arXiv subjects

Weiqiang Wang

Publications and source records attributed to Weiqiang Wang.

At least 235 records · Page 13Linked to original sources

arXiv2021

Serre-Lusztig relations for $\imath$quantum groups

Let $(\bf U, \bf U^\imath)$ be a quantum symmetric pair of Kac-Moody type. The $\imath$quantum groups $\bf U^\imath$ and the universal $\imath$quantum groups $\widetilde{\bf U}^\imath$ can be viewed as a generalization of quantum groups and Drinfeld doubles $\widetilde{\bf U}$. In this paper we formulate and establish Serre-Lusztig relations for $\imath$quantum groups in terms of $\imath$divided powers, which are an $\imath$-analog of Lusztig's higher order Serre relations for quantum groups. This has applications to braid group symmetries on $\imath$quantum groups.

math.RT↗

arXiv2020

Rethinking Object Detection in Retail Stores

The convention standard for object detection uses a bounding box to represent each individual object instance. However, it is not practical in the industry-relevant applications in the context of warehouses due to severe occlusions among groups of instances of the same categories. In this paper, we propose a new task, ie, simultaneously object localization and counting, abbreviated as Locount, which requires algorithms to localize groups of objects of interest with the number of instances. However, there does not exist a dataset or benchmark designed for such a task. To this end, we collect a large-scale object localization and counting dataset with rich annotations in retail stores, which consists of 50,394 images with more than 1.9 million object instances in 140 categories. Together with this dataset, we provide a new evaluation protocol and divide the training and testing subsets to fairly evaluate the performance of algorithms for Locount, developing a new benchmark for the Locount task. Moreover, we present a cascaded localization and counting network as a strong baseline, which gradually classifies and regresses the bounding boxes of objects with the predicted numbers of instances enclosed in the bounding boxes, trained in an end-to-end manner. Extensive experiments are conducted on the proposed dataset to demonstrate its significance and the analysis discussions on failure cases are provided to indicate future directions. Dataset is available at https://isrc.iscas.ac.cn/gitlab/research/locount-dataset.

cs.CV↗

arXiv2020

Towards Spatio-Temporal Video Scene Text Detection via Temporal Clustering

With only bounding-box annotations in the spatial domain, existing video scene text detection (VSTD) benchmarks lack temporal relation of text instances among video frames, which hinders the development of video text-related applications. In this paper, we systematically introduce a new large-scale benchmark, named as STVText4, a well-designed spatial-temporal detection metric (STDM), and a novel clustering-based baseline method, referred to as Temporal Clustering (TC). STVText4 opens a challenging yet promising direction of VSTD, termed as ST-VSTD, which targets at simultaneously detecting video scene texts in both spatial and temporal domains. STVText4 contains more than 1.4 million text instances from 161,347 video frames of 106 videos, where each instance is annotated with not only spatial bounding box and temporal range but also four intrinsic attributes, including legibility, density, scale, and lifecycle, to facilitate the community. With continuous propagation of identical texts in the video sequence, TC can accurately output the spatial quadrilateral and temporal range of the texts, which sets a strong baseline for ST-VSTD. Experiments demonstrate the efficacy of our method and the great academic and practical value of the STVText4. The dataset and code will be available soon.

cs.CV↗

arXiv2020

Hall algebras and quantum symmetric pairs II: reflection functors

Recently the authors initiated an $\imath$Hall algebra approach to (universal) $\imath$quantum groups arising from quantum symmetric pairs. In this paper we construct and study BGP type reflection functors which lead to isomorphisms of the $\imath$Hall algebras associated to acyclic $\imath$quivers. For Dynkin quivers, these symmetries on $\imath$Hall algebras induce automorphisms of universal $\imath$quantum groups, which are shown to satisfy the braid group relations associated to the restricted Weyl group of a symmetric pair; conjecturally these continue to hold for acyclic quivers/Kac-Moody setting. This leads to a conceptual construction of $q$-root vectors and PBW bases for (universal) quasi-split $\imath$quantum groups of ADE type.

math.RT↗

arXiv2020

Reinterpreting CTC training as iterative fitting

The connectionist temporal classification (CTC) enables end-to-end sequence learning by maximizing the probability of correctly recognizing sequences during training. The outputs of a CTC-trained model tend to form a series of spikes separated by strongly predicted blanks, know as the spiky problem. To figure out the reason for it, we reinterpret the CTC training process as an iterative fitting task that is based on frame-wise cross-entropy loss. It offers us an intuitive way to compare target probabilities with model outputs for each iteration, and explain how the model outputs gradually turns spiky. Inspired by it, we put forward two ways to modify the CTC training. The experiments demonstrate that our method can well solve the spiky problem and moreover, lead to faster convergence over various training settings. Beside this, the reinterpretation of CTC, as a brand new perspective, may be potentially useful in other situations. The code is publicly available at https://github.com/hzli-ucas/caffe/tree/ctc.

cs.CV↗

arXiv2020

Formulae of $\imath$-divided powers in ${\mathbf U}_q(\mathfrak{sl}_2)$

The existence of the $\imath$-canonical basis (also known as the $\imath$-divided powers) for the coideal subalgebra of the quantum $\mathfrak{sl}_2$ were established by Bao and Wang, with conjectural explicit formulae. In this paper we prove the conjectured formulae of these $\imath$-divided powers. This is achieved by first establishing closed formulae of the $\imath$-divided powers in basis for quantum $\mathfrak{sl}_2$ and then formulae for the $\imath$-canonical basis in terms of Lusztig's divided powers in each finite-dimensional simple module of quantum $\mathfrak{sl}_2$. These formulae exhibit integrality and positivity properties.

math.RT↗

arXiv2020

A Serre presentation for the $\imath$quantum groups

Let $(\bf U, \bf U^\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node. We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations. The verification of new $\imath$Serre relations is reduced to some new q-binomial identities. Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters.

math.RT↗

arXiv2020

Characters as Graphs: Recognizing Online Handwritten Chinese Characters via Spatial Graph Convolutional Network

Chinese is one of the most widely used languages in the world, yet online handwritten Chinese character recognition (OLHCCR) remains challenging. To recognize Chinese characters, one popular choice is to adopt the 2D convolutional neural network (2D-CNN) on the extracted feature images, and another one is to employ the recurrent neural network (RNN) or 1D-CNN on the time-series features. Instead of viewing characters as either static images or temporal trajectories, here we propose to represent characters as geometric graphs, retaining both spatial structures and temporal orders. Accordingly, we propose a novel spatial graph convolution network (SGCN) to effectively classify those character graphs for the first time. Specifically, our SGCN incorporates the local neighbourhood information via spatial graph convolutions and further learns the global shape properties with a hierarchical residual structure. Experiments on IAHCC-UCAS2016, ICDAR-2013, and UNIPEN datasets demonstrate that the SGCN can achieve comparable recognition performance with the state-of-the-art methods for character recognition.

cs.CV↗

arXiv2020

Quantum key distribution with dissipative Kerr soliton generated by on-chip microresonators

Quantum key distribution (QKD) can distribute symmetric key bits between remote legitimate users with the guarantee of quantum mechanics principles. For practical applications, the compact and robust photonic components for QKD are essential, and there are increasing attention to integrate the source, detector and modulators on a photonic chip. However, the massive and parallel QKD based on wavelength multiplexing are still challenge, due to the limited coherent light sources on the chip. Here, we introduce the Kerr dissipative soliton in a microresonator, which provides the locked coherent frequency comb with 49GHz frequency spacing, for QKD. We demonstrate the parallel QKD by demulplexing the coherent comb lines form the soliton, and showing the potential of Gbps secret key rate if the hundreds of channels covering C and L bands are fully exploited. The demonstrated soliton based QKD architecture are compatible with the efforts of quantum photonic integrated circuits, which are compact, robust and low-cost, and provides a competitive platform of practical QKD chip.

quant-ph↗

arXiv2020

Long distance measurement using single soliton microcomb

Dispersive interferometry (DPI) takes a major interest in optical frequency comb (OFC) based long distance laser-based light detection and ranging (LIDAR) for the merits of strong anti-interference ability and long coherent length. However, the mismatch between the repetition rate of OFC and the resolution of optical spectrum acquisition system induces a large dead-zone which is a major obstacle for practical applications. Here, a new DPI LIDAR on the strength of high-repetition-rate soliton microcomb is demonstrated, which reaches a minimum Allan deviation of 27 nm for an outdoor 1179 m ranging experiment. The proposed scheme approaches a compact, high-accuracy, and none-dead-zone long distance ranging system, opening up new opportunities for emerging applications of frontier scientific researches and advanced manufacturing.

physics.ins-det↗

arXiv2020

The $q$-Schur algebras and $q$-Schur dualities of finite type

We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra and Hecke algebra associated to $W$. We then realize geometrically the $q$-Schur algebra and duality, and construct a canonical basis for the $q$-Schur algebra with positivity. With suitable choices of $X_{\texttt f}$ in classical types, we recover the $q$-Schur algebras in the literature. Our $q$-Schur algebras are closely related to the category $\mathcal O$, where the type $G_2$ is studied in detail.

math.RT↗

arXiv2020

Canonical bases for tensor products and super Kazhdan-Lusztig theory

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category $\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).

math.QA↗

arXiv2019

A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs

We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category O of the ortho-symplectic Lie superalgebras $\mathfrak{osp}(2m+1|2n)$. In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.

math.RT↗

arXiv2019

Affine Hecke algebras and quantum symmetric pairs

We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and affine Schur algebra. Then we construct monomial bases and canonical bases for the affine Schur algebra. The multiplication formula allows us to establish a stabilization property of the family of affine Schur algebras that leads to the modified version of an algebra ${\mathbf K}^{\mathfrak c}_n$. We show that ${\mathbf K}^{\mathfrak c}_n$ is a coideal subalgebra of quantum affine algebra ${\bf U}(\hat{\mathfrak{gl}}_n)$, and $\big({\mathbf U}(\hat{ \mathfrak{gl}}_n), {\mathbf K}^{\mathfrak c}_n)$ forms a quantum symmetric pair. The modified coideal subalgebra is shown to admit monomial and stably canonical bases. We also formulate several variants of the affine Schur algebra and the (modified) coideal subalgebra above, as well as their monomial and canonical bases. This work provides a new and algebraic approach which complements and sheds new light on our previous geometric approach on the subject. In the appendix by four of the authors, new length formulas for the Weyl groups of affine classical types are obtained in a symmetrized fashion.

math.QA↗

arXiv2019

Guided Attention Network for Object Detection and Counting on Drones

Object detection and counting are related but challenging problems, especially for drone based scenes with small objects and cluttered background. In this paper, we propose a new Guided Attention Network (GANet) to deal with both object detection and counting tasks based on the feature pyramid. Different from the previous methods relying on unsupervised attention modules, we fuse different scales of feature maps by using the proposed weakly-supervised Background Attention (BA) between the background and objects for more semantic feature representation. Then, the Foreground Attention (FA) module is developed to consider both global and local appearance of the object to facilitate accurate localization. Moreover, the new data argumentation strategy is designed to train a robust model in various complex scenes. Extensive experiments on three challenging benchmarks (i.e., UAVDT, CARPK and PUCPR+) show the state-of-the-art detection and counting performance of the proposed method compared with existing methods.

cs.CV↗

arXiv2019

Quantum supergroups VI. Roots of $1$

A quantum covering group is an algebra with parameters $q$ and $π$ subject to $π^2=1$ and it admits an integral form; it specializes to the usual quantum group at $π=1$ and to a quantum supergroup of anisotropic type at $π=-1$. In this paper we establish the Frobenius-Lusztig homomorphism and Lusztig-Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at $π=1$ recovers Lusztig's constructions for quantum groups at roots of 1.

math.QA↗

arXiv2019

Stability of the centers of group algebras of $GL_n(q)$

The center $\mathscr{Z}_n(q)$ of the integral group algebra of the general linear group $GL_n(q)$ over a finite field admits a filtration with respect to the reflection length. We show that the structure constants of the associated graded algebras $\mathscr{G}_n(q)$ are independent of $n$, and this stability leads to a universal stable center with positive integer structure constants which governs the algebras $\mathscr{G}_n(q)$ for all $n$. Various structure constants of the stable center are computed and several conjectures are formulated. Analogous stability properties for symmetric groups and wreath products were established earlier by Farahat-Higman and the second author.

math.RT↗

arXiv2019

Anti-commuting varieties

We study the anti-commuting variety which consists of pairs of anti-commuting $n\times n$ matrices. We provide an explicit description of its irreducible components and their dimensions. The GIT quotient of the anti-commuting variety with respect to the conjugation action of $GL_n$ is shown to be of pure dimension $n$. We also show the semi-nilpotent anti-commuting variety (in which one matrix is required to be nilpotent) is of pure dimension $n^2$ and describe its irreducible components.

math.AG↗