I. THE COMPLEXITY OFBIOLOGICAL RESPONSESFor an organism, to be living or notdepends on its response to foreign matters.Facing the increasing amount and diversi-ty of chemicals, natural and synthetic, tounderstand the ...I. THE COMPLEXITY OFBIOLOGICAL RESPONSESFor an organism, to be living or notdepends on its response to foreign matters.Facing the increasing amount and diversi-ty of chemicals, natural and synthetic, tounderstand the principles of the biologicalresponses becomes extremely importantin pursuing the way of rational utiliza-tion and governing the foreign matters.However, most biological responses aretoo complex to explore their nature. Forinstance, the risk to human beings andorganisms related to the application ofrare earths in agriculture, forestation, fish-ery and husbandry has been argued展开更多
A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Lin...A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Links of the same feature have the same cost. It is proved that the problem of finding ?routing tree of the minimum cost for a given set of tasks of two features is NP-complete.展开更多
A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the numbe...A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n^4,n^3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.展开更多
Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and...Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.展开更多
文摘I. THE COMPLEXITY OFBIOLOGICAL RESPONSESFor an organism, to be living or notdepends on its response to foreign matters.Facing the increasing amount and diversi-ty of chemicals, natural and synthetic, tounderstand the principles of the biologicalresponses becomes extremely importantin pursuing the way of rational utiliza-tion and governing the foreign matters.However, most biological responses aretoo complex to explore their nature. Forinstance, the risk to human beings andorganisms related to the application ofrare earths in agriculture, forestation, fish-ery and husbandry has been argued
基金This research was supported in part by the NSF grants DCB-8501226 and DCR-8696135. Part of this work was done while the first author was at the Mathematical Sciences Research Institute, Berkeley, California, and while the second author was at the Departm
文摘A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Links of the same feature have the same cost. It is proved that the problem of finding ?routing tree of the minimum cost for a given set of tasks of two features is NP-complete.
基金This work is supported in part by the Foundation of Zhongshan University Advanced Research Centrein part by the National Natural Science Foundation of China
文摘A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity.We prove that the cost of locating all zeros of a polynomial of degree n to an accuracy of ε(measured by the number of evaluations of the polynomial)grows no faster than O(max{n^4,n^3log_2(n/ε)}).This work is in response to a question raised in a paper by S.Smale as to the efficiency of piecewise linear methods in solving equations.In comparison with a few results reported,the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.
文摘Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.
