Non‐Negative Matrices and Markov Chains
By V. Isham, Eugene Seneta. 1983
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Citations in the corpus
- Stochastic Gradient Push for Distributed Deep Learning (2018, background): “Drawing inspiration from the theory of Markov chains (Seneta, 1981), the mixing matrices P (k) are designed to be column stochastic (each column must sum to 1).”
- LexRank: Graph-based Lexical Centrality as Salience in Text Summarization (2004, background): “e is reachable from any other state, i.e. for all i,j there exists an n such that Xn(i,j) 6= 0. A Markov chain is aperiodic if for all i, gcd{n : Xn(i,i) > 0} = 1. By the Perron-Frobenius theorem (Seneta, 1981), an irreducible and aperiodic Markov chain is guaranteed to converge to a unique stati”
- A tutorial on modeling and analysis of dynamic social networks. Part I (2017, background): “As shown in the next subsection, Theorem 12 can be derived from the standard results on the Markov chains convergence [82], using the duality between Markov chains and the French-DeGroot opinion dynamics.”
- LexRank: Graph-based Centrality as Salience in Text Summarization (2004, methodology): “By the Perron-Frobenius theorem (Seneta, 1981), an irreducible and aperiodic Markov chain is guaranteed to converge to a unique stationary distribution.”
- GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES (2001, unknown): “5 of (5) assures that if R(A) is aperiodic”
- Concave Perron–Frobenius Theory and applications (2001, unknown): “, [1, 8, 10].”
- A tutorial on the positive realization problem (2004, background): “have been the subject of study in the mathematical sciences from long ago (see, for example, [82]–[91]).”
- Multi-Antenna Wireless Powered Communication With Energy Beamforming (2013, methodology): “ing problem given in (13) into an equivalent spectral radius minimization problem, where the spectral radius of a matrix B, denoted by ρ(B), is defined as its maximum eigenvalue in absolute value [8], [9]. Define D(W) = Diag n 1 kwH 1h k2 ,··· , 1 kwH Kh Kk2 o , σ(W) = [(1−τ¯)σ2kw 1k2,··· ,(1− τ¯)σ2kw”
- Stochastic Consensus Seeking With Noisy and Directed Inter-Agent Communication: Fixed and Randomly Varying Topologies (2010, background): “Now we may summarize the following properties based on standard results on Markov chains [29].”