Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such...Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such problems usually consume time and memory,especially for large-size problems.Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems,especially the generative model of the deep neural networks.In this work,we propose a resource allocation deep autoencoder network,as one of the promising generative models,for enabling spectrum sharing in underlay device-to-device(D2D)communication by solving linear sum assignment problems(LSAPs).Specifically,we investigate the performance of three different architectures for the conditional variational autoencoders(CVAE).The three proposed architecture are the convolutional neural network(CVAECNN)autoencoder,the feed-forward neural network(CVAE-FNN)autoencoder,and the hybrid(H-CVAE)autoencoder.The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques,such as the Hungarian algorithm,due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time.Moreover,the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.展开更多
In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric ...In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.展开更多
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical...In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.展开更多
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis...Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.展开更多
A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then...A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.展开更多
Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum represent...Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.展开更多
Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/...Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.展开更多
In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming pro...In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.展开更多
On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘prob...On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.展开更多
[背景]电焊工接触含多种金属的电焊烟尘引起肺功能下降,既往研究多集中于单一金属与肺功能间的关联,较少关注到金属混合暴露的肺功能健康损害。[目的]本研究旨在评估电焊工尿液和血液中多种金属浓度与肺功能指标间的关联,探讨影响肺功...[背景]电焊工接触含多种金属的电焊烟尘引起肺功能下降,既往研究多集中于单一金属与肺功能间的关联,较少关注到金属混合暴露的肺功能健康损害。[目的]本研究旨在评估电焊工尿液和血液中多种金属浓度与肺功能指标间的关联,探讨影响肺功能的关键金属成分,为职业健康风险评估提供参考依据。[方法]对上海市某造船厂电焊工和对照组工人进行问卷调查、肺功能检测,并收集尿液和血液样本。采用电感耦合等离子体质谱法(ICP-MS)检测尿液和血液中钒、铬、锰等12种金属浓度。Spearman相关用于分析血液、尿液中金属间的关联性。应用多重线性回归、加权分位数之和回归(WQS)和贝叶斯核机器回归(BKMR)剖析金属混合暴露与肺功能指标用力肺活量(FVC)、用力肺活量占预计值百分比(FVC%)、第1秒用力呼气容积(FEV_(1))、第1秒用力呼气容积占预计值百分比(FEV_(1)%)和一秒率(FEV_(1)/FVC)间的关系。[结果]本研究共纳入445名工人,焊工组322人(72.36%),对照组123人(27.64%),总人群平均年龄为(37.64±8.80)岁,87.19%为男性。电焊工尿镉(0.88 vs 0.58μg·L^(-1))以及血铬(5.86 vs5.06μg·L^(-1))、锰(24.24 vs 21.38μg·L^(-1))浓度均显著高于对照组(P<0.05)。Spearman相关结果显示尿液和血液中金属元素间相关系数范围为-0.46~0.68。在校正混杂因素后,多重线性回归结果提示电焊工尿钼与FVC、FEV_(1)间呈负相关;血钼与FVC、FVC%、FEV_(1)、FEV_(1)%以及血铜与FEV_(1)/FVC间呈负相关。WQS结果表明电焊工血液、尿液金属混合浓度每增加1个四分位数水平,FEV_(1)、FVC分别平均下降0.112 L、0.353 L,铜、锌、钒、锑等金属贡献较大。BKMR显示电焊工血液、尿液中金属浓度与FVC、FVC%、FEV_(1)、FEV_(1)%间呈下降趋势,单变量暴露反应-关系中血液、尿液钼浓度与FVC、FVC%、FEV_(1)、FEV_(1)大致呈线性下降趋势;电焊工尿液中不同金属作用于FEV_(1)%时,镉与锰、镍、钒间,钒与铁、钼、锌、铜间可能具有交互作用。[结论]多金属混合暴露引起电焊工肺功能下降,贡献较大的金属有钼、锑、铜和锌等。展开更多
基金supported in part by the China NSFC Grant 61872248Guangdong NSF 2017A030312008+1 种基金Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No.161064)GDUPS (2015)
文摘Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such problems usually consume time and memory,especially for large-size problems.Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems,especially the generative model of the deep neural networks.In this work,we propose a resource allocation deep autoencoder network,as one of the promising generative models,for enabling spectrum sharing in underlay device-to-device(D2D)communication by solving linear sum assignment problems(LSAPs).Specifically,we investigate the performance of three different architectures for the conditional variational autoencoders(CVAE).The three proposed architecture are the convolutional neural network(CVAECNN)autoencoder,the feed-forward neural network(CVAE-FNN)autoencoder,and the hybrid(H-CVAE)autoencoder.The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques,such as the Hungarian algorithm,due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time.Moreover,the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.
基金Supported by the Scientific Research Foundation of Hubei Provincial Education Department of China(Q20174503)the National Science Foundation of Hubei Polytechnic University of China(12xjz14A and 17xjz03A)。
文摘In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.
文摘In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.
文摘Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in [1]. Our approach is based on the use of linear programming and is solvable in polynomial time. The algorithm we developed can be implemented and parallelized in a very easy way.
基金supported by the National Natural Science Foundation of China (51179039)the Ph.D. Programs Foundation of Ministry of Education of China (20102304110021)
文摘A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347026,11147009,and 11244005)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Scientific Research Project of Liaocheng,China
文摘Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.
文摘Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.
文摘In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.
文摘On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.
文摘[背景]电焊工接触含多种金属的电焊烟尘引起肺功能下降,既往研究多集中于单一金属与肺功能间的关联,较少关注到金属混合暴露的肺功能健康损害。[目的]本研究旨在评估电焊工尿液和血液中多种金属浓度与肺功能指标间的关联,探讨影响肺功能的关键金属成分,为职业健康风险评估提供参考依据。[方法]对上海市某造船厂电焊工和对照组工人进行问卷调查、肺功能检测,并收集尿液和血液样本。采用电感耦合等离子体质谱法(ICP-MS)检测尿液和血液中钒、铬、锰等12种金属浓度。Spearman相关用于分析血液、尿液中金属间的关联性。应用多重线性回归、加权分位数之和回归(WQS)和贝叶斯核机器回归(BKMR)剖析金属混合暴露与肺功能指标用力肺活量(FVC)、用力肺活量占预计值百分比(FVC%)、第1秒用力呼气容积(FEV_(1))、第1秒用力呼气容积占预计值百分比(FEV_(1)%)和一秒率(FEV_(1)/FVC)间的关系。[结果]本研究共纳入445名工人,焊工组322人(72.36%),对照组123人(27.64%),总人群平均年龄为(37.64±8.80)岁,87.19%为男性。电焊工尿镉(0.88 vs 0.58μg·L^(-1))以及血铬(5.86 vs5.06μg·L^(-1))、锰(24.24 vs 21.38μg·L^(-1))浓度均显著高于对照组(P<0.05)。Spearman相关结果显示尿液和血液中金属元素间相关系数范围为-0.46~0.68。在校正混杂因素后,多重线性回归结果提示电焊工尿钼与FVC、FEV_(1)间呈负相关;血钼与FVC、FVC%、FEV_(1)、FEV_(1)%以及血铜与FEV_(1)/FVC间呈负相关。WQS结果表明电焊工血液、尿液金属混合浓度每增加1个四分位数水平,FEV_(1)、FVC分别平均下降0.112 L、0.353 L,铜、锌、钒、锑等金属贡献较大。BKMR显示电焊工血液、尿液中金属浓度与FVC、FVC%、FEV_(1)、FEV_(1)%间呈下降趋势,单变量暴露反应-关系中血液、尿液钼浓度与FVC、FVC%、FEV_(1)、FEV_(1)大致呈线性下降趋势;电焊工尿液中不同金属作用于FEV_(1)%时,镉与锰、镍、钒间,钒与铁、钼、锌、铜间可能具有交互作用。[结论]多金属混合暴露引起电焊工肺功能下降,贡献较大的金属有钼、锑、铜和锌等。
