Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the...Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.展开更多
The problem of determining the number of steps needed to find the greatest common divisor of two positive integers by Euclidean algorithm has been investigated in elementary number theory for decades. Different upper ...The problem of determining the number of steps needed to find the greatest common divisor of two positive integers by Euclidean algorithm has been investigated in elementary number theory for decades. Different upper bounds have been found for this problem. Here, we provide a sharp upper bound for a function which has a direct relation to the numbers whom the greatest common divisor we are trying to calculate. We mainly use some features of Fibonacci numbers as our tools.展开更多
A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree...A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice.展开更多
为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时...为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时间序列通过基于序列重要点(Series Importance Point, SIP)的时间序列线性分段(Piecewise Linear Represent, PLR)算法(PLR_SIP)得到数条时间子序列;然后采用欧氏距离进行时间子序列的相似性分析,并基于改进的局部离群因子(Local Outlier Factor, LOF)算法计算每条时间子序列的局部离群因子;最后将其与设定的阈值相比较,从而识别出监测数据的异常。为验证该算法的准确性与工程实用性,对某公路大跨度斜拉桥健康监测数据进行异常识别。结果表明:采用PLR_SIP算法对原始时间序列压缩分割得到的时间子序列能够准确地反映原序列的变化趋势和范围;改进的LOF算法突破了传统LOF算法仅能识别离群值这类无持续时间异常的局限性,能够排除噪声的干扰,实现对离群、缺失和漂移3种异常的识别。该算法无需定义训练集,直接以原始监测数据作为算法的输入,同时能够自适应调整阈值参数,具有良好的可扩展性、实时性、准确性和高效性,适用于处理实时、大量的桥梁健康监测数据。展开更多
An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before...An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before those programmes are applied in real situations. This study aims to find the optimum input setting for a double inverted pendulum（DIP）, which requires an appropriate input to be able to stand and to achieve robust stability even when the system model is unknown. Such a DIP input could be widely applied in engineering fields for optimizing unknown systems with a limited budget. Previous studies have used various mathematical approaches to optimize settings for DIP, then have designed control algorithms or physical mathematical models.This study did not adopt a mathematical approach for the DIP controller because our DIP has five input parameters within its nondeterministic system model. This paper proposes a novel algorithm, named Uni Neuro, that integrates neural networks（NNs） and a uniform design（UD） in a model formed by input and response to the experimental data（metamodel）. We employed a hybrid UD multiobjective genetic algorithm（HUDMOGA） for obtaining the optimized setting input parameters. The UD was also embedded in the HUDMOGA for enriching the solution set, whereas each chromosome used for crossover, mutation, and generation of the UD was determined through a selection procedure and derived individually. Subsequently, we combined the Euclidean distance and Pareto front to improve the performance of the algorithm. Finally, DIP equipment was used to confirm the settings. The proposed algorithm can produce 9 alternative configured input parameter values to swing-up then standing in robust stability of the DIP from only 25 training data items and 20 optimized simulation results. In comparison to the full factorial design, this design can save considerable experiment time because the metamodel can be formed by only 25 experiments using the UD. Furthermore, the proposed algorithm can be applied to nonlinear systems with multiple constraints.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.展开更多
Minimum Partial Euclidean Distance (MPED) based K-best algorithm is proposed to detect the best signal for MIMO (Multiple Input Multiple Output) detector. It is based on Breadth-first search method. The proposed algor...Minimum Partial Euclidean Distance (MPED) based K-best algorithm is proposed to detect the best signal for MIMO (Multiple Input Multiple Output) detector. It is based on Breadth-first search method. The proposed algorithm is independent of the number of transmitting/receiving antennas and constellation size. It provides a high throughput and reduced Bit Error Rate (BER) with the performance close to Maximum Likelihood Detection (MLD) method. The main innovations are the nodes that are expanded and visited based on MPED algorithm and it keeps track of finally selecting the best candidates at each cycle. It allows its complexity to scale linearly with the modulation order. Using Quadrature Amplitude Modulation (QAM) the complex domain input signals are modulated and are converted into wavelet packets and these packets are transmitted using Additive White Gaussian Noise (AWGN) channel. Then from the number of received signals the best signal is detected using MPED based K-best algorithm. It provides the exact best node solution with reduced complexity. The pipelined VLSI architecture is the best suited for implementation because the expansion and sorting cores are data driven. The proposed method is implemented targeting Xilinx Virtex 5 device for a 4 × 4, 64-QAM system and it achieves throughput of 1.1 Gbps. The results of resource utilization are tabulated and compared with the existing algorithms.展开更多
文摘Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.
文摘The problem of determining the number of steps needed to find the greatest common divisor of two positive integers by Euclidean algorithm has been investigated in elementary number theory for decades. Different upper bounds have been found for this problem. Here, we provide a sharp upper bound for a function which has a direct relation to the numbers whom the greatest common divisor we are trying to calculate. We mainly use some features of Fibonacci numbers as our tools.
基金the National Natural Science Foundation of China (70471065)the Shanghai Leading Academic Discipline Project (T0502).
文摘A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice.
文摘为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时间序列通过基于序列重要点(Series Importance Point, SIP)的时间序列线性分段(Piecewise Linear Represent, PLR)算法(PLR_SIP)得到数条时间子序列;然后采用欧氏距离进行时间子序列的相似性分析,并基于改进的局部离群因子(Local Outlier Factor, LOF)算法计算每条时间子序列的局部离群因子;最后将其与设定的阈值相比较,从而识别出监测数据的异常。为验证该算法的准确性与工程实用性,对某公路大跨度斜拉桥健康监测数据进行异常识别。结果表明:采用PLR_SIP算法对原始时间序列压缩分割得到的时间子序列能够准确地反映原序列的变化趋势和范围;改进的LOF算法突破了传统LOF算法仅能识别离群值这类无持续时间异常的局限性,能够排除噪声的干扰,实现对离群、缺失和漂移3种异常的识别。该算法无需定义训练集,直接以原始监测数据作为算法的输入,同时能够自适应调整阈值参数,具有良好的可扩展性、实时性、准确性和高效性,适用于处理实时、大量的桥梁健康监测数据。
基金supported by Indonesian Government(No.BPPLN DIKTI 3+1)
文摘An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before those programmes are applied in real situations. This study aims to find the optimum input setting for a double inverted pendulum（DIP）, which requires an appropriate input to be able to stand and to achieve robust stability even when the system model is unknown. Such a DIP input could be widely applied in engineering fields for optimizing unknown systems with a limited budget. Previous studies have used various mathematical approaches to optimize settings for DIP, then have designed control algorithms or physical mathematical models.This study did not adopt a mathematical approach for the DIP controller because our DIP has five input parameters within its nondeterministic system model. This paper proposes a novel algorithm, named Uni Neuro, that integrates neural networks（NNs） and a uniform design（UD） in a model formed by input and response to the experimental data（metamodel）. We employed a hybrid UD multiobjective genetic algorithm（HUDMOGA） for obtaining the optimized setting input parameters. The UD was also embedded in the HUDMOGA for enriching the solution set, whereas each chromosome used for crossover, mutation, and generation of the UD was determined through a selection procedure and derived individually. Subsequently, we combined the Euclidean distance and Pareto front to improve the performance of the algorithm. Finally, DIP equipment was used to confirm the settings. The proposed algorithm can produce 9 alternative configured input parameter values to swing-up then standing in robust stability of the DIP from only 25 training data items and 20 optimized simulation results. In comparison to the full factorial design, this design can save considerable experiment time because the metamodel can be formed by only 25 experiments using the UD. Furthermore, the proposed algorithm can be applied to nonlinear systems with multiple constraints.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
文摘Minimum Partial Euclidean Distance (MPED) based K-best algorithm is proposed to detect the best signal for MIMO (Multiple Input Multiple Output) detector. It is based on Breadth-first search method. The proposed algorithm is independent of the number of transmitting/receiving antennas and constellation size. It provides a high throughput and reduced Bit Error Rate (BER) with the performance close to Maximum Likelihood Detection (MLD) method. The main innovations are the nodes that are expanded and visited based on MPED algorithm and it keeps track of finally selecting the best candidates at each cycle. It allows its complexity to scale linearly with the modulation order. Using Quadrature Amplitude Modulation (QAM) the complex domain input signals are modulated and are converted into wavelet packets and these packets are transmitted using Additive White Gaussian Noise (AWGN) channel. Then from the number of received signals the best signal is detected using MPED based K-best algorithm. It provides the exact best node solution with reduced complexity. The pipelined VLSI architecture is the best suited for implementation because the expansion and sorting cores are data driven. The proposed method is implemented targeting Xilinx Virtex 5 device for a 4 × 4, 64-QAM system and it achieves throughput of 1.1 Gbps. The results of resource utilization are tabulated and compared with the existing algorithms.
