation settings.
In this paper, we aim to advance the research of multi-modal pre-training on E-commerce and subsequently contribute a large-scale dataset, named M5Product, which consists of over 6 million multimodal pairs, covering more than 6,000 categories and 5,0
00 attributes. Generally, existing multi-modal datasets are either limited in scale or modality diversity. Differently, our M5Product is featured from the following aspects. First, the M5Product dataset is 500 times larger than the public multimodal dataset with the same number of modalities and nearly twice larger compared with the largest available text-image cross-modal dataset. Second, the dataset contains rich information of multiple modalities including image, text, table, video and audio, in which each modality can capture different views of semantic information (e.g. category, attributes, affordance, brand, preference) and complements the other. Third, to better accommodate with real-world problems, a few portion of M5Product contains incomplete modality pairs and noises while having the long-tailed distribution, which aligns well with real-world scenarios. Finally, we provide a baseline model M5-MMT that makes the first attempt to integrate the different modality configuration into an unified model for feature fusion to address the great challenge for semantic alignment. We also evaluate various multi-model pre-training state-of-the-arts for benchmarking their capabilities in learning from unlabeled data under the different number of modalities on the M5Product dataset. We conduct extensive experiments on four downstream tasks and provide some interesting findings on these modalities. Our dataset and related code are available at https://xiaodongsuper.github.io/M5Product_dataset.
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of this, a n
ew second-order energy-conserving implicit scheme is proposed. Numerical simulations of Galactic model hosting a BL Lacertae object and magnetized rotating black hole background support these analytical results. The new method with appropriate time steps is used to explore the effects of varying the parameters on the presence of chaos in the two physical models. Chaos easily occurs in the Galactic model as the mass of the nucleus, the internal perturbation parameter, and the anisotropy of the potential of the elliptical galaxy increase. The dynamics of charged particles around the magnetized Kerr spacetime is easily chaotic for larger energies of the particles, smaller initial angular momenta of the particles, and stronger magnetic fields. The chaotic properties are not necessarily weakened when the black hole spin increases. The new method can be used for any six-dimensional Hamiltonian problems, including globally hyperbolic spacetimes with readily available (3+1) split coordinates.
Nowadays, customers demands for E-commerce are more diversified, which introduces more complications to the product retrieval industry. Previous methods are either subject to single-modal input or perform supervised image-level product retrieval, thu
s fail to accommodate real-life scenarios where enormous weakly annotated multi-modal data are present. In this paper, we investigate a more realistic setting that aims to perform weakly-supervised multi-modal instance-level product retrieval among fine-grained product categories. To promote the study of this challenging task, we contribute Product1M, one of the largest multi-modal cosmetic datasets for real-world instance-level retrieval. Notably, Product1M contains over 1 million image-caption pairs and consists of two sample types, i.e., single-product and multi-product samples, which encompass a wide variety of cosmetics brands. In addition to the great diversity, Product1M enjoys several appealing characteristics including fine-grained categories, complex combinations, and fuzzy correspondence that well mimic the real-world scenes. Moreover, we propose a novel model named Cross-modal contrAstive Product Transformer for instance-level prodUct REtrieval (CAPTURE), that excels in capturing the potential synergy between multi-modal inputs via a hybrid-stream transformer in a self-supervised manner.CAPTURE generates discriminative instance features via masked multi-modal learning as well as cross-modal contrastive pretraining and it outperforms several SOTA cross-modal baselines. Extensive ablation studies well demonstrate the effectiveness and the generalization capacity of our model. Dataset and codes are available at https: //github.com/zhanxlin/Product1M.
The generation of squeezed light in semiconductor materials opens opportunities for building on-chip devices that are operated at the quantum level. Here we study theoretically a squeezed light source of polariton dark solitons confined in a geometri
c potential well of semiconductor microcavities in the strong coupling regime. We show that polariton dark solitons of odd and even parities can be created by tuning the potential depth. When driving the potential depth linearly, a bistability of solitons with the two different parities can be induced. Strong intensity squeezing is obtained near the turning point of the bistability due to the large nonlinear interaction, which can be controlled by Feshbach resonance. The phase diagram of the bistability and squeezing of the dark solitons is obtained through large scale numerical calculations. Our study contributes to the current efforts in realizing topological excitations and squeezed light sources with solid-state devices.
Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the
Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions.
Database Management System (DBMS) plays a core role in modern software from mobile apps to online banking. It is critical that DBMS should provide correct data to all applications. When the DBMS returns incorrect data, a correctness bug is triggered.
Current production-level DBMSs still suffer from insufficient testing due to the limited hand-written test cases. Recently several works proposed to automatically generate many test cases with query transformation, a process of generating an equivalent query pair and testing a DBMS by checking whether the system returns the same result set for both queries. However, all of them still heavily rely on manual work to provide a transformation which largely confines their exploration of the valid input query space. This paper introduces duplicate-sensitivity guided transformation synthesis which automatically finds new transformations by first synthesizing many candidates then filtering the nonequivalent ones. Our automated synthesis is achieved by mutating a query while keeping its duplicate sensitivity, which is a necessary condition for query equivalence. After candidate synthesis, we keep the mutant query which is equivalent to the given one by using a query equivalent checker. Furthermore, we have implemented our idea in a tool Eqsql and used it to test the production-level DBMSs. In two months, we detected in total 30 newly confirmed and unique bugs in MySQL, TiDB and CynosDB.
This paper describes a variational auto-encoder based non-autoregressive text-to-speech (VAENAR-TTS) model. The autoregressive TTS (AR-TTS) models based on the sequence-to-sequence architecture can generate high-quality speech, but their sequential d
ecoding process can be time-consuming. Recently, non-autoregressive TTS (NAR-TTS) models have been shown to be more efficient with the parallel decoding process. However, these NAR-TTS models rely on phoneme-level durations to generate a hard alignment between the text and the spectrogram. Obtaining duration labels, either through forced alignment or knowledge distillation, is cumbersome. Furthermore, hard alignment based on phoneme expansion can degrade the naturalness of the synthesized speech. In contrast, the proposed model of VAENAR-TTS is an end-to-end approach that does not require phoneme-level durations. The VAENAR-TTS model does not contain recurrent structures and is completely non-autoregressive in both the training and inference phases. Based on the VAE architecture, the alignment information is encoded in the latent variable, and attention-based soft alignment between the text and the latent variable is used in the decoder to reconstruct the spectrogram. Experiments show that VAENAR-TTS achieves state-of-the-art synthesis quality, while the synthesis speed is comparable with other NAR-TTS models.
In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all splitting parts
have analytical solutions as explicit functions of proper time. To cope with this difficulty, we introduce a time transformation function to the Hamiltonian of Kerr geometry so as to obtain a time-transformed Hamiltonian consisting of five splitting parts, whose analytical solutions are explicit functions of the new coordinate time. The chosen time transformation function can cause time steps to be adaptive, but it is mainly used to implement the desired splitting of the time transformed Hamiltonian. In this manner, new explicit symplectic algorithms are easily available. Unlike Runge Kutta integrators, the newly proposed algorithms exhibit good long term behavior in the conservation of Hamiltonian quantities when appropriate fixed coordinate time steps are considered. They are better than same order implicit and explicit mixed symplectic algorithms and extended phase space explicit symplectic like methods in computational efficiency. The proposed idea on the construction of explicit symplectic integrators is suitable for not only the Kerr metric but also many other relativistic problems, such as a Kerr black hole immersed in a magnetic field, a Kerr Newman black hole with an external magnetic field, axially symmetric core shell systems, and five dimensional black ring metrics.
