Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach ge...Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].展开更多
Fatigue damage increases with the applied loading cycles in a cumulative manner and the material deteriorates with the corrosion time. A cumulative fatigue damage rule under the alternative of corrosion or cyclic load...Fatigue damage increases with the applied loading cycles in a cumulative manner and the material deteriorates with the corrosion time. A cumulative fatigue damage rule under the alternative of corrosion or cyclic loading was proposed. The specimens of aluminum alloy LY12-CZ soaked in corrosive liquid for different times were tested under the constant amplitude cyclic loading to obtain S-N curves. The test was carried out to verify the proposed cumulative fatigue damage rule under the different combinations among corrosion time, loading level, and the cycle numbers. It was shown that the predicted residual fatigue lives showed a good agreement with the experimental results and the proposed rule was simple and can be easily adopted.展开更多
Detecting remote homology proteins is a challenging problem for both basic research and drug development. Although there are a couple of methods to deal with this problem, the benchmark datasets based on which the exi...Detecting remote homology proteins is a challenging problem for both basic research and drug development. Although there are a couple of methods to deal with this problem, the benchmark datasets based on which the existing methods were trained and tested contain many high homologous samples as reflected by the fact that the cutoff threshold was set at 95%. In this study, we reconstructed the benchmark dataset by setting the threshold at 40%, meaning none of the proteins included in the benchmark dataset has more than 40% pairwise sequence identity with any other in the same subset. Using the new benchmark dataset, we proposed a new predictor called “dRHP-GreyFun” based on the grey modeling and functional domain approach. Rigorous cross-validations have indicated that the new predictor is superior to its counterparts in both enhancing success rates and reducing computational cost. The predictor can be downloaded from https://github.com/jcilwz/dRHP-GreyFun.展开更多
Mitochondrial dysfunction in Parkinson＇s disease：Mitochondria are the primary energy generator of the cell and they are important for cell survival and apoptosis.Defective mitochondrial homeostasis is frequently rep...Mitochondrial dysfunction in Parkinson＇s disease：Mitochondria are the primary energy generator of the cell and they are important for cell survival and apoptosis.Defective mitochondrial homeostasis is frequently reported in human diseases especially those affecting the brain.展开更多
The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of me...The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.展开更多
While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge t...While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.展开更多
Alzheimer’s disease(AD)is a very complex disease that causes brain failure,then eventually,dementia ensues.It is a global health problem.99%of clinical trials have failed to limit the progression of this disease.The ...Alzheimer’s disease(AD)is a very complex disease that causes brain failure,then eventually,dementia ensues.It is a global health problem.99%of clinical trials have failed to limit the progression of this disease.The risks and barriers to detecting AD are huge as pathological events begin decades before appearing clinical symptoms.Therapies for AD are likely to be more helpful if the diagnosis is determined early before the final stage of neurological dysfunction.In this regard,the need becomes more urgent for biomarker-based detection.A key issue in understanding AD is the need to solve complex and high-dimensional datasets and heterogeneous biomarkers,such as genetics,magnetic resonance imaging(MRI),cerebrospinal fluid(CSF),and cognitive scores.Establishing an interpretable reasoning system and performing interoperability that achieves in terms of a semantic model is potentially very useful.Thus,our aim in this work is to propose an interpretable approach to detect AD based on Alzheimer’s disease diagnosis ontology(ADDO)and the expression of semantic web rule language(SWRL).This work implements an ontology-based application that exploits three different machine learning models.These models are random forest(RF),JRip,and J48,which have been used along with the voting ensemble.ADNI dataset was used for this study.The proposed classifier’s result with the voting ensemble achieves a higher accuracy of 94.1%and precision of 94.3%.Our approach provides effective inference rules.Besides,it contributes to a real,accurate,and interpretable classifier model based on various AD biomarkers for inferring whether the subject is a normal cognitive(NC),significant memory concern(SMC),early mild cognitive impairment(EMCI),late mild cognitive impairment(LMCI),or AD.展开更多
Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and ...Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.展开更多
Although great differences exist between the trade systems of different countries,internationaltrade must go on in line with the customary international trade rules.As China’s economy developsand the socialist market...Although great differences exist between the trade systems of different countries,internationaltrade must go on in line with the customary international trade rules.As China’s economy developsand the socialist market economic system emerges,China is basically qualified to link up withcustomary international trade rules.In the Ninth Five-Year Plan period,China’s reform of its foreigntrade system aims at setting up a trade system that conforms with international trade practice.Forthe purpose,the author of this article suggests that a neutral trade policy should be adopted inaccordance with the international practice since it does not hinder exports,nor restrict imports toan excessive degree.展开更多
文摘Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].
基金supported by the National Natural Science Foundation of China(No.10377007)
文摘Fatigue damage increases with the applied loading cycles in a cumulative manner and the material deteriorates with the corrosion time. A cumulative fatigue damage rule under the alternative of corrosion or cyclic loading was proposed. The specimens of aluminum alloy LY12-CZ soaked in corrosive liquid for different times were tested under the constant amplitude cyclic loading to obtain S-N curves. The test was carried out to verify the proposed cumulative fatigue damage rule under the different combinations among corrosion time, loading level, and the cycle numbers. It was shown that the predicted residual fatigue lives showed a good agreement with the experimental results and the proposed rule was simple and can be easily adopted.
文摘Detecting remote homology proteins is a challenging problem for both basic research and drug development. Although there are a couple of methods to deal with this problem, the benchmark datasets based on which the existing methods were trained and tested contain many high homologous samples as reflected by the fact that the cutoff threshold was set at 95%. In this study, we reconstructed the benchmark dataset by setting the threshold at 40%, meaning none of the proteins included in the benchmark dataset has more than 40% pairwise sequence identity with any other in the same subset. Using the new benchmark dataset, we proposed a new predictor called “dRHP-GreyFun” based on the grey modeling and functional domain approach. Rigorous cross-validations have indicated that the new predictor is superior to its counterparts in both enhancing success rates and reducing computational cost. The predictor can be downloaded from https://github.com/jcilwz/dRHP-GreyFun.
文摘Mitochondrial dysfunction in Parkinson＇s disease：Mitochondria are the primary energy generator of the cell and they are important for cell survival and apoptosis.Defective mitochondrial homeostasis is frequently reported in human diseases especially those affecting the brain.
基金the National Natural Science Foundation of China (50275113).
文摘The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.
基金Supported by the National Science Council at Taiwan through Grants No. NSC 97-2112-M-009-008-MY3
文摘While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.
基金This work was supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2021R1A2C1011198).
文摘Alzheimer’s disease(AD)is a very complex disease that causes brain failure,then eventually,dementia ensues.It is a global health problem.99%of clinical trials have failed to limit the progression of this disease.The risks and barriers to detecting AD are huge as pathological events begin decades before appearing clinical symptoms.Therapies for AD are likely to be more helpful if the diagnosis is determined early before the final stage of neurological dysfunction.In this regard,the need becomes more urgent for biomarker-based detection.A key issue in understanding AD is the need to solve complex and high-dimensional datasets and heterogeneous biomarkers,such as genetics,magnetic resonance imaging(MRI),cerebrospinal fluid(CSF),and cognitive scores.Establishing an interpretable reasoning system and performing interoperability that achieves in terms of a semantic model is potentially very useful.Thus,our aim in this work is to propose an interpretable approach to detect AD based on Alzheimer’s disease diagnosis ontology(ADDO)and the expression of semantic web rule language(SWRL).This work implements an ontology-based application that exploits three different machine learning models.These models are random forest(RF),JRip,and J48,which have been used along with the voting ensemble.ADNI dataset was used for this study.The proposed classifier’s result with the voting ensemble achieves a higher accuracy of 94.1%and precision of 94.3%.Our approach provides effective inference rules.Besides,it contributes to a real,accurate,and interpretable classifier model based on various AD biomarkers for inferring whether the subject is a normal cognitive(NC),significant memory concern(SMC),early mild cognitive impairment(EMCI),late mild cognitive impairment(LMCI),or AD.
基金Supported by the Natural Science Foundation of Zhejiang Province（Y6090361）
文摘Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.
文摘Although great differences exist between the trade systems of different countries,internationaltrade must go on in line with the customary international trade rules.As China’s economy developsand the socialist market economic system emerges,China is basically qualified to link up withcustomary international trade rules.In the Ninth Five-Year Plan period,China’s reform of its foreigntrade system aims at setting up a trade system that conforms with international trade practice.Forthe purpose,the author of this article suggests that a neutral trade policy should be adopted inaccordance with the international practice since it does not hinder exports,nor restrict imports toan excessive degree.
