arXiv subjects
Publications and source records attributed to Yong Wang.
In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski-Sitarz-Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators, particularly in the cases of on 4-dimensional manifolds with boundary.
Action advising endeavors to leverage supplementary guidance from expert teachers to alleviate the issue of sampling inefficiency in Deep Reinforcement Learning (DRL). Previous agent-specific action advising methods are hindered by imperfections in the agent itself, while agent-agnostic approaches exhibit limited adaptability to the learning agent. In this study, we propose a novel framework called Agent-Aware trAining yet Agent-Agnostic Action Advising (A7) to strike a balance between the two. The underlying concept of A7 revolves around utilizing the similarity of state features as an indicator for soliciting advice. However, unlike prior methodologies, the measurement of state feature similarity is performed by neither the error-prone learning agent nor the agent-agnostic advisor. Instead, we employ a proxy model to extract state features that are both discriminative (adaptive to the agent) and generally applicable (robust to agent noise). Furthermore, we utilize behavior cloning to train a model for reusing advice and introduce an intrinsic reward for the advised samples to incentivize the utilization of expert guidance. Experiments are conducted on the GridWorld, LunarLander, and six prominent scenarios from Atari games. The results demonstrate that A7 significantly accelerates the learning process and surpasses existing methods (both agent-specific and agent-agnostic) by a substantial margin. Our code will be made publicly available.
In [19], a general Dabrowski-Sitarz-Zalecki type theorem for odd dimensional manifolds with boundary was proved. In this paper, we give the proof of the another general Dabrowski-Sitarz-Zalecki type theorem for the spectral Einstein functional associated with the Dirac operator on odd dimensional manifolds with boundary.
Online A/B tests have become increasingly popular and important for social platforms. However, accurately estimating the global average treatment effect (GATE) has proven to be challenging due to network interference, which violates the Stable Unit Treatment Value Assumption (SUTVA) and poses a great challenge to experimental design. Existing network experimental design research was mostly based on the unbiased Horvitz-Thompson (HT) estimator with substantial data trimming to ensure unbiasedness at the price of high resultant estimation variance. In this paper, we strive to balance the bias and variance in designing randomized network experiments. Under a potential outcome model with 1-hop interference, we derive the bias and variance of the standard HT estimator and reveal their relation to the network topological structure and the covariance of the treatment assignment vector. We then propose to formulate the experimental design problem to optimize the covariance matrix of the treatment assignment vector to achieve the bias and variance balance by minimizing a well-crafted upper bound of the mean squared error (MSE) of the estimator, which allows us to decouple the unknown interference effect component and the experimental design component. An efficient projected gradient descent algorithm is presented to implement the desired randomization scheme. Finally, we carry out extensive simulation studies 2 to demonstrate the advantages of our proposed method over other existing methods in many settings, with different levels of model misspecification.
Quantum computing offers significant speedup compared to classical computing, which has led to a growing interest among users in learning and applying quantum computing across various applications. However, quantum circuits, which are fundamental for implementing quantum algorithms, can be challenging for users to understand due to their underlying logic, such as the temporal evolution of quantum states and the effect of quantum amplitudes on the probability of basis quantum states. To fill this research gap, we propose QuantumEyes, an interactive visual analytics system to enhance the interpretability of quantum circuits through both global and local levels. For the global-level analysis, we present three coupled visualizations to delineate the changes of quantum states and the underlying reasons: a Probability Summary View to overview the probability evolution of quantum states; a State Evolution View to enable an in-depth analysis of the influence of quantum gates on the quantum states; a Gate Explanation View to show the individual qubit states and facilitate a better understanding of the effect of quantum gates. For the local-level analysis, we design a novel geometrical visualization Dandelion Chart to explicitly reveal how the quantum amplitudes affect the probability of the quantum state. We thoroughly evaluated QuantumEyes as well as the novel QuantumEyes integrated into it through two case studies on different types of quantum algorithms and in-depth expert interviews with 12 domain experts. The results demonstrate the effectiveness and usability of our approach in enhancing the interpretability of quantum circuits.
We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms a delta measure ({\it i.e.}, concentration) at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary problem for the compressible Navier-Stokes-Poisson equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at a certain time, it is proved that no delta measure ({\it i.e.}, concentration) in space-time is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration.
Satellite-based greenhouse gases (GHG) sensing technologies play a critical role in the study of global carbon emissions and climate change. However, none of the existing satellite-based GHG sensing technologies can achieve the measurement of broad bandwidth, high temporal-spatial resolution, and high sensitivity at the same time. Recently, dual-comb spectroscopy (DCS) has been proposed as a superior candidate technology for GHG sensing because it can measure broadband spectra with high temporal-spatial resolution and high sensitivity. The main barrier to DCS's display on satellites is its short measurement distance in open air achieved thus far. Prior research has not been able to implement DCS over 20 km of open-air path. Here, by developing a bistatic setup using time-frequency dissemination and high-power optical frequency combs, we have implemented DCS over a 113 km turbulent horizontal open-air path. Our experiment successfully measured GHG with 7 nm spectral bandwidth and a 10 kHz frequency and achieved a CO2 sensing precision of <2 ppm in 5 minutes and <0.6 ppm in 36 minutes. Our results represent a significant step towards advancing the implementation of DCS as a satellite-based technology and improving technologies for GHG monitoring
In this paper, we establish the proof of general Kastler-Kalau-Walze type theorems for conformal perturbations of dirac Operators on even dimensional compact manifolds with (respectively without) boundary.
In this paper, we define the spectral Einstein functional associated with the sub-signature operator for manifolds with boundary. Motivated by the spectral Einstein functional and the sub-signature operator, we relate them to the noncommutative residue for manifolds with boundary. And we give the proof of the Dabrowski-Sitarz-Zalecki type theorems for the spectral Einstein functional associated with the sub-signature operator on 4-dimensional manifolds with boundary.
For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale problems by reconstructing the loss function and associating it with special neural network architectures. New PINN methods derived from the improved PINN framework differ from the conventional PINN method mainly in two aspects. First, the new methods use a novel loss function by modifying the standard loss function through a (grouping) regularization strategy. The regularization strategy implements a different power operation on each loss term so that all loss terms composing the loss function are of approximately the same order of magnitude, which makes all loss terms be optimized synchronously during the optimization process. Second, for the multi-frequency or high-frequency problems, in addition to using the modified loss function, new methods upgrade the neural network architecture from the common fully-connected neural network to special network architectures such as the Fourier feature architecture, and the integrated architecture developed by us. The combination of the above two techniques leads to a significant improvement in the computational accuracy of multi-scale problems. Several challenging numerical examples demonstrate the effectiveness of the proposed methods. The proposed methods not only significantly outperform the conventional PINN method in terms of computational efficiency and computational accuracy, but also compare favorably with the state-of-the-art methods in the recent literature. The improved PINN framework facilitates better application of PINNs to multi-scale problems.
Taxi drivers often take much time to navigate the streets to look for passengers, which leads to high vacancy rates and wasted resources. Empty taxi cruising remains a big concern for taxi companies. Analyzing the pick-up point selection behavior can solve this problem effectively, providing suggestions for taxi management and dispatch. Many studies have been devoted to analyzing and recommending hot-spot regions of pick-up points, which can make it easier for drivers to pick up passengers. However, the selection of pick-up points is complex and affected by multiple factors, such as convenience and traffic management. Most existing approaches cannot produce satisfactory results in real-world applications because of the changing travel demands and the lack of interpretability. In this paper, we introduce a visual analytics system, T-PickSeer, for taxi company analysts to better explore and understand the pick-up point selection behavior of passengers. We explore massive taxi GPS data and employ an overview-to-detail approach to enable effective analysis of pick-up point selection. Our system provides coordinated views to compare different regularities and characteristics in different regions. Also, our system assists in identifying potential pick-up points and checking the performance of each pick-up point. Three case studies based on a real-world dataset and interviews with experts have demonstrated the effectiveness of our system.
Dynamic multi-objective optimisation (DMO) handles optimisation problems with multiple (often conflicting) objectives in varying environments. Such problems pose various challenges to evolutionary algorithms, which have popularly been used to solve complex optimisation problems, due to their dynamic nature and resource restrictions in changing environments. This paper proposes vector autoregressive evolution (VARE) consisting of vector autoregression (VAR) and environment-aware hypermutation to address environmental changes in DMO. VARE builds a VAR model that considers mutual relationship between decision variables to effectively predict the moving solutions in dynamic environments. Additionally, VARE introduces EAH to address the blindness of existing hypermutation strategies in increasing population diversity in dynamic scenarios where predictive approaches are unsuitable. A seamless integration of VAR and EAH in an environment-adaptive manner makes VARE effective to handle a wide range of dynamic environments and competitive with several popular DMO algorithms, as demonstrated in extensive experimental studies. Specially, the proposed algorithm is computationally 50 times faster than two widely-used algorithms (i.e., TrDMOEA and MOEA/D-SVR) while producing significantly better results.
Automated visualization recommendation facilitates the rapid creation of effective visualizations, which is especially beneficial for users with limited time and limited knowledge of data visualization. There is an increasing trend in leveraging machine learning (ML) techniques to achieve an end-to-end visualization recommendation. However, existing ML-based approaches implicitly assume that there is only one appropriate visualization for a specific dataset, which is often not true for real applications. Also, they often work like a black box, and are difficult for users to understand the reasons for recommending specific visualizations. To fill the research gap, we propose AdaVis, an adaptive and explainable approach to recommend one or multiple appropriate visualizations for a tabular dataset. It leverages a box embedding-based knowledge graph to well model the possible one-to-many mapping relations among different entities (i.e., data features, dataset columns, datasets, and visualization choices). The embeddings of the entities and relations can be learned from dataset-visualization pairs. Also, AdaVis incorporates the attention mechanism into the inference framework. Attention can indicate the relative importance of data features for a dataset and provide fine-grained explainability. Our extensive evaluations through quantitative metric evaluations, case studies, and user interviews demonstrate the effectiveness of AdaVis.
Data visualization is a powerful tool for exploring and communicating insights in various domains. To automate visualization choice for datasets, a task known as visualization recommendation has been proposed. Various machine-learning-based approaches have been developed for this purpose, but they often require a large corpus of dataset-visualization pairs for training and lack natural explanations for their results. To address this research gap, we propose LLM4Vis, a novel ChatGPT-based prompting approach to perform visualization recommendation and return human-like explanations using very few demonstration examples. Our approach involves feature description, demonstration example selection, explanation generation, demonstration example construction, and inference steps. To obtain demonstration examples with high-quality explanations, we propose a new explanation generation bootstrapping to iteratively refine generated explanations by considering the previous generation and template-based hint. Evaluations on the VizML dataset show that LLM4Vis outperforms or performs similarly to supervised learning models like Random Forest, Decision Tree, and MLP in both few-shot and zero-shot settings. The qualitative evaluation also shows the effectiveness of explanations generated by LLM4Vis. We make our code publicly available at \href{https://github.com/demoleiwang/LLM4Vis}{https://github.com/demoleiwang/LLM4Vis}.
In this paper, we give the proof of the general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem on odd dimensional compact manifolds with boundary.
In [5], [6] and [8], the authors gave some modular forms over $Γ^0(2)$. In this note, we proceed with the study of cancellation formulas relating to the modular forms.
Designers need to consider not only perceptual effectiveness but also visual styles when creating an infographic. This process can be difficult and time consuming for professional designers, not to mention non-expert users, leading to the demand for automated infographics design. As a first step, we focus on timeline infographics, which have been widely used for centuries. We contribute an end-to-end approach that automatically extracts an extensible timeline template from a bitmap image. Our approach adopts a deconstruction and reconstruction paradigm. At the deconstruction stage, we propose a multi-task deep neural network that simultaneously parses two kinds of information from a bitmap timeline: 1) the global information, i.e., the representation, scale, layout, and orientation of the timeline, and 2) the local information, i.e., the location, category, and pixels of each visual element on the timeline. At the reconstruction stage, we propose a pipeline with three techniques, i.e., Non-Maximum Merging, Redundancy Recover, and DL GrabCut, to extract an extensible template from the infographic, by utilizing the deconstruction results. To evaluate the effectiveness of our approach, we synthesize a timeline dataset (4296 images) and collect a real-world timeline dataset (393 images) from the Internet. We first report quantitative evaluation results of our approach over the two datasets. Then, we present examples of automatically extracted templates and timelines automatically generated based on these templates to qualitatively demonstrate the performance. The results confirm that our approach can effectively extract extensible templates from real-world timeline infographics.
By some SL(2, Z) modular forms introduced in [4] and [9], we construct some Γ^0(2) and Γ_0(2) modular forms and obtain some new cancellation formulas for spin manifolds and spin^c manifolds respectively. As corollaries, we get some divisibility results of index of twisted Dirac operators on spin manifolds and spin^c manifolds .