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Zhen Lei

Zhen Lei appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Computer Visionmath.APMachine Learningmath-phmath.MPcond-mat.quant-gashep-phmath.NANeural and Evolutionary Computingnlin.SINumerical Analysisphysics.soc-phquant-phSocial and Information NetworksSoftware Engineering

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Published work

61 published item(s)

preprint2026arXiv

CellScientist: Dual-Space Hierarchical Orchestration for Closed-Loop Refinement of Virtual Cell Models

Virtual Cell Modeling (VCM) requires models that not only predict perturbation responses, but also support targeted revision when predictions fail. Current LLM-assisted modeling workflows face a refinement-routing problem: prediction discrepancies are observed through executable implementations, but the relevant revision may involve the modeling assumption, representation design, implementation, or task constraint. Without structured feedback propagation across these levels, iterative refinement may repair code while failing to revise the assumption responsible for the discrepancy. We propose CellScientist, a dual-space hierarchical framework that couples a high-level hypothesis space with a low-level executable implementation space. CellScientist represents modeling decisions as structured states, realizes them as admissible programs under task and interface constraints, and routes execution discrepancies back to targeted hypothesis or implementation updates. This enables a closed Hypothesis -> Implementation -> Hypothesis loop where failures become structured signals for model refinement rather than debugging events. Across morphology and transcriptomic benchmarks, with additional single-cell perturbation evaluations, the final executable models selected by CellScientist improve over reference baselines under fixed split and evaluation protocols, while the workflow produces auditable refinement traces.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Self-similarity Driven Scale-invariant Learning for Weakly Supervised Person Search

Weakly supervised person search aims to jointly detect and match persons with only bounding box annotations. Existing approaches typically focus on improving the features by exploring relations of persons. However, scale variation problem is a more severe obstacle and under-studied that a person often owns images with different scales (resolutions). On the one hand, small-scale images contain less information of a person, thus affecting the accuracy of the generated pseudo labels. On the other hand, the similarity of cross-scale images is often smaller than that of images with the same scale for a person, which will increase the difficulty of matching. In this paper, we address this problem by proposing a novel one-step framework, named Self-similarity driven Scale-invariant Learning (SSL). Scale invariance can be explored based on the self-similarity prior that it shows the same statistical properties of an image at different scales. To this end, we introduce a Multi-scale Exemplar Branch to guide the network in concentrating on the foreground and learning scale-invariant features by hard exemplars mining. To enhance the discriminative power of the features in an unsupervised manner, we introduce a dynamic multi-label prediction which progressively seeks true labels for training. It is adaptable to different types of unlabeled data and serves as a compensation for clustering based strategy. Experiments on PRW and CUHK-SYSU databases demonstrate the effectiveness of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Surveillance Face Anti-spoofing

Face Anti-spoofing (FAS) is essential to secure face recognition systems from various physical attacks. However, recent research generally focuses on short-distance applications (i.e., phone unlocking) while lacking consideration of long-distance scenes (i.e., surveillance security checks). In order to promote relevant research and fill this gap in the community, we collect a large-scale Surveillance High-Fidelity Mask (SuHiFiMask) dataset captured under 40 surveillance scenes, which has 101 subjects from different age groups with 232 3D attacks (high-fidelity masks), 200 2D attacks (posters, portraits, and screens), and 2 adversarial attacks. In this scene, low image resolution and noise interference are new challenges faced in surveillance FAS. Together with the SuHiFiMask dataset, we propose a Contrastive Quality-Invariance Learning (CQIL) network to alleviate the performance degradation caused by image quality from three aspects: (1) An Image Quality Variable module (IQV) is introduced to recover image information associated with discrimination by combining the super-resolution network. (2) Using generated sample pairs to simulate quality variance distributions to help contrastive learning strategies obtain robust feature representation under quality variation. (3) A Separate Quality Network (SQN) is designed to learn discriminative features independent of image quality. Finally, a large number of experiments verify the quality of the SuHiFiMask dataset and the superiority of the proposed CQIL.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Beyond 3DMM: Learning to Capture High-fidelity 3D Face Shape

3D Morphable Model (3DMM) fitting has widely benefited face analysis due to its strong 3D priori. However, previous reconstructed 3D faces suffer from degraded visual verisimilitude due to the loss of fine-grained geometry, which is attributed to insufficient ground-truth 3D shapes, unreliable training strategies and limited representation power of 3DMM. To alleviate this issue, this paper proposes a complete solution to capture the personalized shape so that the reconstructed shape looks identical to the corresponding person. Specifically, given a 2D image as the input, we virtually render the image in several calibrated views to normalize pose variations while preserving the original image geometry. A many-to-one hourglass network serves as the encode-decoder to fuse multiview features and generate vertex displacements as the fine-grained geometry. Besides, the neural network is trained by directly optimizing the visual effect, where two 3D shapes are compared by measuring the similarity between the multiview images rendered from the shapes. Finally, we propose to generate the ground-truth 3D shapes by registering RGB-D images followed by pose and shape augmentation, providing sufficient data for network training. Experiments on several challenging protocols demonstrate the superior reconstruction accuracy of our proposal on the face shape.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Deep Learning for Face Anti-Spoofing: A Survey

Face anti-spoofing (FAS) has lately attracted increasing attention due to its vital role in securing face recognition systems from presentation attacks (PAs). As more and more realistic PAs with novel types spring up, traditional FAS methods based on handcrafted features become unreliable due to their limited representation capacity. With the emergence of large-scale academic datasets in the recent decade, deep learning based FAS achieves remarkable performance and dominates this area. However, existing reviews in this field mainly focus on the handcrafted features, which are outdated and uninspiring for the progress of FAS community. In this paper, to stimulate future research, we present the first comprehensive review of recent advances in deep learning based FAS. It covers several novel and insightful components: 1) besides supervision with binary label (e.g., '0' for bonafide vs. '1' for PAs), we also investigate recent methods with pixel-wise supervision (e.g., pseudo depth map); 2) in addition to traditional intra-dataset evaluation, we collect and analyze the latest methods specially designed for domain generalization and open-set FAS; and 3) besides commercial RGB camera, we summarize the deep learning applications under multi-modal (e.g., depth and infrared) or specialized (e.g., light field and flash) sensors. We conclude this survey by emphasizing current open issues and highlighting potential prospects.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

HP-Capsule: Unsupervised Face Part Discovery by Hierarchical Parsing Capsule Network

Capsule networks are designed to present the objects by a set of parts and their relationships, which provide an insight into the procedure of visual perception. Although recent works have shown the success of capsule networks on simple objects like digits, the human faces with homologous structures, which are suitable for capsules to describe, have not been explored. In this paper, we propose a Hierarchical Parsing Capsule Network (HP-Capsule) for unsupervised face subpart-part discovery. When browsing large-scale face images without labels, the network first encodes the frequently observed patterns with a set of explainable subpart capsules. Then, the subpart capsules are assembled into part-level capsules through a Transformer-based Parsing Module (TPM) to learn the compositional relations between them. During training, as the face hierarchy is progressively built and refined, the part capsules adaptively encode the face parts with semantic consistency. HP-Capsule extends the application of capsule networks from digits to human faces and takes a step forward to show how the neural networks understand homologous objects without human intervention. Besides, HP-Capsule gives unsupervised face segmentation results by the covered regions of part capsules, enabling qualitative and quantitative evaluation. Experiments on BP4D and Multi-PIE datasets show the effectiveness of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Nested Collaborative Learning for Long-Tailed Visual Recognition

The networks trained on the long-tailed dataset vary remarkably, despite the same training settings, which shows the great uncertainty in long-tailed learning. To alleviate the uncertainty, we propose a Nested Collaborative Learning (NCL), which tackles the problem by collaboratively learning multiple experts together. NCL consists of two core components, namely Nested Individual Learning (NIL) and Nested Balanced Online Distillation (NBOD), which focus on the individual supervised learning for each single expert and the knowledge transferring among multiple experts, respectively. To learn representations more thoroughly, both NIL and NBOD are formulated in a nested way, in which the learning is conducted on not just all categories from a full perspective but some hard categories from a partial perspective. Regarding the learning in the partial perspective, we specifically select the negative categories with high predicted scores as the hard categories by using a proposed Hard Category Mining (HCM). In the NCL, the learning from two perspectives is nested, highly related and complementary, and helps the network to capture not only global and robust features but also meticulous distinguishing ability. Moreover, self-supervision is further utilized for feature enhancement. Extensive experiments manifest the superiority of our method with outperforming the state-of-the-art whether by using a single model or an ensemble.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Radiation of the energy-critical wave equation with compact support

We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions $3 \le d \le 5$, with compactly supported initial data. In particular, it is shown that nontrivial global solutions with compact spatial support must be radiative in the sense that at least one of the following is true: (1) $\int_{|x|> |t|} \left( |\partial_t u|^2 + |\nabla u|^2 \right) \mathrm{d}x \ge η_1(u) > 0, \ \mathrm{for} \ \mathrm{all} \ t \ge 0 \ \mathrm{or} \ \mathrm{all} \ t \le 0,$ (2) $\int_{|x|> -\varepsilon +|t|} \left( |\partial_t u|^2 + |\nabla u|^2 \right) \mathrm{d}x \ge η_2(\varepsilon, u) > 0, \ \mathrm{for} \ \mathrm{all} \ t \in \mathbb{R}, \varepsilon > 0.$ In space dimensions 3 and 4, a nontrivial soliton background is also considered. As an application, we obtain partial results on the rigidity conjecture concerning solutions with the compactness property, including a new proof for the global existence of such solutions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Solving parametric partial differential equations with deep rectified quadratic unit neural networks

Implementing deep neural networks for learning the solution maps of parametric partial differential equations (PDEs) turns out to be more efficient than using many conventional numerical methods. However, limited theoretical analyses have been conducted on this approach. In this study, we investigate the expressive power of deep rectified quadratic unit (ReQU) neural networks for approximating the solution maps of parametric PDEs. The proposed approach is motivated by the recent important work of G. Kutyniok, P. Petersen, M. Raslan and R. Schneider (Gitta Kutyniok, Philipp Petersen, Mones Raslan, and Reinhold Schneider. A theoretical analysis of deep neural networks and parametric pdes. Constructive Approximation, pages 1-53, 2021), which uses deep rectified linear unit (ReLU) neural networks for solving parametric PDEs. In contrast to the previously established complexity-bound $\mathcal{O}\left(d^3\log_{2}^{q}(1/ ε) \right)$ for ReLU neural networks, we derive an upper bound $\mathcal{O}\left(d^3\log_{2}^{q}\log_{2}(1/ ε) \right)$ on the size of the deep ReQU neural network required to achieve accuracy $ε>0$, where $d$ is the dimension of reduced basis representing the solutions. Our method takes full advantage of the inherent low-dimensionality of the solution manifolds and better approximation performance of deep ReQU neural networks. Numerical experiments are performed to verify our theoretical result.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Weakly Aligned Feature Fusion for Multimodal Object Detection

To achieve accurate and robust object detection in the real-world scenario, various forms of images are incorporated, such as color, thermal, and depth. However, multimodal data often suffer from the position shift problem, i.e., the image pair is not strictly aligned, making one object has different positions in different modalities. For the deep learning method, this problem makes it difficult to fuse multimodal features and puzzles the convolutional neural network (CNN) training. In this article, we propose a general multimodal detector named aligned region CNN (AR-CNN) to tackle the position shift problem. First, a region feature (RF) alignment module with adjacent similarity constraint is designed to consistently predict the position shift between two modalities and adaptively align the cross-modal RFs. Second, we propose a novel region of interest (RoI) jitter strategy to improve the robustness to unexpected shift patterns. Third, we present a new multimodal feature fusion method that selects the more reliable feature and suppresses the less useful one via feature reweighting. In addition, by locating bounding boxes in both modalities and building their relationships, we provide novel multimodal labeling named KAIST-Paired. Extensive experiments on 2-D and 3-D object detection, RGB-T, and RGB-D datasets demonstrate the effectiveness and robustness of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Face Synthesis for Eyeglass-Robust Face Recognition

In the application of face recognition, eyeglasses could significantly degrade the recognition accuracy. A feasible method is to collect large-scale face images with eyeglasses for training deep learning methods. However, it is difficult to collect the images with and without glasses of the same identity, so that it is difficult to optimize the intra-variations caused by eyeglasses. In this paper, we propose to address this problem in a virtual synthesis manner. The high-fidelity face images with eyeglasses are synthesized based on 3D face model and 3D eyeglasses. Models based on deep learning methods are then trained on the synthesized eyeglass face dataset, achieving better performance than previous ones. Experiments on the real face database validate the effectiveness of our synthesized data for improving eyeglass face recognition performance.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Improving Face Anti-Spoofing by 3D Virtual Synthesis

Face anti-spoofing is crucial for the security of face recognition systems. Learning based methods especially deep learning based methods need large-scale training samples to reduce overfitting. However, acquiring spoof data is very expensive since the live faces should be re-printed and re-captured in many views. In this paper, we present a method to synthesize virtual spoof data in 3D space to alleviate this problem. Specifically, we consider a printed photo as a flat surface and mesh it into a 3D object, which is then randomly bent and rotated in 3D space. Afterward, the transformed 3D photo is rendered through perspective projection as a virtual sample. The synthetic virtual samples can significantly boost the anti-spoofing performance when combined with a proposed data balancing strategy. Our promising results open up new possibilities for advancing face anti-spoofing using cheap and large-scale synthetic data.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Towards Fast, Accurate and Stable 3D Dense Face Alignment

Existing methods of 3D dense face alignment mainly concentrate on accuracy, thus limiting the scope of their practical applications. In this paper, we propose a novel regression framework named 3DDFA-V2 which makes a balance among speed, accuracy and stability. Firstly, on the basis of a lightweight backbone, we propose a meta-joint optimization strategy to dynamically regress a small set of 3DMM parameters, which greatly enhances speed and accuracy simultaneously. To further improve the stability on videos, we present a virtual synthesis method to transform one still image to a short-video which incorporates in-plane and out-of-plane face moving. On the premise of high accuracy and stability, 3DDFA-V2 runs at over 50fps on a single CPU core and outperforms other state-of-the-art heavy models simultaneously. Experiments on several challenging datasets validate the efficiency of our method. Pre-trained models and code are available at https://github.com/cleardusk/3DDFA_V2.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bridging the Gap Between Anchor-based and Anchor-free Detection via Adaptive Training Sample Selection

Object detection has been dominated by anchor-based detectors for several years. Recently, anchor-free detectors have become popular due to the proposal of FPN and Focal Loss. In this paper, we first point out that the essential difference between anchor-based and anchor-free detection is actually how to define positive and negative training samples, which leads to the performance gap between them. If they adopt the same definition of positive and negative samples during training, there is no obvious difference in the final performance, no matter regressing from a box or a point. This shows that how to select positive and negative training samples is important for current object detectors. Then, we propose an Adaptive Training Sample Selection (ATSS) to automatically select positive and negative samples according to statistical characteristics of object. It significantly improves the performance of anchor-based and anchor-free detectors and bridges the gap between them. Finally, we discuss the necessity of tiling multiple anchors per location on the image to detect objects. Extensive experiments conducted on MS COCO support our aforementioned analysis and conclusions. With the newly introduced ATSS, we improve state-of-the-art detectors by a large margin to $50.7\%$ AP without introducing any overhead. The code is available at https://github.com/sfzhang15/ATSS

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Deep Spatial Gradient and Temporal Depth Learning for Face Anti-spoofing

Face anti-spoofing is critical to the security of face recognition systems. Depth supervised learning has been proven as one of the most effective methods for face anti-spoofing. Despite the great success, most previous works still formulate the problem as a single-frame multi-task one by simply augmenting the loss with depth, while neglecting the detailed fine-grained information and the interplay between facial depths and moving patterns. In contrast, we design a new approach to detect presentation attacks from multiple frames based on two insights: 1) detailed discriminative clues (e.g., spatial gradient magnitude) between living and spoofing face may be discarded through stacked vanilla convolutions, and 2) the dynamics of 3D moving faces provide important clues in detecting the spoofing faces. The proposed method is able to capture discriminative details via Residual Spatial Gradient Block (RSGB) and encode spatio-temporal information from Spatio-Temporal Propagation Module (STPM) efficiently. Moreover, a novel Contrastive Depth Loss is presented for more accurate depth supervision. To assess the efficacy of our method, we also collect a Double-modal Anti-spoofing Dataset (DMAD) which provides actual depth for each sample. The experiments demonstrate that the proposed approach achieves state-of-the-art results on five benchmark datasets including OULU-NPU, SiW, CASIA-MFSD, Replay-Attack, and the new DMAD. Codes will be available at https://github.com/clks-wzz/FAS-SGTD.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Domain Balancing: Face Recognition on Long-Tailed Domains

Long-tailed problem has been an important topic in face recognition task. However, existing methods only concentrate on the long-tailed distribution of classes. Differently, we devote to the long-tailed domain distribution problem, which refers to the fact that a small number of domains frequently appear while other domains far less existing. The key challenge of the problem is that domain labels are too complicated (related to race, age, pose, illumination, etc.) and inaccessible in real applications. In this paper, we propose a novel Domain Balancing (DB) mechanism to handle this problem. Specifically, we first propose a Domain Frequency Indicator (DFI) to judge whether a sample is from head domains or tail domains. Secondly, we formulate a light-weighted Residual Balancing Mapping (RBM) block to balance the domain distribution by adjusting the network according to DFI. Finally, we propose a Domain Balancing Margin (DBM) in the loss function to further optimize the feature space of the tail domains to improve generalization. Extensive analysis and experiments on several face recognition benchmarks demonstrate that the proposed method effectively enhances the generalization capacities and achieves superior performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Efficient Algorithms towards Network Intervention

Research suggests that social relationships have substantial impacts on individuals' health outcomes. Network intervention, through careful planning, can assist a network of users to build healthy relationships. However, most previous work is not designed to assist such planning by carefully examining and improving multiple network characteristics. In this paper, we propose and evaluate algorithms that facilitate network intervention planning through simultaneous optimization of network degree, closeness, betweenness, and local clustering coefficient, under scenarios involving Network Intervention with Limited Degradation - for Single target (NILD-S) and Network Intervention with Limited Degradation - for Multiple targets (NILD-M). We prove that NILD-S and NILD-M are NP-hard and cannot be approximated within any ratio in polynomial time unless P=NP. We propose the Candidate Re-selection with Preserved Dependency (CRPD) algorithm for NILD-S, and the Objective-aware Intervention edge Selection and Adjustment (OISA) algorithm for NILD-M. Various pruning strategies are designed to boost the efficiency of the proposed algorithms. Extensive experiments on various real social networks collected from public schools and Web and an empirical study are conducted to show that CRPD and OISA outperform the baselines in both efficiency and effectiveness.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

LAMP-HQ: A Large-Scale Multi-Pose High-Quality Database and Benchmark for NIR-VIS Face Recognition

Near-infrared-visible (NIR-VIS) heterogeneous face recognition matches NIR to corresponding VIS face images. However, due to the sensing gap, NIR images often lose some identity information so that the recognition issue is more difficult than conventional VIS face recognition. Recently, NIR-VIS heterogeneous face recognition has attracted considerable attention in the computer vision community because of its convenience and adaptability in practical applications. Various deep learning-based methods have been proposed and substantially increased the recognition performance, but the lack of NIR-VIS training samples leads to the difficulty of the model training process. In this paper, we propose a new Large-Scale Multi-Pose High-Quality NIR-VIS database LAMP-HQ containing 56,788 NIR and 16,828 VIS images of 573 subjects with large diversities in pose, illumination, attribute, scene and accessory. We furnish a benchmark along with the protocol for NIR-VIS face recognition via generation on LAMP-HQ, including Pixel2Pixel, CycleGAN, and ADFL. Furthermore, we propose a novel exemplar-based variational spectral attention network to produce high-fidelity VIS images from NIR data. A spectral conditional attention module is introduced to reduce the domain gap between NIR and VIS data and then improve the performance of NIR-VIS heterogeneous face recognition on various databases including the LAMP-HQ.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Learning Meta Face Recognition in Unseen Domains

Face recognition systems are usually faced with unseen domains in real-world applications and show unsatisfactory performance due to their poor generalization. For example, a well-trained model on webface data cannot deal with the ID vs. Spot task in surveillance scenario. In this paper, we aim to learn a generalized model that can directly handle new unseen domains without any model updating. To this end, we propose a novel face recognition method via meta-learning named Meta Face Recognition (MFR). MFR synthesizes the source/target domain shift with a meta-optimization objective, which requires the model to learn effective representations not only on synthesized source domains but also on synthesized target domains. Specifically, we build domain-shift batches through a domain-level sampling strategy and get back-propagated gradients/meta-gradients on synthesized source/target domains by optimizing multi-domain distributions. The gradients and meta-gradients are further combined to update the model to improve generalization. Besides, we propose two benchmarks for generalized face recognition evaluation. Experiments on our benchmarks validate the generalization of our method compared to several baselines and other state-of-the-arts. The proposed benchmarks will be available at https://github.com/cleardusk/MFR.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Multi-Modal Face Anti-Spoofing Based on Central Difference Networks

Face anti-spoofing (FAS) plays a vital role in securing face recognition systems from presentation attacks. Existing multi-modal FAS methods rely on stacked vanilla convolutions, which is weak in describing detailed intrinsic information from modalities and easily being ineffective when the domain shifts (e.g., cross attack and cross ethnicity). In this paper, we extend the central difference convolutional networks (CDCN) \cite{yu2020searching} to a multi-modal version, intending to capture intrinsic spoofing patterns among three modalities (RGB, depth and infrared). Meanwhile, we also give an elaborate study about single-modal based CDCN. Our approach won the first place in "Track Multi-Modal" as well as the second place in "Track Single-Modal (RGB)" of ChaLearn Face Anti-spoofing Attack Detection Challenge@CVPR2020 \cite{liu2020cross}. Our final submission obtains 1.02$\pm$0.59\% and 4.84$\pm$1.79\% ACER in "Track Multi-Modal" and "Track Single-Modal (RGB)", respectively. The codes are available at{https://github.com/ZitongYu/CDCN}.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

SADet: Learning An Efficient and Accurate Pedestrian Detector

Although the anchor-based detectors have taken a big step forward in pedestrian detection, the overall performance of algorithm still needs further improvement for practical applications, \emph{e.g.}, a good trade-off between the accuracy and efficiency. To this end, this paper proposes a series of systematic optimization strategies for the detection pipeline of one-stage detector, forming a single shot anchor-based detector (SADet) for efficient and accurate pedestrian detection, which includes three main improvements. Firstly, we optimize the sample generation process by assigning soft tags to the outlier samples to generate semi-positive samples with continuous tag value between $0$ and $1$, which not only produces more valid samples, but also strengthens the robustness of the model. Secondly, a novel Center-$IoU$ loss is applied as a new regression loss for bounding box regression, which not only retains the good characteristics of IoU loss, but also solves some defects of it. Thirdly, we also design Cosine-NMS for the postprocess of predicted bounding boxes, and further propose adaptive anchor matching to enable the model to adaptively match the anchor boxes to full or visible bounding boxes according to the degree of occlusion, making the NMS and anchor matching algorithms more suitable for occluded pedestrian detection. Though structurally simple, it presents state-of-the-art result and real-time speed of $20$ FPS for VGA-resolution images ($640 \times 480$) on challenging pedestrian detection benchmarks, i.e., CityPersons, Caltech, and human detection benchmark CrowdHuman, leading to a new attractive pedestrian detector.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Semi-Siamese Training for Shallow Face Learning

Most existing public face datasets, such as MS-Celeb-1M and VGGFace2, provide abundant information in both breadth (large number of IDs) and depth (sufficient number of samples) for training. However, in many real-world scenarios of face recognition, the training dataset is limited in depth, i.e. only two face images are available for each ID. $\textit{We define this situation as Shallow Face Learning, and find it problematic with existing training methods.}$ Unlike deep face data, the shallow face data lacks intra-class diversity. As such, it can lead to collapse of feature dimension and consequently the learned network can easily suffer from degeneration and over-fitting in the collapsed dimension. In this paper, we aim to address the problem by introducing a novel training method named Semi-Siamese Training (SST). A pair of Semi-Siamese networks constitute the forward propagation structure, and the training loss is computed with an updating gallery queue, conducting effective optimization on shallow training data. Our method is developed without extra-dependency, thus can be flexibly integrated with the existing loss functions and network architectures. Extensive experiments on various benchmarks of face recognition show the proposed method significantly improves the training, not only in shallow face learning, but also for conventional deep face data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

UA-DETRAC: A New Benchmark and Protocol for Multi-Object Detection and Tracking

In recent years, numerous effective multi-object tracking (MOT) methods are developed because of the wide range of applications. Existing performance evaluations of MOT methods usually separate the object tracking step from the object detection step by using the same fixed object detection results for comparisons. In this work, we perform a comprehensive quantitative study on the effects of object detection accuracy to the overall MOT performance, using the new large-scale University at Albany DETection and tRACking (UA-DETRAC) benchmark dataset. The UA-DETRAC benchmark dataset consists of 100 challenging video sequences captured from real-world traffic scenes (over 140,000 frames with rich annotations, including occlusion, weather, vehicle category, truncation, and vehicle bounding boxes) for object detection, object tracking and MOT system. We evaluate complete MOT systems constructed from combinations of state-of-the-art object detection and object tracking methods. Our analysis shows the complex effects of object detection accuracy on MOT system performance. Based on these observations, we propose new evaluation tools and metrics for MOT systems that consider both object detection and object tracking for comprehensive analysis.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

CRAFT Objects from Images

Object detection is a fundamental problem in image understanding. One popular solution is the R-CNN framework and its fast versions. They decompose the object detection problem into two cascaded easier tasks: 1) generating object proposals from images, 2) classifying proposals into various object categories. Despite that we are handling with two relatively easier tasks, they are not solved perfectly and there's still room for improvement. In this paper, we push the "divide and conquer" solution even further by dividing each task into two sub-tasks. We call the proposed method "CRAFT" (Cascade Region-proposal-network And FasT-rcnn), which tackles each task with a carefully designed network cascade. We show that the cascade structure helps in both tasks: in proposal generation, it provides more compact and better localized object proposals; in object classification, it reduces false positives (mainly between ambiguous categories) by capturing both inter- and intra-category variances. CRAFT achieves consistent and considerable improvement over the state-of-the-art on object detection benchmarks like PASCAL VOC 07/12 and ILSVRC.

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preprint2016arXiv

Embedding Deep Metric for Person Re-identication A Study Against Large Variations

Person re-identification is challenging due to the large variations of pose, illumination, occlusion and camera view. Owing to these variations, the pedestrian data is distributed as highly-curved manifolds in the feature space, despite the current convolutional neural networks (CNN)'s capability of feature extraction. However, the distribution is unknown, so it is difficult to use the geodesic distance when comparing two samples. In practice, the current deep embedding methods use the Euclidean distance for the training and test. On the other hand, the manifold learning methods suggest to use the Euclidean distance in the local range, combining with the graphical relationship between samples, for approximating the geodesic distance. From this point of view, selecting suitable positive i.e. intra-class) training samples within a local range is critical for training the CNN embedding, especially when the data has large intra-class variations. In this paper, we propose a novel moderate positive sample mining method to train robust CNN for person re-identification, dealing with the problem of large variation. In addition, we improve the learning by a metric weight constraint, so that the learned metric has a better generalization ability. Experiments show that these two strategies are effective in learning robust deep metrics for person re-identification, and accordingly our deep model significantly outperforms the state-of-the-art methods on several benchmarks of person re-identification. Therefore, the study presented in this paper may be useful in inspiring new designs of deep models for person re-identification.

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preprint2016arXiv

Global Well-posedness of the Incompressible Magnetohydrodynamics

This paper studies the Cauchy problem of the incompressible magnetohydrodynamic systems with or without viscosity $ν$. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all $ν\geq 0$ and all space dimension $n \geq 2$. Such a result holds true uniformly in nonnegative viscosity parameter. The proof is based on the inherent strong null structure of the systems which was first introduced for incompressible elastodynamics by the second author in \cite{Lei14} and Alinhac's ghost weight technique.

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preprint2016arXiv

Learning Discriminative Features with Class Encoder

Deep neural networks usually benefit from unsupervised pre-training, e.g. auto-encoders. However, the classifier further needs supervised fine-tuning methods for good discrimination. Besides, due to the limits of full-connection, the application of auto-encoders is usually limited to small, well aligned images. In this paper, we incorporate the supervised information to propose a novel formulation, namely class-encoder, whose training objective is to reconstruct a sample from another one of which the labels are identical. Class-encoder aims to minimize the intra-class variations in the feature space, and to learn a good discriminative manifolds on a class scale. We impose the class-encoder as a constraint into the softmax for better supervised training, and extend the reconstruction on feature-level to tackle the parameter size issue and translation issue. The experiments show that the class-encoder helps to improve the performance on benchmarks of classification and face recognition. This could also be a promising direction for fast training of face recognition models.

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preprint2016arXiv

On the Two-Dimensional Muskat Problem with Monotone Large Initial Data

We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [26]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function.

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preprint2016arXiv

Some New Symmetric Relations and the Prediction of Left and Right Handed Neutrino Masses using Koide's Relation

Masses of the three generations of charged leptons are known to completely satisfy the Koide's mass relation. But the question remains if such a relation exists for neutrinos? In this paper, by considering SeeSaw mechanism as the mechanism generating tiny neutrino masses, we show how neutrinos satisfy the Koide's mass relation, on the basis of which we systematically give exact values of not only left but also right handed neutrino masses.

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preprint2015arXiv

A priori bound on the velocity in axially symmetric Navier-Stokes equations

Let $v$ be the velocity of Leray-Hopf solutions to the axially symmetric three-dimensional Navier-Stokes equations. Under suitable conditions for initial values, we prove the following a priori bound \[ |v(x, t)| \le \frac{C}{r^2} |\ln r|^{1/2}, \]where $r \in (0, 1/2)$ is the distance from $x$ to the z axis, and $C$ is a constant depending only on the initial value. This provides a pointwise upper bound (worst case scenario) for possible singularities while the recent papers \cite{CSTY2} and \cite{KNSS} gave a lower bound. The gap is polynomial order 1 modulo a half log term.

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preprint2015arXiv

Constrained Deep Metric Learning for Person Re-identification

Person re-identification aims to re-identify the probe image from a given set of images under different camera views. It is challenging due to large variations of pose, illumination, occlusion and camera view. Since the convolutional neural networks (CNN) have excellent capability of feature extraction, certain deep learning methods have been recently applied in person re-identification. However, in person re-identification, the deep networks often suffer from the over-fitting problem. In this paper, we propose a novel CNN-based method to learn a discriminative metric with good robustness to the over-fitting problem in person re-identification. Firstly, a novel deep architecture is built where the Mahalanobis metric is learned with a weight constraint. This weight constraint is used to regularize the learning, so that the learned metric has a better generalization ability. Secondly, we find that the selection of intra-class sample pairs is crucial for learning but has received little attention. To cope with the large intra-class variations in pedestrian images, we propose a novel training strategy named moderate positive mining to prevent the training process from over-fitting to the extreme samples in intra-class pairs. Experiments show that our approach significantly outperforms state-of-the-art methods on several benchmarks of person re-identification.

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preprint2015arXiv

Convolutional Channel Features

Deep learning methods are powerful tools but often suffer from expensive computation and limited flexibility. An alternative is to combine light-weight models with deep representations. As successful cases exist in several visual problems, a unified framework is absent. In this paper, we revisit two widely used approaches in computer vision, namely filtered channel features and Convolutional Neural Networks (CNN), and absorb merits from both by proposing an integrated method called Convolutional Channel Features (CCF). CCF transfers low-level features from pre-trained CNN models to feed the boosting forest model. With the combination of CNN features and boosting forest, CCF benefits from the richer capacity in feature representation compared with channel features, as well as lower cost in computation and storage compared with end-to-end CNN methods. We show that CCF serves as a good way of tailoring pre-trained CNN models to diverse tasks without fine-tuning the whole network to each task by achieving state-of-the-art performances in pedestrian detection, face detection, edge detection and object proposal generation.

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preprint2015arXiv

Criticality of the Axially Symmetric Navier-Stokes Equations

Smooth solutions to the axi-symmetric Navier-Stokes equations obey the following maximum principle: $$\sup_{t\geq 0}\|rv^θ(t, \cdot)\|_{L^\infty} \leq \|rv^θ(0, \cdot)\|_{L^\infty}.$$ We prove that all solutions with initial data in $H^{\frac{1}{2}}$ is smooth globally in time if $rv^θ$ satisfies a kind of Form Boundedness Condition (FBC) which is invariant under the natural scaling of the Navier-Stokes equations. In particular, if $rv^θ$ satisfies \begin{equation}\nonumber \sup_{t \geq 0}|rv^θ(t, r, z)| \leq C_\ast|\ln r|^{- 2},\ \ r \leq δ_0 \in (0, \frac{1}{2}),\ C_\ast < \infty, \end{equation} then our FBC is satisfied. Here $δ_0$ and $C_\ast$ are independent of neither the profile nor the norm of the initial data. So the gap from regularity is logarithmic in nature. We also prove the global regularity of solutions if $\|rv^θ(0, \cdot)\|_{L^\infty}$ or $\sup_{t \geq 0}\|rv^θ(t, \cdot)\|_{L^\infty(r \leq r_0)}$ is small but the smallness depends on certain dimensionless quantity of the initial data.

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preprint2015arXiv

Global Regularity to the Navier-Stokes Equations for A Class of Large Initial Data

We prove that for initial data of the form \begin{equation}\nonumber u_0^ε(x) = (v_0^h(x_ε), ε^{-1}v_0^n(x_ε))^T,\quad x_ε= (x_h, εx_n)^T, n \geq 4, \end{equation} the Cauchy problem of the incompressible Navier-Stokes equations on $\mathbb{R}^n$ is globally well-posed for all small $ε> 0$, provided that the initial velocity profile $v_0$ is analytic in $x_n$ and certain norm of $v_0$ is sufficiently small but independent of $ε$.

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preprint2015arXiv

Structure of Helicity and Global Solutions of Incompressible Navier-Stokes Equation

In this paper we derive a new energy identity for the three-dimensional incompressible Navier-Stokes equations by a special structure of helicity. The new energy functional is critical with respect to the natural scalings of the Navier-Stokes equations. Moreover, it is conditionally coercive. As an application we construct a family of finite energy smooth solutions to the Navier-Stokes equations whose critical norms can be arbitrarily large.

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preprint2014arXiv

Aggregate channel features for multi-view face detection

Face detection has drawn much attention in recent decades since the seminal work by Viola and Jones. While many subsequences have improved the work with more powerful learning algorithms, the feature representation used for face detection still can't meet the demand for effectively and efficiently handling faces with large appearance variance in the wild. To solve this bottleneck, we borrow the concept of channel features to the face detection domain, which extends the image channel to diverse types like gradient magnitude and oriented gradient histograms and therefore encodes rich information in a simple form. We adopt a novel variant called aggregate channel features, make a full exploration of feature design, and discover a multi-scale version of features with better performance. To deal with poses of faces in the wild, we propose a multi-view detection approach featuring score re-ranking and detection adjustment. Following the learning pipelines in Viola-Jones framework, the multi-view face detector using aggregate channel features shows competitive performance against state-of-the-art algorithms on AFW and FDDB testsets, while runs at 42 FPS on VGA images.

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preprint2014arXiv

Deep Metric Learning for Practical Person Re-Identification

Various hand-crafted features and metric learning methods prevail in the field of person re-identification. Compared to these methods, this paper proposes a more general way that can learn a similarity metric from image pixels directly. By using a "siamese" deep neural network, the proposed method can jointly learn the color feature, texture feature and metric in a unified framework. The network has a symmetry structure with two sub-networks which are connected by Cosine function. To deal with the big variations of person images, binomial deviance is used to evaluate the cost between similarities and labels, which is proved to be robust to outliers. Compared to existing researches, a more practical setting is studied in the experiments that is training and test on different datasets (cross dataset person re-identification). Both in "intra dataset" and "cross dataset" settings, the superiorities of the proposed method are illustrated on VIPeR and PRID.

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preprint2014arXiv

Learning Face Representation from Scratch

Pushing by big data and deep convolutional neural network (CNN), the performance of face recognition is becoming comparable to human. Using private large scale training datasets, several groups achieve very high performance on LFW, i.e., 97% to 99%. While there are many open source implementations of CNN, none of large scale face dataset is publicly available. The current situation in the field of face recognition is that data is more important than algorithm. To solve this problem, this paper proposes a semi-automatical way to collect face images from Internet and builds a large scale dataset containing about 10,000 subjects and 500,000 images, called CASIAWebFace. Based on the database, we use a 11-layer CNN to learn discriminative representation and obtain state-of-theart accuracy on LFW and YTF. The publication of CASIAWebFace will attract more research groups entering this field and accelerate the development of face recognition in the wild.

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preprint2014arXiv

Local Well-posedness of the three dimensional compressible Euler--Poisson equations with physical vacuum

This paper is concerned with the three dimensional compressible Euler--Poisson equations with moving physical vacuum boundary condition. This fluid system is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local existence of classical solutions for initial data in certain weighted Sobolev spaces is established in the case that the adiabatic index satisfies $1 < γ< 3$.

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preprint2014arXiv

Shared Representation Learning for Heterogeneous Face Recognition

After intensive research, heterogenous face recognition is still a challenging problem. The main difficulties are owing to the complex relationship between heterogenous face image spaces. The heterogeneity is always tightly coupled with other variations, which makes the relationship of heterogenous face images highly nonlinear. Many excellent methods have been proposed to model the nonlinear relationship, but they apt to overfit to the training set, due to limited samples. Inspired by the unsupervised algorithms in deep learning, this paper proposes an novel framework for heterogeneous face recognition. We first extract Gabor features at some localized facial points, and then use Restricted Boltzmann Machines (RBMs) to learn a shared representation locally to remove the heterogeneity around each facial point. Finally, the shared representations of local RBMs are connected together and processed by PCA. Two problems (Sketch-Photo and NIR-VIS) and three databases are selected to evaluate the proposed method. For Sketch-Photo problem, we obtain perfect results on the CUFS database. For NIR-VIS problem, we produce new state-of-the-art performance on the CASIA HFB and NIR-VIS 2.0 databases.

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preprint2013arXiv

Fast Matching by 2 Lines of Code for Large Scale Face Recognition Systems

In this paper, we propose a method to apply the popular cascade classifier into face recognition to improve the computational efficiency while keeping high recognition rate. In large scale face recognition systems, because the probability of feature templates coming from different subjects is very high, most of the matching pairs will be rejected by the early stages of the cascade. Therefore, the cascade can improve the matching speed significantly. On the other hand, using the nested structure of the cascade, we could drop some stages at the end of feature to reduce the memory and bandwidth usage in some resources intensive system while not sacrificing the performance too much. The cascade is learned by two steps. Firstly, some kind of prepared features are grouped into several nested stages. And then, the threshold of each stage is learned to achieve user defined verification rate (VR). In the paper, we take a landmark based Gabor+LDA face recognition system as baseline to illustrate the process and advantages of the proposed method. However, the use of this method is very generic and not limited in face recognition, which can be easily generalized to other biometrics as a post-processing module. Experiments on the FERET database show the good performance of our baseline and an experiment on a self-collected large scale database illustrates that the cascade can improve the matching speed significantly.

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preprint2013arXiv

On Axially Symmetric Incompressible Magnetohydrodynamics in Three Dimensions

The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a constant magnetic field, whose global regularity problem is known as a Clay Millennium Prize Problem. In this article, we prove the global regularity of axially symmetric solutions to the ideal MHD in three dimensions for a family of non-trivial magnetic fields. The proofs are based on the special structures of MHD and can of course also applied to the resistive MHD. Our result might indicate that there are richer fantastic research topics in MHD than Navier-Stokes equations.

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preprint2013arXiv

On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In \cite{HL09}, Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler and Navier-Stokes equations is that the convection term is neglected in the 3D model. In \cite{HSW09}, the authors proved that the 3D inviscid model can develop a finite time singularity starting from smooth initial data on a rectangular domain. A global well-posedness result was also proved for a class of smooth initial data under some smallness condition. The analysis in \cite{HSW09} does not apply to the case when the domain is axisymmetric and unbounded in the radial direction. In this paper, we prove that the 3D inviscid model with an appropriate Neumann-Robin boundary condition will develop a finite time singularity starting from smooth initial data in an axisymmetric domain. Moreover, we prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition.

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preprint2012arXiv

Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics

We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/ε]$, for initial data of the form $εU_0$, where $T$ depends only on some Sobolev norm of $U_0$. We show that for such data there exists a unique solution on a time interval $[0, \exp{T}/ε]$, provided that $ε$ is sufficiently small. This is achieved by careful consideration of the structure of the nonlinearity. The incompressible elasticity equation is inherently linearly degenerate in the isotropic case; in other words, the equation satisfies a null condition. This is essential for time decay estimates. The pressure, which arises as a Lagrange multiplier to enforce the incompressibility constraint, is estimated in a novel way as a nonlocal nonlinear term with null structure. The proof employs the generalized energy method of Klainerman, enhanced by weighted $L^2$ estimates and the ghost weight introduced by Alinhac.

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preprint2012arXiv

Finite Time Blow-up of a 3D Model for Incompressible Euler Equations

We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In \cite{HL09a}, we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence presented in \cite{HL09a} seems to support that the 3D model may develop a finite time singularity. In this paper, we prove rigorously that the 3D inviscid model develops a finite time singularity for a family of smooth initial data whose energy is finite and conserved in time.

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preprint2012arXiv

Global solutions for micro-macro models of polymeric fluids

We provide a new proof for the global well-posedness of systems coupling fluids and polymers in two space dimensions. Compared to the well-known existing method based on the losing a priori estimates, our method is more direct and much simpler. The co-rotational FENE dumbbell model and the coupling Smoluchowski and Navier-Stokes equations are studied as examples to illustrate our main ideas.

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preprint2012arXiv

Global Solutions of Evolutionary Faddeev Model With Small Initial Data

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1 + n}$ to the unit sphere $\mathbb{S}^2$, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.

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preprint2012arXiv

On a family of exact solutions to the incompressible liquid crystals in two dimensions

In this paper we construct a family of exact strong solutions to the two-dimensional incompressible liquid crystal equations with finite energy. The initial velocity is chosen to be rotationally symmetric and the image of the initial orientation of the liquid crystal is a non-trivial curve on the unit sphere. It turns out that this family of initial data evolves globally in time by liquid crystal flow and may shrink to a single point as time goes to infinity.

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preprint2012arXiv

Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions

We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global well-posedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin in \cite{DingLin} and Lin-Lin-Wang in \cite{LinLinWang}. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under certain angle condition. Our proof is based on a frequency localization argument combined with the concentration-compactness approach which can be of independent interest.

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preprint2012arXiv

Rotation-Strain Decomposition for the Incompressible Viscoelasticity in Two Dimensions

In \cite{Lei}, the author derived an exact rotation-strain model in two dimensions for the motion of incompressible viscoelastic materials via the polar decomposition of the deformation tensor. Based on the rotation-strain model, the author constructed a family of large global classical solutions for the 2D incompressible viscoelasticity. To get such a global well-posedness result, the equation for the rotation angle was essential to explore the underlying weak dissipative structure of the whole viscoelastic system even though the momentum equation for the velocity field and the transport equation for the strain tensor have already formed a closed subsystem. In this paper, we revisit such a result without making use of the equation of the rotation angle. The proof relies on a new identity satisfied by the strain matrix. The smallness assumptions are only imposed on the $H^2$ norm of initial velocity field and the initial strain matrix, which implies that the deformation tensor is allowed being away from the equilibrium of 2 in the maximum norm.

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preprint2012arXiv

Singularities of solutions to compressible Euler equations with vacuum

Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be symmetric and the initial sound speed is required to vanish at the origin. They are smooth in Sobolev space $H^3$, but not required to have a compact support. It is shown that the $H^3$ norm of the velocity field and the sound speed will blow up in a finite time.

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preprint2010arXiv

A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations

Let $v(x, t)= v^r e_r + v^θe_θ+ v^z e_z$ be a solution to the three-dimensional incompressible axially-symmetric Navier-Stokes equations. Denote by $b = v^r e_r + v^z e_z$ the radial-axial vector field. Under a general scaling invariant condition on $b$, we prove that the quantity $Γ= r v^θ$ is Hölder continuous at $r = 0$, $t = 0$. As an application, we give a partial proof of a conjecture on Liouville property by Koch-Nadirashvili-Seregin-Sverak in \cite{KNSS} and Seregin-Sverak in \cite{SS}. As another application, we prove that if $b \in L^\infty([0, T], BMO^{-1})$, then $v$ is regular. This provides an answer to an open question raised by Koch and Tataru in \cite{KochTataru} about the uniqueness and regularity of Navier-Stokes equations in the axially-symmetric case.

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preprint2010arXiv

Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.

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preprint2010arXiv

Structure of Singularities of 3D Axi-symmetric Navier-Stokes Equations

Let $v$ be a solution of the axially symmetric Navier-Stokes equation. We determine the structure of certain (possible) maximal singularity of $v$ in the following sense. Let $(x_0, t_0)$ be a point where the flow speed $Q_0 = |v(x_0, t_0)|$ is comparable with the maximum flow speed at and before time $t_0$. We show after a space-time scaling with the factor $Q_0$ and the center $(x_0, t_0)$, the solution is arbitrarily close in $C^{2, 1, α}_{\rm local}$ norm to a nonzero constant vector in a fixed parabolic cube, provided that $r_0 Q_0$ is sufficiently large. Here $r_0$ is the distance from $x_0$ to the $z$ axis. Similar results are also shown to be valid if $|r_0v(x_0, t_0)|$ is comparable with the maximum of $|rv(x, t)|$ at and before time $t_0$.

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preprint2009arXiv

On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.

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