arXiv subjects

Jie Xu

Publications and source records attributed to Jie Xu.

At least 361 records · Page 20Linked to original sources

arXiv2023

The Conformal Laplacian and The Kazdan-Warner Problem: Zero First Eigenvalue Case

In this article, we first show that given a smooth function $ S $ either on closed manifolds $ (M, g) $ or compact manifolds $ (\bar{M}, g) $ with non-empty boundary, both for dimensions at least $ 3 $, the condition $ S \equiv 0 $, or $ S $ changes sign and $ \int_{M} S \dvol < 0 $ (with zero mean curvature if the boundary is not empty), is both the necessary and sufficient condition for prescribing scalar curvature problems within conformal class $ [g] $, provided that the first eigenvalue of the conformal Laplacian is zero. We then extend the same necessary and sufficient condition, in terms of prescribing Gauss curvature function and zero geodesic curvature, to compact Riemann surfaces with non-empty boundary, provided that the Euler characteristic is zero. These results are the first full extensions since the results of Kazdan and Warner \cite{KW2} on 2-dimensional torus, and of Escobar and Schoen \cite{ESS} on closed manifolds for dimensions $ 3 $ and $ 4 $. We then give results of prescribing nonzero scalar and mean curvature problems on $ (\bar{M}, g) $, still with zero first eigenvalue and dimensions at least $ 3 $. Analogously, results of prescribing Gauss and geodesic curvature problems on compact Riemann surfaces with boundary are given for zero Euler characteristic case. Lastly, we show a generalization of the Han-Li conjecture. Technically the key step for manifolds with dimensions at least $ 3 $ is to apply both the local variational methods, local Yamabe-type equations and a new version of the monotone iteration scheme. The key features include the smoothness of the upper solution, the technical difference between constant and non-constant prescribing scalar curvature functions, etc.

math.DG↗

arXiv2023

Trichotomy Theorem for Prescribed Scalar and Mean Curvatures on Compact Manifolds with Boundaries

In this article, we give results of prescribing scalar and mean curvature functions for metrics either pointwise conformal or conformally equivalent to a Riemannian metric that is equipped on a compact manifold with boundary, with dimensions at least $ 3 $. The results are classified by the sign of the first eigenvalue of the conformal Laplacian. This leads to a "Trichotomy Theorem" in terms of both scalar and mean curvature functions, which is a full extension of the "Trichotomy Theorem" given by Kazdan and Warner. We also discuss prescribing Gauss and geodesic curvature problems on compact Riemann surfaces with boundary for metrics either pointwise conformal or conformally equivalent to the original metric, provided that the Euler characteristic is negative. The key step is a general version of monotone iteration scheme which handle the zeroth order nonlinear term on the boundary conditions.

math.DG↗

arXiv2022

Prescribed Scalar Curvature on Compact Manifolds Under Conformal Deformation

We give sufficient and "almost" necessary conditions for the prescribed scalar curvature problems within the conformal class of a Riemannian metric $ g $ for both closed manifolds and compact manifolds with boundary, including the interesting cases $ \mathbb{S}^{n} $ or some quotient of $ \mathbb{S}^{n} $, in dimensions $ n \geqslant 3 $, provided that the first eigenvalues of conformal Laplacian (with appropriate boundary conditions if necessary) are positive. When the manifold is not some quotient of $ \mathbb{S}^{n} $, we show that, on one hand, any smooth function that is a positive constant within some open subset of the manifold with arbitrary positive measure, and has no restriction on the rest of the manifold, is a prescribed scalar curvature function of some metric under conformal change; on the other hand, any smooth function $ S $ is almost a prescribed scalar curvature function of Yamabe metric within the conformal class $ [g] $ in the sense that an appropriate perturbation of $ S $ that defers with $ S $ within an arbitrarily small open subset is a prescribed scalar curvature function of Yamabe metric. When the manifold is either $ \mathbb{S}^{n} $ or $ \mathbb{S}^n / Γ$ with Kleinian group $ Γ$ we show that any positive function that satisfies a technical analytical condition, called CONDITION B, can be realized as a prescribed scalar curvature functions on these manifolds.

math.DG↗

arXiv2022

RoSGAS: Adaptive Social Bot Detection with Reinforced Self-Supervised GNN Architecture Search

Social bots are referred to as the automated accounts on social networks that make attempts to behave like human. While Graph Neural Networks (GNNs) has been massively applied to the field of social bot detection, a huge amount of domain expertise and prior knowledge is heavily engaged in the state-of-the art approaches to design a dedicated neural network architecture for a specific classification task. Involving oversized nodes and network layers in the model design, however, usually causes the over-smoothing problem and the lack of embedding discrimination. In this paper, we propose RoSGAS, a novel Reinforced and Self-supervised GNN Architecture Search framework to adaptively pinpoint the most suitable multi-hop neighborhood and the number of layers in the GNN architecture. More specifically, we consider the social bot detection problem as a user-centric subgraph embedding and classification task. We exploit heterogeneous information network to present the user connectivity by leveraging account metadata, relationships, behavioral features and content features. RoSGAS uses a multi-agent deep reinforcement learning (RL) mechanism for navigating the search of optimal neighborhood and network layers to learn individually the subgraph embedding for each target user. A nearest neighbor mechanism is developed for accelerating the RL training process, and RoSGAS can learn more discriminative subgraph embedding with the aid of self-supervised learning. Experiments on 5 Twitter datasets show that RoSGAS outperforms the state-of-the-art approaches in terms of accuracy, training efficiency and stability, and has better generalization when handling unseen samples.

cs.SI↗

arXiv2022

Electrical switching of ferro-rotational order in nano-thick 1T-TaS$_2$ crystals

Hysteretic switching of domain states is a salient character of all ferroic materials and the foundation for their multifunctional applications. Ferro-rotational order is emerging as a new type of ferroic order featuring structural rotations, but its controlled switching remains elusive due to its invariance under both time reversal and spatial inversion. Here, we demonstrate electrical switching of ferro-rotational domain states in nanometer-thick 1T-TaS$_2$ crystals in its charge-density-wave phases. Cooling from the high-symmetry phase to the ferro-rotational phase under an external electric field induces domain state switching and domain wall formation, realized in a simple two-terminal configuration using a volt-scale voltage. Although the electric field does not couple with the order due to symmetry mismatch, it drives domain wall propagation to give rise to reversible, durable, and nonvolatile isothermal state switching at room temperature. These results pave the path for manipulation of the ferro-rotational order and its nanoelectronic applications.

cond-mat.mtrl-sci↗

arXiv2022

Giant efficiency of long-range orbital torque in Co/Nb bilayers

We report unambiguously experimental evidence of a strong orbital current in Nb films with weak spin-orbit coupling via the spin-torque ferromagnetic resonance (ST-FMR) spectrum for Fe/Nb and Co/Nb bilayers. The sign change of the damping-like torque in Co/Nb demonstrates a large spin-orbit correlation and thus great efficiency of orbital torque in Co/Nb. By studying the efficiency as a function of the thickness of Nb sublayer, we reveal a long orbital diffusion length (~3.1 nm) of Nb. Further planar Hall resistance (PHE) measurements at positive and negative applying current confirm the nonlocal orbital transport in ferromagnetic-metal/Nb heterostructures.

physics.app-ph↗

arXiv2022

Assemble Them All: Physics-Based Planning for Generalizable Assembly by Disassembly

Assembly planning is the core of automating product assembly, maintenance, and recycling for modern industrial manufacturing. Despite its importance and long history of research, planning for mechanical assemblies when given the final assembled state remains a challenging problem. This is due to the complexity of dealing with arbitrary 3D shapes and the highly constrained motion required for real-world assemblies. In this work, we propose a novel method to efficiently plan physically plausible assembly motion and sequences for real-world assemblies. Our method leverages the assembly-by-disassembly principle and physics-based simulation to efficiently explore a reduced search space. To evaluate the generality of our method, we define a large-scale dataset consisting of thousands of physically valid industrial assemblies with a variety of assembly motions required. Our experiments on this new benchmark demonstrate we achieve a state-of-the-art success rate and the highest computational efficiency compared to other baseline algorithms. Our method also generalizes to rotational assemblies (e.g., screws and puzzles) and solves 80-part assemblies within several minutes.

cs.RO↗

arXiv2022

AD-BERT: Using Pre-trained contextualized embeddings to Predict the Progression from Mild Cognitive Impairment to Alzheimer's Disease

Objective: We develop a deep learning framework based on the pre-trained Bidirectional Encoder Representations from Transformers (BERT) model using unstructured clinical notes from electronic health records (EHRs) to predict the risk of disease progression from Mild Cognitive Impairment (MCI) to Alzheimer's Disease (AD). Materials and Methods: We identified 3657 patients diagnosed with MCI together with their progress notes from Northwestern Medicine Enterprise Data Warehouse (NMEDW) between 2000-2020. The progress notes no later than the first MCI diagnosis were used for the prediction. We first preprocessed the notes by deidentification, cleaning and splitting, and then pretrained a BERT model for AD (AD-BERT) based on the publicly available Bio+Clinical BERT on the preprocessed notes. The embeddings of all the sections of a patient's notes processed by AD-BERT were combined by MaxPooling to compute the probability of MCI-to-AD progression. For replication, we conducted a similar set of experiments on 2563 MCI patients identified at Weill Cornell Medicine (WCM) during the same timeframe. Results: Compared with the 7 baseline models, the AD-BERT model achieved the best performance on both datasets, with Area Under receiver operating characteristic Curve (AUC) of 0.8170 and F1 score of 0.4178 on NMEDW dataset and AUC of 0.8830 and F1 score of 0.6836 on WCM dataset. Conclusion: We developed a deep learning framework using BERT models which provide an effective solution for prediction of MCI-to-AD progression using clinical note analysis.

cs.CL↗

arXiv2022

Pushing AI to Wireless Network Edge: An Overview on Integrated Sensing, Communication, and Computation towards 6G

Pushing artificial intelligence (AI) from central cloud to network edge has reached board consensus in both industry and academia for materializing the vision of artificial intelligence of things (AIoT) in the sixth-generation (6G) era. This gives rise to an emerging research area known as edge intelligence, which concerns the distillation of human-like intelligence from the huge amount of data scattered at wireless network edge. In general, realizing edge intelligence corresponds to the process of sensing, communication, and computation, which are coupled ingredients for data generation, exchanging, and processing, respectively. However, conventional wireless networks design the sensing, communication, and computation separately in a task-agnostic manner, which encounters difficulties in accommodating the stringent demands of ultra-low latency, ultra-high reliability, and high capacity in emerging AI applications such as auto-driving. This thus prompts a new design paradigm of seamless integrated sensing, communication, and computation (ISCC) in a task-oriented manner, which comprehensively accounts for the use of the data in the downstream AI applications. In view of its growing interest, this article provides a timely overview of ISCC for edge intelligence by introducing its basic concept, design challenges, and enabling techniques, surveying the state-of-the-art development, and shedding light on the road ahead.

cs.IT↗

arXiv2022

Coordinated Transmit Beamforming for Multi-antenna Network Integrated Sensing and Communication

This paper studies a multi-antenna network integrated sensing and communication (ISAC) system, in which a set of multi-antenna base stations (BSs) employ the coordinated transmit beamforming to serve their respectively associated single-antenna communication users (CUs), and at the same time reuse the reflected information signals to perform joint target detection. In particular, we consider two target detection scenarios depending on the time synchronization among BSs. In Scenario \uppercase\expandafter{\romannumeral1}, these BSs are synchronized and can exploit the target-reflected signals over both the direct links (from each BS to target to itself) and the cross links (from each BS to target to other BSs) for joint detection. In Scenario \uppercase\expandafter{\romannumeral2}, these BSs are not synchronized and can only utilize target-reflected signals over the direct links for joint detection. For each scenario, we derive the detection probability under a specific false alarm probability at any given target location. Based on the derivation, we optimize the coordinated transmit beamforming at the BSs to maximize the minimum detection probability over a particular target area, while ensuring the minimum signal-to-interference-plus-noise ratio (SINR) constraints at the CUs, subject to the maximum transmit power constraints at the BSs. We use the semi-definite relaxation (SDR) technique to obtain highly-quality solutions to the formulated problems. Numerical results show that for each scenario, the proposed design achieves higher detection probability than the benchmark scheme based on communication design. It is also shown that the time synchronization among BSs is beneficial in enhancing the detection performance as more reflected signal paths are exploited.

cs.IT↗

arXiv2022

Transmit Optimization for Multi-functional MIMO Systems Integrating Sensing, Communication, and Powering

This paper unifies integrated sensing and communication (ISAC) and simultaneous wireless information and power transfer (SWIPT), by investigating a new multi-functional multiple-input multiple-output (MIMO) system integrating wireless sensing, communication, and powering. In this system, one multi-antenna hybrid access point (H-AP) transmits wireless signals to communicate with one multi-antenna information decoding (ID) receiver, wirelessly charge one multi-antenna energy harvesting (EH) receiver, and perform radar sensing for a point target based on the echo signal at the same time. Under this setup, we aim to reveal the fundamental performance tradeoff limits of sensing, communication, and powering, in terms of the estimation Cram{é}r-Rao bound (CRB), achievable communication rate, and harvested energy level, respectively. Towards this end, we define the achievable CRB-rate-energy (C-R-E) region and characterize its Pareto boundary by maximizing the achievable rate at the ID receiver, subject to the estimation CRB requirement for target sensing, the harvested energy requirement at the EH receiver, and the maximum transmit power constraint at the H-AP. We obtain the semi-closed-form optimal transmit covariance solution to the formulated problem by applying advanced convex optimization techniques. Numerical results show the optimal C-R-E region boundary achieved by our proposed design, as compared to the benchmark scheme based on time switching.

cs.IT↗

arXiv2022

Cramér-Rao Bound Minimization for IRS-Enabled Multiuser Integrated Sensing and Communication with Extended Target

This paper investigates an intelligent reflecting surface (IRS) enabled multiuser integrated sensing and communication (ISAC) system, which consists of one multi-antenna base station (BS), one IRS, multiple single-antenna communication users (CUs), and one extended target at the non-line-of-sight (NLoS) region of the BS. The IRS is deployed to not only assist the communication from the BS to the CUs, but also enable the BS's NLoS target sensing based on the echo signals from the BS-IRS-target-IRS-BS link. To provide full degrees of freedom for sensing, we suppose that the BS sends additional dedicated sensing signals combined with the information signals. Accordingly, we consider two types of CU receivers, namely Type-I and Type-II receivers, which do not have and have the capability of cancelling the interference from the sensing signals, respectively. Under this setup, we jointly optimize the transmit beamforming at the BS and the reflective beamforming at the IRS to minimize the Cramér-Rao bound (CRB) for estimating the target response matrix with respect to the IRS, subject to the minimum signal-to-interference-plus-noise ratio (SINR) constraints at the CUs and the maximum transmit power constraint at the BS. We present efficient algorithms to solve the highly non-convex SINR-constrained CRB minimization problems, by using the techniques of alternating optimization and semi-definite relaxation. Numerical results show that the proposed design achieves lower estimation CRB than other benchmark schemes, and the sensing signal interference pre-cancellation is beneficial when the number of CUs is greater than one.

eess.SP↗

arXiv2022

The Boundary Yamabe Problem, I: Minimal Boundary Case

We apply iteration schemes and perturbation methods to provide a complete solution of the boundary Yamabe problem with minimal boundary scenario, or equivalently, the existence of a real, positive, smooth solution of $ -\frac{4(n -1)}{n - 2} Δ_{g} u + S_{g} u = λu^{\frac{n+2}{n - 2}} $ in $ M $, $ \frac{\partial u}{\partial ν} + \frac{n-2}{2} h_{g} u = 0 $ on $ \partial M $. Thus $ g $ is conformal to to the metric $ \tilde{g} = u^{\frac{4}{n -2}} g $ of constant scalar curvature $ λ$ with minimal boundary. In contrast to the classical method of calculus of variations with assumptions on Weyl tensors and classification of types of points on $ \partial M $, the boundary Yamabe problem is fully solved here in three cases classified by the sign of the first eigenvalue $ η_{1} $ of the conformal Laplacian with Robin condition. When $ η_{1} < 0 $, a pair of global sub-solution and super-solution are constructed. When $ η_{1} > 0 $, a perturbed boundary Yamabe equation $ -\frac{4(n -1)}{n - 2} Δ_{g} u_β + \left( S_{g} + β\right) u_β = λ_β u_β^{\frac{n+2}{n - 2}} $ in $ M $, $ \frac{\partial u_β}{\partial ν} + \frac{n-2}{2} h_{g} u_β = 0 $ on $ \partial M $ is solved with $ β< 0 $. The boundary Yamabe equation is then solved by taking $ β\rightarrow 0^{-} $. The signs of scalar curvature $ S_{g} $ and mean curvature $ h_{g} $ play important roles in this existence result.

math.DG↗

arXiv2022

Intelligent Reflecting Surface Enabled Sensing: Cramér-Rao Lower Bound Optimization

This paper investigates intelligent reflecting surface (IRS) enabled non-line-of-sight (NLoS) wireless sensing, in which an IRS is deployed to assist an access point (AP) to sense a target in its NLoS region. It is assumed that the AP is equipped with multiple antennas and the IRS is equipped with a uniform linear array. The AP aims to estimate the target's direction-of-arrival (DoA) with respect to the IRS, based on the echo signals from the AP-IRS-target-IRS-AP link. Under this setup, we jointly design the transmit beamforming at the AP and the reflective beamforming at the IRS to minimize the Cramér-Rao lower bound (CRLB) on estimation error. Towards this end, we first obtain the CRLB expression for estimating the DoA in closed form. Next, we optimize the joint beamforming design to minimize the CRLB, via alternating optimization, semi-definite relaxation, and successive convex approximation. Numerical results show that the proposed design based on CRLB minimization achieves improved sensing performance in terms of mean squared error, as compared to the traditional schemes with signal-to-noise ratio maximization and separate beamforming.

eess.SP↗

arXiv2022

Solving the Yamabe-Type Equations on Closed Manifolds by Iteration Schemes

We introduce a double iterative scheme and local variational method to solve the Yamabe-type equation $ - \frac{4(n - 1)}{n - 2}Δ_{g} u + (S_{g} + β) u = λu^{\frac{n + 2}{n - 2}} $ for some constant $ β\leqslant 0 $, locally on Riemannian domain $ (Ω, g) $ with trivial Dirichlet condition and globally on closed manifolds $ (M, g) $; the dimensions of $ Ω$ and $ M $ are at least 3. In contrast to the traditional global variational method, these Yamabe-type equations on closed manifolds are analyzed by local analysis and monotone iteration scheme. In particular, we do not need to use the Weyl tensor. In particular, the sign of the first eigenvalue $ η_{1} $ of conformal Laplacian $ \Box_{g} u : = - \frac{4(n - 1)}{n - 2}Δ_{g} u + S_{g} u $ plays the central role. When letting $ β\rightarrow 0 $ from the left, we reproof the classical Yamabe problem as a natural consequence of the Yamabe-type equations. The results are classified by the sign of $ η_{1} $.

math.DG↗

arXiv2022

Deep Clustering: A Comprehensive Survey

Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering, which can learn clustering-friendly representations using deep neural networks, has been broadly applied in a wide range of clustering tasks. Existing surveys for deep clustering mainly focus on the single-view fields and the network architectures, ignoring the complex application scenarios of clustering. To address this issue, in this paper we provide a comprehensive survey for deep clustering in views of data sources. With different data sources and initial conditions, we systematically distinguish the clustering methods in terms of methodology, prior knowledge, and architecture. Concretely, deep clustering methods are introduced according to four categories, i.e., traditional single-view deep clustering, semi-supervised deep clustering, deep multi-view clustering, and deep transfer clustering. Finally, we discuss the open challenges and potential future opportunities in different fields of deep clustering.

cs.LG↗

arXiv2022

MIMO Integrated Sensing and Communication: CRB-Rate Tradeoff

This paper studies a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, in which a multi-antenna base station (BS) sends unified wireless signals to estimate one sensing target and communicate with a multi-antenna communication user (CU) simultaneously. We consider both the point and extended target models. For the point target case, the BS estimates the target angle and we adopt the Cramér-Rao bound (CRB) for angle estimation as the sensing performance metric. For the extended target case, the BS estimates the complete target response matrix, and we consider three different sensing performance metrics including the trace, the maximum eigenvalue, and the determinant of the CRB matrix for target response matrix estimation. For each of the four scenarios with different CRB measures, we investigate the fundamental tradeoff between the CRB for estimation and the data rate for communication, by characterizing the Pareto boundary of the achievable CRB-rate (C-R) region. In particular, we formulate a new MIMO rate maximization problem for each scenario, by optimizing the transmit covariance matrix at the BS, subject to a different form of maximum CRB constraint and its maximum transmit power constraint. For these problems, we obtain their optimal solutions in semi-closed forms by using advanced convex optimization techniques. For the point target case, the optimal solution is obtained by diagonalizing a \emph{composite channel matrix} via singular value decomposition (SVD) together with water-filling-like power allocation over these decomposed subchannels. For the three scenarios in the extended target case, the optimal solutions are obtained by diagonalizing the \emph{communication channel} via SVD, together with proper power allocation over two orthogonal sets of subchannels. Numerical results are conducted to validate the proposed design.

cs.IT↗

arXiv2022

Closed-Loop Control of Direct Ink Writing via Reinforcement Learning

Enabling additive manufacturing to employ a wide range of novel, functional materials can be a major boost to this technology. However, making such materials printable requires painstaking trial-and-error by an expert operator, as they typically tend to exhibit peculiar rheological or hysteresis properties. Even in the case of successfully finding the process parameters, there is no guarantee of print-to-print consistency due to material differences between batches. These challenges make closed-loop feedback an attractive option where the process parameters are adjusted on-the-fly. There are several challenges for designing an efficient controller: the deposition parameters are complex and highly coupled, artifacts occur after long time horizons, simulating the deposition is computationally costly, and learning on hardware is intractable. In this work, we demonstrate the feasibility of learning a closed-loop control policy for additive manufacturing using reinforcement learning. We show that approximate, but efficient, numerical simulation is sufficient as long as it allows learning the behavioral patterns of deposition that translate to real-world experiences. In combination with reinforcement learning, our model can be used to discover control policies that outperform baseline controllers. Furthermore, the recovered policies have a minimal sim-to-real gap. We showcase this by applying our control policy in-vivo on a single-layer, direct ink writing printer.

cs.GR↗