How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a ...How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.展开更多
This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
This study proposes a novel gradient‐based neural network model with an activated variable parameter,named as the activated variable parameter gradient‐based neural network(AVPGNN)model,to solve time‐varying constr...This study proposes a novel gradient‐based neural network model with an activated variable parameter,named as the activated variable parameter gradient‐based neural network(AVPGNN)model,to solve time‐varying constrained quadratic programming(TVCQP)problems.Compared with the existing models,the AVPGNN model has the following advantages:(1)avoids the matrix inverse,which can significantly reduce the computing complexity;(2)introduces the time‐derivative of the time‐varying param-eters in the TVCQP problem by adding an activated variable parameter,enabling the AVPGNN model to achieve a predictive calculation that achieves zero residual error in theory;(3)adopts the activation function to accelerate the convergence rate.To solve the TVCQP problem with the AVPGNN model,the TVCQP problem is transformed into a non‐linear equation with a non‐linear compensation problem function based on the Karush Kuhn Tucker conditions.Then,a variable parameter with an activation function is employed to design the AVPGNN model.The accuracy and convergence rate of the AVPGNN model are rigorously analysed in theory.Furthermore,numerical experiments are also executed to demonstrate the effectiveness and superiority of the proposed model.Moreover,to explore the feasibility of the AVPGNN model,appli-cations to the motion planning of a robotic manipulator and the portfolio selection of marketed securities are illustrated.展开更多
With the continuous and rapid growth of transport demand,scheduling strategy of warehouse has become a key issue in the field of logistics transportation.The structural differences of the warehouse,the automated stora...With the continuous and rapid growth of transport demand,scheduling strategy of warehouse has become a key issue in the field of logistics transportation.The structural differences of the warehouse,the automated storage and retrieval system(AS/RS)model and the two-end dual stackers scheduling model(TDSM)are considered,and a new improved genetic algorithm(NIGA)is proposed.It can adjust the algorithm structure according to the density of population fitness value,and effectively optimize the stacker path.In the TDSM,an improved anti-collision principle is proposed to avoid collision of two stackers.Besides,combined with the optimal anti-collision boundary inspection mechanism,the best working area for the two stackers is allocated by using NIGA.Finally,the new improved GA is compared with GA and the adaptive GA on specific storage and retrieval tasks.The simulation results show that the proposed NIGA well outperforms other GAs in most instances,which indicates that it is an effective approach for the AS/RS and the TDSM scheduling optimization problem.展开更多
In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane unde...In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity;our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. <em>Mathematica</em> [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.展开更多
Automatically solving math word problems,which involves comprehension,cognition,and reasoning,is a crucial issue in artificial intelligence research.Existing math word problem solvers mainly work on word-level relatio...Automatically solving math word problems,which involves comprehension,cognition,and reasoning,is a crucial issue in artificial intelligence research.Existing math word problem solvers mainly work on word-level relationship extraction and the generation of expression solutions while lacking consideration of the clause-level relationship.To this end,inspired by the theory of two levels of process in comprehension,we propose a novel clause-level relationship-aware math solver(CLRSolver)to mimic the process of human comprehension from lower level to higher level.Specifically,in the lower-level processes,we split problems into clauses according to their natural division and learn their semantics.In the higher-level processes,following human′s multi-view understanding of clause-level relationships,we first apply a CNN-based module to learn the dependency relationships between clauses from word relevance in a local view.Then,we propose two novel relationship-aware mechanisms to learn dependency relationships from the clause semantics in a global view.Next,we enhance the representation of clauses based on the learned clause-level dependency relationships.In expression generation,we develop a tree-based decoder to generate the mathematical expression.We conduct extensive experiments on two datasets,where the results demonstrate the superiority of our framework.展开更多
Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimiza...Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems. Papers containing new ideas, creative ap-proaches and/or innovative applications as well as invited reviews are expected toappear regularly in the journal.Instructions for AuthorsTo speed up the refereeing and publication processes, all transactions and com-munications between the journal and the authors will be done electronically.All manuscripts should be in the form PDF or postscript or MS Word files.展开更多
Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimiza...Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-展开更多
Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimiza...Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-展开更多
The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From ...The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).展开更多
The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From ...The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).展开更多
基金National Natural Science Foundation of China,Grant/Award Number:92370117。
文摘How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
基金supported in part by the University of Macao(File No.MYRG2018‐00053‐FST)in part by the Open Research Fund of the Beijing Key Laboratory of Big Data Technology for Food Safety(Project No.BTBD‐2021KF05)in part by the Major Science and Technology Special Project of Yunnan Province(202102AD080006).
文摘This study proposes a novel gradient‐based neural network model with an activated variable parameter,named as the activated variable parameter gradient‐based neural network(AVPGNN)model,to solve time‐varying constrained quadratic programming(TVCQP)problems.Compared with the existing models,the AVPGNN model has the following advantages:(1)avoids the matrix inverse,which can significantly reduce the computing complexity;(2)introduces the time‐derivative of the time‐varying param-eters in the TVCQP problem by adding an activated variable parameter,enabling the AVPGNN model to achieve a predictive calculation that achieves zero residual error in theory;(3)adopts the activation function to accelerate the convergence rate.To solve the TVCQP problem with the AVPGNN model,the TVCQP problem is transformed into a non‐linear equation with a non‐linear compensation problem function based on the Karush Kuhn Tucker conditions.Then,a variable parameter with an activation function is employed to design the AVPGNN model.The accuracy and convergence rate of the AVPGNN model are rigorously analysed in theory.Furthermore,numerical experiments are also executed to demonstrate the effectiveness and superiority of the proposed model.Moreover,to explore the feasibility of the AVPGNN model,appli-cations to the motion planning of a robotic manipulator and the portfolio selection of marketed securities are illustrated.
基金supported by Anhui Provincial Natural Science Foundation,the youth top-notch talent of Anhui Polytechnic University and University-level research project of Anhui Polytechnic University(No.Xjky019201904)Natural Science Foundation of Anhui Province(Grant/Award Number:1708085ME129)Key Project of Natural Science Research in Colleges and Universities of Anhui Province(kj2019a0147).
文摘With the continuous and rapid growth of transport demand,scheduling strategy of warehouse has become a key issue in the field of logistics transportation.The structural differences of the warehouse,the automated storage and retrieval system(AS/RS)model and the two-end dual stackers scheduling model(TDSM)are considered,and a new improved genetic algorithm(NIGA)is proposed.It can adjust the algorithm structure according to the density of population fitness value,and effectively optimize the stacker path.In the TDSM,an improved anti-collision principle is proposed to avoid collision of two stackers.Besides,combined with the optimal anti-collision boundary inspection mechanism,the best working area for the two stackers is allocated by using NIGA.Finally,the new improved GA is compared with GA and the adaptive GA on specific storage and retrieval tasks.The simulation results show that the proposed NIGA well outperforms other GAs in most instances,which indicates that it is an effective approach for the AS/RS and the TDSM scheduling optimization problem.
文摘In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity;our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. <em>Mathematica</em> [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.
基金supported by National Key Research and Development Program of China(No.2021YFF0901003)National Natural Science Foundation of China(Nos.61922073,U20A20229,and 62106244)。
文摘Automatically solving math word problems,which involves comprehension,cognition,and reasoning,is a crucial issue in artificial intelligence research.Existing math word problem solvers mainly work on word-level relationship extraction and the generation of expression solutions while lacking consideration of the clause-level relationship.To this end,inspired by the theory of two levels of process in comprehension,we propose a novel clause-level relationship-aware math solver(CLRSolver)to mimic the process of human comprehension from lower level to higher level.Specifically,in the lower-level processes,we split problems into clauses according to their natural division and learn their semantics.In the higher-level processes,following human′s multi-view understanding of clause-level relationships,we first apply a CNN-based module to learn the dependency relationships between clauses from word relevance in a local view.Then,we propose two novel relationship-aware mechanisms to learn dependency relationships from the clause semantics in a global view.Next,we enhance the representation of clauses based on the learned clause-level dependency relationships.In expression generation,we develop a tree-based decoder to generate the mathematical expression.We conduct extensive experiments on two datasets,where the results demonstrate the superiority of our framework.
文摘Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems. Papers containing new ideas, creative ap-proaches and/or innovative applications as well as invited reviews are expected toappear regularly in the journal.Instructions for AuthorsTo speed up the refereeing and publication processes, all transactions and com-munications between the journal and the authors will be done electronically.All manuscripts should be in the form PDF or postscript or MS Word files.
文摘Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-
文摘Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-
文摘The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).
文摘The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).
