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Wyszukujesz frazę "graph Laplacian" wg kryterium: Temat

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    Wyświetlanie 1-12 z 12
    Tytuł:
    A generalization of the graph Laplacian with application to a distributed consensus algorithm
    Autorzy:
    Zhai, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/331278.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    graph Laplacian
    generalized graph Laplacian
    adjacency weights
    distributed consensus algorithm
    cooperative control
    Opis:
    In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 2; 353-360
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A matrix inequality based design method for consensus problems in multi-agent systems
    Autorzy:
    Zhai, G.
    Okuno, S.
    Imae, J.
    Kobayashi, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/930012.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system wieloagentowy
    konsensus
    sterowanie zdecentralizowane
    nierówność macierzy
    LMI
    multi-agent systems
    consensus
    decentralized control
    graph Laplacian
    matrix inequality
    Opis:
    In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 4; 639-646
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Frames and factorization of graph Laplacians
    Autorzy:
    Jorgensen, P.
    Tian, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255936.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    unbounded operators
    deficiency-indices
    Hilbert space
    boundary values
    weighted graph
    reproducing kernel
    Dirichlet form
    graph Laplacian
    resistance network
    harmonic analysis
    frame
    Parseval frame
    Friedrichs extension
    reversible random walk
    resistance distance
    energy Hilbert space
    Opis:
    Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space [formula] of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in [formula] we characterize the Priedrichs extension of the [formula]-graph Laplacian. We consider infinite connected network-graphs G = (V, E), V for vertices, and E for edges. To every conductance function c on the edges E of G, there is an associated pair [formula] where [formula] in an energy Hilbert space, and Δ (=Δc) is the c-graph Laplacian; both depending on the choice of conductance function c. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in [formula] consisting of dipoles. Now Δ is a well-defined semibounded Hermitian operator in both of the Hilbert [formula] and [formula]. It is known to automatically be essentially selfadjoint as an [formula]-operator, but generally not as an [formula] operator. Hence as an [formula] operator it has a Friedrichs extension. In this paper we offer two results for the Priedrichs extension: a characterization and a factorization. The latter is via [formula].
    Źródło:
    Opuscula Mathematica; 2015, 35, 3; 293-332
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An upper bound on the Laplacian spectral radius of the signed graphs
    Autorzy:
    Li, Hong-Hai
    Li, Jiong-Sheng
    Powiązania:
    https://bibliotekanauki.pl/articles/743035.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Laplacian matrix
    signed graph
    mixed graph
    largest Laplacian eigenvalue
    upper bound
    Opis:
    In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2008, 28, 2; 345-359
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number
    Autorzy:
    Luo, Jing
    Zhu, Zhongxun
    Wan, Runze
    Powiązania:
    https://bibliotekanauki.pl/articles/31341799.pdf
    Data publikacji:
    2017-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Laplacian characteristic polynomial
    Laplacian-like energy
    tricyclic graph
    Opis:
    Let $ \phi (L(G)) = \text{det}(x I−L(G)) = \Sigma_{k=0}^n (−1)^k c_k (G) x^{n−k} $ be the Laplacian characteristic polynomial of $G$. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in $ \mathcal{G}_{n,n+2} (i) $ (the set of all tricyclic graphs with fixed order $n$ and matching number $i$). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on $ \phi (L(G)) $, is also determined in $ \mathcal{G}_{n,n+2} (i) $.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 3; 505-522
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the second largest eigenvalue of a mixed graph
    Autorzy:
    Zhou, Jun
    Fan, Yi-Zheng
    Wang, Yi
    Powiązania:
    https://bibliotekanauki.pl/articles/743812.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed graph
    Laplacian eigenvalue
    degree
    Opis:
    Let G be a mixed graph. We discuss the relation between the second largest eigenvalue λ₂(G) and the second largest degree d₂(G), and present a sufficient condition for λ₂(G) ≥ d₂(G).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 2; 373-384
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Balancedness and the Least Laplacian Eigenvalue of Some Complex Unit Gain Graphs
    Autorzy:
    Belardo, Francesco
    Brunetti, Maurizio
    Reff, Nathan
    Powiązania:
    https://bibliotekanauki.pl/articles/31540652.pdf
    Data publikacji:
    2020-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    gain graph
    Laplacian eigenvalues
    balanced graph
    algebraic frustration
    Opis:
    Let \(\mathbb{T}_4 = {±1, ±i}\) be the subgroup of 4-th roots of unity inside \(\mathbb{T}\), the multiplicative group of complex units. A complex unit gain graph \(\Phi\) is a simple graph $Γ = (V(Γ) = {v_1, . . ., v_n}, E(Γ))$ equipped with a map \(\varphi:\overrightarrow{E}(Γ)→\mathbb{T}\) defined on the set of oriented edges such that \(\varphi(v_iv_j) = \varphi(v_jv_i)^{−1}\). The gain graph \(\Phi\) is said to be balanced if for every cycle $C = v_{i_1}v_{i_2} . . . v_{i_k}v_{i_1}$ we have \(\varphi(v_{i_1}v_{i_2})\varphi(v_{i_2}v_{i_3}) . . . \varphi(v_{i_k}v_{i_1}) = 1\). It is known that \(\Phi\) is balanced if and only if the least Laplacian eigenvalue \(\lambda_n(\Phi)\) is 0. Here we show that, if \(\Phi\) is unbalanced and \(\varphi(\Phi) ⊆ \mathbb{T}_4\), the eigenvalue \(\lambda_n(\Phi)\) measures how far is \(\Phi\) from being balanced. More precisely, let \(ν(\Phi)\) (respectively, \(∈(\Phi)\)) be the number of vertices (respectively, edges) to cancel in order to get a balanced gain subgraph. We show that \(\lambda_n(\Phi) ≤ ν(\Phi) ≤ ∈(\Phi)\). We also analyze the case when \(\lambda_n(\Phi) = ν(\Phi)\). In fact, we identify the structural conditions on \(\Phi\) that lead to such equality.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 2; 417-433
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two
    Autorzy:
    Gong, Shi-Cai
    Fan, Yi-Zheng
    Powiązania:
    https://bibliotekanauki.pl/articles/743659.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    unicyclic graph
    mixed graph
    Laplacian eigenvalue
    matching number
    spectrum
    Opis:
    This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 1; 69-82
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
    Autorzy:
    Fan, Yi-Zheng
    Wu, Song
    Powiązania:
    https://bibliotekanauki.pl/articles/743077.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    unicyclic graph
    Laplacian matrix
    spectral radius
    Opis:
    The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2008, 28, 3; 487-499
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The signless Laplacian spectral radius of graphs with given number of cut vertices
    Autorzy:
    Cui, Lin
    Fan, Yi-Zheng
    Powiązania:
    https://bibliotekanauki.pl/articles/744527.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    cut vertex
    signless Laplacian matrix
    spectral radius
    Opis:
    In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 1; 85-93
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number
    Autorzy:
    Su, Li
    Li, Hong-Hai
    Zhang, Jing
    Powiązania:
    https://bibliotekanauki.pl/articles/30148000.pdf
    Data publikacji:
    2014-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    clique number
    kite graph
    signless Laplacian
    spectral radius
    Opis:
    In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph $PK_{n-\omega,\omega}$ among all connected graphs with $n$ vertices and clique number $\omega$. In addition, we show that the spectral radius $\mu$ of $PK_{m,\omega}$ $(m\geq1)$ satisfies $$\frac{1}{2}(2\omega-1+\sqrt{4\omega^{2}-12\omega+17})\leq\mu\leq 2\omega-1.$$ More precisely, for $m>1$, $\mu$ satisfies the equation \[ \mu-\omega-\frac{\omega-1}{\mu-2\omega+3}=a_m\sqrt{\mu^2-4\mu}+\frac{1}{t_1}, \] where $a_m=\frac{1}{1-t_1^{2m+3}}$ and $t_{1}=\frac{\mu-2+\sqrt{(\mu-2)^{2}-4}}{2}$. At last the spectral radius $\mu(PK_{\infty,\omega})$ of the infinite graph $PK_{\infty,\omega}$ is also discussed.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 1; 95-102
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constrained spectral clustering via multi-layer graph embeddings on a Grassmann manifold
    Autorzy:
    Trokicić, Aleksandar
    Todorović, Branimir
    Powiązania:
    https://bibliotekanauki.pl/articles/329780.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    spectral clustering
    constrained clustering
    multilayer graph
    Grassmann manifold
    Nyström method
    Laplacian matrix
    grupowanie widmowe
    graf wielowarstwowy
    metoda Nyströma
    macierz Laplaciana
    Opis:
    We present two algorithms in which constrained spectral clustering is implemented as unconstrained spectral clustering on a multi-layer graph where constraints are represented as graph layers. By using the Nystrom approximation in one of the algorithms, we obtain time and memory complexities which are linear in the number of data points regardless of the number of constraints. Our algorithms achieve superior or comparative accuracy on real world data sets, compared with the existing state-of-the-art solutions. However, the complexity of these algorithms is squared with the number of vertices, while our technique, based on the Nyström approximation method, has linear time complexity. The proposed algorithms efficiently use both soft and hard constraints since the time complexity of the algorithms does not depend on the size of the set of constraints.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 1; 125-137
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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