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Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年 282卷 98-110页

作者： Przybylowicz, Pawel AGH Univ Sci & Technol Fac Appl Math PL-30059 Krakow Poland

We consider strong one-point approximation of solutions of scalar stochastic differential equations (SDEs) with irregular coefficients. The drift coefficient a : [0, T] x R -> R is assumed to be Lipschitz continuous with respect to the space variable but only measurable with respect to the time variable. For the diffusion coefficient b : [0, T] -> R we assume that it is only piecewise Holder continuous with Holder exponent Q is an element of (0,1]. We show that, roughly speaking, the error of any algorithm, which uses n values of the diffusion coefficient, cannot converge to zero faster than n(-min)[Q, 1/2] as n -> +infinity. This best speed of convergence is achieved by the randomized Euler scheme. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Non-standard assumptions One-point approximation Lower bounds Asymptotic error optimal algorithm Monte Carlo methods

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Analysis of Aerosol Optical Mixing Using the EOMOS Model From Typical AERONET Sites

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GEOPHYSICAL RESEARCH LETTERS 2024年第18期51卷

作者： Yan, Gang Sun, Bingqiang Gao, Chenxu Chen, Yunqian Chen, Jianmin Fudan Univ Inst Atmospher Sci Dept Atmospher & Ocean Sci Shanghai Peoples R China Fudan Univ IRDR Int Ctr Excellence Risk Interconnect & Govern Shanghai Peoples R China Fudan Univ Dept Environm Sci & Engn Shanghai Key Lab Atmospher Particle Pollut & Preve Shanghai Peoples R China

Satellite remote sensing predominantly employs optical properties for aerosol classification, often neglecting aerosol mixing and lacking validation accuracy. This study defines five aerosol types: marine, continental, dust, urban-industrial, and biomass-burning. Proposing the external optical mixing optimization solver (EOMOS) model based on the external mixing assumption, the model's accuracy is enhanced by approximately 95.0% through constraints and optimization. Perturbation experiments on particle size distribution and complex refractive index validate the model's robustness. The EOMOS model analyzes aerosol mixing states, and quantifies contributions to aerosol optical depth (AOD) for each aerosol type, surpassing traditional methods by at least 139.7%. Additionally, the EOMOS model examines trends in aerosol type AOD, revealing a noticeable post-2013 reduction in AOD of urban-industrial aerosols in Beijing, suggesting pollution mitigation. In Brazil, urban-industrial and biomass-burning aerosol AODs were 328.1% and 107.7% higher in 2005, 2007, and 2010, primarily due to fire impact. Plain Language Summary Aerosols are tiny particles suspended in the atmosphere, and have complex impacts on climate, human health, and the environment. This study analyzes the external mixing state of aerosols based on optical properties and provides a practical and feasible method for characterizing them. Five primary aerosol types were predefined and their mixing states were determined by relating them to optical observations. The results revealed that urban-industrial aerosols in Beijing have gradually decreased since 2013, partly due to the implementation of the "Action Plan for the Prevention and Control of Air Pollution (2013-2017)" by the Chinese government. However, they remain the predominant pollutants, with peak concentrations occurring in July. In contrast, the Brazilian region experienced a sudden increase in biomass-burning aerosols in 2005, 2007, and 2010 due to wil

关键词： aerosol classification external optical mixing optimization solver (EOMOS) model optimal algorithm

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Hybrid GA-BF based intelligent PID controller tuning for AVR system

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APPLIED SOFT COMPUTING 2011年第1期11卷 11-22页

作者： Kim, Dong Hwa Hanbat Natl Univ Dept Instrumentat & Control Eng Taejon 305719 South Korea

This paper deals with hybrid system (GA-BF) based on the conventional GA (Genetic algorithm) and BF (Bacterial Foraging) which is the social foraging behavior of bacteria. A variety of test function is introduced and simulated to illustrate the characteristics and performance by mutation, crossover, variation of step size, variation of chemotactic step, and variation of lifetime of bacteria in the proposed hybrid system GA-BF. The simulated results represent that the proposed method is highly satisfactory. This approach provides us with novel hybrid model based on foraging behavior and also with a possible new connection between evolutionary forces in social foraging and distributed nongradient optimization algorithm design for global optimization over noisy surfaces. (c) 2010 Published by Elsevier B.V.

关键词： Genetic algorithm Bacterial Foraging optimization Hybrid system optimal algorithm

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A theoretical framework of uplink macroscopic optimization for multicell systems with multiuser detection

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2004年第6期53卷 1769-1779页

作者： Lau, V Univ Sci & Technol Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China

In this paper, we consider a system with K client users (single antenna), n(B) base stations (each has single antenna), as well as a centralized controller. All the base stations operate at the same frequency and have optimal multiuser detection (MUD) per base station. The MUD at the base station is able to cancel only the intracell interference but not the intercell interference. A client user is associated with a single base station at any time. We consider a general problem of uplink macroscopic optimization (or macroscopic resource management) where the centralized controller dynamically determines an appropriate association mapping of the K users with respect to the n(B) base stations over a macroscopic time scale. We propose a novel multicell capacity region as well as an analytical framework for the above macroscopic optimization problem. A simple conventional rule is to associate a user with the strongest base station (camp-on-the-strongest-cell) and this has been widely employed in conventional cellular systems. However, based on the optimization framework, we found that this conventional approach is in fact not optimal when MUD is employed at the base station. We show that the optimal macroscopic optimization algorithm is of exponential complexity and we propose a simple greedy algorithm as a feasible solution. It is shown that the macroscopic optimization gain over the conventional approach increases with decreasing path loss exponent due to large area of overlapping.

关键词： macroscopic scheduling multiaccess information theory multicell scheduling multiuser detection (MUD) optimal algorithm proportional fairness utility functions

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On the complexity of computing quadrature formulas for marginal distributions of SDEs

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JOURNAL OF COMPLEXITY 2015年第1期31卷 110-145页

作者： Mueller-Gronbach, Thomas Ritter, Klaus Yaroslavtseva, Larisa Univ Passau Fak Informat & Math D-94032 Passau Germany Tech Univ Kaiserslautern Fachbereich Math D-67653 Kaiserslautern Germany

We study the problem of approximating the distribution of the solution of a d-dimensional system of stochastic differential equations (SDEs) at a single time point by a probability measure with finite support, i.e., by a quadrature formula with positive weights summing up to one. We consider deterministic algorithms that may use finitely many evaluations of the drift coefficient and the diffusion coefficient and we analyze their worst case behavior with respect to classes of SDEs, which are specified in terms of smoothness constraints for the coefficients of the equation. The worst case error of an algorithm is defined in terms of a metric on the space of probability measures on the state space of the solution, which is induced by a class of test functions f: R-d -> R. For the definition of the worst case cost of an algorithm we either consider the size of the support of the approximating probability measure or the number of evaluations of the coefficients of the equation or the total computational cost within the real number model without pricing precomputation. We show that the order of convergence of the corresponding minimal errors is rid, min(s(1), s(2))/d and min(r, s(1), s(2))/d, respectively, up to an arbitrarily small power, where the parameters r, s(1) and s(2) denote the smoothness of the test functions, the drift coefficients and the diffusion coefficients, respectively. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Quadrature of SDEs Quantization of SDEs Worst case analysis Lower bounds optimal algorithm Deterministic algorithm

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On the complexity of searching for a maximum of a function on a quantum computer

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QUANTUM INFORMATION PROCESSING 2006年第1期5卷 31-41页

作者： Gocwin, Maciej AGH Univ Sci & Technol Dept Appl Math PL-30059 Krakow Poland

We deal with the problem of finding a maximum of a function from the Holder class on a quantum computer We show matching lower and upper bounds oil the complexity of this problem. We prove upper bounds by constructing an alogorithm that uses a pre-exisiting quantum algorithm for finding maximum of a discrete sequence. To prove lower bounds we use results for finding the logical OR of sequence of bits. We show that quantum computation yields a quadratic speed-up over deterministic and randomized algorithms.

关键词： numerical optimization optimal algorithm quantum computing query complexity

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A branch and bound algorithm for disassembly scheduling with assembly product structure

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2009年第3期60卷 419-430页

作者： Kim, H-J Lee, D-H Xirouchakis, P. Kwon, O. K. Inha Univ Asia Pacific Sch Logist Grad Sch Logist Inchon 402751 South Korea Hanyang Univ Seoul 133791 South Korea Ecole Polytech Fed Lausanne Swiss Fed Inst Technol CH-1015 Lausanne Switzerland

This paper considers a production planning problem in disassembly systems, which is the problem of determining the quantity and timing of disassembling end-of-use/life products in order to satisfy the demand of their parts or components over a planning horizon. The case of single product type without parts commonality is considered for the objective of minimizing the sum of setup and inventory holding costs. To show the complexity of the problem, we prove that the problem is NP-hard. Then, after deriving the properties of optimal solutions, a branch and bound algorithm is suggested that incorporates the Lagrangean relaxation-based upper and lower bounds. Computational experiments are performed on a number of randomly generated problems and the test results indicate that the branch and bound algorithm can give optimal solutions up to moderate-sized problems in a reasonable computation time. A Lagrangean heuristic for a viable alternative for large-sized problems is also suggested and compared with the existing heuristics to show its effectiveness.

关键词： environmental studies production and scheduling optimal algorithm

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Data privacy preservation algorithm with k-anonymity

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WORLD WIDE WEB-INTERNET AND WEB INFORMATION SYSTEMS 2021年第5期24卷 1551-1561页

作者： Mahanan, Waranya Chaovalitwongse, W. Art Natwichai, Juggapong Chiang Mai Univ Fac Engn Dept Comp Engn Data Engn Lab Chiang Mai Thailand Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA Chiang Mai Univ Fac Engn & Data Analyt Dept Comp Engn Data Engn Lab Chiang Mai Thailand Chiang Mai Univ Knowledge Synth Healthcare Ctr Chiang Mai Thailand

With growing concern of data privacy violations, privacy preservation processes become more intense. The k-anonymity method, a widely applied technique, transforms the data such that the publishing datasets must have at least k tuples to have the same link-able attribute, quasi-identifiers, values. From the observations, we found that, in a certain domain, all quasi-identifiers of the datasets, can have the same data type. This type of attribute is considered as an Identical Generalization Hierarchy (IGH) data. An IGH data has a particular set of characteristics that could utilize for enhancing the efficiency of heuristic privacy preservation algorithms. In this paper, we propose a data privacy preservation heuristic algorithm on IGH data. The algorithm is developed from the observations on the anonymous property of the problem structure that can eliminate the privacy constraints consideration. The experiment results are presented that the proposed algorithm could effectively preserve data privacy and also reduce the number of visited nodes for ensuring the privacy protection, which is the most time-consuming process, compared to the most efficient existing algorithm by at most 21%.

关键词： Data privacy preservation k-anonymity optimal algorithm

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Bilevel parameters identification for the multi-stage nonlinear impulsive system in microorganisms fed-batch cultures

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2008年第3期9卷 1068-1077页

作者： Shen, Lijuan Wang, Yan Feng, Enmin Xiu, Zhilong Luoyuang Normal Univ Dept Math Luoyang 471022 Henan Peoples R China Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China Dalian Univ Technol Dept Biotechnol Dalian 116012 Peoples R China

Considering the abrupt jump of the substrate and different characters of the bacterial in the lag phase, the exponential phase and the stationary phase this paper proposes the multi-stage nonlinear impulsive system for the fed-batch fermentation from glycerol to 1,3-propanediol (1,3-PD) and establishes the bilevel identification system for its sensitive parameters. The properties of the solutions for the nonlinear multi-stage dynamical system are investigated and identifiability of the parameters is proved. Finally an optimal algorithm is constructed to obtain the optimal solution of the identification model and the numerical example is then discussed to illustrate the algorithm. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： bilevel identification multi-stage impulsive system optimal algorithm fed-batch cultures

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Early 21st Century cyclone climatology: a 3D *** Characterization

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INTERNATIONAL JOURNAL OF CLIMATOLOGY 2021年第7期41卷 4019-4046页

作者： Lakkis, Susan G. Canziani, Pablo O. Rodriguez, Joaquin O. Yuchechen, Adrian E. O'Neill, Alan Albers, Kim H. Hodges, Kevin Pontificia Univ Catolica Argentina Fac Ingn & Ciencias Agr Buenos Aires DF Argentina Univ Tecnol Nacl Fac Reg Buenos Aires Unidad Invest & Desarrollo Ingn Buenos Aires DF Argentina Consejo Nacl Invest Cient & Tecn Buenos Aires DF Argentina Univ Reading Dept Meteorol Reading Berks England Karlsruhe Inst Technol Inst Meteorol & Climate Res Karlsruhe Germany

Extra-tropical cyclones are a relevant feature in the climate at middle and high latitudes. Despite their importance, most studies typically focus only on cyclones identified at a single atmospheric level and on events close to the surface. This paper provides a new perspective on the Southern Hemisphere (SH) cyclone events based on the multilevel cyclone tracking algorithm STACKER. The algorithm, using relative vorticity, detects the raw tracks at single levels and objectively combines them to provide the 3D events and their evolutionary timeline. As a result, a 3D cyclone climatology, based on ECMWF Reanalysis ERA-I data from 12 pressure levels in the troposphere and lowermost stratosphere is presented. To the best of our knowledge, this is the first analysis carried out throughout the troposphere and the lowermost extratropical/subpolar stratosphere in order to give a comprehensive picture of the cyclone events as physical entities throughout their lifetime. Cyclone properties analysed are track densities, translational velocity, vorticity and lifetimes. For the subtropical and extra-tropical SH, results support many previous ideas about cyclone characteristics, but new insights are also obtained. A total of 58,231 multilevel cyclone events lasting at least 2 days were detected, with vertical structures spanning two or more levels. This means an average of 303 cyclone events of all types per month, between 2001 and 2017, disregarding seasonality. Results show that cyclones are most frequently detected at the lowest levels of 925 and 700 hPa. By considering that cyclonic systems can be grouped into families according to their vertical extent, results per month on average show that shallow systems are the most frequent events with approximately 248 systems detected, followed by 43 intermediary and 11 deep events. Shallow and deep systems have a large percentage of events with genesis at 925 and 700 hPa. Density statistics show that shallow events are present at all

关键词： 3D cyclone climatology dynamic programming feature tracking multilevel structures optimal algorithm relative vorticity STACKER

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