76 research outputs found
Example of a directed network, where V<sub>s</sub> = {x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>,x<sub>4</sub>,x<sub>5</sub>,x<sub>6</sub>,x<sub>7</sub>}, V<sub>c</sub> = {u<sub>1</sub>,u<sub>2</sub>,u<sub>3</sub>}, E<sub>s</sub> = {(x<sub>1</sub>,x<sub>2</sub>),(x<sub>1</sub>,x<sub>3</sub>),(x<sub>2</sub>,x<sub>4</sub>),(x<sub>2</sub>,x<sub>5</sub>),(x<sub>3</sub>,x<sub>6</sub>),(x<sub>3</sub>,x<sub>7</sub>),(x<sub>4</sub>,x<sub>2</sub>),(x<sub>5</sub>,x<sub>6</sub>),(x<sub>7</sub>,x<sub>7</sub>)}, E<sub>c</sub> = {(u<sub>1</sub>, x<sub>1</sub>),(u<sub>2</sub>, x<sub>2</sub>),(u<sub>3</sub>, x<sub>3</sub>)}, a<sub>ij</sub> (i = 1,2,…,7; j = 1,2,…,7) ∈ V<sub>s</sub> × V<sub>s</sub>, b<sub>ij</sub>(i = 1,2,3; j = 1,2,…,7) ∈ V<sub>c</sub> × V<sub>s.</sub>, <i>w</i><sub>24</sub> > 0 and <i>w</i><sub>42</sub> > 0.
<p>Example of a directed network, where V<sub>s</sub> = {x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>,x<sub>4</sub>,x<sub>5</sub>,x<sub>6</sub>,x<sub>7</sub>}, V<sub>c</sub> = {u<sub>1</sub>,u<sub>2</sub>,u<sub>3</sub>}, E<sub>s</sub> = {(x<sub>1</sub>,x<sub>2</sub>),(x<sub>1</sub>,x<sub>3</sub>),(x<sub>2</sub>,x<sub>4</sub>),(x<sub>2</sub>,x<sub>5</sub>),(x<sub>3</sub>,x<sub>6</sub>),(x<sub>3</sub>,x<sub>7</sub>),(x<sub>4</sub>,x<sub>2</sub>),(x<sub>5</sub>,x<sub>6</sub>),(x<sub>7</sub>,x<sub>7</sub>)}, E<sub>c</sub> = {(u<sub>1</sub>, x<sub>1</sub>),(u<sub>2</sub>, x<sub>2</sub>),(u<sub>3</sub>, x<sub>3</sub>)}, a<sub>ij</sub> (i = 1,2,…,7; j = 1,2,…,7) ∈ V<sub>s</sub> × V<sub>s</sub>, b<sub>ij</sub>(i = 1,2,3; j = 1,2,…,7) ∈ V<sub>c</sub> × V<sub>s.</sub>, <i>w</i><sub>24</sub> > 0 and <i>w</i><sub>42</sub> > 0.</p
A parallel adaptive quantum genetic algorithm for the controllability of arbitrary networks - Fig 9
<p>Fitness and penalty curves as a function of iterating generation for (a) ER with ⟨k⟩ = 4.0, (b) SF with ⟨k⟩ = 4.0 and γ = 2.1, and (c) SW with ⟨k⟩ = 4.0. The red dotted line with a square is the best fitness corresponding to D<sub>best</sub> at the current generation, the blue dashed line with a circle is the mean fitness of all control schemes at each generation, and the black line with a triangle is the penalty term corresponding to D<sub>best</sub> at each generation.</p
Performance comparison of PAQGA, MMT, and MM on several large real-directed, -weighted and–unweighted networks in terms of N<sub>cm</sub> and computational time.
<p>For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p
Performance comparison of PAQGA and parallel GA on different networks using eight MATLAB® workers in terms of n<sub>cm</sub>, the minimum iterating generations, and computational time.
<p>For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p
Performance comparison of PAQGA, GA, and EO on different networks in terms of <i>n</i><sub><i>cm</i></sub>, the minimum iterating generations, and computational time.
<p>Power-law index of SF networks in these experiments was γ = 2.1. ‘/’ indicates that the corresponding results were not available for the computational time limit. For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p
Impact of and C on N<sub>cm</sub> of SW networks.
<p>(a) N<sub>cm</sub> as a function of with fixed C. When C = 1, the network is fully connected and can be steered to any state with only one controller. (b) N<sub>cm</sub> as a function of C with fixed ⟨k⟩. Networks are directed with N = P = 500.</p
Illustration of how new control scheme D* functions in the network topology.
<p>(a) Original network with seven state nodes and five candidate control nodes. (b) Input matrix changes into B* = BD*M after choosing u* = {u<sub>1</sub>,u<sub>2</sub>,u<sub>3</sub>} as new control nodes. New network has seven state nodes and three control nodes.</p
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