The Schrödinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral...

The f-electron spectral function of the Falicov-Kimball model is calculated via a Keldysh-based many-body formalism originally developed by Brandt and Urbanek. We provide results for both the Bethe lattice and the hypercubic lattice at half filling. Since the numerical computations are quite sensitive to the discretization along the Kadanoff-Baym contour and to the maximum cutoff in time that i...

Predictive state representations (PSRs) model dynamical systems using appropriately chosen predictions about future observations as a representation of the current state. In contrast to the hidden states posited by HMMs or RNNs, PSR states are directly observable in the training data; this gives rise to a moment-matching spectral algorithm for learning PSRs that is computationally efficient and...

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients and the input amplitude is subject to second and fourth moment constraints. The main focus is on the power-limited (i.e., wideband, low-power) regime. First the structure of the capacity-achieving input signals is investigat...

LSI +61 303 is one of the few X-ray binaries with Be star companion from which both radio and high-energy gamma-ray emission have been observed. We present XMM-Newton and INTEGRAL observations which reveal variability of the X-ray spectral index of the system. The X-ray spectrum is hard (photon index Γ ≃ 1.5) during the orbital phases of both high and low X-ray flux. However, the spectrum softe...

LSI +61 303 is one of the few X-ray binaries with Be star companion from which both radio and high-energy gamma-ray emission have been observed. We present XMM-Newton and INTEGRAL observations which reveal variability of the X-ray spectral index of the system. The X-ray spectrum is hard (photon index Γ ≃ 1.5) during the orbital phases of both high and low X-ray flux. However, the spectrum softe...

The microscopic connections between solvation dynamics and the experimentally measured dynamic emission Stokes shift are explored by molecular dynamics simulation using the hydrated electron as a fully quantum mechanical probe. Solvent response functions are computed using the method of spectral reconstruction at various time resolutions for both fluorescence and stimulated emission and compare...

Consider a random sample from a bivariate distribution function F in the max-domain of attraction of an extreme-value distribution function G. This G is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of F . A major issue in multivariate extreme-value theory is the estimation of the spectral measure Φp with respect to the L...