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We present a bound on the exponent exp(A) of an n × n primitive matrix A in terms of its boolean rank b = b(A); namely exp(A) ≤ (b − 1)2 + 2. Further, we show that for each 2 ≤ b ≤ n − 1, there is an n × n primitive matrix A with b(A) = b... more
We present a bound on the exponent exp(A) of an n × n primitive matrix A in terms of its boolean rank b = b(A); namely exp(A) ≤ (b − 1)2 + 2. Further, we show that for each 2 ≤ b ≤ n − 1, there is an n × n primitive matrix A with b(A) = b such
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We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link/node. We obtain analytic formulas for the probability of success, when the agent's tool is the free... more
We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link/node. We obtain analytic formulas for the probability of success, when the agent's tool is the free evolution of a single excitation on an XX spin system paired with the network. We completely characterize the parameters allowing for an advantageous solution. From the results emerges an optimal (deterministic) algorithm for quantum search, therefore gaining a quadratic speed-up with respect to the optimal classical analogue, and in line with well-known results in quantum computation. When attempting to detect a faulty node, the chosen setting appears to be very fragile and the probability of success too small to be of any direct use.
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The iterative aggregation/disaggregation (IAD) method is an improvement of the PageRank algorithm used by the search engine Google to compute stationary probabilities of very large Markov chains. In this paper the convergence, in exact... more
The iterative aggregation/disaggregation (IAD) method is an improvement of the PageRank algorithm used by the search engine Google to compute stationary probabilities of very large Markov chains. In this paper the convergence, in exact arithmetic, of the IAD method is analyzed. The IAD method is expressed as the power method preconditioned by an incomplete LU factorization. This leads to a
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Abstract: Recent works have shown that Markov chain theory can be used to model and realistically describe road network dynamics. Properties of the Markov transition matrix such as the Perron eigenvector, the second eigenvalue, and the... more
Abstract: Recent works have shown that Markov chain theory can be used to model and realistically describe road network dynamics. Properties of the Markov transition matrix such as the Perron eigenvector, the second eigenvalue, and the Kemeny constant have nice ...
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Cutpoint Decoupling and First Passage Times for Random Walks on Graphs. [SIAM Journal on Matrix Analysis and Applications 20, 860 (1999)]. Stephen J. Kirkland, Michael Neumann. Abstract. One approach to the computations ...
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ABSTRACT A bigraph (bipartite graph) is called semi-complete, if it has an adjacency matrix of the form A=0BB T 0, where B is such a matrix that its sum with the transposed matrix B T has the term 0 on the main diagonal and the term 1... more
ABSTRACT A bigraph (bipartite graph) is called semi-complete, if it has an adjacency matrix of the form A=0BB T 0, where B is such a matrix that its sum with the transposed matrix B T has the term 0 on the main diagonal and the term 1 elsewhere. (Such a matrix is an adjacency matrix of a tournament.) The paper studies properties of such bigraphs, namely regularity, connectedness and spectral properties. Among other results it is proved that a regular semi-complete bigraph has four distinct eigenvalues if and only if the mentioned matrix B is an adjacency matrix of a doubly regular tournament, i.e. a tournament in which each pair of vertices dominates the same number of vertices. These tournaments are also studied.Reviewer: B.Zelinka (Liberec)
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ABSTRACT Of interest here is a characterization of the undirected graphs G such that the Laplacian matrix associated with G can be diagonalized by some Hadamard matrix. Many interesting and fundamental properties are presented for such... more
ABSTRACT Of interest here is a characterization of the undirected graphs G such that the Laplacian matrix associated with G can be diagonalized by some Hadamard matrix. Many interesting and fundamental properties are presented for such graphs along with a partial characterization of the cographs that have this property.
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The M-Matrix Group Generalized Inverse Problem for Weighted Trees. [SIAM Journal on Matrix Analysis and Applications 19, 226 (1998)]. Stephen J. Kirkland, Michael Neumann. Abstract. We characterize all weighted trees whose ...