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21.
To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence. 相似文献
22.
《Journal of computational and graphical statistics》2013,22(4):807-825
We present CARTscans, a graphical tool that displays predicted values across a fourdimensional subspace. We show how these plots are useful for understanding the structure and relationships between variables in a wide variety of models, including (but not limited to) regression trees, ensembles of trees, and linear regressions with varying degrees of interactions. In addition, the common visualization framework allows diverse complex models to be visually compared in a way that illuminates the similarities and differences in the underlying methods, facilitates the choice of a particular model structure, and provides a useful check for implausible predictions of future observations in regions with little or no data. 相似文献
23.
Khodakhast Bibak 《International journal of quantum chemistry》2013,113(8):1209-1212
For a graph G, a “spanning tree” in G is a tree that has the same vertex set as G. The number of spanning trees in a graph (network) G, denoted by t(G), is an important invariant of the graph (network) with lots of decisive applications in many disciplines. In the article by Sato (Discrete Math. 2007, 307, 237), the number of spanning trees in an (r, s)‐semiregular graph and its line graph are obtained. In this article, we give short proofs for the formulas without using zeta functions. Furthermore, by applying the formula that enumerates the number of spanning trees in the line graph of an (r, s)‐semiregular graph, we give a new proof of Cayley's Theorem. © 2013 Wiley Periodicals, Inc. 相似文献
25.
Zhongzhi Zhang Shuigeng Zhou Tao Zou Lichao Chen Jihong Guan 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(2):259-264
We make a mapping from Sierpinski fractals to a new class
of networks, the incompatibility networks, which are scale-free,
small-world, disassortative, and maximal planar graphs. Some
relevant characteristics of the networks such as degree
distribution, clustering coefficient, average path length, and
degree correlations are computed analytically and found to be
peculiarly rich. The method of network representation can be applied
to some real-life systems making it possible to study the complexity
of real networked systems within the framework of complex network
theory. 相似文献
26.
给定2个图G 1 ![]()
![]()
和G 2 ![]()
![]()
,设G 1 ![]()
![]()
的边集E ( G 1 ) = { e 1 , e 2 , ? , e m 1 } ![]()
![]()
,则图G 1 ⊙ G 2 ![]()
![]()
可由一个G 1 ![]()
![]()
,m 1 ![]()
![]()
个G 2 ![]()
![]()
通过在G 1 ![]()
![]()
对应的每条边外加一个孤立点,新增加的点记为U = { u 1 , u 2 , ? , u m 1 } ![]()
![]()
,将u i ![]()
![]()
分别与第i ![]()
![]()
个G 2 ![]()
![]()
的所有点以及G 1 ![]()
![]()
中的边e i ![]()
![]()
的端点相连得到,其中i = ? 1,2 , ? , m 1 ![]()
![]()
。得到:(i)当G 1 ![]()
![]()
是正则图,G 2 ![]()
![]()
是正则图或完全二部图时,确定了G 1 ⊙ G 2 ![]()
![]()
的邻接谱(A -谱)。(ii)当G 1 ![]()
![]()
是正则图,G 2 ![]()
![]()
是任意图时,给出了G 1 ⊙ G 2 ![]()
![]()
的拉普拉斯谱(L -谱)。(iii)当G 1 ![]()
![]()
和G 2 ![]()
![]()
都是正则图时,给出了G 1 ⊙ G 2 ![]()
![]()
的无符号拉普拉斯谱(Q -谱)。作为以上结论的应用,构建了无限多对A -同谱图、L -同谱图和Q -同谱图;同时当G 1 ![]()
![]()
是正则图时,确定了G 1 ⊙ G 2 ![]()
![]()
支撑树的数量和Kirchhoff指数。 相似文献
27.
线性同胚于星象函数的一族解析函数 总被引:4,自引:0,他引:4
本文定义了线性同胚于星象函数的-族解析函数A(,α).我们导出A(α)中函数的积分表达式:借助算子理论研究A(,α)族的包含关系并确定它的闭凸包、闭凸包的极值点和它的支撑点;利用一个阶微分从属证明关于实部的二个不等式.最后,我们还证明A(,α)中函数的偏差定理. 相似文献
28.
We examine factorizations of complete graphs K2n into caterpillars of diameter 5. First we present a construction generalizing some previously known methods. Then we use the new method along with some previous partial results to give a complete characterization of caterpillars of diameter 5, which factorize the complete graph K2n. 相似文献
29.
Samy Chammaa Dr. Bianca Sperl Anke G. Roth Aybike Yektaoglu Steffen Renner Dr. Thorsten Berg Prof. Dr. Christoph Arenz Prof. Dr. Athanassios Giannis Prof. Dr. Tudor I. Oprea Dr. Daniel Rauh Dr. Markus Kaiser Dr. Herbert Waldmann Prof. Dr. 《Angewandte Chemie (International ed. in English)》2010,49(21):3666-3670
30.