Breast cancer diagnosis through mammography is a pivotal application within medical image-based diagnostics,integral for early detection and effective treatment.While deep learning has significantly advanced the analy...Breast cancer diagnosis through mammography is a pivotal application within medical image-based diagnostics,integral for early detection and effective treatment.While deep learning has significantly advanced the analysis of mammographic images,challenges such as low contrast,image noise,and the high dimensionality of features often degrade model performance.Addressing these challenges,our study introduces a novel method integrating Genetic Algorithms(GA)with pre-trained Convolutional Neural Network(CNN)models to enhance feature selection and classification accuracy.Our approach involves a systematic process:first,we employ widely-used CNN architectures(VGG16,VGG19,MobileNet,and DenseNet)to extract a broad range of features from the Medical Image Analysis Society(MIAS)mammography dataset.Subsequently,a GA optimizes these features by selecting the most relevant and least redundant,aiming to overcome the typical pitfalls of high dimensionality.The selected features are then utilized to train several classifiers,including Linear and Polynomial Support Vector Machines(SVMs),K-Nearest Neighbors,Decision Trees,and Random Forests,enabling a robust evaluation of the method’s effectiveness across varied learning algorithms.Our extensive experimental evaluation demonstrates that the integration of MobileNet and GA significantly improves classification accuracy,from 83.33%to 89.58%,underscoring the method’s efficacy.By detailing these steps,we highlight the innovation of our approach which not only addresses key issues in breast cancer imaging analysis but also offers a scalable solution potentially applicable to other domains within medical imaging.展开更多
Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining perform...Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining performance,but they still require huge computational resource and may miss many HUIs.Due to the good combination of EA and graphics processing unit(GPU),we propose a parallel genetic algorithm(GA)based on the platform of GPU for mining HUIM(PHUI-GA).The evolution steps with improvements are performed in central processing unit(CPU)and the CPU intensive steps are sent to GPU to eva-luate with multi-threaded processors.Experiments show that the mining performance of PHUI-GA outperforms the existing EAs.When mining 90%HUIs,the PHUI-GA is up to 188 times better than the existing EAs and up to 36 times better than the CPU parallel approach.展开更多
Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up t...Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up to 7G.Furthermore,it improves the array gain and directivity,increasing the detection range and angular resolution of radar systems.This study proposes two highly efficient SLL reduction techniques.These techniques are based on the hybridization between either the single convolution or the double convolution algorithms and the genetic algorithm(GA)to develop the Conv/GA andDConv/GA,respectively.The convolution process determines the element’s excitations while the GA optimizes the element spacing.For M elements linear antenna array(LAA),the convolution of the excitation coefficients vector by itself provides a new vector of excitations of length N=(2M−1).This new vector is divided into three different sets of excitations including the odd excitations,even excitations,and middle excitations of lengths M,M−1,andM,respectively.When the same element spacing as the original LAA is used,it is noticed that the odd and even excitations provide a much lower SLL than that of the LAA but with amuch wider half-power beamwidth(HPBW).While the middle excitations give the same HPBWas the original LAA with a relatively higher SLL.Tomitigate the increased HPBWof the odd and even excitations,the element spacing is optimized using the GA.Thereby,the synthesized arrays have the same HPBW as the original LAA with a two-fold reduction in the SLL.Furthermore,for extreme SLL reduction,the DConv/GA is introduced.In this technique,the same procedure of the aforementioned Conv/GA technique is performed on the resultant even and odd excitation vectors.It provides a relatively wider HPBWthan the original LAA with about quad-fold reduction in the SLL.展开更多
In a brand new era,with chaotic scenario that exists within the world,people are undermined with diverse psychological assaults.There have been numerous sensible approaches on the way to understand and lessen those at...In a brand new era,with chaotic scenario that exists within the world,people are undermined with diverse psychological assaults.There have been numerous sensible approaches on the way to understand and lessen those attacks.Bioscrypt developments have verified to be one of the beneficial approaches for intercepting these troubles.Identifying recognition through human iris organ is said as one of the well-known biometric strategies because of its reliability and higher accurate return in comparison to different developments.Reviewing beyond literatures,terrible imaging condition,low flexibility of version,and small length iris image dataset are the constraints desiring solutions.Among these kinds of developments,the iris popularity structures are suitable gear for the human identification.Iris popularity has been an energetic studies location for the duration of previous couple of decades,due to its extensive packages in the areas,from airports to native land protection border protection.In the past,various functions and methods for iris recognition have been presented.Despite of the very fact that there are many approaches published in this field,there are still liberal amount of problems in this methodology like tedious and computational intricacy.We suggest an all-encompassing deep learning architecture for iris recognition supported by a genetic algorithm and a wavelet transformation,which may jointly learn the feature representation and perform recognition to realize high efficiency.With just a few training photos from each class,we train our model on a well-known iris recognition dataset and demonstrate improvements over prior methods.We think that this architecture can be frequently employed for various biometric recognition jobs,assisting in the development of a more scalable and precise system.The exploratory aftereffects of the proposed technique uncover that the strategy is effective inside the iris acknowledgment.展开更多
In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying result...In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying results by using conventional linear sta- tistical methods. Recursive feature elimination based on support vector machine (SVM RFE) is an effective algorithm for gene selection and cancer classification, which are integrated into a consistent framework. In this paper, we propose a new method to select parameters of the aforementioned algorithm implemented with Gaussian kernel SVMs as better alternatives to the common practice of selecting the apparently best parameters by using a genetic algorithm to search for a couple of optimal parameter. Fast implementation issues for this method are also discussed for pragmatic reasons. The proposed method was tested on two repre- sentative hereditary breast cancer and acute leukaemia datasets. The experimental results indicate that the proposed method per- forms well in selecting genes and achieves high classification accuracies with these genes.展开更多
Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it...Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it avoids converging to the local optimum. However, it takes too much CPU time in the late process of GA. On the other hand, in the late process Simulated Annealing (SA) converges faster than GA but it is easily trapped to local optimum. In this letter, a useful method that unifies GA and SA is introduced, which utilizes the advantage of the global search ability of GA and fast convergence of SA. The experimental results show that the proposed algorithm outperforms GA in terms of CPU time without degradation of performance. It also achieves highly comparable placement cost compared to the state-of-the-art results obtained by Versatile Place and Route (VPR) Tool.展开更多
Accurate prediction of chemical composition of vacuum gas oil （VGO） is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks （ANN） based on a...Accurate prediction of chemical composition of vacuum gas oil （VGO） is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks （ANN） based on a genetic algorithm （GA） is developed for predicting VGO saturates. The number of neurons in the hidden layer, the momentum and the learning rates are determined by using the genetic algorithm. The inputs for the artificial neural networks model are five physical properties, namely, average boiling point, density, molecular weight, viscosity and refractive index. It is verified that the genetic algorithm could find the optimal structural parameters and training parameters of ANN. In addition, an artificial neural networks model based on a genetic algorithm was tested and the results indicated that the VGO saturates can be efficiently predicted. Compared with conventional artificial neural networks models, this approach can improve the prediction accuracy.展开更多
The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the slid...The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.展开更多
Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture ...Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture design process. However, the design of a fixture relies heavily on the designerts expertise and experience up to now. Therefore, a new approach to loeator layout determination for workpieces with arbitrary complex surfaces is pro- posed for the first time. Firstly, based on the fuzzy judgment method, the proper locating reference and locator - numbers are determined with consideration of surface type, surface area and position tolerance. Secondly, the lo- cator positions are optimized by genetic algorithm（GA）. Finally, a typical example shows that the approach is su- perior to the experiential method and can improve positioning accuracy effectively.展开更多
In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoen...In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoenergetic PDDs where two steps are involved.First the spectrum is modeled as a prior analytical function with two parameters αand Ep optimized with the GA.Secondly the linac photon spectrum is modeled as a discretization constrained model optimized with the GA. The solved analytical function in the first step is used to generate initial solutions for the GA’s first run in this step.The method is applied to the Varian iX linear accelerator to derive the energy spectra of its 6 and 15 MV photon beams.The experimental results show that both the reconstructed spectrums and the derived PDDs with the proposed method are in good agreement with those calculated using the Monte Carlo simulation.展开更多
The influences of biological,chemical,and flow processes on soil structure through microbially induced carbonate precipitation(MICP)are not yet fully understood.In this study,we use a multi-level thresholding segmenta...The influences of biological,chemical,and flow processes on soil structure through microbially induced carbonate precipitation(MICP)are not yet fully understood.In this study,we use a multi-level thresholding segmentation algorithm,genetic algorithm(GA)enhanced Kapur entropy(KE)(GAE-KE),to accomplish quantitative characterization of sandy soil structure altered by MICP cementation.A sandy soil sample was treated using MICP method and scanned by the synchrotron radiation(SR)micro-CT with a resolution of 6.5 mm.After validation,tri-level thresholding segmentation using GAE-KE successfully separated the precipitated calcium carbonate crystals from sand particles and pores.The spatial distributions of porosity,pore structure parameters,and flow characteristics were calculated for quantitative characterization.The results offer pore-scale insights into the MICP treatment effect,and the quantitative understanding confirms the feasibility of the GAE-KE multi-level thresholding segmentation algorithm.展开更多
A genetic algorithm (GA)-based method is proposed to solve the nonlinearoptimization problem of minimum zone cylindricity evaluation. First, the background of the problemis introduced. Then the mathematical model and ...A genetic algorithm (GA)-based method is proposed to solve the nonlinearoptimization problem of minimum zone cylindricity evaluation. First, the background of the problemis introduced. Then the mathematical model and the fitness function are derived from themathematical definition of dimensioning and tolerancing principles. Thirdly with the least squaressolution as the initial values, the whole implementation process of the algorithm is realized inwhich some key techniques, for example, variables representing, population initializing and suchbasic operations as selection, crossover and mutation, are discussed in detail. Finally, examplesare quoted to verify the proposed algorithm. The computation results indicate that the GA-basedoptimization method performs well on cylindricity evaluation. The outstanding advantages concludehigh accuracy, high efficiency and capabilities of solving complicated nonlinear and large spaceproblems.展开更多
基金The authors extend their appreciation to the Deputyship for Research&Innovation,“Ministry of Education”in Saudi Arabia for funding this research work through the project number (IFKSUDR_D127).
文摘Breast cancer diagnosis through mammography is a pivotal application within medical image-based diagnostics,integral for early detection and effective treatment.While deep learning has significantly advanced the analysis of mammographic images,challenges such as low contrast,image noise,and the high dimensionality of features often degrade model performance.Addressing these challenges,our study introduces a novel method integrating Genetic Algorithms(GA)with pre-trained Convolutional Neural Network(CNN)models to enhance feature selection and classification accuracy.Our approach involves a systematic process:first,we employ widely-used CNN architectures(VGG16,VGG19,MobileNet,and DenseNet)to extract a broad range of features from the Medical Image Analysis Society(MIAS)mammography dataset.Subsequently,a GA optimizes these features by selecting the most relevant and least redundant,aiming to overcome the typical pitfalls of high dimensionality.The selected features are then utilized to train several classifiers,including Linear and Polynomial Support Vector Machines(SVMs),K-Nearest Neighbors,Decision Trees,and Random Forests,enabling a robust evaluation of the method’s effectiveness across varied learning algorithms.Our extensive experimental evaluation demonstrates that the integration of MobileNet and GA significantly improves classification accuracy,from 83.33%to 89.58%,underscoring the method’s efficacy.By detailing these steps,we highlight the innovation of our approach which not only addresses key issues in breast cancer imaging analysis but also offers a scalable solution potentially applicable to other domains within medical imaging.
基金This work was supported by the National Natural Science Foundation of China(62073155,62002137,62106088,62206113)the High-End Foreign Expert Recruitment Plan(G2023144007L)the Fundamental Research Funds for the Central Universities(JUSRP221028).
文摘Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining performance,but they still require huge computational resource and may miss many HUIs.Due to the good combination of EA and graphics processing unit(GPU),we propose a parallel genetic algorithm(GA)based on the platform of GPU for mining HUIM(PHUI-GA).The evolution steps with improvements are performed in central processing unit(CPU)and the CPU intensive steps are sent to GPU to eva-luate with multi-threaded processors.Experiments show that the mining performance of PHUI-GA outperforms the existing EAs.When mining 90%HUIs,the PHUI-GA is up to 188 times better than the existing EAs and up to 36 times better than the CPU parallel approach.
基金Research Supporting Project Number(RSPD2023R 585),King Saud University,Riyadh,Saudi Arabia.
文摘Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up to 7G.Furthermore,it improves the array gain and directivity,increasing the detection range and angular resolution of radar systems.This study proposes two highly efficient SLL reduction techniques.These techniques are based on the hybridization between either the single convolution or the double convolution algorithms and the genetic algorithm(GA)to develop the Conv/GA andDConv/GA,respectively.The convolution process determines the element’s excitations while the GA optimizes the element spacing.For M elements linear antenna array(LAA),the convolution of the excitation coefficients vector by itself provides a new vector of excitations of length N=(2M−1).This new vector is divided into three different sets of excitations including the odd excitations,even excitations,and middle excitations of lengths M,M−1,andM,respectively.When the same element spacing as the original LAA is used,it is noticed that the odd and even excitations provide a much lower SLL than that of the LAA but with amuch wider half-power beamwidth(HPBW).While the middle excitations give the same HPBWas the original LAA with a relatively higher SLL.Tomitigate the increased HPBWof the odd and even excitations,the element spacing is optimized using the GA.Thereby,the synthesized arrays have the same HPBW as the original LAA with a two-fold reduction in the SLL.Furthermore,for extreme SLL reduction,the DConv/GA is introduced.In this technique,the same procedure of the aforementioned Conv/GA technique is performed on the resultant even and odd excitation vectors.It provides a relatively wider HPBWthan the original LAA with about quad-fold reduction in the SLL.
文摘In a brand new era,with chaotic scenario that exists within the world,people are undermined with diverse psychological assaults.There have been numerous sensible approaches on the way to understand and lessen those attacks.Bioscrypt developments have verified to be one of the beneficial approaches for intercepting these troubles.Identifying recognition through human iris organ is said as one of the well-known biometric strategies because of its reliability and higher accurate return in comparison to different developments.Reviewing beyond literatures,terrible imaging condition,low flexibility of version,and small length iris image dataset are the constraints desiring solutions.Among these kinds of developments,the iris popularity structures are suitable gear for the human identification.Iris popularity has been an energetic studies location for the duration of previous couple of decades,due to its extensive packages in the areas,from airports to native land protection border protection.In the past,various functions and methods for iris recognition have been presented.Despite of the very fact that there are many approaches published in this field,there are still liberal amount of problems in this methodology like tedious and computational intricacy.We suggest an all-encompassing deep learning architecture for iris recognition supported by a genetic algorithm and a wavelet transformation,which may jointly learn the feature representation and perform recognition to realize high efficiency.With just a few training photos from each class,we train our model on a well-known iris recognition dataset and demonstrate improvements over prior methods.We think that this architecture can be frequently employed for various biometric recognition jobs,assisting in the development of a more scalable and precise system.The exploratory aftereffects of the proposed technique uncover that the strategy is effective inside the iris acknowledgment.
基金Project supported by the National Basic Research Program (973) of China (No. 2002CB312200) and the Center for Bioinformatics Pro-gram Grant of Harvard Center of Neurodegeneration and Repair,Harvard Medical School, Harvard University, Boston, USA
文摘In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying results by using conventional linear sta- tistical methods. Recursive feature elimination based on support vector machine (SVM RFE) is an effective algorithm for gene selection and cancer classification, which are integrated into a consistent framework. In this paper, we propose a new method to select parameters of the aforementioned algorithm implemented with Gaussian kernel SVMs as better alternatives to the common practice of selecting the apparently best parameters by using a genetic algorithm to search for a couple of optimal parameter. Fast implementation issues for this method are also discussed for pragmatic reasons. The proposed method was tested on two repre- sentative hereditary breast cancer and acute leukaemia datasets. The experimental results indicate that the proposed method per- forms well in selecting genes and achieves high classification accuracies with these genes.
基金Supported by School of Engineering, Napier University, United Kingdom, and partially supported by the National Natural Science Foundation of China (No.60273093).
文摘Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it avoids converging to the local optimum. However, it takes too much CPU time in the late process of GA. On the other hand, in the late process Simulated Annealing (SA) converges faster than GA but it is easily trapped to local optimum. In this letter, a useful method that unifies GA and SA is introduced, which utilizes the advantage of the global search ability of GA and fast convergence of SA. The experimental results show that the proposed algorithm outperforms GA in terms of CPU time without degradation of performance. It also achieves highly comparable placement cost compared to the state-of-the-art results obtained by Versatile Place and Route (VPR) Tool.
文摘Accurate prediction of chemical composition of vacuum gas oil （VGO） is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks （ANN） based on a genetic algorithm （GA） is developed for predicting VGO saturates. The number of neurons in the hidden layer, the momentum and the learning rates are determined by using the genetic algorithm. The inputs for the artificial neural networks model are five physical properties, namely, average boiling point, density, molecular weight, viscosity and refractive index. It is verified that the genetic algorithm could find the optimal structural parameters and training parameters of ANN. In addition, an artificial neural networks model based on a genetic algorithm was tested and the results indicated that the VGO saturates can be efficiently predicted. Compared with conventional artificial neural networks models, this approach can improve the prediction accuracy.
文摘The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.
基金Supported by the Natural Science Foundation of Jiangxi Province(2009GZC0104)the Science and Technology Research Project of Jiangxi Provincial Department of Education(GJJ10521)~~
文摘Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture design process. However, the design of a fixture relies heavily on the designerts expertise and experience up to now. Therefore, a new approach to loeator layout determination for workpieces with arbitrary complex surfaces is pro- posed for the first time. Firstly, based on the fuzzy judgment method, the proper locating reference and locator - numbers are determined with consideration of surface type, surface area and position tolerance. Secondly, the lo- cator positions are optimized by genetic algorithm（GA）. Finally, a typical example shows that the approach is su- perior to the experiential method and can improve positioning accuracy effectively.
文摘In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoenergetic PDDs where two steps are involved.First the spectrum is modeled as a prior analytical function with two parameters αand Ep optimized with the GA.Secondly the linac photon spectrum is modeled as a discretization constrained model optimized with the GA. The solved analytical function in the first step is used to generate initial solutions for the GA’s first run in this step.The method is applied to the Varian iX linear accelerator to derive the energy spectra of its 6 and 15 MV photon beams.The experimental results show that both the reconstructed spectrums and the derived PDDs with the proposed method are in good agreement with those calculated using the Monte Carlo simulation.
基金supported by the National Natural Science Foundation of China(Grant Nos.42077232 and 42077235)the Key Research and Development Plan of Jiangsu Province(Grant No.BE2022156).
文摘The influences of biological,chemical,and flow processes on soil structure through microbially induced carbonate precipitation(MICP)are not yet fully understood.In this study,we use a multi-level thresholding segmentation algorithm,genetic algorithm(GA)enhanced Kapur entropy(KE)(GAE-KE),to accomplish quantitative characterization of sandy soil structure altered by MICP cementation.A sandy soil sample was treated using MICP method and scanned by the synchrotron radiation(SR)micro-CT with a resolution of 6.5 mm.After validation,tri-level thresholding segmentation using GAE-KE successfully separated the precipitated calcium carbonate crystals from sand particles and pores.The spatial distributions of porosity,pore structure parameters,and flow characteristics were calculated for quantitative characterization.The results offer pore-scale insights into the MICP treatment effect,and the quantitative understanding confirms the feasibility of the GAE-KE multi-level thresholding segmentation algorithm.
基金This project is supported by National Natural Science Foundation of China (No.59975025)
文摘A genetic algorithm (GA)-based method is proposed to solve the nonlinearoptimization problem of minimum zone cylindricity evaluation. First, the background of the problemis introduced. Then the mathematical model and the fitness function are derived from themathematical definition of dimensioning and tolerancing principles. Thirdly with the least squaressolution as the initial values, the whole implementation process of the algorithm is realized inwhich some key techniques, for example, variables representing, population initializing and suchbasic operations as selection, crossover and mutation, are discussed in detail. Finally, examplesare quoted to verify the proposed algorithm. The computation results indicate that the GA-basedoptimization method performs well on cylindricity evaluation. The outstanding advantages concludehigh accuracy, high efficiency and capabilities of solving complicated nonlinear and large spaceproblems.
