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Researcher profile

Jiaqi Yang

Jiaqi Yang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer VisionMachine Learningmath.APArtificial IntelligenceRoboticsmath.DSeess.IVInformation Theorymath.FAmath.ITmath.NANumerical Analysisphysics.optics

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Published work

24 published item(s)

preprint2026arXiv

Efficient Feature-Free Initialization for Monocular Visual-Inertial Systems Using a Feed-Forward 3D Model

Fast and reliable initialization is critical for monocular visual-inertial navigation systems (VINS), as it establishes the starting conditions for subsequent state estimation. Despite steady progress, most existing methods heavily rely on visual feature correspondences and require 3-4 seconds of sensory data for successful initialization, which limits their applicability and efficiency. With the advent of feed-forward 3D models that can directly predict point clouds from images, we revisit the visual-inertial initialization problem from a concise perspective. In this work, we propose a feature-free initialization framework that leverages up-to-scale point clouds predicted by a feed-forward 3D model, thereby obviating the need for visual feature tracking and estimation. This design substantially reduces system complexity and improves the reliability of initialization. Experiments on public datasets demonstrate that the proposed feature-free initialization method achieves the highest success rate, exceeding 90%, and significantly reduces the data duration required for successful initialization, typically to under 1.2 s. We further validate our method on a self-collected dataset covering various indoor and outdoor scenarios, demonstrating robust performance, particularly in visually degraded environments where existing methods often fail. The code and dataset are available at https://github.com/Yuantai-Z/FF-VIO-Init.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

On the well-posedness of two-dimensional Muskat problem with an elastic interface

We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36], we demonstrate that the problem is locally well-posed in $H^s$ for $s\geq 2$ for arbitrary initial data. Furthermore, for the one-phase case and the stable two-phase case $(ρ^+ \leq ρ^-)$, we establish global well-posedness for small initial data in $H^s$ when $s> \frac{3}{2}$.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Self-heterodyne spectroscopy via a non-uniformly spaced frequency comb

Frequency comb spectroscopy has significantly advanced molecular spectroscopy across scientific research and diverse applications. Among its key performance metrics especially for time-resolved studies, sensitivity and measurement speed are paramount. However, a long-standing compromise between these parameters arises from the need for noise reduction. Here, we introduce a comb spectroscopy system that overcomes this limitation using a single frequency comb of non-uniformly spaced modes. The comb is generated using an extremely simple setup, composed of a continuous-wave (CW) fiber laser and a single-sideband phase modulator (SSM). Our approach delivers optical-to-radio-frequency conversion comparable to dual-comb spectroscopy (DCS) but through a simplified self-heterodyning architecture. By leveraging the intrinsic mutual coherence of the comb, this design achieves a noise-equivalent absorption coefficient (NEA) of 5.0*10^(-6) Hz^(-1/2)--an order-of-magnitude improvement over state-of-the-art DCS, coupled with long-term stability. The system resolves weak molecular overtone spectra on nanosecond timescales, in a single-shot measurement, at a signal-to-noise ratio of 128. This integration of high sensitivity, resolution, and speed resolves the core trade-off that has long constrained time-resolved spectroscopic analysis.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

StableHand: Quality-Aware Flow Matching for World-Space Dual-Hand Motion Estimation from Egocentric Video

Recovering world space 4D motion of two interacting hands from egocentric video is a fundamental capability for supervising robot policy learning, where wrist trajectories track the end-effector and finger articulations specify the grasp pose. Two major challenges arise in this setting: hands frequently leave the camera view for extended periods due to head motion, and persistent hand-object interactions cause severe occlusions of one or both hands. Existing methods uniformly condition on noisy hand motion observations without accounting for their per-frame reliability, leading to substantial performance degradation. Our key insight is that accurate world space hand motion estimation is tightly coupled with the quality of per-frame hand observations. To this end, we decompose the quality of hand motion observations extracted from an off-the-shelf hand pose estimator into four channels: wrist global translation and finger articulations for both hands. We propose StableHand, a quality-aware flow-matching framework conditioned on these four-channel quality signals, which are predicted by a learned quality network. We naturally incorporate the quality signals into the flow-matching process through a per-channel forward schedule, a quality-adjusted velocity target, AdaLN modulation of the DiT denoiser, and a quality-aware ODE initialization. This unified generative process preserves high-quality observations while reconstructing unreliable ones using a learned bimanual motion prior. Experiments on HOT3D and ARCTIC, two egocentric benchmarks featuring long missing-hand spans and persistent hand-object occlusions, show that StableHand achieves state-of-the-art performance across all reported metrics, reducing W-MPJPE by 20-25% compared to the strongest baseline, with the largest gains on heavily occluded ARCTIC sequences.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Topology-Attention ConvLSTM Network and Its Application to EM Images

Structural accuracy of segmentation is important for finescale structures in biomedical images. We propose a novel TopologyAttention ConvLSTM Network (TACNet) for 3D image segmentation in order to achieve high structural accuracy for 3D segmentation tasks. Specifically, we propose a Spatial Topology-Attention (STA) module to process a 3D image as a stack of 2D image slices and adopt ConvLSTM to leverage contextual structure information from adjacent slices. In order to effectively transfer topology-critical information across slices, we propose an Iterative-Topology Attention (ITA) module that provides a more stable topology-critical map for segmentation. Quantitative and qualitative results show that our proposed method outperforms various baselines in terms of topology-aware evaluation metrics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Characterization of smooth solutions to the Navier-Stokes equations in a pipe with two types of slip boundary conditions

Smooth solutions of the stationary Navier-Stokes equations in an infinitely long pipe, equipped with the Navier-slip or Navier-Hodge-Lions boundary condition, are considered in this paper. Three main results are presented. First, when equipped with the Navier-slip boundary condition, it is shown that, $W^{1,\infty}$ axially symmetric solutions with zero flux at one cross section, must be swirling solutions: $u=(- C x_2, C x_1,0)$, and $x_3-$periodic solutions must be helical solutions: $u=(-C_1x_2,C_1x_1,C_2)$. Second, also equipped with the Navier-slip boundary condition, if the swirl or vertical component of the axially symmetric solution is independent of the vertical variable $x_3$, solutions are also proven to be helical solutions. In the case of the vertical component being independent of $x_3$, the $W^{1,\infty}$ assumption is not needed. In the case of the swirl component being independent of $x_3$, the $W^{1,\infty}$ assumption can be relaxed extensively such that the horizontal radial component of the velocity, $u_r$, can grow exponentially with respect to the distance to the origin. Also, by constructing a counterexample, we show that the growing assumption on $u_r$ is optimal. Third, when equipped with the Navier-Hodge-Lions boundary condition, we can show that if the gradient of the velocity grows sublinearly, then the solution, enjoying the Liouville-type theorem, is a trivial shear flow: $(0,0,C)$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

DEVO: Depth-Event Camera Visual Odometry in Challenging Conditions

We present a novel real-time visual odometry framework for a stereo setup of a depth and high-resolution event camera. Our framework balances accuracy and robustness against computational efficiency towards strong performance in challenging scenarios. We extend conventional edge-based semi-dense visual odometry towards time-surface maps obtained from event streams. Semi-dense depth maps are generated by warping the corresponding depth values of the extrinsically calibrated depth camera. The tracking module updates the camera pose through efficient, geometric semi-dense 3D-2D edge alignment. Our approach is validated on both public and self-collected datasets captured under various conditions. We show that the proposed method performs comparable to state-of-the-art RGB-D camera-based alternatives in regular conditions, and eventually outperforms in challenging conditions such as high dynamics or low illumination.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Nearly Minimax Algorithms for Linear Bandits with Shared Representation

We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors and closes the gap in existing results [Yang et al., 2021]. Our main technique include a more efficient estimator for the low-rank linear feature extractor and an accompanied novel analysis for this estimator.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Phasic Self-Imitative Reduction for Sparse-Reward Goal-Conditioned Reinforcement Learning

It has been a recent trend to leverage the power of supervised learning (SL) towards more effective reinforcement learning (RL) methods. We propose a novel phasic approach by alternating online RL and offline SL for tackling sparse-reward goal-conditioned problems. In the online phase, we perform RL training and collect rollout data while in the offline phase, we perform SL on those successful trajectories from the dataset. To further improve sample efficiency, we adopt additional techniques in the online phase including task reduction to generate more feasible trajectories and a value-difference-based intrinsic reward to alleviate the sparse-reward issue. We call this overall algorithm, PhAsic self-Imitative Reduction (PAIR). PAIR substantially outperforms both non-phasic RL and phasic SL baselines on sparse-reward goal-conditioned robotic control problems, including a challenging stacking task. PAIR is the first RL method that learns to stack 6 cubes with only 0/1 success rewards from scratch.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Provable Model-based Nonlinear Bandit and Reinforcement Learning: Shelve Optimism, Embrace Virtual Curvature

This paper studies model-based bandit and reinforcement learning (RL) with nonlinear function approximations. We propose to study convergence to approximate local maxima because we show that global convergence is statistically intractable even for one-layer neural net bandit with a deterministic reward. For both nonlinear bandit and RL, the paper presents a model-based algorithm, Virtual Ascent with Online Model Learner (ViOlin), which provably converges to a local maximum with sample complexity that only depends on the sequential Rademacher complexity of the model class. Our results imply novel global or local regret bounds on several concrete settings such as linear bandit with finite or sparse model class, and two-layer neural net bandit. A key algorithmic insight is that optimism may lead to over-exploration even for two-layer neural net model class. On the other hand, for convergence to local maxima, it suffices to maximize the virtual return if the model can also reasonably predict the size of the gradient and Hessian of the real return.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Revisiting Some Common Practices in Cooperative Multi-Agent Reinforcement Learning

Many advances in cooperative multi-agent reinforcement learning (MARL) are based on two common design principles: value decomposition and parameter sharing. A typical MARL algorithm of this fashion decomposes a centralized Q-function into local Q-networks with parameters shared across agents. Such an algorithmic paradigm enables centralized training and decentralized execution (CTDE) and leads to efficient learning in practice. Despite all the advantages, we revisit these two principles and show that in certain scenarios, e.g., environments with a highly multi-modal reward landscape, value decomposition, and parameter sharing can be problematic and lead to undesired outcomes. In contrast, policy gradient (PG) methods with individual policies provably converge to an optimal solution in these cases, which partially supports some recent empirical observations that PG can be effective in many MARL testbeds. Inspired by our theoretical analysis, we present practical suggestions on implementing multi-agent PG algorithms for either high rewards or diverse emergent behaviors and empirically validate our findings on a variety of domains, ranging from the simplified matrix and grid-world games to complex benchmarks such as StarCraft Multi-Agent Challenge and Google Research Football. We hope our insights could benefit the community towards developing more general and more powerful MARL algorithms. Check our project website at https://sites.google.com/view/revisiting-marl.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Stability of a point charge for the repulsive Vlasov-Poisson system

We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small gas, i.e.\ measures of the form $δ_{(\mathcal{X}(t),\mathcal{V}(t))}+μ^2d{\bf x}d{\bf v}$ for some $(\mathcal{X}, \mathcal{V}):\mathbb{R}\to\mathbb{R}^6$ and a small gas distribution $μ:\mathbb{R}\to L^2_{{\bf x},{\bf v}}$, and study asymptotic dynamics in the associated initial value problem. If initially suitable moments on $μ_0=μ(t=0)$ are small, we obtain a global solution of the above form, and the electric field generated by the gas distribution $μ$ decays at an almost optimal rate. Assuming in addition boundedness of suitable derivatives of $μ_0$, the electric field decays at an optimal rate and we derive a modified scattering dynamics for the motion of the point charge and the gas distribution. Our proof makes crucial use of the Hamiltonian structure. The linearized system is transport by the Kepler ODE, which we integrate exactly through an asymptotic action-angle transformation. Thanks to a precise understanding of the associated kinematics, moment and derivative control is achieved via a bootstrap analysis that relies on the decay of the electric field associated to $μ$. The asymptotic behavior can then be deduced from the properties of Poisson brackets in asymptotic action coordinates.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Unsupervised Learning of 3D Semantic Keypoints with Mutual Reconstruction

Semantic 3D keypoints are category-level semantic consistent points on 3D objects. Detecting 3D semantic keypoints is a foundation for a number of 3D vision tasks but remains challenging, due to the ambiguity of semantic information, especially when the objects are represented by unordered 3D point clouds. Existing unsupervised methods tend to generate category-level keypoints in implicit manners, making it difficult to extract high-level information, such as semantic labels and topology. From a novel mutual reconstruction perspective, we present an unsupervised method to generate consistent semantic keypoints from point clouds explicitly. To achieve this, the proposed model predicts keypoints that not only reconstruct the object itself but also reconstruct other instances in the same category. To the best of our knowledge, the proposed method is the first to mine 3D semantic consistent keypoints from a mutual reconstruction view. Experiments under various evaluation metrics as well as comparisons with the state-of-the-arts demonstrate the efficacy of our new solution to mining semantic consistent keypoints with mutual reconstruction.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

VECtor: A Versatile Event-Centric Benchmark for Multi-Sensor SLAM

Event cameras have recently gained in popularity as they hold strong potential to complement regular cameras in situations of high dynamics or challenging illumination. An important problem that may benefit from the addition of an event camera is given by Simultaneous Localization And Mapping (SLAM). However, in order to ensure progress on event-inclusive multi-sensor SLAM, novel benchmark sequences are needed. Our contribution is the first complete set of benchmark datasets captured with a multi-sensor setup containing an event-based stereo camera, a regular stereo camera, multiple depth sensors, and an inertial measurement unit. The setup is fully hardware-synchronized and underwent accurate extrinsic calibration. All sequences come with ground truth data captured by highly accurate external reference devices such as a motion capture system. Individual sequences include both small and large-scale environments, and cover the specific challenges targeted by dynamic vision sensors.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Persistence and Smooth Dependence on Parameters of Periodic Orbits in Functional Differential Equations Close to an ODE or an Evolutionary PDE

We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that, under some mild assumptions, if the ODE has a nondegenerate periodic orbit, then the FDE has a smooth periodic orbit. Moreover, we get smooth dependence of the periodic orbit and its frequency on parameters with high regularity. The result also applies to FDEs which are perturbations of some evolutionary partial differential equations(PDEs). The proof consists in solving functional equations satisfied by the parameterization of the periodic orbit and the frequency using a fixed point approach. We do not need to consider the smoothness of the evolution or even the phase space of the FDEs.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

3D Correspondence Grouping with Compatibility Features

We present a simple yet effective method for 3D correspondence grouping. The objective is to accurately classify initial correspondences obtained by matching local geometric descriptors into inliers and outliers. Although the spatial distribution of correspondences is irregular, inliers are expected to be geometrically compatible with each other. Based on such observation, we propose a novel representation for 3D correspondences, dubbed compatibility feature (CF), to describe the consistencies within inliers and inconsistencies within outliers. CF consists of top-ranked compatibility scores of a candidate to other correspondences, which purely relies on robust and rotation-invariant geometric constraints. We then formulate the grouping problem as a classification problem for CF features, which is accomplished via a simple multilayer perceptron (MLP) network. Comparisons with nine state-of-the-art methods on four benchmarks demonstrate that: 1) CF is distinctive, robust, and rotation-invariant; 2) our CF-based method achieves the best overall performance and holds good generalization ability.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Cross-Modal Image Fusion Method Guided by Human Visual Characteristics

The characteristics of feature selection, nonlinear combination and multi-task auxiliary learning mechanism of the human visual perception system play an important role in real-world scenarios, but the research of image fusion theory based on the characteristics of human visual perception is less. Inspired by the characteristics of human visual perception, we propose a robust multi-task auxiliary learning optimization image fusion theory. Firstly, we combine channel attention model with nonlinear convolutional neural network to select features and fuse nonlinear features. Then, we analyze the impact of the existing image fusion loss on the image fusion quality, and establish the multi-loss function model of unsupervised learning network. Secondly, aiming at the multi-task auxiliary learning mechanism of human visual perception system, we study the influence of multi-task auxiliary learning mechanism on image fusion task on the basis of single task multi-loss network model. By simulating the three characteristics of human visual perception system, the fused image is more consistent with the mechanism of human brain image fusion. Finally, in order to verify the superiority of our algorithm, we carried out experiments on the combined vision system image data set, and extended our algorithm to the infrared and visible image and the multi-focus image public data set for experimental verification. The experimental results demonstrate the superiority of our fusion theory over state-of-arts in generality and robustness.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

AE-Net: Autonomous Evolution Image Fusion Method Inspired by Human Cognitive Mechanism

In order to solve the robustness and generality problems of the image fusion task,inspired by the human brain cognitive mechanism, we propose a robust and general image fusion method with autonomous evolution ability, and is therefore denoted with AE-Net. Through the collaborative optimization of multiple image fusion methods to simulate the cognitive process of human brain, unsupervised learning image fusion task can be transformed into semi-supervised image fusion task or supervised image fusion task, thus promoting the evolutionary ability of network model weight. Firstly, the relationship between human brain cognitive mechanism and image fusion task is analyzed and a physical model is established to simulate human brain cognitive mechanism. Secondly, we analyze existing image fusion methods and image fusion loss functions, select the image fusion method with complementary features to construct the algorithm module, establish the multi-loss joint evaluation function to obtain the optimal solution of algorithm module. The optimal solution of each image is used to guide the weight training of network model. Our image fusion method can effectively unify the cross-modal image fusion task and the same modal image fusion task, and effectively overcome the difference of data distribution between different datasets. Finally, extensive numerical results verify the effectiveness and superiority of our method on a variety of image fusion datasets, including multi-focus dataset, infrared and visi-ble dataset, medical image dataset and multi-exposure dataset. Comprehensive experiments demonstrate the superiority of our image fusion method in robustness and generality. In addition, experimental results also demonstate the effectiveness of human brain cognitive mechanism to improve the robustness and generality of image fusion.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

LRF-Net: Learning Local Reference Frames for 3D Local Shape Description and Matching

The local reference frame (LRF) acts as a critical role in 3D local shape description and matching. However, most of existing LRFs are hand-crafted and suffer from limited repeatability and robustness. This paper presents the first attempt to learn an LRF via a Siamese network that needs weak supervision only. In particular, we argue that each neighboring point in the local surface gives a unique contribution to LRF construction and measure such contributions via learned weights. Extensive analysis and comparative experiments on three public datasets addressing different application scenarios have demonstrated that LRF-Net is more repeatable and robust than several state-of-the-art LRF methods (LRF-Net is only trained on one dataset). In addition, LRF-Net can significantly boost the local shape description and 6-DoF pose estimation performance when matching 3D point clouds.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Non-linear and Selective Fusion of Cross-Modal Images

The human visual perception system has strong robustness in image fusion. This robustness is based on human visual perception system's characteristics of feature selection and non-linear fusion of different features. In order to simulate the human visual perception mechanism in image fusion tasks, we propose a multi-source image fusion framework that combines illuminance factors and attention mechanisms. The framework effectively combines traditional image features and modern deep learning features. First, we perform multi-scale decomposition of multi-source images. Then, the visual saliency map and the deep feature map are combined with the illuminance fusion factor to perform high-low frequency nonlinear fusion. Secondly, the characteristics of high and low frequency fusion are selected through the channel attention network to obtain the final fusion map. By simulating the nonlinear characteristics and selection characteristics of the human visual perception system in image fusion, the fused image is more in line with the human visual perception mechanism. Finally, we validate our fusion framework on public datasets of infrared and visible images, medical images and multi-focus images. The experimental results demonstrate the superiority of our fusion framework over state-of-arts in visual quality, objective fusion metrics and robustness.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Numerical computation of periodic orbits and isochrons for state-dependent delay perturbation of an ODE in the plane

We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differential equation with a limit cycle. Note that the space of solutions of an SDDE is infinite dimensional. We compute a two parameter family of solutions of the SDDE which converge to the solutions of the ODE as the perturbation goes to zero in a neighborhood of the limit cycle. The method we use formulates functional equations among periodic functions (or functions converging exponentially to periodic). The functional equations express that the functions solve the SDDE. Therefore, rather than evolving initial data and finding solutions of a certain shape, we consider spaces of functions with the desired shape and require that they are solutions. The mathematical theory of these invariance equations is developed in a companion paper, which develops "a posteriori" theorems. They show that, if there is a sufficiently approximate solution (with respect to some explicit condition numbers), then there is a true solution close to the approximate one. Since the numerical methods produce an approximate solution, and provide estimates of the condition numbers, we can make sure that the numerical solutions we consider approximate true solutions. In this paper, we choose a systematic way to approximate functions by a finite set of numbers (Taylor-Fourier series) and develop a toolkit of algorithms that implement the operators -- notably composition -- that enter into the theory. We also present several implementation results and present the results of running the algorithms and their implementation in some representative cases.

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preprint2020arXiv

On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces

In this paper we derive regular criteria in Lorentz spaces for Leray-Hopf weak solutions $v$ of the three-dimensional Navier-Stokes equations based on the formal equivalence relation $π\cong|v|^2$, where $π$ denotes the fluid pressure and $v$ the fluid velocity. It is called the mixed pressure-velocity problem (the P-V problem). It is shown that if $\fπ{(e^{-|x|^2}+|v|)^θ}\in L^p(0,T;L^{q,\infty})\,,$ where $0\leqθ\leq1$ and $\f2p+\f3q=2-θ$, then $v$ is regular on $(0,T]$. Note that, if $\Om$ is periodic, we may replace $\,e^{-|x|^2} \,$ by a positive constant. This result improves a 2018 statement obtained by one of the authors. Furthermore, as an integral part of our contribution, we give an overview on the known results on the P-V problem, and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin (L-P-S) type.

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preprint2020arXiv

On the Shinbrot's criteria for energy equality to Newtonian fluids: A simplified proof, and an extension of the range of application

We show that the classical Shinbrot&#39;s criteria to guarantee that a Leray-Hopf solution satisfies the energy equality follows trivially from the $L^4( (0\,,T)\timesΩ))$ Lions-Prodi particular case. Moreover we extend Shinbrot&#39;s result to space coefficients $ r \in (3,\,4)\,.$ In this last case our condition coincides with Shinbrot condition for $r=4$, but for $r<4$ it is more restrictive than the classical one, $ 2/p + 2/r = 1\,.$ It looks significant that in correspondence to the extreme values $r=3$ and $r=\infty$, and just for these two values, the conditions become respectively $u \in L^\infty(L^3)$ and $u \in L^2(L^\infty)$, which imply regularity by appealing to classical Ladyzhenskaya-Prodi-Serrin (L-P-S) type conditions. However, for values $r\in (3,\infty)$ the L-P-S condition does not apply, even for the more demanding case $\,3<r<4\,.$ The proofs are quite trivial, by appealing to interpolation, with $L^\infty(L^2)$ in the first case and with $L^2(L^6)$ in the second case. The central position of this old classical problem in Fluid-Mechanics, together with the simplicity of the proofs (in particular the novelty of the second result) looks at least curious. This may be considered a merit of this very short note.

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preprint2019arXiv

Evaluating Local Geometric Feature Representations for 3D Rigid Data Matching

Local geometric descriptors remain an essential component for 3D rigid data matching and fusion. The devise of a rotational invariant local geometric descriptor usually consists of two steps: local reference frame (LRF) construction and feature representation. Existing evaluation efforts have mainly been paid on the LRF or the overall descriptor, yet the quantitative comparison of feature representations remains unexplored. This paper fills this gap by comprehensively evaluating nine state-of-the-art local geometric feature representations. Our evaluation is on the ground that ground-truth LRFs are leveraged such that the ranking of tested feature representations are more convincing as opposed to existing studies. The experiments are deployed on six standard datasets with various application scenarios (shape retrieval, point cloud registration, and object recognition) and data modalities (LiDAR, Kinect, and Space Time) as well as perturbations including Gaussian noise, shot noise, data decimation, clutter, occlusion, and limited overlap. The evaluated terms cover the major concerns for a feature representation, e.g., distinctiveness, robustness, compactness, and efficiency. The outcomes present interesting findings that may shed new light on this community and provide complementary perspectives to existing evaluations on the topic of local geometric feature description. A summary of evaluated methods regarding their peculiarities is also presented to guide real-world applications and new descriptor crafting.

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