When a transition probability matrix is represented as the product of two stochastic matrices, swapping the factors of the multiplication yields another transition matrix that retains some fundamental characteristics of the original. Since the new matrix can be much smaller than its precursor, replacing the former for the latter can lead to significant savings in terms of computational effort. ...

fept nanoparticles with thermally stable room-temperature ferromagnetism are investigated. the monodisperse nanoparticles are prepared by chemical synthesis and a salt-matrix annealing technique. structural and magnetic characterizations confirm the phase transition from the disordered face-centered cubic structure. in this paper, 3 nm fept nanoparticles are first synthesized by superhydride re...

Adapting the competitions method of Freivalds to the setting of unbounded-error prob-abilistic computation, we prove that, for any 2 (0; 1], Band-Mat-Inv(n) is log-space complete for the class of languages recognized by log-space unbounded-error probabilistic Turing machines (PL). This extends the result of Jung that Band-Mat-Inv(n) is log-space complete for PL, and may open new possibilities f...

We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and ...

We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain thres...