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OPTIMAL CONTROL OF AN SIR EPIDEMIC MODEL BASED ON dynamic programming APPROACH

Journal of Mathematical Sciences (United States) 2024年第1期289卷 14-27页

作者： Bouremani, Touffik Slimani, Yacine Laboratory of Applied Mathematics (LaMA) Faculty of Technology Ferhat Abbas University Setif 1 Setif 19000 Algeria Laboratory of Intelligent System (LSI) Faculty of Technology Ferhat Abbas University Setif 1 Setif 19000 Algeria

This paper investigates optimal control of a susceptible-infected-recovered (SIR) epidemic model using the dynamic programming approach. In fact, our study focuses on the modified model by incorporating it with a Bolza-type objective function. We use a certain refinement of Cauchy’s method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a certain admissible control. The optimality is justified by using one of the well-known verification theorems, which provides an argument for sufficient optimality conditions. Through numerical tests, we demonstrate how adjustments to the infection and recovery rates, guided by the optimization framework provided by the guidance function, can significantly impact epidemic outcomes. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

关键词： Differential inclusion dynamic programming method Hamiltonian flow Optimal control SIR model Value function Verification theorem

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Error-resilient Video Multicast with Layered Hybrid FEC/ARQ over Broadband Wireless Networks

Error-resilient Video Multicast with Layered Hybrid FEC/ARQ ...

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54th Annual IEEE Global Telecommunications Conference (GLOBECOM)

作者： Jin, Junfeng Ji, Yusheng Zhao, Baohua Hao, Zhou Liu, Zhi Univ Sci & Technol China Sch Comp Sci Hefei 230027 Anhui Peoples R China Natl Inst Informat Tokyo 1018430 Japan

ISBN: (纸本)9781424492688

Video multicast over broadband wireless networks suffers from packet losses induced by fading wireless channels and user heterogeneity in channel conditions within a multicast group. A promising solution to these problems is the use of layered hybrid FEC/ARQ for scalable video multicast. However, how to allocate the radio resources to multiple video layers and how to address the cross-layer combination of application layer hybrid FEC/ARQ and physical layer MCS (modulation and coding schemes) for each video layer, is not a trivial issue. We prove that this problem is NP-hard and propose an optimal Error-resilient Video Multicast (ERVM) framework in infrastructure-based broadband wireless networks. To avoid user heterogeneity and feedback implosion, we use a weighted designated user group to send light-weight feedback messages. The ERVM algorithm is based on the dynamic programming method with a pseudo-polynomial run time, and can get the optimal transmission configuration to maximize the expected utility for the designated user group, which is a probabilistic function of the received video rate. Simulation results show that our ERVM algorithm offers significant improvements over the conventional single-layer FEC/ARQ scheme and the layered FEC scheme. Furthermore, our weighted designated user group with light-weight and accurate feedbacks is better than other user feedback schemes.

关键词： Algorithm design and analysis Automatic repeat request ERVM algorithm Forward error correction MCS physical layer NP-hard problem PSNR Streaming media Wireless networks application layered hybrid FEC-ARQ automatic repeat request broadband networks computational complexity dynamic programming dynamic programming method error-resilient video multicast framework fading channels fading wireless channels feedback forward error correction infrastructure-based broadband wireless networks modulation and coding schemes modulation coding multicast protocols network coding packet losses probability pseudo-polynomial run time radio networks radio resource allocation received video rate probabilistic function resource allocation single-layer FEC-ARQ scheme user feedback schemes user heterogeneity video coding weighted designated user group

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12th IEEE International Conference on e-Business Engineering (ICEBE)

作者： Wang, Shaopeng Wen, Yingyou Zhao, Hong Northeastern Univ Dept Informat Sci & Engn Shenyang Peoples R China

ISBN: (纸本)9781467380027

Aiming at the problem that the NAIVE algorithm which is taken to handle the similarity query based on LCSS over data stream window (SQLSW) cannot get query results until calculations on all elements in the full dynamic programming matrix are finished, the SQLSW query processing algorithm based on Possible Solution domain optimization strategy (SQLSW-PS) is proposed. It defines possible solution (PS) domain of the dynamic programming matrix about every window. Based on characters of matrix members in the PS domain and the similarity query, it can get query result on the condition that the LCSS similarity function value has not been obtained yet, and reduce lots of computations related to matrix members. It is revealed by extensive experiments that the SQLSW-PS outperforms current algorithms in time, and is effective in handling the SQLSW query.

关键词： data stream data mining similarity query LCSS dynamic programming method

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The Bi-level programming Model between the Manufacture and the Supplier

The Bi-level Programming Model between the Manufacture and t...

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16th International Conference on Management Science and Engineering

作者： Hu Chang-ying Renmin Univ China Sch Informat Beijing 100872 Peoples R China

ISBN: (纸本)9781424439706

We consider a serial supply chain consisting of a supplier and a manufacturer, where production, inventory, transportation, backlogging and subcontracting decisions are integrated. A sequence of deterministic but non-stationary demands of the manufacturer for single good needs to be satisfied by the supplier over a finite horizon. In each period, the supplier can produce items by himself, also can use the subcontracting option if he can not satisfy the manufacturer's need, or due to the cost consideration. Generally, manufacturer's order decisions can influence the supplier's profits straightly, and on the contrary, supplier's plan of production also can influence the cost of manufacturer. Hence, it is not appropriate to take them as one group with public benefit sometimes. We establish a bi-level programming model in which the manufacturer is the leader, the supplier is the follower and the production and subcontracting capacities are stationary. The manufacturer as the leader, first gives the decisions of ordering, aiming to reduce the cost of himself, then the follower-supplier, decides his plan of production or subcontracting according to the manufacture's order to minimize his own cost. By solving the model, we can get the relative optimal schemes satisfied by both of the manufacturer and the supplier.

关键词： bi-level programming model dynamic programming method penalty function method polynomial time supply chain management

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Island Partition of the Distribution System With Distributed Generation Based on Improved dynamic programming 6

Island Partition of the Distribution System With Distributed...

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China International Conference on Electricity Distribution (CICED)

作者： Zhang, Cheng Long Yang, Zhi Chao Ge, Le Yuan, Xiao Dong Nanjing Inst Technol Sch Elect Power Engn Nanjing 211167 Jiangsu Peoples R China Jiangsu Elect Power Res Inst Nanjing 210000 Jiangsu Peoples R China

ISBN: (纸本)9781479941254

A novel optimal island partition model of the distribution system with distributed generation (DG) is proposed and a distributed islanding method based on improved dynamic programming is applied to this model. This paper changes the islanding problem into minimum spanning tree to obtain connected graph. Since the load priority, controllable/uncontrollable load, and the restrictions of power balance, voltage and equipment capability are all taken into account, therefore, the proposed model and method can meet the demand of the practical engineering very well;Based on inclusion-exclusion theorem and dynamic programming theory, the distribution system containing DGs is divided into multiple tree knapsack problems. It effectively reduces the overlap between the various issues intersect. Each TKP is solved by the improved dynamic programming method. Through the island merging process, it can achieve the optimal division of the island. The numerical examples show that: the algorithm can improve the speed and accuracy of problem solving.

关键词： Optimal island partition. Distribution system Distributed generation (DG) Tree knapsack problem (TKP) dynamic programming method

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Diurnal variation of salivary cortisol and amylase activity in fatigued state

Diurnal variation of salivary cortisol and amylase activity ...

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5th International Conference on Impact of Environmental Factors on Health

作者： Nakajima, Y. Takahashi, T. Yamaguchi, M. Iwate Univ Grad Sch Engn Morioka Iwate Japan

ISBN: (纸本)9781845642013

Saliva has great potential as a bio-fluid for point-of-use measurement of the human stress response. The purpose of this study was to evaluate the diurnal variation of salivary cortisol (CORT) and salivary amylase activity (SAA) under the condition of a fatigued state. The subjects were I I emergency medical doctors who worked for the Department of Emergency and Critical Care Medicine in 24 h-shifts, and their diurnal variations were measured three times in one month during the 24h-shift workday. As a control experiment, 6 subjects' diurnal variations were measured during a holiday period. The saliva samples were collected 4 times in total during an examination. The mean CORT of a workday showed its lowest value of 1.07 +/- 0.55 ng/ml before sleep (24:00), and was highest at 4.76 +/- 3.16 ng/ml at the start of a daytime duty (9:00) (p < 0.01). In contrast, the mean CORT of a holiday showed its lowest value of 1.48 +/- 1.00 ng/ml in the afternoon and a highest value of 4.74 +/- 2.76 ng/ml the next morning (p < 0.05). The mean SAA of a workday showed its lowest value of 59.3 +/- 31.5 kU/l during a daytime duty (12:00- 14:00) and was highest at 112.7 +/- 90.1 kU/l at the start of night-time duty (18:00). These salivary biomarkers CORT and SAA on both workdays and holidays showed diurnal variation. In particular, the diurnal variation of CORT followed a well-defined 'bath-tub' shaped curve. A negative correlation of -0.36 was observed between the individual's CORT and SAA in workdays and of -0.62 in holidays, as determined by using the dynamic programming method. It was suggested that the fatigued state of humans is possibly reflected in the diurnal variations of CORT and SAA.

关键词： diurnal variation cortisol amylase fatigued slate dynamic programming method

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Comparison of Body Shape Descriptors for Biometric Recognition using MMW Images 22

Comparison of Body Shape Descriptors for Biometric Recogniti...

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22nd International Conference on Pattern Recognition (ICPR)

作者： Gonzalez-Sosa, Ester Vera-Rodriguez, Ruben Fierrez, Julian Ortega-Garcia, Javier Univ Autonoma Madrid EPS Biometr Recognit Grp ATVS E-28049 Madrid Spain

ISBN: (纸本)9781479952083

The use of Millimetre wave images has been proposed recently in the biometric field to overcome certain limitations when using images acquired at visible frequencies. In this paper, several body shape-based techniques were applied to model the silhouette of images of people acquired at 94 GHz. We put forward several methods for the parameterization and classification stage with the objective of finding the best configuration in terms of biometric recognition performance. Contour coordinates, shape contexts, Fourier descriptors and silhouette landmarks were used as feature approaches and for classification we utilized Euclidean distance and a dynamic programming method. Results showed that the dynamic programming algorithm improved the performance of the system with respect to the baseline Euclidean distance and the necessity of a minimum resolution of the contour to achieve promising equal error rates. The use of the contour coordinates is the most suitable feature to use in the system regarding the performance and the computational cost involved when having at least 3 images for model training. Besides, Fourier descriptors are more robust against rotations, which may be of interest when dealing with few training images.

关键词： Fourier analysis biometrics (access control) dynamic programming shape recognition Euclidean distance Fourier descriptors MMW images baseline Euclidean distance biometric recognition body shape descriptors body shape-based techniques contour coordinates dynamic programming method image silhouette millimetre wave images model training shape contexts silhouette landmarks Biomedical imaging Context Databases Feature extraction Heuristic algorithms Protocols Shape Biometric recognition Fourier descriptors Euclidean distance dynamic programming Biomedical imaging shape recognition Heuristic algorithms Fourier analysis Feature extraction Model trains protocols images Database Pattern recognition

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Effect of lifetime uncertainty on consumption/investment with luxury bequest motives

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FINANCE RESEARCH LETTERS 2016年 17卷 275-279页

作者： Choi, Sungsub Kim, Sungjun Shim, Gyoocheol Pohang Univ Sci & Technol Dept Math Pohang 37673 South Korea Ajou Univ Dept Financial Engn Suwon 16499 South Korea

We study optimal consumption/investment of a retiree who has luxury bequest motives and faces the nonnegative bequest constraint His lifetime is uncertain but actuarially fair life insurance-annuity policies are available. We obtain a closed form solution by using a dynamic programming method, and investigate the effects of lifetime uncertainty and the presence of life insurance-annuity on the consumption/investment policies. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Consumption Investment Luxury bequest Lifetime uncertainty Normegative bequest constraint dynamic programming method

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A Fast method for Exactly Optimum Linear Decomposition of Index Generation Functions

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JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING 2022年第3-4期38卷 387-405页

作者： Nagayama, Shinobu Sasao, Tsutomu Butler, Jon T. Hiroshima City Univ Dept Comp & Network Engn Hiroshima Japan Meiji Univ Dept Comp Sci Kawasaki Kanagawa Japan Naval Postgrad Sch Dept Elect & Comp Engn Monterey CA USA

Linear decomposition of index generation functions is a representation of index generation functions using two kinds of functions: linear functions and a function storing indices. Minimization of the number of linear functions in a linear decomposition is required for efficient implementation of index generation functions. This paper proposes a fast method to exactly minimize the number of linear functions, and shows its time and space complexities. The complexities are large because of the exact optimization method. But, experimental results show that actual computation time and memory size are quite small. This is because the proposed method searches for an optimum solution efficiently based on a dynamic programming method using zero-suppressed binary decision diagrams (ZDDs).

关键词： Index generation functions functional decomposition linear decomposition zero-suppressed binary decision diagrams logic design dynamic programming method

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Optimizing insuring critical path problem under uncertainty based on GP-BPSO algorithm

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SCIENTIA IRANICA 2018年第6期25卷 3713-3722页

作者： Li, Z. Li, B. Tianjin Univ Coll Management & Econ Tianjin 300072 Peoples R China

This study considers a novel class of hi-level fuzzy random programming problems of insuring critical path. In this study, duration of each task is considered as a fuzzy random variable and follows the known possibility and probability distributions. Because an effective way to directly solve the problem does not exist, we first reduce the chance constraint to two equivalent random subproblems under two different kinds of risk attitudes. Then, we use Sample Average Approximation (SAA) method for reformulating the equivalent random programming subproblems as the approximation problems. Since the approximation problems are also difficult to solve, we explore a hybrid Genotype Phenotype Binary Particle Swarm Optimization algorithm (GP-BPSO) for resolving two equivalent subproblems, in which dynamic programming method (DPM) is used for finding the solution in the lower-level programming. At last, a series of simulation examples are provided for demonstrating the validity of the hybrid GP-BPSO compared with the hybrid BPSO algorithm. (C) 2018 Sharif University of Technology. All rights reserved.

关键词： Insuring critical path Bi-level fuzzy random programming Hybrid algorithm dynamic programming method Task duration Project management problem Sample average approximation

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