Generalized Projective Representations for sl(n+1)

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of $sl(n+1)$ to a non-homogenous representation on the tensor space of any finite-dimensional irreducible $gl(n)$-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible $sl(n+1)$-modules, which are in general not highest-weight type, for any given finite-dimensional irreducible $sl(n)$-module. The results could also be used to study the quantum field theory with the projective group as the symmetry.Comment: 24page

An Approach for Chinese-Japanese Named Entity Equivalents Extraction Using Inductive Learning and Hanzi-Kanji Mapping Table

Named Entity Translation Equivalents extraction plays a critical role in machine translation (MT) and cross language information retrieval (CLIR). Traditional methods are often based on large-scale parallel or comparable corpora. However, the applicability of these studies is constrained, mainly because of the scarcity of parallel corpora of the required scale, especially for language pairs of Chinese and Japanese. In this paper, we propose a method considering the characteristics of Chinese and Japanese to automatically extract the Chinese-Japanese Named Entity (NE) translation equivalents based on inductive learning (IL) from monolingual corpora. The method adopts the Chinese Hanzi and Japanese Kanji Mapping Table (HKMT) to calculate the similarity of the NE instances between Japanese and Chinese. Then, we use IL to obtain partial translation rules for NEs by extracting the different parts from high similarity NE instances in Chinese and Japanese. In the end, the feedback processing updates the Chinese and Japanese NE entity similarity and rule sets. Experimental results show that our simple, efficient method, which overcomes the insufficiency of the traditional methods, which are severely dependent on bilingual resource. Compared with other methods, our method combines the language features of Chinese and Japanese with IL for automatically extracting NE pairs. Our use of a weak correlation bilingual text sets and minimal additional knowledge to extract NE pairs effectively reduces the cost of building the corpus and the need for additional knowledge. Our method may help to build a large-scale Chinese-Japanese NE translation dictionary using mono-lingual corpora

Noise and Speckle Reduction in Doppler Blood Flow Spectrograms Using an Adaptive Pulse-Coupled Neural Network

A novel method, called adaptive pulse coupled neural network (AD-PCNN) using a two-stage denoising strategy, is proposed to reduce noise and speckle in the spectrograms of Doppler blood flow signals. AD-PCNN contains an adaptive thresholding PCNN and a threshold decaying PCNN. Firstly, PCNN pulses based on the adaptive threshold filter a part of background noise in the spectrogram while isolating the remained noise and speckles. Subsequently, the speckles and noise of the denoised spectrogram are detected by the pulses generated through the threshold decaying PCNN and then are iteratively removed by the intensity variation to speckle or noise neurons. The relative root mean square (RRMS) error of the maximum frequency extracted from the AD-PCNN spectrogram of the simulated Doppler blood flow signals is decreased 25.2% on average compared to that extracted from the MPWD (matching pursuit with Wigner Distribution) spectrogram, and the RRMS error of the AD-PCNN spectrogram is decreased 10.8% on average compared to MPWD spectrogram. Experimental results of synthetic and clinical signals show that the proposed method is better than the MPWD in improving the accuracy of the spectrograms and their maximum frequency curves

Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in the Navier-Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution

Contextual Modeling for 3D Dense Captioning on Point Clouds

3D dense captioning, as an emerging vision-language task, aims to identify and locate each object from a set of point clouds and generate a distinctive natural language sentence for describing each located object. However, the existing methods mainly focus on mining inter-object relationship, while ignoring contextual information, especially the non-object details and background environment within the point clouds, thus leading to low-quality descriptions, such as inaccurate relative position information. In this paper, we make the first attempt to utilize the point clouds clustering features as the contextual information to supply the non-object details and background environment of the point clouds and incorporate them into the 3D dense captioning task. We propose two separate modules, namely the Global Context Modeling (GCM) and Local Context Modeling (LCM), in a coarse-to-fine manner to perform the contextual modeling of the point clouds. Specifically, the GCM module captures the inter-object relationship among all objects with global contextual information to obtain more complete scene information of the whole point clouds. The LCM module exploits the influence of the neighboring objects of the target object and local contextual information to enrich the object representations. With such global and local contextual modeling strategies, our proposed model can effectively characterize the object representations and contextual information and thereby generate comprehensive and detailed descriptions of the located objects. Extensive experiments on the ScanRefer and Nr3D datasets demonstrate that our proposed method sets a new record on the 3D dense captioning task, and verify the effectiveness of our raised contextual modeling of point clouds

Less Emphasis on Difficult Layer Regions: Curriculum Learning for Singularly Perturbed Convection-Diffusion-Reaction Problems

Although Physics-Informed Neural Networks (PINNs) have been successfully applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging convection-diffusion-reaction problems. In this paper, we investigate the reason of this failure from a domain distribution perspective, and identify that learning multi-scale fields simultaneously makes the network unable to advance its training and easily get stuck in poor local minima. We show that the widespread experience of sampling more collocation points in high-loss layer regions hardly help optimize and may even worsen the results. These findings motivate the development of a novel curriculum learning method that encourages neural networks to prioritize learning on easier non-layer regions while downplaying learning on harder layer regions. The proposed method helps PINNs automatically adjust the learning emphasis and thereby facilitate the optimization procedure. Numerical results on typical benchmark equations show that the proposed curriculum learning approach mitigates the failure modes of PINNs and can produce accurate results for very sharp boundary and interior layers. Our work reveals that for equations whose solutions have large scale differences, paying less attention to high-loss regions can be an effective strategy for learning them accurately.Comment: 22 page