Search Results for author: Yi Liu

Found 79 papers, 16 papers with code

Evolutionary Action Selection for Gradient-based Policy Learning

no code implementations12 Jan 2022 Yan Ma, Tianxing Liu, Bingsheng Wei, Yi Liu, Kang Xu, Wei Li

To better integrate these two approaches and avoid the drawbacks caused by the introduction of EA, we devote ourselves to devising a more efficient and reasonable method of combining EA and DRL.

Continuous Control

FamilySeer: Towards Optimized Tensor Codes by Exploiting Computation Subgraph Similarity

no code implementations1 Jan 2022 Shanjun Zhang, Mingzhen Li, Hailong Yang, Yi Liu, Zhongzhi Luan, Depei Qian

Currently, the DL compilers partition the input DL models into several subgraphs and leverage the auto-tuning to find the optimal tensor codes of these subgraphs.

PP-HumanSeg: Connectivity-Aware Portrait Segmentation with a Large-Scale Teleconferencing Video Dataset

1 code implementation14 Dec 2021 Lutao Chu, Yi Liu, Zewu Wu, Shiyu Tang, Guowei Chen, Yuying Hao, Juncai Peng, Zhiliang Yu, Zeyu Chen, Baohua Lai, Haoyi Xiong

This work is the first to construct a large-scale video portrait dataset that contains 291 videos from 23 conference scenes with 14K fine-labeled frames and extensions to multi-camera teleconferencing.

Portrait Segmentation Semantic Segmentation

Direct Training via Backpropagation for Ultra-low Latency Spiking Neural Networks with Multi-threshold

no code implementations25 Nov 2021 Changqing Xu, Yi Liu, YinTang Yang

In our proposed training method, we proposed three approximated derivative for spike activity to solve the problem of the non-differentiable issue which cause difficulties for direct training SNNs based on BP.

Damped Anderson Mixing for Deep Reinforcement Learning: Acceleration, Convergence, and Stabilization

no code implementations NeurIPS 2021 Ke Sun, Yafei Wang, Yi Liu, Yingnan Zhao, Bo Pan, Shangling Jui, Bei Jiang, Linglong Kong

Anderson mixing has been heuristically applied to reinforcement learning (RL) algorithms for accelerating convergence and improving the sampling efficiency of deep RL.

Locally Adaptive Structure and Texture Similarity for Image Quality Assessment

no code implementations16 Oct 2021 Keyan Ding, Yi Liu, Xueyi Zou, Shiqi Wang, Kede Ma

The latest advances in full-reference image quality assessment (IQA) involve unifying structure and texture similarity based on deep representations.

Image Quality Assessment Image Super-Resolution

Resource-constrained Federated Edge Learning with Heterogeneous Data: Formulation and Analysis

no code implementations14 Oct 2021 Yi Liu, Yuanshao Zhu, James J. Q. Yu

Similarly, due to the heterogeneity of the connected remote devices, FEEL faces the challenge of heterogeneous data and non-IID (Independent and Identically Distributed) data.

Ensemble Learning Multi-class Classification

Dyn-Backdoor: Backdoor Attack on Dynamic Link Prediction

no code implementations8 Oct 2021 Jinyin Chen, Haiyang Xiong, Haibin Zheng, Jian Zhang, Guodong Jiang, Yi Liu

Backdoor attacks induce the DLP methods to make wrong prediction by the malicious training data, i. e., generating a subgraph sequence as the trigger and embedding it to the training data.

Dynamic Link Prediction

Towards Understanding Distributional Reinforcement Learning: Regularization, Optimization, Acceleration and Sinkhorn Algorithm

no code implementations7 Oct 2021 Ke Sun, Yingnan Zhao, Yi Liu, Enze Shi, Yafei Wang, Aref Sadeghi, Xiaodong Yan, Bei Jiang, Linglong Kong

Distributional reinforcement learning~(RL) is a class of state-of-the-art algorithms that estimate the whole distribution of the total return rather than only its expectation.

Atari Games Distributional Reinforcement Learning

BioCopy: A Plug-And-Play Span Copy Mechanism in Seq2Seq Models

no code implementations EMNLP (sustainlp) 2021 Yi Liu, Guoan Zhang, Puning Yu, Jianlin Su, Shengfeng Pan

Copy mechanisms explicitly obtain unchanged tokens from the source (input) sequence to generate the target (output) sequence under the neural seq2seq framework.

TAG

Exploring the Training Robustness of Distributional Reinforcement Learning against Noisy State Observations

no code implementations17 Sep 2021 Ke Sun, Yi Liu, Yingnan Zhao, Hengshuai Yao, Shangling Jui, Linglong Kong

In real scenarios, state observations that an agent observes may contain measurement errors or adversarial noises, misleading the agent to take suboptimal actions or even collapse while training.

Density Estimation Distributional Reinforcement Learning

BoA-PTA, A Bayesian Optimization Accelerated Error-Free SPICE Solver

no code implementations31 Jul 2021 Wei W. Xing, Xiang Jin, Yi Liu, Dan Niu, Weishen Zhao, Zhou Jin

One of the greatest challenges in IC design is the repeated executions of computationally expensive SPICE simulations, particularly when highly complex chip testing/verification is involved.

Variational Inference

Swap-Free Fat-Water Separation in Dixon MRI using Conditional Generative Adversarial Networks

no code implementations29 Jul 2021 Nicolas Basty, Marjola Thanaj, Madeleine Cule, Elena P. Sorokin, Yi Liu, Jimmy D. Bell, E. Louise Thomas, Brandon Whitcher

Using data from the UK Biobank Dixon MRI, our model is able to predict highly accurate fat and water channels that are free from artifacts.

Style Transfer

EGC2: Enhanced Graph Classification with Easy Graph Compression

no code implementations16 Jul 2021 Jinyin Chen, Dunjie Zhang, Zhaoyan Ming, Mingwei Jia, Yi Liu

To achieve lower complexity defense applied to various graph classification models, EGC$^2$ utilizes a centrality-based edge importance index to compress graphs, filtering out trivial structures and even adversarial perturbations of the input graphs, thus improves its robustness.

Graph Classification

Markov Decision Process modeled with Bandits for Sequential Decision Making in Linear-flow

no code implementations1 Jul 2021 Wenjun Zeng, Yi Liu

In membership/subscriber acquisition and retention, we sometimes need to recommend marketing content for multiple pages in sequence.

Decision Making Q-Learning

A Map of Bandits for E-commerce

no code implementations1 Jul 2021 Yi Liu, Lihong Li

The rich body of Bandit literature not only offers a diverse toolbox of algorithms, but also makes it hard for a practitioner to find the right solution to solve the problem at hand.

Mask-Embedded Discriminator With Region-Based Semantic Regularization for Semi-Supervised Class-Conditional Image Synthesis

no code implementations CVPR 2021 Yi Liu, Xiaoyang Huo, Tianyi Chen, Xiangping Zeng, Si Wu, Zhiwen Yu, Hau-San Wong

Semi-supervised generative learning (SSGL) makes use of unlabeled data to achieve a trade-off between the data collection/annotation effort and generation performance, when adequate labeled data are not available.

Image Generation

Optical Mouse: 3D Mouse Pose From Single-View Video

no code implementations17 Jun 2021 Bo Hu, Bryan Seybold, Shan Yang, David Ross, Avneesh Sud, Graham Ruby, Yi Liu

We present a method to infer the 3D pose of mice, including the limbs and feet, from monocular videos.

FineAction: A Fine-Grained Video Dataset for Temporal Action Localization

no code implementations24 May 2021 Yi Liu, LiMin Wang, Xiao Ma, Yali Wang, Yu Qiao

Second, the coarse action classes often lead to the ambiguous annotations of temporal boundaries, which are inappropriate for temporal action localization.

Temporal Action Localization Temporal Localization +1

Machine Learning Regression based Single Event Transient Modeling Method for Circuit-Level Simulation

no code implementations22 May 2021 Changqing Xu, Yi Liu, XinFang Liao, JiaLiang Cheng, YinTang Yang

A multilayer feedfordward neural network is used to build the SET pulse current model by learning the data from TCAD simulation.

The ADENUIM Telescope- A new beam telescope for the DESY II Test Beam Facility

no code implementations22 Feb 2021 Yi Liu, Yao Teng, Chenfei Yang, Changqing Feng, Ingrid-Maria Gregor, Lennart Huth, Marcel Stanitzki

The coincident signal of all scintillators is used as trigger and then used as a trigger and distributed to the entire system, including all the telescope planes and any devices under test from test beam users.

Instrumentation and Detectors Instrumentation and Methods for Astrophysics High Energy Physics - Experiment

Spherical Message Passing for 3D Graph Networks

1 code implementation9 Feb 2021 Yi Liu, Limei Wang, Meng Liu, Xuan Zhang, Bora Oztekin, Shuiwang Ji

Thus, our SMP represents a complete and accurate architecture for learning from 3D graphs in the SCS.

Representation Learning

PaddleSeg: A High-Efficient Development Toolkit for Image Segmentation

1 code implementation15 Jan 2021 Yi Liu, Lutao Chu, Guowei Chen, Zewu Wu, Zeyu Chen, Baohua Lai, Yuying Hao

The toolkit aims to help both developers and researchers in the whole process of designing segmentation models, training models, optimizing performance and inference speed, and deploying models.

Autonomous Driving Human Part Segmentation +2

A Multi-Stage Attentive Transfer Learning Framework for Improving COVID-19 Diagnosis

no code implementations14 Jan 2021 Yi Liu, Shuiwang Ji

The method is then integrated to the last stage of the proposed transfer learning framework to reuse the complex patterns learned from the same CT images.

Computed Tomography (CT) COVID-19 Diagnosis +3

CleftNet: Augmented Deep Learning for Synaptic Cleft Detection from Brain Electron Microscopy

no code implementations12 Jan 2021 Yi Liu, Shuiwang Ji

The effectiveness of our methods is evaluated on both online and offline tasks.

Social Media, Content Moderation, and Technology

no code implementations12 Jan 2021 Yi Liu, Pinar Yildirim, Z. John Zhang

This means that platforms under different revenue models can have different incentives to improve their content moderation technology.

Semi-Supervised Single-Stage Controllable GANs for Conditional Fine-Grained Image Generation

no code implementations ICCV 2021 Tianyi Chen, Yi Liu, Yunfei Zhang, Si Wu, Yong Xu, Feng Liangbing, Hau San Wong

To ensure disentanglement among the variables, we maximize mutual information between the class-independent variable and synthesized images, map real images to the latent space of a generator to perform consistency regularization of cross-class attributes, and incorporate class semantic-based regularization into a discriminator's feature space.

Image Generation

RC-SSFL: Towards Robust and Communication-efficient Semi-supervised Federated Learning System

no code implementations8 Dec 2020 Yi Liu, Xingliang Yuan, Ruihui Zhao, Yifeng Zheng, Yefeng Zheng

Extensive case studies on two real-world datasets demonstrate that RC-SSFL can maintain the performance comparable to typical FL in the presence of poisoning attacks and reduce communication overhead by $2 \times \sim 4 \times $.

Federated Learning Quantization

Towards Communication-efficient and Attack-Resistant Federated Edge Learning for Industrial Internet of Things

no code implementations8 Dec 2020 Yi Liu, Ruihui Zhao, Jiawen Kang, Abdulsalam Yassine, Dusit Niyato, Jialiang Peng

Second, we propose an asynchronous local differential privacy mechanism, which improves communication efficiency and mitigates gradient leakage attacks by adding well-designed noise to the gradients of edge nodes.

Edge-computing

A Systematic Literature Review on Federated Learning: From A Model Quality Perspective

no code implementations1 Dec 2020 Yi Liu, Li Zhang, Ning Ge, Guanghao Li

In this process, the server uses an incentive mechanism to encourage clients to contribute high-quality and large-volume data to improve the global model.

Federated Learning

Topology-Aware Graph Pooling Networks

no code implementations19 Oct 2020 Hongyang Gao, Yi Liu, Shuiwang Ji

In addition, graph topology is incorporated in global voting to compute the importance score of each node globally in the entire graph.

Graph Classification

Large-Scale Analysis of Iliopsoas Muscle Volumes in the UK Biobank

1 code implementation12 Aug 2020 Julie Fitzpatrick, Nicolas Basty, Madeleine Cule, Yi Liu, Jimmy D. Bell, E. Louise Thomas, Brandon Whitcher

We also found that iliopsoas volume was significantly related to height, BMI and age, and that there was an acceleration in muscle volume decrease in men with age.

Scalable and Communication-efficient Decentralized Federated Edge Learning with Multi-blockchain Framework

no code implementations10 Aug 2020 Jiawen Kang, Zehui Xiong, Chunxiao Jiang, Yi Liu, Song Guo, Yang Zhang, Dusit Niyato, Cyril Leung, Chunyan Miao

This framework can achieve scalable and flexible decentralized FEL by individually manage local model updates or model sharing records for performance isolation.

Cryptography and Security

PR-NN: RNN-based Detection for Coded Partial-Response Channels

2 code implementations30 Jul 2020 Simeng Zheng, Yi Liu, Paul H. Siegel

In this paper, we investigate the use of recurrent neural network (RNN)-based detection of magnetic recording channels with inter-symbol interference (ISI).

Federated Learning in the Sky: Aerial-Ground Air Quality Sensing Framework with UAV Swarms

no code implementations23 Jul 2020 Yi Liu, Jiangtian Nie, Xuandi Li, Syed Hassan Ahmed, Wei Yang Bryan Lim, Chunyan Miao

To this end, this paper proposes a new federated learning-based aerial-ground air quality sensing framework for fine-grained 3D air quality monitoring and forecasting.

Federated Learning

Deep Anomaly Detection for Time-series Data in Industrial IoT: A Communication-Efficient On-device Federated Learning Approach

no code implementations19 Jul 2020 Yi Liu, Sahil Garg, Jiangtian Nie, Yang Zhang, Zehui Xiong, Jiawen Kang, M. Shamim Hossain

Third, to adapt the proposed framework to the timeliness of industrial anomaly detection, we propose a gradient compression mechanism based on Top-\textit{k} selection to improve communication efficiency.

Anomaly Detection Federated Learning +1

Deep Learning of High-Order Interactions for Protein Interface Prediction

no code implementations18 Jul 2020 Yi Liu, Hao Yuan, Lei Cai, Shuiwang Ji

However, these methods do not incorporate the important sequential information from amino acid chains and the high-order pairwise interactions.

Protein Interface Prediction

Image Processing and Quality Control for Abdominal Magnetic Resonance Imaging in the UK Biobank

2 code implementations2 Jul 2020 Nicolas Basty, Yi Liu, Madeleine Cule, E. Louise Thomas, Jimmy D. Bell, Brandon Whitcher

An end-to-end image analysis pipeline is presented for the abdominal MRI protocol used in the UK Biobank on the first 38, 971 participants.

Variable Selection via Thompson Sampling

no code implementations1 Jul 2020 Yi Liu, Veronika Rockova

Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning.

Interpretable Machine Learning Stochastic Optimization +1

Assessing the Impact of COVID-19 on the Objective and Analysis of Oncology Clinical Trials -- Application of the Estimand Framework

no code implementations8 Jun 2020 Evgeny Degtyarev, Kaspar Rufibach, Yue Shentu, Godwin Yung, Michelle Casey, Stefan Englert, Feng Liu, Yi Liu, Oliver Sailer, Jonathan Siegel, Steven Sun, Rui Tang, Jiangxiu Zhou

We identify key intercurrent events that may occur due to COVID-19 in oncology clinical trials with a focus on time-to-event endpoints and discuss considerations pertaining to the other estimand attributes introduced in the ICH E9 addendum.

Federated Learning for 6G Communications: Challenges, Methods, and Future Directions

no code implementations4 Jun 2020 Yi Liu, Xingliang Yuan, Zehui Xiong, Jiawen Kang, Xiaofei Wang, Dusit Niyato

As the 5G communication networks are being widely deployed worldwide, both industry and academia have started to move beyond 5G and explore 6G communications.

Federated Learning

Exemplar-based Generative Facial Editing

no code implementations31 May 2020 Jingtao Guo, Yi Liu, Zhenzhen Qian, Zuowei Zhou

Image synthesis has witnessed substantial progress due to the increasing power of generative model.

Image Generation

Activation functions are not needed: the ratio net

1 code implementation14 May 2020 Chi-Chun Zhou, Hai-Long Tu, Yue-Jie Hou, Zhen Ling, Yi Liu, Jian Hua

We compare the effectiveness and efficiency of the ratio net and that of the RBF and the MLP with various kinds of activation functions in the classification task on the mnist database of handwritten digits and the Internet Movie Database (IMDb) which is a binary sentiment analysis dataset.

General Classification Sentiment Analysis

A Secure Federated Learning Framework for 5G Networks

no code implementations12 May 2020 Yi Liu, Jialiang Peng, Jiawen Kang, Abdullah M. Iliyasu, Dusit Niyato, Ahmed A. Abd El-Latif

In this article, we propose a blockchain-based secure FL framework to create smart contracts and prevent malicious or unreliable participants from involving in FL.

Federated Learning

Privacy-preserving Traffic Flow Prediction: A Federated Learning Approach

no code implementations19 Mar 2020 Yi Liu, James J. Q. Yu, Jiawen Kang, Dusit Niyato, Shuyu Zhang

Through extensive case studies on a real-world dataset, it is shown that FedGRU's prediction accuracy is 90. 96% higher than the advanced deep learning models, which confirm that FedGRU can achieve accurate and timely traffic prediction without compromising the privacy and security of raw data.

Federated Learning Traffic Prediction

The Deep Learning Compiler: A Comprehensive Survey

1 code implementation6 Feb 2020 Mingzhen Li, Yi Liu, Xiaoyan Liu, Qingxiao Sun, Xin You, Hailong Yang, Zhongzhi Luan, Lin Gan, Guangwen Yang, Depei Qian

In this paper, we perform a comprehensive survey of existing DL compilers by dissecting the commonly adopted design in details, with emphasis on the DL oriented multi-level IRs, and frontend/backend optimizations.

MulGAN: Facial Attribute Editing by Exemplar

no code implementations28 Dec 2019 Jingtao Guo, Zhenzhen Qian, Zuowei Zhou, Yi Liu

These methods encode attribute-related information in images into the predefined region of the latent feature space by employing a pair of images with opposite attributes as input to train model, the face attribute transfer between the input image and the exemplar can be achieved by exchanging their attribute-related latent feature region.

THUEE system description for NIST 2019 SRE CTS Challenge

no code implementations25 Dec 2019 Yi Liu, Tianyu Liang, Can Xu, Xianwei Zhang, Xianhong Chen, Wei-Qiang Zhang, Liang He, Dandan song, Ruyun Li, Yangcheng Wu, Peng Ouyang, Shouyi Yin

This paper describes the systems submitted by the department of electronic engineering, institute of microelectronics of Tsinghua university and TsingMicro Co. Ltd. (THUEE) to the NIST 2019 speaker recognition evaluation CTS challenge.

Speaker Recognition

PPGAN: Privacy-preserving Generative Adversarial Network

no code implementations4 Oct 2019 Yi Liu, Jialiang Peng, James J. Q. Yu, Yi Wu

To address this issue, we propose a Privacy-preserving Generative Adversarial Network (PPGAN) model, in which we achieve differential privacy in GANs by adding well-designed noise to the gradient during the model learning procedure.

Employing Deep Part-Object Relationships for Salient Object Detection

1 code implementation ICCV 2019 Yi Liu, Qiang Zhang, Dingwen Zhang, Jungong Han

In the second step, we feed the primary capsules into two identical streams, within each of which low-level capsules (parts) will be assigned to their familiar high-level capsules (object) via a locally connected routing.

RGB Salient Object Detection Salient Object Detection

Building Change Detection for Remote Sensing Images Using a Dual Task Constrained Deep Siamese Convolutional Network Model

no code implementations17 Sep 2019 Yi Liu, Chao Pang, Zongqian Zhan, Xiaomeng Zhang, Xue Yang

In recent years, building change detection methods have made great progress by introducing deep learning, but they still suffer from the problem of the extracted features not being discriminative enough, resulting in incomplete regions and irregular boundaries.

Building change detection for remote sensing images Change Detection +2

Open DNN Box by Power Side-Channel Attack

no code implementations21 Jul 2019 Yun Xiang, Zhuangzhi Chen, Zuohui Chen, Zebin Fang, Haiyang Hao, Jinyin Chen, Yi Liu, Zhefu Wu, Qi Xuan, Xiaoniu Yang

However, recent studies indicate that they are also vulnerable to adversarial attacks.

Global Pixel Transformers for Virtual Staining of Microscopy Images

no code implementations1 Jul 2019 Yi Liu, Hao Yuan, Zhengyang Wang, Shuiwang Ji

It is also shown that our proposed global pixel transformer layer is useful to improve the fluorescence image prediction results.

MV-C3D: A Spatial Correlated Multi-View 3D Convolutional Neural Networks

no code implementations15 Jun 2019 Qi Xuan, Fuxian Li, Yi Liu, Yun Xiang

Experimental results on ModelNet10 and ModelNet40 datasets show that our MV-C3D technique can achieve outstanding performance with multi-view images which are captured from partial angles with less range.

3D Object Recognition

Normalization Gradients are Least-squares Residuals

no code implementations ICLR 2019 Yi Liu

Batch Normalization (BN) and its variants have seen widespread adoption in the deep learning community because they improve the training of deep neural networks.

Estimation of Inter-Sentiment Correlations Employing Deep Neural Network Models

no code implementations24 Nov 2018 Xinzhi Wang, Shengcheng Yuan, HUI ZHANG, Yi Liu

By contrast, in objective news bodies and titles, it is easy to regard text as caused love (gd).

DSNet: Deep and Shallow Feature Learning for Efficient Visual Tracking

no code implementations6 Nov 2018 Qiangqiang Wu, Yan Yan, Yanjie Liang, Yi Liu, Hanzi Wang

In recent years, Discriminative Correlation Filter (DCF) based tracking methods have achieved great success in visual tracking.

Image Classification Visual Tracking

An Efficient Bandit Algorithm for Realtime Multivariate Optimization

no code implementations22 Oct 2018 Daniel N. Hill, Houssam Nassif, Yi Liu, Anand Iyer, S. V. N. Vishwanathan

We further apply our algorithm to optimize a message that promotes adoption of an Amazon service.

Multi-glance Reading Model for Text Understanding

no code implementations WS 2018 Pengcheng Zhu, Yujiu Yang, Wenqiang Gao, Yi Liu

Based on the multi-glance mechanism, we design two types of recurrent neural network models for repeated reading: Glance Cell Model (GCM) and Glance Gate Model (GGM).

Document Classification Machine Translation +2

Multi-Modal Coreference Resolution with the Correlation between Space Structures

no code implementations21 Apr 2018 Qibin Zheng, Xingchun Diao, Jianjun Cao, Xiaolei Zhou, Yi Liu, Hongmei Li

In this paper, we bring a extrinsic correlation between the space structures of each modalities in coreference resolution.

Coreference Resolution

Comparison of Multiple Features and Modeling Methods for Text-dependent Speaker Verification

no code implementations14 Jul 2017 Yi Liu, Liang He, Yao Tian, Zhuzi Chen, Jia Liu, Michael T. Johnson

Additionally, we also find that even though bottleneck features perform well for text-independent speaker verification, they do not outperform MFCCs on the most challenging Imposter-Correct trials on RedDots.

Speaker Identification Speaker Recognition +2

Teaching Compositionality to CNNs

no code implementations CVPR 2017 Austin Stone, Huayan Wang, Michael Stark, Yi Liu, D. Scott Phoenix, Dileep George

Convolutional neural networks (CNNs) have shown great success in computer vision, approaching human-level performance when trained for specific tasks via application-specific loss functions.

Object Recognition

Sparse Representation based Multi-sensor Image Fusion: A Review

no code implementations12 Feb 2017 Qiang Zhang, Yi Liu, Rick S. Blum, Jungong Han, DaCheng Tao

As a result of several successful applications in computer vision and image processing, sparse representation (SR) has attracted significant attention in multi-sensor image fusion.

Dictionary Learning Infrared And Visible Image Fusion

A backward pass through a CNN using a generative model of its activations

no code implementations8 Nov 2016 Huayan Wang, Anna Chen, Yi Liu, Dileep George, D. Scott Phoenix

Neural networks have shown to be a practical way of building a very complex mapping between a pre-specified input space and output space.

Hierarchical compositional feature learning

no code implementations7 Nov 2016 Miguel Lázaro-Gredilla, Yi Liu, D. Scott Phoenix, Dileep George

We introduce the hierarchical compositional network (HCN), a directed generative model able to discover and disentangle, without supervision, the building blocks of a set of binary images.

Formula of Volume of Revolution with Integration by Parts and Extension

no code implementations4 Sep 2016 Yi Liu, Jingwei Liu

A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly monotone and differential function.

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