Yong-Geun Oh, Rui Wang
We introduce a canonical affine connection on the contact manifold $(Q,ξ)$, which is associated to each contact triad $(Q,λ,J)$ where $λ$ is a contact form and $J:ξ\to ξ$ is an endomorphism with $J^2 = -id$ compatible to $dλ$. We call it the \emph{contact triad connection} of $(Q,λ,J)$ and prove its existence and uniqueness. The connection is canonical in that the pull-back connection $φ^*\nabla$ of a triad connection $\nabla$ becomes the triad connection of the pull-back triad $(Q, φ^*λ, φ^*J)$ for any diffeomorphism $φ:Q \to Q$ satisfying $φ^*λ= λ$ (sometimes called a strict contact diffeomorphism). It also preserves both the triad metric $$ g_{(λ,J)} = dλ(\cdot, J\cdot) + λ\otimes λ$$ and $J$ regarded as an endomorphism on $TQ = \mathbb R\{X_λ\}\oplus ξ$, and is characterized by its torsion properties and the requirement that the contact form $λ$ be holomorphic in the $CR$-sense. In particular, the connection restricts to a Hermitian connection $\nabla^π$ on the Hermitian vector bundle $(ξ,J,g_ξ)$ with $g_ξ= dλ(\cdot, J\cdot)|_ξ$, which we call the \emph{contact Hermitian connection} of $(ξ,J,g_ξ)$. These connections greatly simplify tensorial calculations in the sequels \cite{oh-wang1}, \cite{oh-wang2} performed in the authors' analytic study of the map $w$, called contact instantons, which satisfy the nonlinear elliptic system of equations $\overline{\partial}^πw = 0, \, d(w^*λ\circ j) = 0$ in the contact triad $(Q,λ,J)$.
Yong-Geun Oh, Rui Wang
This is a sequel to the papers [OW1], [OW2]. In [OW1], the authors introduced a canonical affine connection on $M$ associated to the contact triad $(M,λ,J)$. In [OW2], they used the connection to establish a priori $W^{k,p}$-coercive estimates for maps $w: \dot Σ\to M$ satisfying $\overline{\partial}^πw= 0, \, d(w^*λ\circ j) = 0$ \emph{without involving symplectization}. We call such a pair $(w,j)$ a contact instanton. In this paper, we first prove a canonical neighborhood theorem of the locus $Q$ foliated by closed Reeb orbits of a Morse-Bott contact form. Then using a general framework of the three-interval method, we establish exponential decay estimates for contact instantons $(w,j)$ of the triad $(M,λ,J)$, with $λ$ a Morse-Bott contact form and $J$ a CR-almost complex structure adapted to $Q$, under the condition that the asymptotic charge of $(w,j)$ at the associated puncture vanishes. We also apply the three-interval method to the symplectization case and provide an alternative approach via tensorial calculations to exponential decay estimates in the Morse-Bott case for the pseudoholomorphic curves on the symplectization of contact manifolds. This was previously established by Bourgeois [Bou] (resp. by Bao [Ba]), by using special coordinates, for the cylindrical (resp. for the asymptotically cylindrical) ends. The exponential decay result for the Morse-Bott case is an essential ingredient in the set-up of the moduli space of pseudoholomorphic curves which plays a central role in contact homology and symplectic field theory (SFT).
Yong-Geun Oh, Rui Wang
In the present article, we develop the analysis of the following nonlinear elliptic system of equations $$ \bar\partial^πw = 0, \, d(w^*λ\circ j) = 0 $$ first introduced by Hofer, associated to each given contact triad $(M,λ,J)$ on a contact manifold $(M,ξ)$. We directly work with this elliptic system on the contact manifold without involving the symplectization process. We establish the local a priori $C^k$ coercive pointwise estimates for all $k \geq 2$ in terms of $\|dw\|_{C^0}$ by doing tensorial calculations on contact manifold itself using the contact triad connection introduced by present the authors. Equipping the punctured Riemann surface $(\dot Σ,j)$ with a cylindrical Kähler metric and isothermal coordinates near every puncture, we prove the asymptotic (subsequence) convergence to the `spiraling' instantons along the `rotating' Reeb orbit for any solution $w$, not necessarily for $w^*λ\circ j$ being exact (i.e., allowing non-zero `charge' $Q \neq 0$), with bounded gradient $\|d w\|_{C^0} < C$ and finite $π$-harmonic energy. For nondegenerate contact forms, we employ the `three-interval method' to prove the exponential convergence to a closed Reeb orbit when $Q = 0$. (The Morse-Bott case using this method is treated in a sequel (arXiv:1311.6196).)
Rui Wang, Joel Lehman, Jeff Clune, Kenneth O. Stanley
While the history of machine learning so far largely encompasses a series of problems posed by researchers and algorithms that learn their solutions, an important question is whether the problems themselves can be generated by the algorithm at the same time as they are being solved. Such a process would in effect build its own diverse and expanding curricula, and the solutions to problems at various stages would become stepping stones towards solving even more challenging problems later in the process. The Paired Open-Ended Trailblazer (POET) algorithm introduced in this paper does just that: it pairs the generation of environmental challenges and the optimization of agents to solve those challenges. It simultaneously explores many different paths through the space of possible problems and solutions and, critically, allows these stepping-stone solutions to transfer between problems if better, catalyzing innovation. The term open-ended signifies the intriguing potential for algorithms like POET to continue to create novel and increasingly complex capabilities without bound. Our results show that POET produces a diverse range of sophisticated behaviors that solve a wide range of environmental challenges, many of which cannot be solved by direct optimization alone, or even through a direct-path curriculum-building control algorithm introduced to highlight the critical role of open-endedness in solving ambitious challenges. The ability to transfer solutions from one environment to another proves essential to unlocking the full potential of the system as a whole, demonstrating the unpredictable nature of fortuitous stepping stones. We hope that POET will inspire a new push towards open-ended discovery across many domains, where algorithms like POET can blaze a trail through their interesting possible manifestations and solutions.
Rui Wang, C. Umit Bas, Zihang Cheng, Thomas Choi, Hao Feng, Zheda Li, XiaoKang Ye, Pan Tang, Seun Sangodoyin, Jorge G. Ponce, Robert Monroe, Thomas Henige, Gary Xu, Jianzhong, Zhang, Jeongho Park, Andreas F. Molisch
This paper investigates the capability of millimeter-wave (mmWave) channel sounders with phased arrays to perform super-resolution parameter estimation, i.e., determine the parameters of multipath components (MPC), such as direction of arrival and delay, with resolution better than the Fourier resolution of the setup. We analyze the question both generally, and with respect to a particular novel multi-beam mmWave channel sounder that is capable of performing multiple-input-multiple-output (MIMO) measurements in dynamic environments. We firstly propose a novel two-step calibration procedure that provides higher-accuracy calibration data that are required for Rimax or SAGE. Secondly, we investigate the impact of center misalignment and residual phase noise on the performance of the parameter estimator. Finally we experimentally verify the calibration results and demonstrate the capability of our sounder to perform super-resolution parameter estimation.
Rui Wang, Yuta Hozumi, Changchuan Yin, Guo-Wei Wei
Coronavirus disease 2019 (COVID-19) is a continuously devastating public health and the world economy. One of the major challenges in controlling the COVID-19 outbreak is its asymptomatic infection and transmission, which are elusive and defenseless in most situations. The pathogenicity and virulence of asymptomatic COVID-19 remain mysterious. Based on the genotyping of 20656 Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) genome isolates, we reveal that asymptomatic infection is linked to SARS-CoV-2 11083G>T mutation, i.e., leucine (L) to phenylalanine (F) substitution at the residue 37 (L37F) of nonstructure protein 6 (NSP6). By analyzing the distribution of 11083G>T in various countries, we unveil that 11083G>T may correlate with the hypotoxicity of SARS-CoV-2. Moreover, we show a global decaying tendency of the 11083G>T mutation ratio indicating that 11083G>T hinders SARS-CoV-2 transmission capacity. Sequence alignment found both NSP6 and residue 37 neighborhoods are relatively conservative over a few coronaviral species, indicating their importance in regulating host cell autophagy to undermine innate cellular defense against viral infection. Using machine learning and topological data analysis, we demonstrate that mutation L37F has made NSP6 energetically less stable. The rigidity and flexibility index and several network models suggest that mutation L37F may have compromised the NSP6 function, leading to a relatively weak SARS-CoV subtype. This assessment is a good agreement with our genotyping of SARS-CoV-2 evolution and transmission across various countries and regions over the past few months.
Rui Wang, Lie-Wen Chen, Ying Zhou
Based on an extended Skyrme interaction that includes the terms in relative momenta up to sixth order, corresponding to the so-called Skyrme pseudopotential up to next-to-next-to-next-to leading order (N3LO), we derive the expressions of Hamiltonian density and single nucleon potential under general non-equilibrium conditions which can be applied in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei. While the conventional Skyrme interactions, which include the terms in relative momenta up to second order, predict an incorrect behavior as a function of energy for nucleon optical potential in nuclear matter, the present extended N3LO Skyrme interaction can give a nice description for the empirical nucleon optical potential. We also construct three interaction sets with different high-density behaviors of the symmetry energy, by fitting both the empirical nucleon optical potential up to energy of $1$ GeV and the empirical properties of isospin asymmetric nuclear matter. These extended N3LO Skyrme interactions will be useful in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei at intermediate and high energies, and they can also be useful in nuclear structure studies within the mean-field model.
Rui Wang, Xiao-Jun Wu, Kai-Xuan Chen, Josef Kittler
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive Definite (SPD) manifold and Grassmann manifold respectively, and some algorithms have been developed on them for classification tasks. Motivated by the inability of existing methods to extract discriminatory features for data on Riemannian manifolds, we propose a novel algorithm which combines multiple manifolds as the features of the original image sets. In order to fuse these manifolds, the well-studied Riemannian kernels have been utilized to map the original Riemannian spaces into high dimensional Hilbert spaces. A metric Learning method has been devised to embed these kernel spaces into a lower dimensional common subspace for classification. The state-of-the-art results achieved on three datasets corresponding to two different classification tasks, namely face recognition and object categorization, demonstrate the effectiveness of the proposed method.
Rui Wang
With the rapid development of computer graphics and vision, several three-dimensional (3D) reconstruction techniques have been proposed and used to obtain the 3D representation of objects in the form of point cloud models, mesh models, and geometric models. The cost of 3D reconstruction is declining due to the maturing of this technology, however, the inexpensive 3D reconstruction scanners on the market may not be able to generate a clear point cloud model as expected. This study systematically reviews some basic types of 3D reconstruction technology and introduces an easy implementation using a linear laser scanner, a camera, and a turntable. The implementation is based on the monovision with laser and has tested several objects like wiki and mug. The accuracy and resolution of the point cloud result are quite satisfying. It turns out everyone can build such a 3D reconstruction system with appropriate procedures.
Jiahui Chen, Rui Wang, Nancy Benovich Gilby, Guo-Wei Wei
The latest severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant Omicron (B.1.1.529) has ushered panic responses around the world due to its contagious and vaccine escape mutations. The essential infectivity and antibody resistance of the SARS-CoV-2 variant are determined by its mutations on the spike (S) protein receptor-binding domain (RBD). However, a complete experimental evaluation of Omicron might take weeks or even months. Here, we present a comprehensive quantitative analysis of Omicron's infectivity, vaccine-breakthrough, and antibody resistance. An artificial intelligence (AI) model, which has been trained with tens of thousands of experimental data points and extensively validated by experimental data on SARS-CoV-2, reveals that Omicron may be over ten times more contagious than the original virus or about twice as infectious as the Delta variant. Based on 132 three-dimensional (3D) structures of antibody-RBD complexes, we unveil that Omicron may be twice more likely to escape current vaccines than the Delta variant. The Food and Drug Administration (FDA)-approved monoclonal antibodies (mAbs) from Eli Lilly may be seriously compromised. Omicron may also diminish the efficacy of mAbs from Celltrion and Rockefeller University. However, its impact on Regeneron mAb cocktail appears to be mild.
Kaifu Gao, Rui Wang, Jiahui Chen, Limei Cheng, Jaclyn Frishcosy, Yuta Huzumi, Yuchi Qiu, Tom Schluckbier, Guo-Wei Wei
The deadly coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has gone out of control globally. Despite much effort by scientists, medical experts, and society in general, the slow progress on drug discovery and antibody therapeutic development, the unknown possible side effects of the existing vaccines, and the high transmission rate of the SARS-CoV-2, remind us of the sad reality that our current understanding of the transmission, infectivity, and evolution of SARS-CoV-2 is unfortunately very limited. The major limitation is the lack of mechanistic understanding of viral-host cell interactions, the viral regulation, protein-protein interactions, including antibody-antigen binding, protein-drug binding, host immune response, etc. This limitation will likely haunt the scientific community for a long time and have a devastating consequence in combating COVID-19 and other pathogens. Notably, compared to the long-cycle, highly cost, and safety-demanding molecular-level experiments, the theoretical and computational studies are economical, speedy, and easy to perform. There exists a tsunami of the literature on molecular modeling, simulation, and prediction of SARS-CoV-2 that has become impossible to fully be covered in a review. To provide the reader a quick update about the status of molecular modeling, simulation, and prediction of SARS-CoV-2, we present a comprehensive and systematic methodology-centered narrative in the nick of time. Aspects such as molecular modeling, Monte Carlo (MC) methods, structural bioinformatics, machine learning, deep learning, and mathematical approaches are included in this review. This review will be beneficial to researchers who are looking for ways to contribute to SARS-CoV-2 studies and those who are assessing the current status in the field.
Junyi Ao, Rui Wang, Long Zhou, Chengyi Wang, Shuo Ren, Yu Wu, Shujie Liu, Tom Ko, Qing Li, Yu Zhang, Zhihua Wei, Yao Qian, Jinyu Li, Furu Wei
Motivated by the success of T5 (Text-To-Text Transfer Transformer) in pre-trained natural language processing models, we propose a unified-modal SpeechT5 framework that explores the encoder-decoder pre-training for self-supervised speech/text representation learning. The SpeechT5 framework consists of a shared encoder-decoder network and six modal-specific (speech/text) pre/post-nets. After preprocessing the input speech/text through the pre-nets, the shared encoder-decoder network models the sequence-to-sequence transformation, and then the post-nets generate the output in the speech/text modality based on the output of the decoder. Leveraging large-scale unlabeled speech and text data, we pre-train SpeechT5 to learn a unified-modal representation, hoping to improve the modeling capability for both speech and text. To align the textual and speech information into this unified semantic space, we propose a cross-modal vector quantization approach that randomly mixes up speech/text states with latent units as the interface between encoder and decoder. Extensive evaluations show the superiority of the proposed SpeechT5 framework on a wide variety of spoken language processing tasks, including automatic speech recognition, speech synthesis, speech translation, voice conversion, speech enhancement, and speaker identification. We release our code and model at https://github.com/microsoft/SpeechT5.
Jiahui Chen, Rui Wang, Guo-Wei Wei
Sep 15, 2021·q-bio.PE·PDF The mechanism of SARS-CoV-2 evolution and transmission is elusive and its understanding, a prerequisite to forecast emerging variants, is of paramount importance. SARS-CoV-2 evolution is driven by the mechanisms at molecular and organism scales and regulated by the transmission pathways at the population scale. In this review, we show that infectivity-based natural selection was discovered as the mechanism for SARS-CoV-2 evolution and transmission in July 2020. In April 2021, we proved beyond all doubt that such a natural selection via infectivity-based transmission pathway remained the sole mechanism for SARS-CoV-2 evolution. However, we reveal that antibody-disruptive co-mutations [Y449S, N501Y] debuted as a new vaccine-resistant transmission pathway of viral evolution in highly vaccinated populations a few months ago. Over one year ago, we foresaw that mutations spike protein RBD residues, 452 and 501, would "have high chances to mutate into significantly more infectious COVID-19 strains". Mutations on these residues underpin prevailing SARS-CoV-2 variants Alpha, Beta, Gamma, Delta, Epsilon, Theta, Kappa, Lambda, and Mu at present and are expected to be vital to emerging variants. We anticipate that viral evolution will combine RBD co-mutations at these two sites, creating future variants that are tens of times more infectious than the original SARS-CoV-2. Additionally, two complementary transmission pathways of viral evolution: infectivity and vaccine-resistant, will prolong our battle with COVID-19 for years. We predict that RBD co-mutation [A411S, L452R, T478K], [L452R, T478K, N501Y], [L452R, T478K, E484K, N501Y], [K417N, L452R, T478K], and [P384L, K417N, E484K, N501Y] will have high chances to grow into dominating variants due to their high infectivity and/or strong ability to break through current vaccines, calling for the development of new vaccines and antibody therapies.
Rui Wang, Xu Tan, Renqian Luo, Tao Qin, Tie-Yan Liu
Neural approaches have achieved state-of-the-art accuracy on machine translation but suffer from the high cost of collecting large scale parallel data. Thus, a lot of research has been conducted for neural machine translation (NMT) with very limited parallel data, i.e., the low-resource setting. In this paper, we provide a survey for low-resource NMT and classify related works into three categories according to the auxiliary data they used: (1) exploiting monolingual data of source and/or target languages, (2) exploiting data from auxiliary languages, and (3) exploiting multi-modal data. We hope that our survey can help researchers to better understand this field and inspire them to design better algorithms, and help industry practitioners to choose appropriate algorithms for their applications.
Rui Wang, Guoyin Wang, Ricardo Henao
Unsupervised domain adaptation seeks to learn an invariant and discriminative representation for an unlabeled target domain by leveraging the information of a labeled source dataset. We propose to improve the discriminative ability of the target domain representation by simultaneously learning tightly clustered target representations while encouraging that each cluster is assigned to a unique and different class from the source. This strategy alleviates the effects of negative transfer when combined with adversarial domain matching between source and target representations. Our approach is robust to differences in the source and target label distributions and thus applicable to both balanced and imbalanced domain adaptation tasks, and with a simple extension, it can also be used for partial domain adaptation. Experiments on several benchmark datasets for domain adaptation demonstrate that our approach can achieve state-of-the-art performance in all three scenarios, namely, balanced, imbalanced and partial domain adaptation.
Rui Wang, Rundong Zhao, Emily Ribando-Gros, Jiahui Chen, Yiying Tong, Guo-Wei Wei
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a unified multiscale paradigm to encompass TDA and geometric analysis. In PSG theory, families of persistent Laplacians (PLs) corresponding to various topological dimensions are constructed via a filtration to sample a given dataset at multiple scales. The harmonic spectra from the null spaces of PLs offer the same topological invariants, namely persistent Betti numbers, at various dimensions as those provided by PH, while the non-harmonic spectra of PLs give rise to additional geometric analysis of the shape of the data. In this work, we develop an open-source software package, called highly efficient robust multidimensional evolutionary spectra (HERMES), to enable broad applications of PSGs in science, engineering, and technology. To ensure the reliability and robustness of HERMES, we have validated the software with simple geometric shapes and complex datasets from three-dimensional (3D) protein structures. We found that the smallest non-zero eigenvalues are very sensitive to data abnormality.
Rui Wang, Yinglong Miao, Kostas E. Bekris
Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery shelf means that the robot cannot directly access all objects and has limited free space. This is harder than tabletop rearrangement where objects are easily accessible with top-down grasps, which simplifies robot-object interactions. This work focuses on problems where such interactions are critical for completing tasks. It proposes a new efficient and complete solver under general constraints for monotone instances, which can be solved by moving each object at most once. The monotone solver reasons about robot-object constraints and uses them to effectively prune the search space. The new monotone solver is integrated with a global planner to solve non-monotone instances with high-quality solutions fast. Furthermore, this work contributes an effective pre-processing tool to significantly speed up online motion planning queries for rearrangement in confined spaces. Experiments further demonstrate that the proposed monotone solver, equipped with the pre-processing tool, results in 57.3% faster computation and 3 times higher success rate than state-of-the-art methods. Similarly, the resulting global planner is computationally more efficient and has a higher success rate, while producing high-quality solutions for non-monotone instances (i.e., only 1.3 additional actions are needed on average). Videos of demonstrating solutions on a real robotic system and codes can be found at https://github.com/Rui1223/uniform_object_rearrangement.
Liang Yu, Qixin Guo, Rui Wang, Minyan Shi, Fucheng Yan, Ran Wang
Artificial intelligence and distributed algorithms have been widely used in mechanical fault diagnosis with the explosive growth of diagnostic data. A novel intelligent fault diagnosis system framework that allows intelligent terminals to offload computational tasks to Mobile edge computing (MEC) servers is provided in this paper, which can effectively address the problems of task processing delays and enhanced computational complexity. As the resources at the MEC and intelligent terminals are limited, performing reasonable resource allocation optimization can improve the performance, especially for a multi-terminals offloading system. In this study, to minimize the task computation delay, we jointly optimize the local content splitting ratio, the transmission/computation power allocation, and the MEC server selection under a dynamic environment with stochastic task arrivals. The challenging dynamic joint optimization problem is formulated as a reinforcement learning (RL) problem, which is designed as the computational offloading policies to minimize the long-term average delay cost. Two deep RL strategies, deep Q-learning network (DQN) and deep deterministic policy gradient (DDPG), are adopted to learn the computational offloading policies adaptively and efficiently. The proposed DQN strategy takes the MEC selection as a unique action while using the convex optimization approach to obtain the local content splitting ratio and the transmission/computation power allocation. Simultaneously, the actions of the DDPG strategy are selected as all dynamic variables, including the local content splitting ratio, the transmission/computation power allocation, and the MEC server selection. Numerical results demonstrate that both proposed strategies perform better than the traditional non-learning schemes.
Zhen Ning, Bo Fu, Dong-Hui Xu, Rui Wang
The quadrupole topological insulator (QTI) has attracted intense studies as a prototype of symmetry-protected higher-order topological phases of matter with a quantized quadrupole moment. The realization of QTIs has been reported in various static settings with periodic structures. Here, we theoretically investigate topological phase transitions and establish the QTI phase in a periodically driven system with disorder. In the clean limit, the Floquet QTI phase emerges from a topologically trivial band structure driven by elliptically polarized irradiation. More strikingly, starting from a pure and static system with trivial topology, we unveil an intriguing QTI phase which necessitates the simultaneous presence of disorder and periodic driving. Furthermore, we reveal that particle-hole symmetry is sufficient to protect the QTI. Our work not only establishes a new strategy to design QTIs but also enriches the symmetry-protected mechanism of higher-order topology.
Qianru Liu, Rui Wang, Yuesheng Xu, Mingsong Yan
We consider a regularization problem whose objective function consists of a convex fidelity term and a regularization term determined by the $\ell_1$ norm composed with a linear transform. Empirical results show that the regularization with the $\ell_1$ norm can promote sparsity of a regularized solution. It is the goal of this paper to understand theoretically the effect of the regularization parameter on the sparsity of the regularized solutions. We establish a characterization of the sparsity under the transform matrix of the solution. When the fidelity term has a special structure and the transform matrix coincides with a identity matrix, the resulting characterization can be taken as a regularization parameter choice strategy with which the regularization problem has a solution having a sparsity of a certain level. We study choices of the regularization parameter so that the regularization term alleviates the ill-posedness and promote sparsity of the resulting regularized solution. Numerical experiments demonstrate that choices of the regularization parameters can balance the sparsity of the solutions of the regularization problem and its approximation to the minimizer of the fidelity function.