arXiv subjects
Publications and source records attributed to Jie He.
In this paper, we use Nash-Moser iteration method to study the local and global behaviours of positive solutions to the nonlinear elliptic equation $Δ_pv +av^{q}=0$ defined on a complete Riemannian manifolds $(M,g)$ where $p>1$, $a$ and $q$ are constants. Under some assumptions on $a$, $p$ and $q$, we derive gradient estimates and Liouville type theorems for such positive solutions.
In this paper the Nash-Moser iteration method is used to study the gradient estimates of solutions to the quasilinear elliptic equation $Δ_p u-|\nabla u|^q+b(x)|u|^{r-1}u=0$ defined on a complete Riemannian manifold $(M,g)$. When $b(x)\equiv0$, a unified Cheng-Yau type estimate of the solutions to this equation is derived. Regardless of whether this equation is defined on a manifold or a region of Euclidean space, certain technical and geometric conditions posed in \cite[Theorem E, F]{MR3261111} are weakened and hence some of the estimates due to Bidaut-Véron, Garcia-Huidobro and Véron (see \cite[Theorem E, F]{MR3261111}) are improved. In addition, we extend their results to the case $p>n=\dim(M)$. When $b(x)$ does not vanish, we can also extend some estimates for positive solutions to the above equation defined on a region of the Euclidean space due to Filippucci-Sun-Zheng \cite{filippucci2022priori} to arbitrary solutions to this equation on a complete Riemannian manifold. Even in the case of Euclidean space, the estimates for positive solutions in \cite{filippucci2022priori} and our results can not cover each other.
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion coefficients. We establish a propagation of chaos result, based on which the McKean-Vlasov equation is approximated by an interacting particle system. A truncated Euler scheme is then proposed for the interacting particle system allowing for a Khasminskii-type condition on the coefficients. To reduce the computational cost, the random batch approximation proposed in [Jin et al., J. Comput. Phys., 400(1), 2020] is extended to the interacting particle system where the interaction could take place in the diffusion term. An almost half order of convergence is proved in $L^p$ sense. Numerical tests are performed to verify the theoretical results.
The binary systems consisting of a Be star and a white dwarf (BeWDs) are very interesting.They can originate from the binaries composed of a Be star and a subdwarf O or B star (BesdOBs), and they can merge into red giants via luminous red nova or can evolve into double WD potentially detected by $LISA$ mission. Using the method of population synthesis, we investigate the formation and the destiny of BeWDs,and discuss the effects of the metallicity ($Z$) and the common envelope evolution parameters. We find that BesdOBs are significant progenitors of BeWDs. About 30\% ($Z=0.0001$)-50\% ($Z=0.02$) of BeWDs come from BesdOBs. About 60\% ($Z=0.0001$) -70\% ($Z=0.02$) of BeWDs turn into red giants via a merger between a WD and a non-degenerated star. About 30\% ($Z=0.0001$) -40\% ($Z=0.02$) of BeWDs evolve into double WDs which are potential gravitational waves of $LISA$ mission at a frequency band between about $3\times10^{-3}$ and $3\times10^{-2}$ Hz. The common envelope evolution parameter introduces an uncertainty with a factor of about 1.3 on BeWD populations in our simulations.
Let $(M,ω)$ be a compact symplectic manifold. We denote by $\ac$ the space of all almost complex structure compatible with $ω$. $\ac$ has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in $\ac$. We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow.
Automated bug priority inference can reduce the time overhead of bug triagers for priority assignments, improving the efficiency of software maintenance. Currently, there are two orthogonal lines for this task, i.e., traditional machine learning based (TML-based) and neural network based (NN-based) approaches. Although these approaches achieve competitive performance, our observation finds that existing approaches face the following two issues: 1) TML-based approaches require much manual feature engineering and cannot learn the semantic information of bug reports; 2) Both TML-based and NN-based approaches cannot effectively address the label imbalance problem because they are difficult to distinguish the semantic difference between bug reports with different priorities. In this paper, we propose CLeBPI (Contrastive Learning for Bug Priority Inference), which leverages pre-trained language model and contrastive learning to tackle the above-mentioned two issues. Specifically, CLeBPI is first pre-trained on a large-scale bug report corpus in a self-supervised way, thus it can automatically learn contextual representations of bug reports without manual feature engineering. Afterward, it is further pre-trained by a contrastive learning objective, which enables it to distinguish semantic differences between bug reports, learning more precise contextual representations for each bug report. When finishing pre-training, we can connect a classification layer to CLeBPI and fine-tune it for bug priority inference in a supervised way. To verify the effectiveness of CLeBPI, we choose four baseline approaches and conduct comparison experiments on a public dataset. The experimental results show that CLeBPI outperforms all baseline approaches by 23.86%-77.80% in terms of weighted average F1-score, showing its effectiveness.
In this paper, we establish the theory of chaos propagation and propose an Euler-Maruyama scheme for McKean-Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst exponent $H \in (0,1)$. Meanwhile, upper bounds for errors in the Euler method is obtained. A numerical example is demonstrated to verify the theoretical results.
A combinatorial recommender (CR) system feeds a list of items to a user at a time in the result page, in which the user behavior is affected by both contextual information and items. The CR is formulated as a combinatorial optimization problem with the objective of maximizing the recommendation reward of the whole list. Despite its importance, it is still a challenge to build a practical CR system, due to the efficiency, dynamics, personalization requirement in online environment. In particular, we tear the problem into two sub-problems, list generation and list evaluation. Novel and practical model architectures are designed for these sub-problems aiming at jointly optimizing effectiveness and efficiency. In order to adapt to online case, a bootstrap algorithm forming an actor-critic reinforcement framework is given to explore better recommendation mode in long-term user interaction. Offline and online experiment results demonstrate the efficacy of proposed JDRec framework. JDRec has been applied in online JD recommendation, improving click through rate by 2.6% and synthetical value for the platform by 5.03%. We will publish the large-scale dataset used in this study to contribute to the research community.
Formal methods provide very powerful tools and techniques for the design and analysis of complex systems. Their practical application remains however limited, due to the widely accepted belief that formal methods require extensive expertise and a steep learning curve. Writing correct formal specifications in form of logical formulas is still considered to be a difficult and error prone task. In this paper we propose DeepSTL, a tool and technique for the translation of informal requirements, given as free English sentences, into Signal Temporal Logic (STL), a formal specification language for cyber-physical systems, used both by academia and advanced research labs in industry. A major challenge to devise such a translator is the lack of publicly available informal requirements and formal specifications. We propose a two-step workflow to address this challenge. We first design a grammar-based generation technique of synthetic data, where each output is a random STL formula and its associated set of possible English translations. In the second step, we use a state-of-the-art transformer-based neural translation technique, to train an accurate attentional translator of English to STL. The experimental results show high translation quality for patterns of English requirements that have been well trained, making this workflow promising to be extended for processing more complex translation tasks.
This paper focuses on the strong convergence of the truncated $θ$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate, which is close to one, is given under the weaker assumption than the monotone condition. To verify our theoretical findings, we present a numerical example.
Large-scale industrial recommender systems are usually confronted with computational problems due to the enormous corpus size. To retrieve and recommend the most relevant items to users under response time limits, resorting to an efficient index structure is an effective and practical solution. The previous work Tree-based Deep Model (TDM) \cite{zhu2018learning} greatly improves recommendation accuracy using tree index. By indexing items in a tree hierarchy and training a user-node preference prediction model satisfying a max-heap like property in the tree, TDM provides logarithmic computational complexity w.r.t. the corpus size, enabling the use of arbitrary advanced models in candidate retrieval and recommendation. In tree-based recommendation methods, the quality of both the tree index and the user-node preference prediction model determines the recommendation accuracy for the most part. We argue that the learning of tree index and preference model has interdependence. Our purpose, in this paper, is to develop a method to jointly learn the index structure and user preference prediction model. In our proposed joint optimization framework, the learning of index and user preference prediction model are carried out under a unified performance measure. Besides, we come up with a novel hierarchical user preference representation utilizing the tree index hierarchy. Experimental evaluations with two large-scale real-world datasets show that the proposed method improves recommendation accuracy significantly. Online A/B test results at a display advertising platform also demonstrate the effectiveness of the proposed method in production environments.
Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor performance of the traditional iterative gradient-based learning algorithms. Although the famous extreme learning machine (ELM) has successfully addressed the problems of slow convergence, it still has computational robustness problems brought by input weights and biases randomly assigned. Thus, in order to overcome the aforementioned problems, in this paper, a novel type neural network based on Gegenbauer orthogonal polynomials, termed as GNN, is constructed and investigated. This model could overcome the computational robustness problems of ELM, while still has comparable structural simplicity and approximation capability. Based on this, we propose a regularized weights direct determination (R-WDD) based on equality-constrained optimization to determine the optimal output weights. The R-WDD tends to minimize the empirical risks and structural risks of the network, thus to lower the risk of over fitting and improve the generalization ability. This leads us to a the final GNN with R-WDD, which is a unified learning mechanism for binary and multi-class classification problems. Finally, as is verified in the various comparison experiments, GNN with R-WDD tends to have comparable (or even better) generalization performances, computational scalability and efficiency, and classification robustness, compared to least square support vector machine (LS-SVM), ELM with Gaussian kernel.
This paper presents low power dissipation, low phase noise ring oscillators (ROs) based on Semiconductor Manufacturing International Corporation (SMIC) 0.18μm CMOS technology at liquid helium temperature (LHT). First, the characterization and modelling of CMOS at LHT are presented. The temperature-dependent device parameters are revised and the model then shows good agreement with the measurement results. The ring oscillator is then designed with energy efficiency optimization by application of forward body biasing (FBB). FBB is proposed to compensate for the threshold voltage (VTH) shift to preserve the benefits of the enhancement of the carrier mobility at 4.2K. The delay per stage (τp), the static current (ISTAT), the dynamic current (IDYN), the power dissipation (P) and the phase noise (L(foff)) are analyzed at both 298 K and 4.2 K, with and without FBB. The performance of the designed RO in terms of speed (τp=179ps), static current (23.55nA/stage), power dissipation (2.13μW) and phase noise (-177.57dBc/Hz@1MHz) can be achieved at 4.2K with the supply voltage (VDD) reduced to 0.9V.
Model-based methods for recommender systems have been studied extensively in recent years. In systems with large corpus, however, the calculation cost for the learnt model to predict all user-item preferences is tremendous, which makes full corpus retrieval extremely difficult. To overcome the calculation barriers, models such as matrix factorization resort to inner product form (i.e., model user-item preference as the inner product of user, item latent factors) and indexes to facilitate efficient approximate k-nearest neighbor searches. However, it still remains challenging to incorporate more expressive interaction forms between user and item features, e.g., interactions through deep neural networks, because of the calculation cost. In this paper, we focus on the problem of introducing arbitrary advanced models to recommender systems with large corpus. We propose a novel tree-based method which can provide logarithmic complexity w.r.t. corpus size even with more expressive models such as deep neural networks. Our main idea is to predict user interests from coarse to fine by traversing tree nodes in a top-down fashion and making decisions for each user-node pair. We also show that the tree structure can be jointly learnt towards better compatibility with users' interest distribution and hence facilitate both training and prediction. Experimental evaluations with two large-scale real-world datasets show that the proposed method significantly outperforms traditional methods. Online A/B test results in Taobao display advertising platform also demonstrate the effectiveness of the proposed method in production environments.
Lung nodules are commonly detected in screening for patients with a risk for lung cancer. Though the status of large nodules can be easily diagnosed by fine needle biopsy or bronchoscopy, small nodules are often difficult to classify on computed tomography (CT). Recent works have shown that shape analysis of lung nodules can be used to differentiate benign lesions from malignant ones, though existing methods are limited in their sensitivity and specificity. In this work we introduced a new 3D shape analysis within the framework of differential geometry to calculate the Wasserstein distance between benign and malignant lung nodules to derive an accurate classification scheme. The Wasserstein distance between the nodules is calculated based on our new spherical optimal mass transport, this new algorithm works directly on sphere by using spherical metric, which is much more accurate and efficient than previous methods. In the process of deformation, the area-distortion factor gives a probability measure on the unit sphere, which forms the Wasserstein space. From known cases of benign and malignant lung nodules, we can calculate a unique optimal mass transport map between their correspondingly deformed Wasserstein spaces. This transportation cost defines the Wasserstein distance between them and can be used to classify new lung nodules into either the benign or malignant class. To the best of our knowledge, this is the first work that utilizes Wasserstein distance for lung nodule classification. The advantages of Wasserstein distance are it is invariant under rigid motions and scalings, thus it intrinsically measures shape distance even when the underlying shapes are of high complexity, making it well suited to classify lung nodules as they have different sizes, orientations, and appearances.
In this paper, we study the geometry of compact complex manifolds with Levi-Civita Ricci-flat metrics and prove that compact complex surfaces admitting Levi-Civita Ricci-flat metrics are Kahler Calabi-Yau surfaces or Hopf surfaces.
Marginal model is a popular instrument for studying longitudinal data and cluster data. This paper investigates the estimator of marginal model with subgroup auxiliary information. To marginal model, we propose a new type of auxiliary information, and combine them with the traditional estimating equations of the quadratic inference function (QIF) method based on the generalized method of moments (GMM). Thus obtaining a more efficient estimator. The asymptotic normality and the test statistics of the proposed estimator are established. The theoretical result shows that the estimator with subgroup information is more efficient than the conventional QIF one. Simulation studies are carried out to examine the performance of the proposed method under finite sample. We apply the proposed method to a real data for illustration.
This paper proposes a novel and efficient method to build a Computer-Aided Diagnoses (CAD) system for lung nodule detection based on Computed Tomography (CT). This task was treated as an Object Detection on Video (VID) problem by imitating how a radiologist reads CT scans. A lung nodule detector was trained to automatically learn nodule features from still images to detect lung nodule candidates with both high recall and accuracy. Unlike previous work which used 3-dimensional information around the nodule to reduce false positives, we propose two simple but efficient methods, Multi-slice propagation (MSP) and Motionless-guide suppression (MLGS), which analyze sequence information of CT scans to reduce false negatives and suppress false positives. We evaluated our method in open-source LUNA16 dataset which contains 888 CT scans, and obtained state-of-the-art result (Free-Response Receiver Operating Characteristic score of 0.892) with detection speed (end to end within 20 seconds per patient on a single NVidia GTX 1080) much higher than existing methods.