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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Network controllability ： ウィキペディア英語版 Network controllability Network Controllability is concerned about the structural controllability of a network. Controllability describes our ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs. This definition agrees well with our intuitive notion of control. The controllability of general directed and weighted complex networks has recently been the subject of intense study by a number of groups, worldwide. ==Background== Consider the canonical linear time-invariant dynamics on a complex network $$ \dot \cdot \mathbf(t) + \mathbf\cdot \mathbf(t) where the vector $\backslash mathbf(t)=(x\_1(t),\backslash cdots,x\_N(t))^\backslash mathrm$ captures the state of a system of $N$ nodes at time $t$. The $N\; \backslash times\; N$ matrix $\backslash mathbf$ describes the system's wiring diagram and the interaction strength between the components. The $N\; \backslash times\; M$ matrix $\backslash mathbf$ identifies the nodes controlled by an outside controller. The system is controlled through the time dependent input vector $\backslash mathbf(t)\; =\; (u\_1(t),\backslash cdots,u\_M(t))^\backslash mathrm$ that the controller imposes on the system. To identify the ''minimum'' number of driver nodes, denoted by $N\_\backslash mathrm$, whose control is sufficient to fully control the system's dynamics, Liu et al.〔Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási, ''Nature'' 473 (2011).〕 attempted to combine the tools from structural control theory, graph theory and statistical physics. They showed〔 that the minimum number of inputs or driver nodes needed to maintain full control of the network is determined by the 'maximum matching’ in the network, that is, the maximum set of links that do not share start or end nodes. They tried〔 to develop an analytical framework, based on the in-out degree distribution, which predicts $n\_\backslash mathrm\; =N\_\backslash mathrm/N$ for scale-free and Erdős–Rényi Graphs. It is however notable, that their formulation〔 would predict same values of $\}^$ and $$ calculated by Liu et al.〔 is notable. It is obvious that if controllability is decided mainly by degree, why are $$ and $$ so different for many real world networks? They argued 〔 (arXiv:1203.5161v1), that this might be due to the effect of degree correlations. However, it has been shown〔 that network controllability can be altered only by using betweenness centrality and closeness centrality, without using degree (graph theory) or degree correlations at all. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Network controllability」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.