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A backward algorithm to Determine the Existence of Legal Firing Sequences in Ordinary Petri Nets

IEEE ROBOTICS AND AUTOMATION LETTERS 2023年第6期8卷 3190-3197页

作者： Su, Yue Qi, Liang Zhou, MengChu Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao 266590 Peoples R China New Jersey Inst Technol Helen & John C Hartmann Dept Elect & Comp Engn Newark NJ 07102 USA Macau Univ Sci & Technol Macao Inst Syst Engn Collaborat Lab Intelligent Sci & Syst Macau 999078 Peoples R China

Petri nets (PNs) are a graphical and mathematical tool to model various event-driven automated systems. Reachability is a fundamental property of PNs. The existence of a non-negative integer solution (NIS) to a state equation is a necessary but not sufficient condition for determining the reachability of PNs, i.e., there may be no legal firing sequence (LFS) corresponding to an NIS of a state equation. Finding an LFS for an NIS of a state equation is an NP-hard problem. However, we determine the reachability of a marking by determining the existence of LFSs rather than finding them. We find that the existence of idling circuits (ICs) or idling-dependent circuits (IDCs) is the root cause that there is an NIS satisfying the state equation but the marking is non-reachable in ordinary PNs. Based on this, a backward algorithm is presented to determine the existence of an LFS for an NIS. It reversely finds paths from the destination marking to the initial one and determines whether there is always an intermediate marking with ICs or IDCs. When the state equation has a finite number of NISs, only the polynomial time is needed to analyze the reachability of ordinary PNs. Experimental results verify the effectiveness and efficiency of the approach. This work represents an important advance in the theory and applications of PNs to automated system design.

关键词： Mathematical models Firing Sufficient conditions Search problems Programming Petri nets NP-hard problem Automated manufacturing systems backward algorithm discrete event systems intelligent automation reachability

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Flying Ad-Hoc Network Routing Protocol Based on backward algorithm 9th

Flying Ad-Hoc Network Routing Protocol Based on Backward Alg...

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9th International Conference on Intelligent IoT as a Service

作者： Yu, Zheng Yu, Jianguo Beijing Univ Posts & Telecommun Sch Elect Engn Beijing 100876 Peoples R China

ISBN: (纸本)9783031705069;9783031705076

To cope with the challenge of nodes moving at high speed, we propose a flying ad hoc routing protocol based on backward algorithm (FANET-BA). When selecting a relay node, the neighboring node who has the maximum path value will be selected as relay node based on the backward algorithm. When a node encounters a routing void, we categorize this problem into two cases namely the half routing void and the whole routing void, then propose solutions for them respectively. Simulation results show that compared with greedy perimeter stateless routing protocol (GPSR), FANET-BA improves throughput by about 89.0% and successful packet delivery rate by about 55.9%.

关键词： Flying Ad Hoc Network backward algorithm The Half Routing Void The Whole Routing Void

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Parallel random block-coordinate forward-backward algorithm: a unified convergence analysis

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MATHEMATICAL PROGRAMMING 2022年第1期193卷 225-269页

作者： Salzo, Saverio Villa, Silvia Ist Italiano Tecnol Via Melen 83 I-16152 Genoa Italy Univ Genoa DIMA Via Dodecaneso 35 I-16146 Genoa Italy

We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results.

关键词： Convex optimization Parallel algorithms Random block-coordinate descent Arbitrary sampling Error bounds Stochastic quasi-Fejé r sequences Forward– backward algorithm Convergence rates

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NUMERICAL APPROACH FOR SIMULATING THE TENSIONING PROCESS OF COMPLEX PRESTRESSED CABLE-NET STRUCTURES

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JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2021年第8期27卷 571-578页

作者： Chen, Deshen Zhang, Yan Qian, Hongliang Wang, Huajie Jin, Xiaofei Harbin Inst Technol Weihai Sch Ocean Engn Weihai Peoples R China Harbin Inst Technol Minist Educ Key Lab Struct Dynam Behav & Control Sch Civil Engn Harbin Peoples R China China Construct First Bldg Grp Corp Ltd Beijing Peoples R China

The stability of cable-net structures depends on the prestress of the system. Due to the large displacement and mutual effect of the cables, it is difficult to simulate the tensioning process and control the forming accuracy. The backward algorithm (BA) has been used to simulate the tensioning process. The traditional BA involves complicated and tedious matrix operations. In this paper, a new numerical method based on the Vector Form Intrinsic Finite Element (VFIFE) method is proposed for BA application. Moreover, the tensioning sequence of a complex cable-net structure is introduced. Subsequently, a new approach for BA application in the simulation of the tensioning process is presented, which combines the VFIFE approach and the notion of form-finding. Finally, a numerical example is simulated in detail and the results of different tensioning stages are analyzed to verify the feasibility of the proposed approach. This study provides a significant reference for improving the construction control and forming accuracy of complex prestressed cable-net structures.

关键词： tensioning process simulation backward algorithm complex cable-net structure computational method Vector Form Intrinsic Finite Element

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Hidden mover-stayer model for disease progression accounting for misclassified and partially observed diagnostic tests: Application to the natural history of human papillomavirus and cervical precancer

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STATISTICS IN MEDICINE 2021年第15期40卷 3460-3476页

作者： Aron, Jordan Albert, Paul S. Wentzensen, Nicolas Cheung, Li C. NCI Biostat Branch Div Canc & Epidemiol Rockville MD 20850 USA NCI Clin Genet Branch Div Canc & Epidemiol Rockville MD USA

Hidden Markov models (HMMs) have been proposed to model the natural history of diseases while accounting for misclassification in state identification. We introduce a discrete time HMM for human papillomavirus (HPV) and cervical precancer/cancer where the hidden and observed state spaces are defined by all possible combinations of HPV, cytology, and colposcopy results. Because the population of women undergoing cervical cancer screening is heterogeneous with respect to sexual behavior, and therefore risk of HPV acquisition and subsequent precancers, we use a mover-stayer mixture model that assumes a proportion of the population will stay in the healthy state and are not subject to disease progression. As each state is a combination of three distinct tests that characterize the cervix, partially observed data arise when at least one but not every test is observed. The standard forward-backward algorithm, used for evaluating the E-step within the E-M algorithm for maximum-likelihood estimation of HMMs, cannot incorporate time points with partially observed data. We propose a new forward-backward algorithm that considers all possible fully observed states that could have occurred across a participant's follow-up visits. We apply our method to data from a large management trial for women with low-grade cervical abnormalities. Our simulation study found that our method has relatively little bias and out preforms simpler methods that resulted in larger bias.

关键词： EM algorithm forward‐ backward algorithm measurement error partial missing data

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Fast iterative algorithms for birefringent filter design

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APPLIED COMPUTING AND INFORMATICS 2021年第2期17卷 250-263页

作者： Boukharouba, Abdelhak Univ 8 Mai 1945 Guelma Fac Sci & Technol Dept Elect & Telecommun Guelma Algeria

Fast iterative algorithms for designing birefringent filters with any specified spectral response are proposed. From the Jones formalism, we derive two polynomials representing the transmitted and rejected response of the filter, respectively. Once the coefficients of the filters are obtained, the orientation angle of each birefringent section and the phase shift introduced by each compensator can be determined by an iterative algorithm that gives an efficient solution to the birefringent filter design problem. Afterward, some design examples are presented to demonstrate the effectiveness of the proposed approach. In comparison with results reported in the literature, this approach provides the best performance in terms of accuracy and time complexity.

关键词： Birefringent filter Forward algorithm backward algorithm PSO

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The Drawback of Image Resizing Based on Seam Carving

The Drawback of Image Resizing Based on Seam Carving

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2015 4th International Conference on Mechatronics,Materials,Chemistry and Computer Engineering(ICMMCCE 2015)

作者： Zijuan Zhang Shaanxi Polytechnic Institute

Lots of image resizing algorithms that based on seam carving belong to the discrete resizing methods. Seam-carving algorithms refer to delete or insert pixel lines in order to resize image's size. Pixel lines horizontally or vertically pass through the whole image, deleting the pixel line to make the reduction, copying the pixel line to make the magnification, processing level(vertical) pixel line could change the height(width) of image. In order to keep the main characteristic content in image, many seam carving algorithms delete or insert pixel line that has the smallest energy each time. Lots of seam carving algorithms can scale the size of image, protect the important content in the original image, achieve good effect about adaptation, but these algorithms will produce many problems, such as deleting distortion excessively.

关键词： seam carving backward algorithm forward image resizing

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Efficient Implementation of Enhanced Min-Sum algorithm for DVB-S2 LDPC Decoder

Efficient Implementation of Enhanced Min-Sum Algorithm for D...

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IEEE International Conference on Consumer Electronics (ICCE)

作者： Park, Sung Ik Kim, Heung Mook Kim, Jeongchang Elect & Telecommun Res Inst Taejon 305606 South Korea Korea Maritime Univ Busan South Korea

ISBN: (纸本)9781479912919

This paper proposes an efficient implementation of enhanced min-sum algorithm (EMSA) for DVB-S2 LDPC decoding. In order to minimize complexity of check node update, the proposed method uses forward and backward algorithm. Simulation results show that the EMSA does not cause serious performance degradation, as compared with sum-product algorithm when decoder input is 9-bit quantized.

关键词： decoding digital video broadcasting parity check codes product codes video coding DVB- S2 LDPC decoder EMSA backward algorithm check node update complexity enhanced min-sum algorithm forward algorithm sum-product algorithm word length 9 bit algorithm design and analysis Approximation methods Complexity theory Decoding Degradation Digital video broadcasting Parity check codes

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Optimal Dual Martingales, Their Analysis, and Application to New algorithms for Bermudan Products

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2013年第1期4卷 86-116页

作者： Schoenmakers, John Zhang, Jianing Huang, Junbo Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany Galaxy Asset Management Co LTD Shanghai 200122 Peoples R China

In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optimal, and a stability theorem concerning martingales which are nearly surely optimal in a sense. Guided by these results we develop a framework of backward algorithms for constructing such a martingale which can be utilized for computing an upper bound of the Bermudan product. The methodology is purely dual in the sense that it does not require certain input approximations to the Snell envelope. In an Ito-Levy environment we outline a particular regression-based backward algorithm which allows for computing dual upper bounds without nested Monte Carlo simulation. Moreover, as a by-product this algorithm also provides approximations to the continuation values of the product, which in turn determine a stopping policy. We hence obtain lower bounds at the same time. We finally supplement our presentation with numerical experiments.

关键词： Bermudan options duality Monte Carlo simulation linear regression surely optimal martingales backward algorithm

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System Level Delay Modeling for Network-on-Chip

System Level Delay Modeling for Network-on-Chip

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4th World Congress on Software Engineering (WCSE)

作者： Fang, Zhou Ning, Wu Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781479928828

To evaluate the performance of delay for Network-on-Chip (NoC) at system-level design as early as possible, a delay estimation methodology based on M/G/1 queuing theory is proposed in the paper. In this methodology, the influence of the finite buffer resources and virtual channels in NoC router on the packet latency is taken into account, and the backward algorithm is used to calculate the network average packet latency. Several experiments with different traffic loads are carried out to evaluate the efficacy of this delay model. Experimental results show that a significant improvement in evaluation speed is achieved with the proposed power model as compared with the RTL-level simulator, while maintaining a minor average error of approximately 8.0% and achieving a speedup of 250 times. As an application, the proposed model has been successfully used to evaluate the performance of different core mappings for MPEG4 decoder in system-level design.

关键词： NoC Delay Model M/G/1 backward algorithm

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