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71.
We present a graphical technique for generating and indexing spin monomials of high‐spin systems. The procedure consists of developing a graph with at most n line segments from each node in a given row to the one immediately lower, where n is the multiplicity of single‐particle spin function. The paths lead to monomials with definite M values at each node. This technique has been used to generate and diagonalize the model spin Hamiltonian. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 389–393, 1999  相似文献   
72.
We consider a problem of searching an element in a partially ordered set (poset). The goal is to find a search strategy which minimizes the number of comparisons. Ben-Asher, Farchi and Newman considered a special case where the partial order has the maximum element and the Hasse diagram is a tree (tree-like posets) and they gave an O(n4log3n)-time algorithm for finding an optimal search strategy for such a partial order. We show that this problem is equivalent to finding edge ranking of a simple tree corresponding to the Hasse diagram, which implies the existence of a linear-time algorithm for this problem.Then we study a more general problem, namely searching in any partial order with maximum element. We prove that such a generalization is hard, and we give an -approximate polynomial-time algorithm for this problem.  相似文献   
73.
The edit distance problem for rooted unordered trees is known to be NP-hard. Based on this fact, this paper studies exponential-time algorithms for the problem. For a general case, an O(min(1.26n1+n2,2b1+b2poly(n1,n2))) time algorithm is presented, where n1 and n2 are the numbers of nodes and b1 and b2 are the numbers of branching nodes in two input trees. This algorithm is obtained by a combination of dynamic programming, exhaustive search, and maximum weighted bipartite matching. For bounded degree trees over a fixed alphabet, it is shown that the problem can be solved in O((1+ϵ)n1+n2) time for any fixed ϵ>0. This result is achieved by avoiding duplicate calculations for identical subsets of small subtrees.  相似文献   
74.
一类优美树     
孟凡洪  苏耕  杨继 《东北数学》2000,16(3):272-278
§1. Preliminary Lemma Using A to denote the cardinal number of a finite set A, we do not explain anymore what are similar to A in this paper. For a given tree T(V,E), if there is a labeling f of its vertices, which satisfiesf[V(T)]={f(u)u∈V(T)}={0,1,2,…,E(T)},lf[E(T)]={lf(uv)=f(u)-f(v), uv∈E(T)}={1,2,…,E(T)},then f is called a graceful labeling of T, and T is called a graceful tree. lf denotes the labeling of edges that is derived from f. In the 1960s, RingedKotzing and A. R…  相似文献   
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Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.  相似文献   
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In this article, we propose localized implementations of the iterative proportional scaling (IPS) procedure by the strategy of partitioning cliques for computing maximum likelihood estimations in large Gaussian graphical models. We first divide the set of cliques into several nonoverlapping and nonempty blocks, and then adjust clique marginals in each block locally. Thus, high-order matrix operations can be avoided and the IPS procedure is accelerated. We modify the Swendsen–Wang Algorithm and apply the simulated annealing algorithm to find an approximation to the optimal partition which leads to the least complexity. This strategy of partitioning cliques can also speed up the existing IIPS and IHT procedures. Numerical experiments are presented to demonstrate the competitive performance of our new implementations and strategies.  相似文献   
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