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Environmental quality affects the formation of generalist and specialist taxa in microbial communities. [PDF]
Yang G +12 more
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A note on the stochastic roots of stochastic matrices
Journal of Systems Science and Systems Engineering, 2003In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In
Qi-Ming He, Eldon A Gunn, He Qi-Ming
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SIAM Journal on Matrix Analysis and Applications, 2010
We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin matrices as they arise in the discretization of linear differential equations with random coefficient functions. These matrices are characterized as the Galerkin representation of polynomial multiplication operators.
Oliver G. Ernst, Elisabeth Ullmann
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We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin matrices as they arise in the discretization of linear differential equations with random coefficient functions. These matrices are characterized as the Galerkin representation of polynomial multiplication operators.
Oliver G. Ernst, Elisabeth Ullmann
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On Stochastic Matrices and Kernels
Theory of Probability & Its Applications, 1967From the introduction: It is well-known, that every stochastic matrix has 1 as an eigenvalue with \((1,\dots, 1)\) as a corresponding eigenvector. Further, a stochastic matrix, as a linear transformation, leaves the positive orthant invariant, of which \((1,\dots, 1)\) is an interior point. Motivated by this, we show in Section.
Natarajan, S. +2 more
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