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Density-matrix functional theory has enjoyed increasing popularity in recent years. For the onebody reduced density matrix, the theory rests on a Hohenberg-Kohn-type theorem which was formulated by Gilbert [1]. Employing some well-known reduced-density-matrix functionals [2] for the exchange-correlation energy, we minimize the total energy with the appropiate constraints ensuring N-representabi...

Discrete moments of the Riemann zeta function were studied by Gonek and Hejhal in the 1980’s. They independently formulated a conjecture concerning the size of these moments. In 1999, Hughes, Keating, and O’Connell, by employing a random matrix model, made this conjecture more precise. Subject to the Riemann hypothesis, we establish upper and lower bounds of the correct order of magnitude in th...

In this work we investigate the behavior of Gaussian processes as a regression technique for reinforcement learning. When confronted with too many mutually dependant learning examples, the matrix inversion needed for prediction of a new target value becomes numerically unstable. By paying attention to using suitable numerical techniques and employing QR-factorization these instabilities can be ...

In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AXB . The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard compressive sensing (CS) theory after converting it to vector form using the Kronecker operation. In this case, the measurement matrix assumes a Kronecker product stru...