arXiv subjects

Tao Zhang

Publications and source records attributed to Tao Zhang.

At least 541 records · Page 30Linked to original sources

arXiv2021

Some extremal results on hypergraph Turán problems

For two $r$-graphs $\mathcal{T}$ and $\mathcal{H}$, let $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ be the maximum number of copies of $\mathcal{T}$ in an $n$-vertex $\mathcal{H}$-free $r$-graph. The determination of Turán number $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ has become the fundamental core problem in extremal graph theory ever since the pioneering work Turán's Theorem was published in $1941$. Although we have some rich results for the simple graph case, only sporadic results have been known for the hypergraph Turán problems. In this paper, we mainly focus on the function $\text{ex}_{r}(n,\mathcal{T},\mathcal{H})$ when $\mathcal{H}$ is one of two different hypergraph extensions of the complete bipartite graph $K_{s,t}$. The first extension is the complete bipartite $r$-graph $K_{s,t}^{(r)}$, which was introduced by Mubayi and Verstraëte~[J. Combin. Theory Ser. A, 106: 237--253, 2004]. Using the powerful random algebraic method, we show that if $s$ is sufficiently larger than $t$, then \[\text{ex}_{r}(n,\mathcal{T},K_{s,t}^{(r)})=Ω(n^{v-\frac{e}{t}}),\] where $\mathcal{T}$ is an $r$-graph with $v$ vertices and $e$ edges. In particular, when $\mathcal{T}$ is an edge or some specified complete bipartite $r$-graph, we can determine their asymptotics. The second important extension is the complete $r$-partite $r$-graph $K_{s_{1},s_{2},\ldots,s_{r}}^{(r)}$, which has been widely studied. When $r=3$, we provide an explicit construction giving \[\text{ex}_{3}(n,K_{2,2,7}^{(3)})\geqslant\frac{1}{27}n^{\frac{19}{7}}+o(n^{\frac{19}{7}}).\] Our construction is based on the Norm graph, and improves the lower bound $Ω(n^{\frac{73}{27}})$ obtained by probabilistic method.

math.CO↗

arXiv2021

An Efficient Calibration Method for Triaxial Gyroscope

This paper presents an efficient servomotor-aided calibration method for the triaxial gyroscope. The entire calibration process only requires approximately one minute, and does not require high-precision equipment. This method is based on the idea that the measurement of the gyroscope should be equal to the rotation speed of the servomotor. A six-observation experimental design is proposed to minimize the maximum variance of the estimated scale factors and biases. In addition, a fast converging recursive linear least square estimation method is presented to reduce computational complexity. The simulation results reflect the robustness of the calibration method under normal and extreme conditions. We experimentally demonstrate the feasibility of the proposed method on a robot arm, and implement the method on a microcontroller. We verify the calibration results of the proposed method by comparing with a traditional turntable approach, and the experiment indicates that the results of these two methods are comparable. By comparing the calibrated low-cost gyroscope reading with the reading from a high-precision gyroscope, we can conclude that our method significantly increases the gyroscope's accuracy.

cs.RO↗

arXiv2021

Evolving Metric Learning for Incremental and Decremental Features

Online metric learning has been widely exploited for large-scale data classification due to the low computational cost. However, amongst online practical scenarios where the features are evolving (e.g., some features are vanished and some new features are augmented), most metric learning models cannot be successfully applied to these scenarios, although they can tackle the evolving instances efficiently. To address the challenge, we develop a new online Evolving Metric Learning (EML) model for incremental and decremental features, which can handle the instance and feature evolutions simultaneously by incorporating with a smoothed Wasserstein metric distance. Specifically, our model contains two essential stages: a Transforming stage (T-stage) and a Inheriting stage (I-stage). For the T-stage, we propose to extract important information from vanished features while neglecting non-informative knowledge, and forward it into survived features by transforming them into a low-rank discriminative metric space. It further explores the intrinsic low-rank structure of heterogeneous samples to reduce the computation and memory burden especially for highly-dimensional large-scale data. For the I-stage, we inherit the metric performance of survived features from the T-stage and then expand to include the new augmented features. Moreover, a smoothed Wasserstein distance is utilized to characterize the similarity relationships among the heterogeneous and complex samples, since the evolving features are not strictly aligned in the different stages. In addition to tackling the challenges in one-shot case, we also extend our model into multishot scenario. After deriving an efficient optimization strategy for both T-stage and I-stage, extensive experiments on several datasets verify the superior performance of our EML model.

cs.LG↗

arXiv2021

NTIRE 2021 Challenge on Perceptual Image Quality Assessment

This paper reports on the NTIRE 2021 challenge on perceptual image quality assessment (IQA), held in conjunction with the New Trends in Image Restoration and Enhancement workshop (NTIRE) workshop at CVPR 2021. As a new type of image processing technology, perceptual image processing algorithms based on Generative Adversarial Networks (GAN) have produced images with more realistic textures. These output images have completely different characteristics from traditional distortions, thus pose a new challenge for IQA methods to evaluate their visual quality. In comparison with previous IQA challenges, the training and testing datasets in this challenge include the outputs of perceptual image processing algorithms and the corresponding subjective scores. Thus they can be used to develop and evaluate IQA methods on GAN-based distortions. The challenge has 270 registered participants in total. In the final testing stage, 13 participating teams submitted their models and fact sheets. Almost all of them have achieved much better results than existing IQA methods, while the winning method can demonstrate state-of-the-art performance.

eess.IV↗

arXiv2021

The Automatic Calibration Unit in JUNO

This paper describes the design and construction of the automatic calibration unit (ACU) for the JUNO experiment. The ACU is a fully automated mechanical system. It is capable of deploying multiple radioactive sources, an ultraviolet (UV) laser source, or an auxiliary sensor such as a temperature sensor, one at a time, into the central detector of JUNO along the central axis. It is designed as a primary tool to precisely calibrate the energy scale of detector, aligning timing for the photosensors, and partially monitoring the position-dependent energy scale variations.

physics.ins-det↗

arXiv2021

Informational Design of Dynamic Multi-Agent System

This work considers a novel information design problem and studies how the craft of payoff-relevant environmental signals solely can influence the behaviors of intelligent agents. The agents' strategic interactions are captured by a Markov game, in which each agent first selects one external signal from multiple signal sources as additional payoff-relevant information and then takes an action. There is a rational information designer (principal) who possesses one signal source and aims to influence the equilibrium behaviors of the agents by designing the information structure of her signals sent to the agents. We propose a direct information design approach that incentivizes each agent to select the signal sent by the principal, such that the design process avoids the predictions of the agents' strategic selection behaviors. We then introduce the design protocol given a goal of the designer which we refer to as obedient implementability (OIL) and characterize the OIL in a class of obedient sequential Markov perfect equilibria (O-SMPE). A design regime is proposed based on an approach which we refer to as the fixed-point alignment that incentivizes the agents to choose the signal sent by the principal, guarantees that the agents' policy profile of taking actions is the policy component of an O-SMPE and the principal's goal is achieved. We then formulate the principal's optimal goal selection problem in terms of information design and characterize the optimization problem by minimizing the fixed-point misalignments. The proposed approach can be applied to elicit desired behaviors of multi-agent systems in competing as well as cooperating settings and be extended to heterogeneous stochastic games in the complete- and the incomplete-information environments.

cs.MA↗

arXiv2021

Distributed Optimization with Global Constraints Using Noisy Measurements

We propose a new distributed optimization algorithm for solving a class of constrained optimization problems in which (a) the objective function is separable (i.e., the sum of local objective functions of agents), (b) the optimization variables of distributed agents, which are subject to nontrivial local constraints, are coupled by global constraints, and (c) only noisy observations are available to estimate (the gradients of) local objective functions. In many practical scenarios, agents may not be willing to share their optimization variables with others. For this reason, we propose a distributed algorithm that does not require the agents to share their optimization variables with each other; instead, each agent maintains a local estimate of the global constraint functions and share the estimate only with its neighbors. These local estimates of constraint functions are updated using a consensus-type algorithm, while the local optimization variables of each agent are updated using a first-order method based on noisy estimates of gradient. We prove that, when the agents adopt the proposed algorithm, their optimization variables converge with probability 1 to an optimal point of an approximated problem based on the penalty method.

math.OC↗

arXiv2021

Zinbiel 2-algebras

The notions of Zinbiel 2-algebras and 2-term $Z_{\infty}$-algebras are introduced. It is proved that the category of Zinbiel 2-algebras and the category of $2$-term $Z_{\infty}$-algebras are equivalent to each other. Crossed module extensions of Zinbiel algebras are studied. Relationship between Zinbiel 2-algebras and dendriform 2-algebras are found.

math.RA↗

arXiv2021

SWFC-ART: A Cost-effective Approach for Fixed-Size-Candidate-Set Adaptive Random Testing through Small World Graphs

Adaptive random testing (ART) improves the failure-detection effectiveness of random testing by leveraging properties of the clustering of failure-causing inputs of most faulty programs: ART uses a sampling mechanism that evenly spreads test cases within a software's input domain. The widely-used Fixed-Sized-Candidate-Set ART (FSCS-ART) sampling strategy faces a quadratic time cost, which worsens as the dimensionality of the software input domain increases. In this paper, we propose an approach based on small world graphs that can enhance the computational efficiency of FSCS-ART: SWFC-ART. To efficiently perform nearest neighbor queries for candidate test cases, SWFC-ART incrementally constructs a hierarchical navigable small world graph for previously executed, non-failure-causing test cases. Moreover, SWFC-ART has shown consistency in programs with high dimensional input domains. Our simulation and empirical studies show that SWFC-ART reduces the computational overhead of FSCS-ART from quadratic to log-linear order while maintaining the failure-detection effectiveness of FSCS-ART, and remaining consistent in high dimensional input domains. We recommend using SWFC-ART in practical software testing scenarios, where real-life programs often have high dimensional input domains and low failure rates.

cs.SE↗

arXiv2021

On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment

This paper studies dynamic mechanism design in a quasilinear Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent's private information, referred to as state, evolves over time. The agent makes decisions of whether to stop or continue and what to report at each period. The principal, on the other hand, chooses decision rules consisting of an allocation rule and a set of payment rules to maximize her ex-ante expected payoff. In order to influence the agent's stopping decision, one of the terminal payment rules is posted-price, i.e., it depends only on the realized stopping time of the agent. We define the incentive compatibility in this dynamic environment in terms of Bellman equations, which is then simplified by establishing a one-shot deviation principle. Given the optimality of the stopping rule, a sufficient condition for incentive compatibility is obtained by constructing the state-dependent payment rules in terms of a set of functions parameterized by the allocation rule. A necessary condition is derived from envelope theorem, which explicitly formulates the state-dependent payment rules in terms of allocation rules. A class of monotone environment is considered to characterize the optimal stopping by a threshold rule. The posted-price payment rules are then pinned down in terms of the allocation rule and the threshold function up to a constant. The incentive compatibility constraints restrict the design of the posted-price payment rule by a regular condition.

math.DS↗

arXiv2021

Search for Light Dark Matter-Electron Scatterings in the PandaX-II Experiment

We report constraints on light dark matter through its interactions with shell electrons in the PandaX-II liquid xenon detector with a total 46.9 tonne$\cdot$day exposure. To effectively search for these very low energy electron recoils, ionization-only signals are selected from the data. 1821 candidates are identified within ionization signal range between 50 to 75 photoelectrons, corresponding to a mean electronic recoil energy from 0.08 to 0.15 keV. The 90% C.L. exclusion limit on the scattering cross section between the dark matter and electron is calculated based on Poisson statistics. Under the assumption of point interaction, we provide the world's most stringent limit within the dark matter mass range from 15 to 30 $\rm MeV/c^2$, with the corresponding cross section from $2.5\times10^{-37}$ to $3.1\times10^{-38}$ cm$^2$.

hep-ex↗

arXiv2021

FC$^2$N: Fully Channel-Concatenated Network for Single Image Super-Resolution

Most current image super-resolution (SR) methods based on convolutional neural networks (CNNs) use residual learning in network structural design, which favors to effective back propagation and hence improves SR performance by increasing model scale. However, residual networks suffer from representational redundancy by introducing identity paths that impede the full exploitation of model capacity. Besides, blindly enlarging network scale can cause more problems in model training, even with residual learning. In this paper, a novel fully channel-concatenated network (FC$^2$N) is presented to make further mining of representational capacity of deep models, in which all interlayer skips are implemented by a simple and straightforward operation, i.e., weighted channel concatenation (WCC), followed by a 1$\times$1 conv layer. Based on the WCC, the model can achieve the joint attention mechanism of linear and nonlinear features in the network, and presents better performance than other state-of-the-art SR models with fewer model parameters. To our best knowledge, FC$^2$N is the first CNN model that does not use residual learning and reaches network depth over 400 layers. Moreover, it shows excellent performance in both largescale and lightweight implementations, which illustrates the full exploitation of the representational capacity of the model.

eess.IV↗

arXiv2021

Low Pass Filter for Anti-aliasing in Temporal Action Localization

In temporal action localization methods, temporal downsampling operations are widely used to extract proposal features, but they often lead to the aliasing problem, due to lacking consideration of sampling rates. This paper aims to verify the existence of aliasing in TAL methods and investigate utilizing low pass filters to solve this problem by inhibiting the high-frequency band. However, the high-frequency band usually contains large amounts of specific information, which is important for model inference. Therefore, it is necessary to make a tradeoff between anti-aliasing and reserving high-frequency information. To acquire optimal performance, this paper learns different cutoff frequencies for different instances dynamically. This design can be plugged into most existing temporal modeling programs requiring only one additional cutoff frequency parameter. Integrating low pass filters to the downsampling operations significantly improves the detection performance and achieves comparable results on THUMOS'14, ActivityNet~1.3, and Charades datasets. Experiments demonstrate that anti-aliasing with low pass filters in TAL is advantageous and efficient.

cs.CV↗

arXiv2021

Bootstrap inference for quantile-based modal regression

In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap methods for the conditional mode. We also extend the preceding analysis to the case where the dimension of the covariate vector is increasing with the sample size. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method.

math.ST↗

arXiv2021

Towards Evaluating the Robustness of Deep Diagnostic Models by Adversarial Attack

Deep learning models (with neural networks) have been widely used in challenging tasks such as computer-aided disease diagnosis based on medical images. Recent studies have shown deep diagnostic models may not be robust in the inference process and may pose severe security concerns in clinical practice. Among all the factors that make the model not robust, the most serious one is adversarial examples. The so-called "adversarial example" is a well-designed perturbation that is not easily perceived by humans but results in a false output of deep diagnostic models with high confidence. In this paper, we evaluate the robustness of deep diagnostic models by adversarial attack. Specifically, we have performed two types of adversarial attacks to three deep diagnostic models in both single-label and multi-label classification tasks, and found that these models are not reliable when attacked by adversarial example. We have further explored how adversarial examples attack the models, by analyzing their quantitative classification results, intermediate features, discriminability of features and correlation of estimated labels for both original/clean images and those adversarial ones. We have also designed two new defense methods to handle adversarial examples in deep diagnostic models, i.e., Multi-Perturbations Adversarial Training (MPAdvT) and Misclassification-Aware Adversarial Training (MAAdvT). The experimental results have shown that the use of defense methods can significantly improve the robustness of deep diagnostic models against adversarial attacks.

cs.CV↗

arXiv2021

Universal central extensions of Hom-Lie antialgebras

We develop a theory of universal central extensions for Hom-Lie antialgebra. It is proved that a Hom-Lie antialgebra admits a universal central extension if and only if it is perfect. Moreover, we show that the kernel of the universal central extension is equal to the second homology group with trivial coefficients.

math.RA↗

arXiv2021

GnetDet: Object Detection Optimized on a 224mW CNN Accelerator Chip at the Speed of 106FPS

Object detection is widely used on embedded devices. With the wide availability of CNN (Convolutional Neural Networks) accelerator chips, the object detection applications are expected to run with low power consumption, and high inference speed. In addition, the CPU load is expected to be as low as possible for a CNN accelerator chip working as a co-processor with a host CPU. In this paper, we optimize the object detection model on the CNN accelerator chip by minimizing the CPU load. The resulting model is called GnetDet. The experimental result shows that the GnetDet model running on a 224mW chip achieves the speed of 106FPS with excellent accuracy.

cs.AR↗

arXiv2021

Crossed modules for Hom-Lie antialgebras

In this paper, we introduced the concept of crossed module for Hom-Lie antialgebras. It is proved that the category of crossed modules for Hom-Lie antialgebras and the category of $Cat^1$-Hom-Lie antialgebras are equivalent to each other. The relationship between the crossed module extension of Hom-Lie antialgebras and the third cohomology group are investigated.

math.RA↗