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Derivatives of Intersection Local Time for Two Independent Symmetricα-stable Processes

Acta Mathematica Sinica,English Series 2024年第5期40卷 1273-1292页

作者： Huan ZHOU Guang Jun SHEN Qian YU Department of Mathematics Anhui Normal UniversityWuhu 241002P.R.China Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106P.R.China

In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder *** we show that this condition is also necessary for the existence of derivatives of intersection local time at the ***,we also study the power variation of the derivatives.

关键词： Symmetric stable processes intersection local time exponential integrability power variation

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AN INDEFINITE-PROXIMAL-BASED STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD

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Journal of Computational Mathematics 2023年第6期41卷 1017-1040页

作者： Yan Gu Bo Jiang Deren Han Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing210016China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing210016China School of Mathematical Sciences Key Laboratory for NSLSCS of Jiangsu ProvinceNanjing Normal UniversityNanjing210023China LMIB School of Mathematics and Systems ScienceBeihang UniversityBeijing100191China Key Laboratory for NSLSCS of Jiangsu Province China

The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear ***,its convergence was not guaranteed without extra *** et al.(SIAM ***.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation *** this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation ***,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting *** show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic *** numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.

关键词： Indefinite proximal Strictly contractive Peaceman-Rachford splitting method Convex minimization Convergence rate

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Turán Numbers of Expanded Intersecting Cliques in 3-graphs

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Journal of the Operations Research Society of China 2024年第4期12卷 952-964页

作者： Yu-Cong Tang Tong Li Gui-Ying Yan School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing211106JiangsuChina Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) Ministry of Industry and Information TechnologyNanjing211106JiangsuChina School of Mathematical Sciences Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China University of Chinese Academy of Sciences Beijing100049China

Let l>r≥*** a 2-graph F,the expansion E^((r))of F is an r-graph obtained from F by adding r-2 new vertices into each *** F is a clique of order l,the Turán number ex(n,F^((r)))was first asymptotically determined by Mubayi(J Comb Theory Ser B 96:122–134,2006)and exactly computed by Pikhurko(J Comb Theory Ser B 103:220–225,2013).Let F_(k,l)be the 2-graph on(l-1)k+1 vertices consisting of k cliques of order l intersecting at exactly one *** determine the exact Turán number ex(n,F_(k,l)^((3)))for all l>3,k≥1,and sufficiently large n,as well as the corresponding extremal graphs.

关键词： Expansion Turán number 3-Graph Intersecting cliques Stability

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MGLGANï1/4ša generative adversarial model based on multi-layer graph convolution net and recurrent neural networks for link prediction

MGLGANï1/4ša generative adversarial model based on multi-l...

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2022 International Conference on Electronic Information Engineering, Big Data, and Computer technology, EIBDCT 2022

作者： Song, Jiantong Xiao, Xiaoqiang Ning, Weixun Zhang, Xu State Key Laboratory of High Performance Computing HuNan ChangSha China Computer School National University of Defense Technology HuNan ChangSha China

ISBN: (纸本)9781510655133

Link prediction is a technology to find existing but unobserved links (static) or predict new links (dynamic) by studying the network topology. In real life, most networks change with time. Some recent works focus on the dynamic prediction of networks, but they do not solve the weight problem in link prediction well. At the same time, the methods based on matrix decomposition and node embedding used in most link prediction tasks have some problems, such as huge amount of calculation or can't better represent the time evolution. In this paper, we extend the method of predicting the weight between nodes in dynamic networks and propose a generative adversarial model based on multi-layer graph convolution and recurrent neural network. The model consists of a generator and discriminator trained during an adversarial process. Multi-layer graph convolution used to approximate the high order similarity of network graph, so as to compensate the time evolution characteristic that RNN network can only deal with low order similarity. Using the process of confrontation training, the model can learn the representation of robust time evolution and predict with high accuracy. Experiments on several real data sets show that our model has good adaptability better than several baseline models. © 2022 SPIE.

关键词： Generative adversarial networks

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Research on internal surface finishing of multi-cro b channels 1

Research on internal surface finishing of multi-cro b channe...

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1st International Conference on Digital Sovereignty, ICDS 2024

作者： Guo, Jiang Li, Qikai Wang, Liang Qin, Pu Lu, Mingyang Wang, Chao State Key Laboratory of High-performance Precision Manufacturing Dalian University of Technology Dalian116024 China Institute of Machinery Manufacturing Technology China Academy of Engineering Physics Mianyang Sichuan621900 China

The quality of the internal surface plays a crucial role in the performance of parts with complex structures, which are widely used in aerospace, biomedical, and other fields. However, due to poor acce bibility, the uniformity of the internal surface of multi-cro b channels are low after finishing with existing methods. To addre b this i bue, this paper proposes a step-by-step abrasive flow machining method according to the characteristics of multi-cro b channel structures. By flexibly setting the positions of inlets and outlets and adjusting finishing parameters in each step, the material removal rate in different sections of the multi-cro b channels can be regulated. Guided by simulation results, the material removal rate in each section becomes consistent after succe bive steps, achieving uniform finishing of the entire channel. To verify this method, a separatable stainle b-steel part with six cro bed channels was finished under an inlet pre bure of 10 MPa for 40 minutes by using SiC abrasive with a size of 75 μm. The internal surface roughne b of the workpiece was reduced from 1.919 μm to le b than 1 μm, with variation in each section controlled to le b than 12%. © 2025 The Author(s).

关键词： Abrasive cutting

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TDLP: Time decay based link prediction method for dynamic networks

TDLP: Time decay based link prediction method for dynamic ne...

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2022 International Conference on Electronic Information Engineering, Big Data, and Computer technology, EIBDCT 2022

作者： Zhang, Xu Xiao, Xiaoqiang Ning, Weixun Song, Jiantong State Key Laboratory of High Performance Computing HuNan ChangSha China Computer School National University of Defense Technology HuNan ChangSha China

ISBN: (纸本)9781510655133

Link prediction aims to find the missing link in current networks or estimate the likelihood the link will appear in the future. In many real-world scenarios, networks can be massive and drastically evolving. Many recent works concentrated on how to solve the procession of massive data, which cares less about the effects of the temporal information. In some dynamic networks, the edge that appears a long time ago will have fewer effects on the appearance of edges in the future. The accuracy of link prediction in dynamic networks can be further improved by adding temporal information in prediction measures. In this paper, we mainly explore the effects of the link temporal information in the graph stream link prediction. We design a graph stream-based framework to solve link prediction problems in dynamic networks which can provide a convenient platform to implement different link prediction methods for dynamic networks, and evaluate these methods on a fair basis. Then, we proposed the Time Decay-based Link Prediction (TDLP) method to improve the efficient of link prediction problem in the dynamic networks. TDLP extends the neighborhood-based measure with time decay functions in graph stream scenarios which can handle temporal information and massive data. Experiment results demonstrate that the accuracy of link prediction for dynamic networks can be efficiently improved in our TDLP method. © 2022 SPIE.

关键词： Metadata

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high-frequency Voltage Signal Fault Diagnosis Based on Multi-channel Hierarchical Structure Capsule-Attention Network 8

High-frequency Voltage Signal Fault Diagnosis Based on Multi...

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8th International Conference on Big Data and Information Analytics, BigDIA 2022

作者： Miao, Qiucheng Xu, Chuanfu Zhan, Jun Zhu, Dong Wu, Chengkun Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Hunan Changsha China

ISBN: (数字)9781665487962

ISBN: (纸本)9781665487962

An important research area for covered conductors is partial discharge detection. However, the complex distribution of high-frequency signals with particular noise and the long tail problem create a considerable obstacle to accurate detection. This paper proposes a Capsule-Attention model with a Multi-channel Hierarchical structure, which separately utilize ResNet and BiGRU to extract short- and long-term high-frequency and pre-filter existing irrelevant information. The capsule layer is good at multidimensional and spatial information representation, and we utilize it to recognize and classify fault conditions. The attention mechanism's weight distribution quantifies the importance of features in the entire signal. Considering the class imbalance of the long-tail distribution of samples, We propose a Focal-MCC (FMCC) loss function. The proposed loss reshapes the typical cross-entropy loss, hence reducing the weights allocated to well-classified instances. Matthews Correlation Coefficient penalizes false positives/false negatives to prevent parameters from falling into local minimums. The experiments indicate that the model proposed is useful in detecting partial discharge faults and has application value. The code is available at https://***/qiumia030/capsule_attention. © 2022 IEEE.

关键词： Failure analysis

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hcaPCG: A Heterogeneous and communication-avoid PCG with Jacobi preconditioner on SW26010-Pro architecture 29

hcaPCG: A Heterogeneous and communication-avoid PCG with Jac...

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29th IEEE International Conference on Parallel and Distributed Systems, ICPADS 2023

作者： Tian, Min Liu, Yue Wang, Li Chen, Yanyan Liu, Qi Pan, Jingshan Qilu University of Technology Shandong Academy of Sciences Key Laboratory of Computing Power Network and Information Security Ministry of Education Shandong Computer Science Center National Supercomputer Center in Jinan China Shandong Fundamental Research Center for Computer Science Shandong Provincial Key Laboratory of Computer Networks China Jinan Institute of Supercomputing Technology Jinan Key Laboratory of High Performance Computing China

ISBN: (纸本)9798350330717

Due to its efficiency and versatility, the preconditioned conjugate gradient algorithm has long been a staple in the realm of iterative linear system solvers. In this paper, we proposed an optimized preconditioned conjugate gradient algorithm tailored for the SW26010-Pro manycore processor, The main work includes: Optimizing data block sizes based on the processor's storage structure;combining thread-level and data-level parallelism, utilizing manual SIMD to improve efficiency;optimizing the memory access pattern by employing direct memory access and overlapping of computation and communication;employing a shared-memory approach to store long vectors across all cores. Furthermore, we design an accelerated algorithm for reduction operations, to avoid data communication. Experimental results show that the hcaPCG yields up to 28.1× speedups on average compared to the original implementation. © 2023 IEEE.

关键词： Communication-avoid Heterogeneous System Jacobi preconditioner PCG algorithm SW26010-Pro

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AH-TDMA: An Adaptive Heterogeneous Tridiagonal Matrix Algorithm on the New Sunway Supercomputer 29

AH-TDMA: An Adaptive Heterogeneous Tridiagonal Matrix Algori...

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29th IEEE International Conference on Parallel and Distributed Systems, ICPADS 2023

作者： Tian, Min Liu, Qi Li, Yanlong Du, Wei Ren, Zenghui Liu, Yue Qilu University of Technology Shandong Academy of Sciences Key Laboratory of Computing Power Network and Information Security Ministry of Education Shandong Computer Science Center National Supercomputer Center in Jinan China Shandong Fundamental Research Center for Computer Science Shandong Provincial Key Laboratory of Computer Networks China Jinan Institute of Supercomputing Technology Jinan Key Laboratory of High Performance Computing China

ISBN: (纸本)9798350330717

The solution of tridiagonal linear systems is used in in various fields and plays a crucial role in numerical simulations. However, there is few efficient solver for tridiagonal linear systems on the new Sunway supercomputer. Based on a three-dimensional heat conduction problem, we propose an adaptive heterogeneous tridiagonal matrix algorithm (AH-TDMA). Our major innovations include: (1) To address computational hotspots within AH-TDMA, a multi-level parallel approach involving MPI+Athread has been adopted. (2) An adaptive data partitioning scheme has been set up to achieve load balance. (3) Employing direct memory access and establishing shared space between registers and main memory, instead of employing discrete memory access, is done to enhance memory access efficiency. (4) The optimization of the loop structure has been made in adjusting the sequencing of the dual-layered loops to reduce communication overhead. The experimental results show that, with one core group, the AH-TDMA achieves a speedup of 99.6 times for hotspot and total time speedup up to 59.4 times compared to the Parallel and Scalable Library for Tridiagonal Matrix Algorithm (PaScal TDMA). The AH-TDMA is scalable up to 2048 core groups, with a parallel efficiency of 69.2%. © 2023 IEEE.

关键词： adaptive heterogeneous algorithm MPI+Athread Sunway supercomputer three-dimensional heat conduction problem tridiagonal linear systems

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DNS Service Optimization Through In-Network Caching on Programmable Switches

DNS Service Optimization Through In-Network Caching on Progr...

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International Conference on Computer and Communications (ICCC)

作者： Fan Yang Cenman Wang Bowen Zheng Ye Tian Anhui Key Laboratory on High Performance Computing School of Computer Science and Technology University of Science and Technology of China Hefei China

ISBN: (数字)9798331507077

ISBN: (纸本)9798331507084

The Domain Name System (DNS) plays a crucial role in contemporary internet infrastructure. Despite the geographical distance of public DNS servers posing a challenge in minimizing domain name resolution latency, there is an increasing reliance on these servers for resolving domain names. One effective approach to mitigate this challenge involves caching DNS query results at network nodes. The storage of cached results commonly employs hash tables due to the variable lengths of domain names. However, within network nodes, hash tables encounter limitations in capacity and susceptibility to hash collisions, potentially leading to inaccuracies in cached results. Current conventional caching strategies have not produced satisfactory storage outcomes. This research introduces a hash-based DNS caching mechanism to tackle these issues. The proposed mechanism presents a unique DNS storage structure on routers and suggests two implementation strategies that incorporate fingerprint verification and Bloom filters. Through analysis and extensive simulations utilizing real-world network topology, the results demonstrate that the hash-based DNS caching mechanism introduced in this study outperforms existing methods in cache hit rate and diminishes query latency.

关键词： Analytical models Filters Network topology Computational modeling Fingerprint recognition Cache storage Topology Domain Name System Servers Optimization

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