CAS Search. (d) We use the greedy algorithm to control the target edges. Yan, G. et al. Monograph 61, 367–392 (1991). In the four situations, the metric value of \(\varepsilon \) on driven edges are all below the baseline, which shows that our algorithm is efficient in the two artificial networks. No search has been performed. & Barabási, A. Controllability of complex networks. As a result, the control efficiency is not high. Get the Edge Controls for Industrial Package; Choose ECS Targets; Build an Image on a Linux Build System. In Fig. This theory addresses how to select as few input nodes as possible to control the chosen target nodes in a nodal linear dynamic system. Kalman, R. E. Mathematical description of linear dynamical systems. For the general case, we also give an approximate algorithm TEC to calculate the minimum number of driven edges and driver nodes to control the states of target edges. 99 ($6.99/Count) This set gives you more for your money. She Is Bomb's edge control for hair cream locks those little hairs in place, for smooth, picture-perfect results. Figure 4 shows the two schemes and the results of the driver nodes and driven edges on an ER network and a SF network. However, we can not understand the dynamics of many complex systems deeply, such as the neural network of the human brain. To evaluate the efficiency of our algorithm, we apply the following metric: which denotes the control efficiencies of the driver nodes (driven edges) in the random and local schemes by \({\varepsilon }_{N}(r)\), \({\varepsilon }_{M}(r)\), \({\varepsilon }_{N}(l)\) and \({\varepsilon }_{M}(l)\). This work was supported by National Natural Science Fund of China (Nos. It is built as a Win32 Visual Studio 2019 project and makes use of both C++ and JavaScript in the WebView2 environment to power its features. An efficient solution is proposed to compute the minimum driven edges and driver nodes. 11, the target edge controllability can also be regarded as a special output controllability problem on the linear graph. ADS Read reviews and buy Carol's Daughter Black Vanilla Edge Control Smoother - 2.0oz at Target. differ in key technologies such as hypervisor virtualization, kernel version, development How Edge Controls for Industrial Achieve Determinism, Get the Edge Controls for Industrial Package. In addition, \(\alpha =\frac{{P}_{D}}{{N}_{D}}\), \({P}_{D}\) is the number of driven edges (driver nodes) under target edge control, and \({N}_{D}\) is the number of driven edges (driver nodes) under switchboard dynamic control of the whole network. Product Image. We list 6 topological features of the networks, including their average degree(AD), diameter(D), average shortest path(ASP), clustering coefficient(CC), assortativity coefficient(AC), and heterogeneity(H). (1) can be rewritten in terms of \({x}_{{\rm{i}}}\). // See our complete legal Notices and Disclaimers. where \({l}_{{\rm{i}},\alpha }=I(\{{i}_{1},{i}_{2},\,\mathrm{...,}\,{i}_{{{\rm{L}}}_{i}}\})\) represents an \({L}_{{\rm{i}}}\times M\) matrix that contains the \(\{{i}_{1},{i}_{2},\,\mathrm{...,}\,{i}_{{{\rm{L}}}_{{\rm{i}}}}\}\) th rows of the identity matrix \(I\). phys. You are using a browser version with limited support for CSS. effects of resolution on the little rock lake food web. Step 1: We are given a directed network \(G\) with target edges(the red lines). The driven edges are {(1,2),(2,3),(4,5)} and the driver nodes are {1,2,4}. In random target edge control, the control efficiencies of the driver nodes of most networks are negative except the metabolic networks, which implies that most networks do not perform well in terms of the driver nodes in the random scheme. However, until recently, WinForms and WPF apps didn’t have access to the Microsoft Edge-powered WebView. analyse the observational uncertainty and the energy required for control and achieve a series of fundamental yet important theories8. For the driven edges in the local scheme, we select target edges in a local manner, the efficiency is satisfactory in all the networks except for the food web. In the other scheme, we select target edges from connected components in a depth-first strategy. Our method does not optimize the control efficiency of the four food webs under both schemes. For vertex \(v\), \({d}_{{\rm{v}}}^{+}\) is the out-degree and \({d}_{{\rm{v}}}^{-}\) is the in-degree. FREE Shipping on orders over $25 shipped by Amazon. 201701D121052). Our algorithm is efficient if the red line is below the baseline. Figure 5a,b show that the control efficiency of driver nodes and driven edges first decrease and then increase as the average degree increases in the random scheme. Get Help Garmin Support Center. MATH Although the method based on k-travel theory is efficiently control tree-like networks with single driven edge (which is shown in Fig. However, the topological structure is not necessarily static. Based on the switchboard dynamics, we use this k-travel theory to give an effective algorithm to find the controllable set of any edge in the directed tree, especially the root edge. Organizing and understanding a winter’s seagrass foodweb network through effective trophic levels. username and JavaScript. See Intel’s Global Human Rights Principles. First, we select the target edges in two different ways: randomly and locally. Dorf, R. C. Modern control systems. Moreover, the whole system can be controlled. CAS Commun 6, 8414, https://doi.org/10.1038/ncomms9414 (2015). & Martinez, N. D. Food-web structure and network theory: The role of connectance and size. Furthermore, the control efficiency on the driven edges is higher than that of the driver nodes. Verified Purchase. Hence, we have. Article 5 Pieces Hair Edge Brush Double Sided Control Hair Brush Comb Combo Pack Smooth Comb Grooming (5 Colors) 4.6 out of 5 stars 1,665. According to the output controllability theorem, edge ei can control all of the edges in \( {\mathcal L} \)i if the generic dimension of the matrix \( {\mathcal L} ={l}_{i,\alpha }[{b}_{{\rm{i}}},A{b}_{i},{A}^{2}{b}_{{\rm{i}}},\,\mathrm{...,}\,{A}^{N-1}{b}_{{\rm{i}}}]\) is \({L}_{{\rm{i}}}\), i.e., if. Model. More value. https://doi.org/10.1103/Rev.Mod.Phys.74.47, https://doi.org/10.1016/S0378-4371(02)00772-0, https://ieeexplore.ieee.org/document/1100557, https://doi.org/10.1088/1367-2630/16/12/123055, https://www.nature.com/articles/ncomms6415, https://doi.org/10.1371/journal.pone.0175375, https://doi.org/10.1038/s41598-017-04463-5, https://doi.org/10.1103/PhysRevE.94.052310, https://doi.org/10.1103/PhysRevE.100.022318, https://doi.org/10.1016/j.physa.2018.08.011, https://science.sciencemag.org/content/286/5439/509, https://doi.org/10.1016/S0304-3800(99)00022-8, https://doi.org/10.1126/science.298.5594.824, https://doi.org/10.1016/j.jmb.2006.04.029, https://doi.org/10.1371/journal.pone.0094998, http://creativecommons.org/licenses/by/4.0/, https://doi.org/10.1038/s41598-020-66524-6. 11 Edge Control Products That Keep Your Hair Laid for Hours. Whether you have naturally curly, wavy, straight, coily, relaxed hair, or locs Miracle Edges offers a long-lasting hold for all hair types and textures. MathSciNet In fact, \(W\) is the adjacency matrix of the linear graph \(L(G)\) on the original graph \(G\). ECS provides several targets that can be built. Mod. For this reason, our algorithm focuses on the optimization of the driven edges. Generally, the states of the outbound edges \({y}_{{\rm{v}}}^{+}\) are affected by the states of the inbound edges \({y}_{{\rm{v}}}^{-}\), the losses of inbound edges \({\tau }_{{\rm{v}}}\otimes {{y}_{{\rm{v}}}}^{+}(t)\) and the external disturbance on the corresponding nodes \({\sigma }_{{\rm{i}}}{u}_{{\rm{i}}}(t)\). However, the number of driven edges in both networks is less, which shows that our algorithm is efficient. The simulation results and analytic calculation show that SF networks with large average degrees are suitable for target edge control, and the local target control obtains a higher control efficiency than the random target control. The D and the ASP are related to the network scale and the average degree, respectively. ADS Wang, X. F. & Chen, G. Pinning control of scale-free dynamical networks. In the local scheme(Fig. Also, the target edge set selected by the random scheme is easier to control than that by the local scheme and the critical scheme. Then, all the targets can be controlled. Proc. ADS or Sci 298(5594), 824–827, https://doi.org/10.1126/science.298.5594.824 (2002). To quantify the efficiency of the target control for a given fraction \(f\), we define the parameter \(\alpha ={P}_{{\rm{D}}}/{N}_{{\rm{D}}}\) for both driver nodes and driven edges in two selection schemes. By Venezia Moorer. (k-travel theory) For a directed tree, we can control the target edges set \({ {\mathcal L} }_{{\rm{i}}}=\{{e}_{{{\rm{i}}}_{1}},{e}_{{{\rm{i}}}_{2}},\,\mathrm{...,}\,{e}_{{{\rm{i}}}_{{L}_{i}}}\}\) by controlling an edge \({e}_{{\rm{i}}}\) provided that \({d}_{{\rm{ik}}}^{{\prime} }\) (the distance from edge \({e}_{{\rm{i}}}\) to edge \({e}_{{\rm{k}}}\)) meets \({d}_{{\rm{ik}}}^{{\prime} }=k-1\) for every integer \(k\in \mathrm{[1,}{L}_{{\rm{i}}}]\). Lu, F., Yang, K. & Qian, Y. Additionally, Gu et al. In addition, we fix the power exponent and the average degree to observe the marginal influence of the two factors on the control efficiency, which is shown in Fig. 19(3), 201–208, https://ieeexplore.ieee.org/document/1100557 (1974). In addtion, the control efficiencies of the driven edges in the two networks are below the baseline which means that we can control the target edges by controlling fewer driven edges. Furong Lu devised the k-travel theory and performed analytical calculations and simulations. Carol’s Daughter Black Vanilla Moisture & Shine Edge Control Smoother for Dry Hair and Dull Hair, with Aloe and Honey, Clear Edge Smoother, Edge … Extending edge target controllability theory to temporal networks and multi-layer networks may be necessary to combine their own characters. where \(W=[{w}_{{\rm{kj}}}]\) and \({w}_{{\rm{kj}}}\) may be nonzero if and only if the head of edge \({e}_{{\rm{k}}}\) is the tail of edge \({e}_{{\rm{j}}}\). The above results inspire us to consider which topological characteristics determine the control efficiency. Natl. Since \({I}_{{{\rm{i}}}_{1}},{I}_{{{\rm{i}}}_{2}},\,\mathrm{...,}\,{I}_{{{\rm{i}}}_{{L}_{i}}}\) are independent, \(gd( {\mathcal L} )={L}_{{\rm{i}}}\). https://doi.org/10.1038/s41598-020-66524-6, DOI: https://doi.org/10.1038/s41598-020-66524-6. where \(\tilde{A},\tilde{B},\tilde{C}\) are structural equivalent to \(A,B,C\), respectively. A 512, 14–26, https://doi.org/10.1016/j.physa.2018.08.011 (2018). Finally, we analyse the influence of the topology on the control efficiency. Here, we mainly study the problem on SF networks20 with the average degree varying from 2 to 10 at intervals of 2 and with the power index varying from 2.2 to 3.4 in a step 0.2. We also use the two schemes to select the target edges, which are random or local. Each jar contains 3.5 oz.She Is Bomb Collection Edge Control: Tames frizzies and flyaways along the edge of the hairline ; Non … Phys. The distance from edge \(e1\) to edge \(e5\) is four, which is the number of nodes between \(e1\) and \(e5\). Target control theory is one of the most important results among these theories. Product Title On Natural Edge Control Hair Colored Gel, Jet Black, ... Average rating: 3.2 out of 5 stars, based on 6 reviews 6 ratings. A 310, 521–531, https://doi.org/10.1016/S0378-4371(02)00772-0 (2002). Select a Install Edge Controls for Industrial. Rev. CAS Microsoft Edge comes complete with features designed to customize your browsing experience and to help make you more productive. We also approximately give the minimal drive nodes and driven edges on the artificial and real networks. According to the exact controllability, the damping matrix \(T\) with identical diagonal elements has no effect on the edge controllability of the network characterized by \(W-T\)14. Control. Biol. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D. & Alon, U. To ask this question, we analyse the effects of average degree and power exponent on the control efficiency. We adopt the local scheme and the random scheme to study the impact of the network topology on the final results. We verify that the approach based on k-travel theory is more efficient than the traditional edge dynamics method because it can control more edges according to output controllability theory (Lemma 1). Because the diameter and ASP of SF network at \(\langle k\rangle \mathrm{=4}\) are higher than in the other cases, the network’s CC is nearly the same, which is shown in Table 4. Therefore, our algorithm is not very efficient for target edge control relative to the SBD theory. In (a,b), the efficiencies of the driver nodes and the driven edges increase monotonically with the degree exponents. Thank you for visiting nature.com. Edge Booster Edge Control Gel Strong Hold Water-Based Pomade - Super Shine & Moisture - Great for Braiding/Relaxed/Natural Hair (Strawberry, 0.85 fl.oz.) 3.9 out of 5 stars 40. A set of target edges with size S may be denoted as \(\{{c}_{1},{c}_{2}\mathrm{,...,}{c}_{{\rm{S}}}\}\). \(f\) denotes the proportion of edges that we selected from the network. As observed from the table, although AC is the dominant factor for \({\varepsilon }_{N}({\rm{r}})\) and ASP is dominant for \({\varepsilon }_{N}({\rm{l}})\), in general, CC is the most influential factor for the control efficiency in local scheme. We show the topological characteristics of these networks in Table 2. Google Scholar. Try these quick links to visit popular site sections. for a basic account. Form k-travel theory, while the distances from every target edge to the root edge are distinct, then we can control the target edges by solely driving the root edge. Subsequently, researchers have made progress modeling the dynamics on the edges of a network. Here, dim(\(C\)) denotes the dimension of the subspace \(C\), through which we simplify the dimension of system as \((A,B,C)\) (e.g., \(dim(A,B,C)\) is denoted as \(d(A,B,C)\)). Profái, M. & Hovel. No expense was spared when loading this product with all of the healthy hair essentials. In the above control process, the target edges or nodes are controlled in some chronological order. MATH When you Give with Bing 2 through Microsoft Rewards, your … Google Scholar. ISSN 2045-2322 (online). ADS If you don't set this policy, there aren't any restrictions on acceptable extension and app types. Target control of complex networks. Menichetti, G., Dall’Asta, L. & Bianconi, G. Control of multilayer networks. Ecol. Unruly edges are no match for these frizz-fighting products. According to the SBD, we need two driver nodes(indicated in green) and three driven edges(indicated in green) to control the whole network. In term of the efficiency of driven edges in the random scheme, the neuronal network, the regulatory networks and the metabolic networks surpass those of the other networks, which means that we need fewer driven edges to control the target edges under the TEC algorithm than that the SBD theory would require on these networks. Moreover, \({b}_{{\rm{i}}}\) is the \(i\) th column of the identity matrix. The numbers of nodes and edges are denoted by \(N\) and \(M\), respectively. 4.3 out of 5 stars 5,483. Mar … Add to cart. ADS Kaleidoscope Miracle Edges is infused with Kaleidoscope Miracle Drops, to keep dry stubborn edges moisturized. To clarify algorithm 1, we first introduce several definitions: (Structurally equivalent). I must say that I wash this out every night because if you apply more the next day for any reason, it will turn a little white. In other words, we use fewer driver nodes or driven edges to control the target edges than with the SBD theory. In artificial networks, we see that the control efficiency of SF networks is closely related to the average degree and the degree exponent. Figure 5c,d show the results in the local scheme, and we observe a similar trend in the random scheme. 99 ($9.99/Count) Get it as soon as Thu, Feb 11. Nature 473, 167–173 https://doi.org/10.1038/nature10011 (2011). When the clustering coefficient is high, the number of driven edges in target control is not siginficantly different from the corresponding number in SBD theory. Pan, Y. J.& Li, X. Moreover, we analyse the topological factors that affect target edge control. This shortcoming has motivated us to give an effective control scheme for the target edges. SET. 201802013), Program for the Young SanJin Scholars of Shanxi. Shop for shea butter edge control online at Target. Earlier this week at Build 2018, Kevin Gallo … MATH The control efficiency increases with the average degree of the SF networks and it is higher on driven edges than on driver nodes. With reagard to controlling the target edges in local scheme, the efficiencies of the driver nodes is high in the electronic circuit networks and the metabolic networks. Phys. When \(\varepsilon =0\), the control efficiency is neutral, which means that to control f fraction of edges in networks, we need \(f\,\ast \,N\) driver nodes(driven edges). // Performance varies by use, configuration and other factors. Article Analysis of the influence factors of the target control efficiencies of SF networks. Pang, S.-P., Wang, W.-X. Install Edge Controls for Industrial. The above theory pertains to the dynamic process on the nodes. Consequently, \({d}_{{\rm{ij}}}^{\,{\prime} }\) is single-valued for any edge pair \((i,j)\) in \(T\). (Edge distance) The distance between two edges is the number of internal nodes on a path that connects the two edges, and it is denoted by d′. The fast drying edge control cream is non-flaking and long-lasting. Google Scholar. (a) A directed network with target edges(the red lines). \(E.\,coli,C.\,elegans\) and \(S.\,cerevisiae\)23 are three metabolic networks. (b) We locate the out-edges of the given nodes on its right, and the in-edges on the left. The efficiency of the driven edges in the random scheme is higher than that in the local scheme. PubMed Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Generally, the target controllability can be regarded as the output controllability of the LTI system. PubMed Does the same hold for real networks? 45, 167–256, https://doi.org/10.1137/S003614450342480 (2003). The generic dimension is used to describe the control range of the edge. IEEE Transactions on Autom. The Mane Choice The Alpha Laid Back Effortlessly Edge Control is gentle enough for daily use. For a specific tree-like network, we propose a k-travel algorithm to obtain the minimum number of drivers to control the collection of target edges. Setting Target Power. Choose from contactless Same Day Delivery, Drive Up and more. In addition, \({M}_{{\rm{D}}}\) is the minimum of the driven edges. Target edge controllability on the two artificial networks. I can't say that about a lot of edge controls due to my natural hair. Analytic calculations show that networks with large assortativity coefficient as well as small average shortest path are efficient in random target edge control, and networks with small clustering coefficient are efficient in local target edge control. For a directed tree-like network, to find the lowest driver nodes or driven edges needed to control the target edges, we propose a new method: k-travel theory. J. Soc. Step 4: In the next iteration, the edges reserved in the left part of the bi-layer bipartite graph are the new target edges in the second iteration. The hold to this is great! Nat. Get the most important science stories of the day, free in your inbox. Thus, We have \({l}_{{\rm{i}},\alpha }{A}^{k}{b}_{{\rm{i}}}={\beta }_{{\rm{k}}}{I}_{{i}_{{\rm{k}}}}\), where \({\beta }_{{\rm{k}}}\) is a nonzero constant. The nodes in graph(c) are the edges in graph(a). Search Results. Phys. In the past decade, the study of the dynamics of complex networks has been a focus of research. Recently, the theory of structural controllability has been extended to temporal networks9,29 and multi-layer networks30. Solving these problems will help further enrich the theory of edge target control. The nodes of \(L(G)\) denote the edges of \(G\), and the edge \({e{\prime} }_{{\rm{ij}}}\) of \(L(G)\) indicates that the head of edge \({e}_{{\rm{i}}}\) is the tail of edge \({e}_{{\rm{j}}}\). Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. (a) The overall control efficiency \(\varepsilon \) on the driver nodes for SF networks varies with the average degree \(\langle k\rangle \) for different degree exponents γ in the random scheme. Moreover, if any entries in \(A\) are zeros, the corresponding entry \(\tilde{A}\) must also be zero, which is applicable for the structurally equivalence of systems \((A,B,C)\) and \((\tilde{A},\tilde{B},\tilde{C})\). The complete list of ECS targets available to CAS Target edge control based on switchboard dynamics and the k-travel theory. Google Scholar. In the local scheme, the target edges are selected from the connected components. In general, when the average degree increases, the control efficiency increases, which can be attributed to the fact that networks gain more connectivity when the average degree is increasing. Target Specialty Products brings extensive experience and expertise in vector control and aerial applications, along with an energetic team that will help deliver successful solutions to customers. 44. build is listed in the table below. Sold & shipped by Unique Beauty. MATH Most targets share the same core features but According to the output controllability theorem, we can control the the edges in \( {\mathcal L} \)i by controlling the edge \({e}_{i}\). Target Specialty Products will support Leading Edge as its exclusive distributor of Leading Edge’s PrecisionVision, DropVision and FleetVision technologies. To obtain Here, M denotes the number of edges in \(G\), and \(\{{i}_{1},{i}_{2},\,\mathrm{...,}\,{i}_{{{\rm{L}}}_{{\rm{i}}}}\}\) are the corresponding indices of the edges set \( {\mathcal L} \)i in L(G). In addition, when the nodal target controllability is based on the structural controllability, our method outperforms the nodal target controllability approach in terms of the computational efficiency with respect to identifying the minimum set of drivers. In each iteration, the times required to calculate the driver nodes and the driven edges are \(O(N)\), and the depth of iteration is \(N\) at most. 5(a–d), we observe that the control efficiency at \(\langle k\rangle \mathrm{=4}\) is lower than the corresponding efficiency in the other cases. convert the problem on structural controllability into a graph maximum matching problem6 and propose the scheme of calculating the number of minimum driver nodes. For more general cases, we present an iterative algorithm to approximate the minimum number of driven edges and driver nodes. Intel’s products and software are intended only to be used in applications that do not cause or contribute to a violation of an internationally recognized human right. Here is a feature matrix comparison of the various targets: You can select the features during the build process. Lin, C. Structural controllability. In this paper, we present a greedy algorithm to solve the problem of target edges’ control and focus on the optimization of the number of driven edges. Two matrices \(A=({a}_{{\rm{i}}j})\) and \(\tilde{A}=({\tilde{a}}_{{\rm{i}}j})\) with the same size are said to be structurally equivalent if the entries of \(A\) being nonzero implies that entries in the corresponding location of \(\tilde{A}\) are also nonzero5. However, in many systems, it is inefficient or unnecessary to address all edges. Build an ECS-B image; Build an ECS-X image; Build an ECS-K image; Build an ECS-R image; Build an ECS-A image; Create a Bootable USB; Install an Image on a Target System; Install CODESYS* on Windows* Machine CAS Build an ECS-B image; Build an ECS-X image; Build an ECS-K image; Build an ECS-R image; Build an ECS-A image; Create a Bootable USB; Install an Image on a Target System; Install CODESYS* on Windows* Machine I wasted my hair last night put the edge control on this morning by the time I got to work an hour and a half later it was flakes and white will not recommend this or use it again Read more. The reason is that we consider the edges in network G as the nodes of its linear graph in our algorithm and make use of target control theory based on the nodes. PubMed Unlike traditional hair gels, this product is made with 100% Australian beeswax that naturally provides superior hold and control without flaking. 360(1), 213–227, https://doi.org/10.1016/j.jmb.2006.04.029 (2006). Edge® 520 . 86 … For a directed tree, all of the paths are unique. The nodes of \(L(G)\) are the edges of \(G\), and the edge \({e}_{{\rm{i}}{\rm{j}}}^{{\rm{{\prime} }}}\) of \(L(G)\) indicates that the head of edge \({e}_{{\rm{i}}}\) is the tail of edge \({e}_{{\rm{j}}}\). \({M}_{{\rm{v}}}\) is a switching matrix that denotes the adjacency relationship between the inbound edges and the outbound edges. Article (c) For the SF network with average degree \(\langle k\rangle \) = 6 and \(\gamma =2.4\), we show that the normalized fraction \(\alpha \) of the driver nodes and the driven edges varies with the target edges’ fraction in the random scheme. prerequisite section ECS Build Setup before continuing this section. PubMed Central here, N is the number of vertexes, c is the number of connected components and \({\beta }_{{\rm{i}}}\) is 1 if the \(i\) th connected component is balanced and zero otherwise. Google Scholar. Appl. Traditionally, we assume that the topological structure remains static and then study its influence on the network dynamics1,2,3,4,5,6. In real networks, the results are similar to the cases in artificial networks. Shining and Conditioning Hair Gel by Dark and Lovely, Extra Hold, All Hair Types, Styling Gel Great for Braiding, Twisting & Smooth Edges, Extra Hold, 4.4 oz. In the local scheme, though we have the same situation as in the random scheme, the local control outperforms the random control. Contents. (d)The overall control efficiency \(\varepsilon \) on the driven edges for SF networks varies with the average degree \(\langle k\rangle \) for different degree exponents γ in the local scheme. Overall, the efficiency of the driver nodes in the ER network is higher than that of the SF network under the two selection schemes. generalize the edge dynamics to undirected networks and show a series of results14,15,16. Christian, R. & Luczkovich, J. This edge control smells so good. The figure shows the distance between two edges along a path. Article Set the target … (e) In fact, we need only one node(a) and one driven edge(\(x1\)) to control the states of the target edges, which can be obtained according to the k-travel theory. Pang et al. Google Scholar. study the application of network controllability to brain networks10. The main results of the switchboard dynamics are as follows13. Liu, Y., Slotine, J. Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily. The red line represents the ratio of the driver nodes obtained by TEC algorithm to the driver nodes controlling the whole system, and the green line is the corresponding ratio of the driven edges. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Choose from contactless Same Day Delivery, Drive Up and more. Is there any correlation between the control efficiency and the topological character? Select Pop-ups and redirects.. Move the Block toggle to On.. E 94, 052310, https://doi.org/10.1103/PhysRevE.94.052310 (2016). This algorithm is based on the k-travel theory, and we call it the TEC (target edge control) algorithm (it is shown in Fig. Gift … Sci. Expand | Collapse. Current Price $8.44 $ 8. Conversely, we employ more driver nodes in random control than in local control. Liu et al. Microsoft Support for Business . Article Network motifs: simple building blocks of complex networks. Tamas Nepusz et al. Pang, S. & Hao, F. Target control of edge dynamics in complex networks. (e) By controlling the driver node calculated from the TEC, we can control the driven edge. Otherwise, the extra target edges are the driven edges \({E}_{{\rm{t}}}\), and the driver nodes are the tail nodes of \({E}_{{\rm{t}}}\), which are denoted by \({D}_{{\rm{t}}}\). In switchboard dynamics, Eq. In particular, the controllability of a complex network, which we assess by determining whether the network can be driven from any initial state to any desired state within a finite time, is considered one of the focal research subjects and has been studied massively. ADS Microsoft is committed to ensuring your apps work on Microsoft Edge. 8, 367–369, https://doi.org/10.1109/9.50361 (1990). Step 5: By controlling the driver nodes calculated from the TEC, we can control the driven edges and then all of the targets can be controlled. \(H\) is a diagonal matrix where the \(i\) th diagonal element \({\sigma }_{i}\) is the tail of the \(i\) th edge. The large-scale organization of metabolic networks. Google Scholar. Article We also apply our algorithm to several real networks, where s838, s420 and s208 are three electronic circuit networks21 whose average degree is between 1.54 and 1.6.
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