arXiv subjects
Publications and source records attributed to Xiang Xu.
In this paper, we prove the singularity formation for Poiseuille laminar flow of full Ericksen-Leslie system modeling nematic liquid crystal flows in dimension two. The singularity is due to the geometric effect at the origin.
The paper considers direct and inverse elastic scattering from a cavity in homogeneous medium with Dirichlet and Neumann boundary conditions. For direct scattering, existence and uniqueness are derived by variation approach. For inverse scattering, Fr$\acute{\rm e}$chet derivatives of the solution operators are investigated, which give local stability for Dirichlet case.
This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.
Mammalian brain is a complex organ that contains billions of neurons. These neurons form various neural circuits that control the perception, cognition, emotion and behavior. Developing in vivo neuronal labeling and imaging techniques is crucial for studying the structure and function of neural circuits. In vivo techniques can provide true physiological information that cannot be provided by ex vivo methods. In this study, we describe a new strategy for in vivo neuronal labeling and quantification using MRI. To demonstrate the ability of this new method, we used neurotropic virus to deliver oatp1a1 gene to the target neural circuit. OATP1A1 protein is expressed on the neuronal membrane and can increase the uptake of a specific MRI contrast agent (Gd-EOB-DTPA). By using T1-weighted images for observation, labeled neurons "light up" on MRI. We further use a dynamic-contrast-enhancement based method to obtain measures that provide quantitative information of labeled neurons in vivo.
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deteministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber.
We present SkexGen, a novel autoregressive generative model for computer-aided design (CAD) construction sequences containing sketch-and-extrude modeling operations. Our model utilizes distinct Transformer architectures to encode topological, geometric, and extrusion variations of construction sequences into disentangled codebooks. Autoregressive Transformer decoders generate CAD construction sequences sharing certain properties specified by the codebook vectors. Extensive experiments demonstrate that our disentangled codebook representation generates diverse and high-quality CAD models, enhances user control, and enables efficient exploration of the design space. The code is available at https://samxuxiang.github.io/skexgen.
We introduce D3D-HOI: a dataset of monocular videos with ground truth annotations of 3D object pose, shape and part motion during human-object interactions. Our dataset consists of several common articulated objects captured from diverse real-world scenes and camera viewpoints. Each manipulated object (e.g., microwave oven) is represented with a matching 3D parametric model. This data allows us to evaluate the reconstruction quality of articulated objects and establish a benchmark for this challenging task. In particular, we leverage the estimated 3D human pose for more accurate inference of the object spatial layout and dynamics. We evaluate this approach on our dataset, demonstrating that human-object relations can significantly reduce the ambiguity of articulated object reconstructions from challenging real-world videos. Code and dataset are available at https://github.com/facebookresearch/d3d-hoi.
This paper presents an explore-and-classify framework for structured architectural reconstruction from an aerial image. Starting from a potentially imperfect building reconstruction by an existing algorithm, our approach 1) explores the space of building models by modifying the reconstruction via heuristic actions; 2) learns to classify the correctness of building models while generating classification labels based on the ground-truth, and 3) repeat. At test time, we iterate exploration and classification, seeking for a result with the best classification score. We evaluate the approach using initial reconstructions by two baselines and two state-of-the-art reconstruction algorithms. Qualitative and quantitative evaluations demonstrate that our approach consistently improves the reconstruction quality from every initial reconstruction.
We propose a new method to detect deepfake images using the cue of the source feature inconsistency within the forged images. It is based on the hypothesis that images' distinct source features can be preserved and extracted after going through state-of-the-art deepfake generation processes. We introduce a novel representation learning approach, called pair-wise self-consistency learning (PCL), for training ConvNets to extract these source features and detect deepfake images. It is accompanied by a new image synthesis approach, called inconsistency image generator (I2G), to provide richly annotated training data for PCL. Experimental results on seven popular datasets show that our models improve averaged AUC over the state of the art from 96.45% to 98.05% in the in-dataset evaluation and from 86.03% to 92.18% in the cross-dataset evaluation.
In this paper we study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the space of $Q$-tensors. This free energy density functional is composed of three quadratic terms as the elastic energy density part, and a singular potential in the bulk part that is considered as a natural enforcement of a physical constraint on the eigenvalues of $Q$. The system is a non-diagonal parabolic system with a singular potential which trends to infinity logarithmically when the eigenvalues of $Q$ approaches the physical boundary. We give a rigorous proof that for rather general initial data with possibly infinite free energy, the system has a unique strong solution after any positive time $t_0$. Furthermore, this unique strong solution detaches from the physical boundary after a sufficiently large time $T_0$. We also give estimate of the Hausdorff measure of the set where the solution touches the physical boundary and thus prove a partial regularity result of the solution in the intermediate stage $(0,T_0)$.
In this paper we revisit a singular bulk potential in the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. This singular potential, called Ball-Majumdar potential, is introduced in [3], and is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. Specifically, we establish blowup rates of both this singular potential and its gradient as Q approaches its physical boundary.
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by examining the well-posedness and regularity of the solution for the equivalent stochastic two-point boundary value problem in the frequency domain. For the inverse problem, the Fourier modulus of the diffusion coefficient of the random source is proved to be uniquely determined by the variance of the Fourier transform of the boundary data. As a phase retrieval for the inverse problem, the PhaseLift method with random masks is applied to recover the diffusion coefficient from its Fourier modulus. Numerical experiments are reported to demonstrate the effectiveness of the proposed method.
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect to the wavenumber, and the Karhunen-Lo$\grave{e}$ve expansion of the random structure, which reconstructs key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.
This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting a sequence of trace formulas, which are deduced by a recursive formula, bridging geometrical and spectrum information explicitly in terms of Fredholm integral equations. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.
We present a mutual information-based framework for unsupervised image-to-image translation. Our MCMI approach treats single-cycle image translation models as modules that can be used recurrently in a multi-cycle translation setting where the translation process is bounded by mutual information constraints between the input and output images. The proposed mutual information constraints can improve cross-domain mappings by optimizing out translation functions that fail to satisfy the Markov property during image translations. We show that models trained with MCMI produce higher quality images and learn more semantically-relevant mappings compared to state-of-the-art image translation methods. The MCMI framework can be applied to existing unpaired image-to-image translation models with minimum modifications. Qualitative experiments and a perceptual study demonstrate the image quality improvements and generality of our approach using several backbone models and a variety of image datasets.
In this paper, we focus on improving the online face liveness detection system to enhance the security of the downstream face recognition system. Most of the existing frame-based methods are suffering from the prediction inconsistency across time. To address the issue, a simple yet effective solution based on temporal consistency is proposed. Specifically, in the training stage, to integrate the temporal consistency constraint, a temporal self-supervision loss and a class consistency loss are proposed in addition to the softmax cross-entropy loss. In the deployment stage, a training-free non-parametric uncertainty estimation module is developed to smooth the predictions adaptively. Beyond the common evaluation approach, a video segment-based evaluation is proposed to accommodate more practical scenarios. Extensive experiments demonstrated that our solution is more robust against several presentation attacks in various scenarios, and significantly outperformed the state-of-the-art on multiple public datasets by at least 40% in terms of ACER. Besides, with much less computational complexity (33% fewer FLOPs), it provides great potential for low-latency online applications.
In this paper, we address a key limitation of existing 2D face recognition methods: robustness to occlusions. To accomplish this task, we systematically analyzed the impact of facial attributes on the performance of a state-of-the-art face recognition method and through extensive experimentation, quantitatively analyzed the performance degradation under different types of occlusion. Our proposed Occlusion-aware face REcOgnition (OREO) approach learned discriminative facial templates despite the presence of such occlusions. First, an attention mechanism was proposed that extracted local identity-related region. The local features were then aggregated with the global representations to form a single template. Second, a simple, yet effective, training strategy was introduced to balance the non-occluded and occluded facial images. Extensive experiments demonstrated that OREO improved the generalization ability of face recognition under occlusions by (10.17%) in a single-image-based setting and outperformed the baseline by approximately (2%) in terms of rank-1 accuracy in an image-set-based scenario.
Thermoelectric materials (TMs) can uniquely convert waste heat into electricity, which provides a potential solution for the global energy crisis that is increasingly severe. Bulk Cu2Se, with ionic conductivity of Cu ions, exhibits a significant enhancement of its thermoelectric figure of merit zT by a factor of ~3 near its structural transition around 400 K. Here, we show a systematic study of the electronic structure of Cu2Se and its temperature evolution using high-resolution angle-resolved photoemission spectroscopy. Upon heating across the structural transition, the electronic states near the corner of the Brillouin zone gradually disappear, while the bands near the centre of Brillouin zone shift abruptly towards high binding energies and develop an energy gap. Interestingly, the observed band reconstruction well reproduces the temperature evolution of the Seebeck coefficient of Cu2Se, providing an electronic origin for the drastic enhancement of the thermoelectric performance near 400 K. The current results not only bridge among structural phase transition, electronic structures, and thermoelectric properties in a condensed matter system, but also provide valuable insights into the search and design of new generation of thermoelectric materials.