In strong-coupling regimes, quantum dynamical effects can alter conventional physics described by perturbation theories, but the simulations of these systems using matrix product states---such as multilevel vibronic that are relevant to energy and electron transfer reactions---suffer from rapid entanglement growth during their real-time evolution, impeding explorations spectra, dynamics, kineti...

Existing nonnegative matrix factorization methods usually focus on learning global structure of the data to construct basis and coefficient matrices, which ignores local that commonly exists among data. To overcome this drawback, in paper, we propose a new type method, learns similarity clustering mutually enhanced way. The learned representation is more representative it better reveals inheren...

Large-scale text datasets have long eluded a family of particularly elegant and effective clustering methods that exploits the power of pair-wise similarities between data points due to the prohibitive cost, timeand space-wise, in operating on a similarity matrix, where the state-of-the-art is at best quadratic in time and in space. We present an extremely fast and simple method also using the ...

Let an n x -matrix A have m < (m ? 2) different eigenvalues ?j of the algebraic multiplicity (j = 1,..., m). It is proved that there are ?j-matrices Aj, each which has a unique eigenvalue ?j, such similar to block-diagonal matrix ?D diag (A1,A2,..., Am). I.e. invertible T, T-1AT ?D. Besides, sharp bound for number kT := ||T||||T-1|| derived. As applications these results we obtain norm estim...

Immune repertoires provide a unique fingerprint reflecting the immune history of individuals, with potential applications in precision medicine. However, question how personal that information is and it can be used to identify individuals has not been explored. Here, we show uniquely identified from just few thousands lymphocytes. We present "Immprint," classifier using an information-theoretic...