Add to cart. Rep. 6, 20706, https://doi.org/10.1038/srep20706 (2016). 99 ($6.99/Count) This set gives you more for your money. Control. To target Edge (version < 79), we can check for -ms-ime-align support, Edge being the only Microsoft browser that supports this property: @supports (-ms-ime-align: auto) { .selector { color: red; } } Or this one-liner (that one works on Edge and all IEs also): _:-ms-lang(x), .selector { color: red; } Further explanation, including variants to support specific versions of Edge, can be found … E 94, 052310, https://doi.org/10.1103/PhysRevE.94.052310 (2016). Setting the policy controls which apps and extensions may be installed in Microsoft Edge, which hosts they can interact with, and limits runtime access. The authors declare no competing interests. Mod. The generic dimension \(gd(A,B,C)\) of the output state space is defined by. We also use the two schemes to select the target edges, which are random or local. AC and ASP′ are the main factors in the random scheme. target link below to view instructions on building. 5.0 out of 5 stars Curls passion fruit control edge. 4.5 out … Additionally, Gu et al. Newman, M. The structure and function of complex networks. Plos one 12(4), e0175375, https://doi.org/10.1371/journal.pone.0175375 (2017). Figure 5c,d show the results in the local scheme, and we observe a similar trend in the random scheme. 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 \(I\). This work was supported by National Natural Science Fund of China (Nos. Generally, the target controllability can be regarded as the output controllability of the LTI system. Given a directed network \(G(V,E)\) where |V| = N and \(|E|=L\) denote the number of vertexes and edges, if \({a}_{{\rm{ji}}}\ne 0\) is in the matrix \(A\), then there is a link from node \(i\) to node \(j\). 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. We show the topological characteristics of these networks in Table 2. (d) The driver nodes and the driven edges that we obtained by using SBD theory. This shortcoming has motivated us to give an effective control scheme for the target edges. 360(1), 213–227, https://doi.org/10.1016/j.jmb.2006.04.029 (2006). 3a–e). Here, we propose the k-travel algorithm to approximately calculate the minimum number of driven edges and driver nodes for a directed tree-like network. Unlike traditional hair gels, this product is made with 100% Australian beeswax that naturally provides superior hold and control without flaking. https://doi.org/10.1038/s41598-020-66524-6, DOI: https://doi.org/10.1038/s41598-020-66524-6. MathSciNet Indus. Complete 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 \({\varepsilon }_{M}(l)\). Best 3-in-1. 99(20), 12917–12922, https://doi.org/10.1073/pnas.192407699 (2002). For a directed network \(G\) with the adjacency matrix of its linear graph: A = [\({a}_{{\rm{ij}}}\)], \({a}_{{\rm{ij}}}\) = 1 if there is a link \(({e}_{{\rm{i}}},{e}_{{\rm{j}}})\) and 0 otherwise. Our research leads to several questions. Scientific Reports Target edge controllability on the two artificial networks. CAS Structural controllability and controlling centerlity of temporal networks. In the real world, the dynamical processes performed in the vast majority of systems are nonlinear. You can now smooth your edges down with confidence. Superfamilies of evolved and designed networks. Install Edge Controls for Industrial. Step 3: We use the greedy algorithm for target edges control. or Keyboard shortcuts are keys or combinations of keys that provide an alternate way to do something you'd typically do with a mouse. + Hair Wax Stick 2.7 Oz. Each jar contains 3.5 oz.She Is Bomb Collection Edge Control: Tames frizzies and flyaways along the edge of the hairline ; Non … This algorithm is based on the k-travel theory, and we call it the TEC (target edge control) algorithm (it is shown in Fig. Target control based on edge dynamics in complex networks, $$\varepsilon =0.5-{\int }_{0}^{1}(\alpha (f))df,$$, $$\{\begin{array}{ccc}\dot{x} & = & Ax+Bu,\\ y & = & Cx,\end{array}$$, \(A\in {R}^{N\times N},B\in {R}^{N\times M}\), $$d(A,B,C)=rank[C(B,AB,{A}^{2}B,\ldots ,{A}^{N-1}B)]=S\mathrm{}.$$, \(X=[{x}_{1},{x}_{2},\cdot \cdot \cdot ,{x}_{{\rm{M}}}]\), \({\tau }_{{\rm{v}}}\otimes {{y}_{{\rm{v}}}}^{+}(t)\), \({\sigma }_{{\rm{i}}}{u}_{{\rm{i}}}(t)\), $${\dot{{y}_{{\rm{v}}}}}^{+}({\rm{t}})={M}_{{\rm{v}}}{y}_{{\rm{v}}}^{-}({\rm{t}})-{\tau }_{v}\otimes {{y}_{{\rm{v}}}}^{+}({\rm{t}})+{\sigma }_{{\rm{i}}}{u}_{{\rm{i}}}({\rm{t}}),$$, \({e}_{{\rm{i}}{\rm{j}}}^{{\rm{{\prime} }}}\), \({d}_{{\rm{v}}}^{-} < {d}_{{\rm{v}}}^{+}\), \({d}_{{\rm{v}}}^{+}={d}_{{\rm{v}}}^{-}\), $${M}_{{\rm{D}}}=\mathop{\sum }\limits_{{\rm{i}}\mathrm{=1}}^{N}max({d}_{{\rm{i}}}^{+}-{d}_{{\rm{i}}}^{-}\mathrm{,0)}+\mathop{\sum }\limits_{{\rm{i}}\mathrm{=1}}^{c}{\beta }_{{\rm{i}}}\mathrm{}.$$, \(\{{c}_{1},{c}_{2}\mathrm{,...,}{c}_{{\rm{S}}}\}\), \(\{{e}_{1},{e}_{2},\ldots ,{e}_{{\rm{S}}}\}\), \({x}_{{{\rm{c}}}_{1}},{x}_{{{\rm{c}}}_{2}},\,\mathrm{...,}\,{x}_{{{\rm{c}}}_{{\rm{S}}}}\), $$gd(A,B,C)=\mathop{{\rm{\max }}}\limits_{\tilde{A},\tilde{B},\tilde{C}}rank(\tilde{A},\tilde{B},\tilde{C}),$$, \({ {\mathcal L} }_{{\rm{i}}}=\{{e}_{{{\rm{i}}}_{1}},{e}_{{{\rm{i}}}_{2}},\,\mathrm{...,}\,{e}_{{{\rm{i}}}_{{L}_{i}}}\}\), \( {\mathcal L} ={l}_{i,\alpha }[{b}_{{\rm{i}}},A{b}_{i},{A}^{2}{b}_{{\rm{i}}},\,\mathrm{...,}\,{A}^{N-1}{b}_{{\rm{i}}}]\), $$gd( {\mathcal L} )=gd({l}_{{\rm{i}},\alpha }[{b}_{{\rm{i}}},A{b}_{{\rm{i}}},{A}^{2}{b}_{{\rm{i}}},\ldots ,{A}^{N-1}{b}_{{\rm{i}}}])={L}_{{\rm{i}}},$$, \({l}_{{\rm{i}},\alpha }=I(\{{i}_{1},{i}_{2},\,\mathrm{...,}\,{i}_{{{\rm{L}}}_{i}}\})\), \(\{{i}_{1},{i}_{2},\,\mathrm{...,}\,{i}_{{{\rm{L}}}_{{\rm{i}}}}\}\), \({l}_{{\rm{i}},\alpha }{A}^{k}{b}_{{\rm{i}}}={\beta }_{{\rm{k}}}{I}_{{i}_{{\rm{k}}}}\), $$gd( {\mathcal L} )=gd[{\beta }_{1}{I}_{{{\rm{i}}}_{1}},{\beta }_{2}{I}_{{{\rm{i}}}_{2}}\mathrm{,...,}{\beta }_{{L}_{{\rm{i}}}}{I}_{{{\rm{i}}}_{{L}_{i}}}].$$, \({I}_{{{\rm{i}}}_{1}},{I}_{{{\rm{i}}}_{2}},\,\mathrm{...,}\,{I}_{{{\rm{i}}}_{{L}_{i}}}\), \((x\mathrm{1,}\,x\mathrm{2,}\,x\mathrm{5)}\), \(\alpha ={P}_{{\rm{D}}}/{N}_{{\rm{D}}}\), \(\alpha ={P}_{{\rm{D}}}/{N}_{{\rm{D}}}=f\). 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. (d–f) are the corresponding figures for the local scheme. This edge control smells so good. To clarify algorithm 1, we first introduce several definitions: (Structurally equivalent). Google Scholar. FREE Shipping on orders over $25 shipped by Amazon. A 310, 521–531, https://doi.org/10.1016/S0378-4371(02)00772-0 (2002). More privacy & control. study the formation of an edge dynamics system and analyse the structural controllability of edge dynamics13, which transforms the edge dynamics in the original networks into the nodal dynamics in the corresponding linear graph. phys. (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. Current Price $8.44 $ 8. We also approximately give the minimal drive nodes and driven edges on the artificial and real networks. build is listed in the table below. 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. Zhang, X. Dorf, R. C. Modern control systems. However, the research on how to control the target edges in switchboard dynamics, which is a dynamical process defined on the edges, has been lacking. Pan, Y. J.& Li, X. Scinece 303, 1538–1542, https://doi.org/10.1126/science.1089167 (2004). \(E.\,coli,C.\,elegans\) and \(S.\,cerevisiae\)23 are three metabolic networks. In this way, we construct a bipartite graph. CAS Simulation results and analytic calculations show that the edge dynamics in dense and homogeneous networks tend to have higher target control efficiency. One person found this helpful. Furthermore, the analysis of the local structure of driver nodes shows that spare and inhomogeneous networks, which emerge in many real systems, tend to choose high-degree and divergent nodes … The process is given in the pseudo-code in the following table. Thus, Gao put forward an approximate algorithm to calculate the fewest driver nodes that can be used to control the target nodes, which effectively reduces the usage of driver nodes11. Choose from contactless Same Day Delivery, Drive Up and more. For general cases, we put forward a greedy algorithm TEC to approximately calculate the minimum number of driven edges and driver nodes. To obtain volume 10, Article number: 9991 (2020) The black line represents the neutral case that (\(\alpha ={P}_{{\rm{D}}}/{N}_{{\rm{D}}}=f\)) as a baseline, which means that we need a fraction \(f\) of the driven edges(driver nodes) to control the fraction \(f\) of the edges. Appl. CAS Sci. Get the most important science stories of the day, free in your inbox. Math. ADS 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. (2) can be written in a linear time-invariant dynamical form \(\dot{X}=AX+Bu\), where \(A\) is the adjacency matrix of the linear graph \(L(G)\) of the original graph \(G\). In the local scheme, the target edges are selected from the connected components. ECS provides several targets that can be built. 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. In fact, \(W\) is the adjacency matrix of the linear graph \(L(G)\) on the original graph \(G\). We apply the TEC algorithm to an ER random network and a BA scale-free network (which are denoted by ER network and SF network). 11 Edge Control Products That Keep Your Hair Laid for Hours.
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