arXiv subjects
Publications and source records attributed to Hui Zhang.
In this paper, we consider compatible Hom-Lie triple systems. Compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie triple systems. As applications of cohomology, we study abelian extensions and deformations of compatible Hom-Lie triple systems.
Gene regulatory relationships can be abstracted as a gene regulatory network (GRN), which plays a key role in characterizing complex cellular processes and pathways. Recently, graph neural networks (GNNs), as a class of deep learning models, have emerged as a useful tool to infer gene regulatory relationships from gene expression data. However, deep learning models have been found to be vulnerable to noise, which greatly hinders the adoption of deep learning in constructing GRNs, because high noise is often unavoidable in the process of gene expression measurement. Can we preferably prototype a robust GNN for constructing GRNs? In this paper, we give a positive answer by proposing a Quadratic Graph Attention Network (Q-GAT) with a dual attention mechanism. We study the changes in the predictive accuracy of Q-GAT and 9 state-of-the-art baselines by introducing different levels of adversarial perturbations. Experiments in the E. coli and S. cerevisiae datasets suggest that Q-GAT outperforms the state-of-the-art models in robustness. Lastly, we dissect why Q-GAT is robust through the signal-to-noise ratio (SNR) and interpretability analyses. The former informs that nonlinear aggregation of quadratic neurons can amplify useful signals and suppress unwanted noise, thereby facilitating robustness, while the latter reveals that Q-GAT can leverage more features in prediction thanks to the dual attention mechanism, which endows Q-GAT with the ability to confront adversarial perturbation. We have shared our code in https://github.com/Minorway/Q-GAT_for_Robust_Construction_of_GRN for readers' evaluation.
The randomzied Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy corruptions, which are common in many practical applications. In this study, we develop a new variant of the randomzied sparse Kaczmarz method with linear convergence guarantees, by making use of a quantile technique to detect corruptions. Moreover, we incorporate averaged block technique into the proposed method to achieve parallel computation and acceleration. Finally, the proposed algorithms are illustrated to be very efficient through extensive numerical experiments.
The single-particle cryo-EM field faces the persistent challenge of preferred orientation, lacking general computational solutions. We introduce cryoPROS, an AI-based approach designed to address the above issue. By generating the auxiliary particles with a conditional deep generative model, cryoPROS addresses the intrinsic bias in orientation estimation for the observed particles. We effectively employed cryoPROS in the cryo-EM single particle analysis of the hemagglutinin trimer, showing the ability to restore the near-atomic resolution structure on non-tilt data. Moreover, the enhanced version named cryoPROS-MP significantly improves the resolution of the membrane protein NaX using the no-tilted data that contains the effects of micelles. Compared to the classical approaches, cryoPROS does not need special experimental or image acquisition techniques, providing a purely computational yet effective solution for the preferred orientation problem. Finally, we conduct extensive experiments that establish the low risk of model bias and the high robustness of cryoPROS.
HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R=100,000 between 0.98 - 2.5 um, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.
Multi-channel speech enhancement seeks to utilize spatial information to distinguish target speech from interfering signals. While deep learning approaches like the dual-path convolutional recurrent network (DPCRN) have made strides, challenges persist in effectively modeling inter-channel correlations and amalgamating multi-level information. In response, we introduce the Parallel Dual-Path Convolutional Recurrent Network (PDPCRN). This acoustic modeling architecture has two key innovations. First, a parallel design with separate branches extracts complementary features. Second, bi-directional modules enable cross-branch communication. Together, these facilitate diverse representation fusion and enhanced modeling. Experimental validation on TIMIT datasets underscores the prowess of PDPCRN. Notably, against baseline models like the standard DPCRN, PDPCRN not only outperforms in PESQ and STOI metrics but also boasts a leaner computational footprint with reduced parameters.
Multi-channel speech enhancement utilizes spatial information from multiple microphones to extract the target speech. However, most existing methods do not explicitly model spatial cues, instead relying on implicit learning from multi-channel spectra. To better leverage spatial information, we propose explicitly incorporating spatial modeling by applying spherical harmonic transforms (SHT) to the multi-channel input. In detail, a hierarchical framework is introduced whereby lower order harmonics capturing broader spatial patterns are estimated first, then combined with higher orders to recursively predict finer spatial details. Experiments on TIMIT demonstrate the proposed method can effectively recover target spatial patterns and achieve improved performance over baseline models, using fewer parameters and computations. Explicitly modeling spatial information hierarchically enables more effective multi-channel speech enhancement.
Multi-channel speech enhancement extracts speech using multiple microphones that capture spatial cues. Effectively utilizing directional information is key for multi-channel enhancement. Deep learning shows great potential on multi-channel speech enhancement and often takes short-time Fourier Transform (STFT) as inputs directly. To fully leverage the spatial information, we introduce a method using spherical harmonics transform (SHT) coefficients as auxiliary model inputs. These coefficients concisely represent spatial distributions. Specifically, our model has two encoders, one for the STFT and another for the SHT. By fusing both encoders in the decoder to estimate the enhanced STFT, we effectively incorporate spatial context. Evaluations on TIMIT under varying noise and reverberation show our model outperforms established benchmarks. Remarkably, this is achieved with fewer computations and parameters. By leveraging spherical harmonics to incorporate directional cues, our model efficiently improves the performance of the multi-channel speech enhancement.
The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast time-stepping discontinuous Galerkin finite element method for the time-fractional diffusion equations, which saves storage and computational time. The optimal error estimate $O(N^{-p-1} + h^{m+1} + \varepsilon N^{rα})$ of the current time-stepping discontinuous Galerkin method is rigorous proved, where $N$ denotes the number of time intervals, $p$ is the degree of polynomial approximation on each time subinterval, $h$ is the maximum space step, $r\ge1$, $m$ is the order of finite element space, and $\varepsilon>0$ can be arbitrarily small. Numerical simulations verify the theoretical analysis.
The step function is one of the simplest and most natural activation functions for deep neural networks (DNNs). As it counts 1 for positive variables and 0 for others, its intrinsic characteristics (e.g., discontinuity and no viable information of subgradients) impede its development for several decades. Even if there is an impressive body of work on designing DNNs with continuous activation functions that can be deemed as surrogates of the step function, it is still in the possession of some advantageous properties, such as complete robustness to outliers and being capable of attaining the best learning-theoretic guarantee of predictive accuracy. Hence, in this paper, we aim to train DNNs with the step function used as an activation function (dubbed as 0/1 DNNs). We first reformulate 0/1 DNNs as an unconstrained optimization problem and then solve it by a block coordinate descend (BCD) method. Moreover, we acquire closed-form solutions for sub-problems of BCD as well as its convergence properties. Furthermore, we also integrate $\ell_{2,0}$-regularization into 0/1 DNN to accelerate the training process and compress the network scale. As a result, the proposed algorithm has a high performance on classifying MNIST and Fashion-MNIST datasets. As a result, the proposed algorithm has a desirable performance on classifying MNIST, FashionMNIST, Cifar10, and Cifar100 datasets.
Collaborative perception is essential to address occlusion and sensor failure issues in autonomous driving. In recent years, theoretical and experimental investigations of novel works for collaborative perception have increased tremendously. So far, however, few reviews have focused on systematical collaboration modules and large-scale collaborative perception datasets. This work reviews recent achievements in this field to bridge this gap and motivate future research. We start with a brief overview of collaboration schemes. After that, we systematically summarize the collaborative perception methods for ideal scenarios and real-world issues. The former focuses on collaboration modules and efficiency, and the latter is devoted to addressing the problems in actual application. Furthermore, we present large-scale public datasets and summarize quantitative results on these benchmarks. Finally, we highlight gaps and overlook challenges between current academic research and real-world applications. The project page is https://github.com/CatOneTwo/Collaborative-Perception-in-Autonomous-Driving
Reducing noise in quantum systems is a major challenge towards the application of quantum technologies. Here, we propose and demonstrate a scheme to reduce noise using a quantum autoencoder with rigorous performance guarantees. The quantum autoencoder learns to compresses noisy quantum states into a latent subspace and removes noise via projective measurements. We find various noise models where we can perfectly reconstruct the original state even for high noise levels. We apply the autoencoder to cool thermal states to the ground state and reduce the cost of magic state distillation by several orders of magnitude. Our autoencoder can be implemented using only unitary transformations without ancillas, making it immediately compatible with the state of the art. We experimentally demonstrate our methods to reduce noise in a photonic integrated circuit. Our results can be directly applied to make quantum technologies more robust to noise.
We investigate the orbit-to-charge conversion in YIG/Pt/nonmagnetic material (NM) trilayer heterostructures. With the additional Ru layer on the top of YIG/Pt stacks, the charge current signal increases nearly an order of magnitude in both longitudinal spin Seebeck effect (SSE) and spin pumping (SP) measurements. Through thickness dependence studies of the Ru metal layer and theoretical model, we quantitatively clarify different contributions of the increased SSE signal that mainly comes from the inverse orbital Hall effect (IOHE) of Ru, and partially comes from the orbital sink effect in the Ru layer. A similar enhancement of SSE(SP) signals is also observed when Ru is replaced by other materials (Ta, W, and Cu), implying the universality of the IOHE in transition metals. Our findings not only suggest a more efficient generation of the charge current via the orbital angular moment channel but also provides crucial insights into the interplay among charge, spin, and orbit.
In this paper, we consider the critical Choquard system with prescribed mass \begin{equation*} \begin{aligned} \left\{ \begin{array}{lll} -Δu+λ_1u=(I_μ\ast |u|^{2^*_μ})|u|^{2^*_μ-2}u+νp(I_μ\ast |v|^q)|u|^{p-2}u\ & \text{in}\quad \mathbb{R}^N,\\ -Δv+λ_2v=(I_μ\ast |v|^{2^*_μ})|v|^{2^*_μ-2}v+νq(I_μ\ast |u|^p)|v|^{q-2}v\ & \text{in}\quad \mathbb{R}^N,\\ \int_{\mathbb{R}^N}u^2=a^2,\quad\int_{\mathbb{R}^N}v^2=b^2, \end{array}\right.\end{aligned} \end{equation*} where $N\geq3$, $0<μ 0$, we study the existence, non-existence and asymptotic behavior of normalized solutions by distinguishing three cases: $L^2$-subcritical case: $p+q<4+\frac{4-2μ}{N}$; $L^2$-critical case: $p+q=4+\frac{4-2μ}{N}$; $L^2$-supercritical case: $p+q>4+\frac{4-2μ}{N}$. In particular, in $L^2$-subcritical case, and either $N\in\{3,4\}$ or $N\geq5$ with $(\frac N2-1)p+\frac {N}{2}q\leq 2N-μ$ and $(\frac N2-1)q+\frac {N}{2}p\leq 2N-μ$, we prove that there exists $ν_0>0$ such that the system has a positive radial normalized ground state for $0<ν<ν_0$. In $L^2$-critical case and $N\in\{3,4\}$, we show there is $ν'_0>0$ such that the system has a positive radial normalized ground state for $0<ν<ν'_0$. In $L^2$-supercritical case and $N\in\{3,4\}$, there are two thresholds $ν_2\geqν_1\geq0$ such that a positive radial normalized solution exists if $ν>ν_2$, and no normalized ground state exists for $ν<ν_1$.
A new fabrication process for superconducting integrated digital circuits is reported. We have developed the "SIMIT Nb04" fabrication technique for superconducting integrated circuits with Nb-based Josephson junctions based on the validated "SIMIT Nb03" process and Chemical Mechanical Planarization (CMP) technology. Seven Nb superconducting layers and one Mo resistor layer are included in the "SIMIT Nb04" process with 19 mask levels. The device structure is composed of active layers including junctions at the bottom, two passive transmission line (PTL) layers in the middle and a DC power layer at the top. The circuit fabrication started with the fabrication of Mo resistors with a target sheet resistance Rsh of 3 $Ω$, followed by the deposition of Nb/Al-AlO$_x$/Nb trilayer Josephson-junction with a target critical current density Jc at 15 kA/cm$^2$. To increase the Al-AlO$_x$ barrier layer etching's repeatability, an additional barrier protection layer was applied. To accomplish high-quality planarization, we created a planarization procedure coupled with dummy filling. To assess the process dependability and controllability, a set of process control monitors (PCMs) for monitoring fabrication and design parameters was designed and monitored. The successful manufacturing and testing of a few small-scale circuits, like our standard library cells, further attests to the viability of our fabrication process for superconducting integrated circuits.
Learning per-point semantic features from the hierarchical feature pyramid is essential for point cloud semantic segmentation. However, most previous methods suffered from ambiguous region features or failed to refine per-point features effectively, which leads to information loss and ambiguous semantic identification. To resolve this, we propose Retro-FPN to model the per-point feature prediction as an explicit and retrospective refining process, which goes through all the pyramid layers to extract semantic features explicitly for each point. Its key novelty is a retro-transformer for summarizing semantic contexts from the previous layer and accordingly refining the features in the current stage. In this way, the categorization of each point is conditioned on its local semantic pattern. Specifically, the retro-transformer consists of a local cross-attention block and a semantic gate unit. The cross-attention serves to summarize the semantic pattern retrospectively from the previous layer. And the gate unit carefully incorporates the summarized contexts and refines the current semantic features. Retro-FPN is a pluggable neural network that applies to hierarchical decoders. By integrating Retro-FPN with three representative backbones, including both point-based and voxel-based methods, we show that Retro-FPN can significantly improve performance over state-of-the-art backbones. Comprehensive experiments on widely used benchmarks can justify the effectiveness of our design. The source is available at https://github.com/AllenXiangX/Retro-FPN
In this paper, we introduce the representation of modified $λ$-differential $3$-Lie algebras and define the cohomology of modified $λ$-differential $3$-Lie algebras with coefficients in a representation. As applications of the proposed cohomology theory, we study linear deformations, abelian extensions and $T^*$-extensions of modified $λ$-differential $3$-Lie algebras.
In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve a quadratic speedup compared to classical Monte Carlo methods. The circuit consists of three modules: a module loading the distribution of asset prices, a module computing the expected payoff, and a module performing the quantum amplitude estimation algorithm to introduce speed-ups. In the distribution module, a generative adversarial network is embedded for efficient learning and loading of asset distributions, which precisely capture the market trends. This work is a step forward in the development of specialized photonic processors for applications in finance, with the potential to improve the efficiency and quality of financial services.