Motivated by WMAP’s confirmation of an anomalously low value of the quadrupole moment of the CMB temperature fluctuations, we investigate the effects on the CMB of cutting off the primordial power spectrum P (k) at low wave numbers. This could arise, for example, from a break in the inflaton potential, a prior period of matter or radiation domination, or an oscillating scalar field which couple...

The paper presents a study of several problems related to spectral factorizations. We assume only a very weak form of coercivity for the p× p spectral function Φ and look at the set Wm of all rectangular, p × m spectral factors. The main object is the arithmetization of the geometry of the set of minimal, stable spectral factors by employing Hardy space techniques and the arithmetic of inner fu...

We consider single particle Schrodinger operators with a gap in the energy spectrum. We construct a countable set of exponentially decaying functions, which form a complete, orthonormal basis set for the states below the spectral gap. Each such function is localized near a closed surface. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces is included.

Voice adaptation describes the process of converting the output of a text-to-speech synthesizer voice to sound like a different voice after a training process in which only a small amount of the desired target speaker’s speech is seen. We employ a locally linear conversion function based on Gaussian mixture models to map bark-scaled line spectral frequencies. We compare performance for three di...

How many Pareto eigenvalues are there in a matrix of a prescribed order? This note provides the best lower bound that it is known up to now for the maximal number of Pareto eigenvalues in a matrix of order n.

Let D ⊂ R be a bounded convex domain which is symmetric relative to both coordinate axes. Assume that [−a, a] × [−b, b], a ≥ b > 0 is the smallest rectangle (with sides parallel to the coordinate axes) containing D. Let {λn}n=1 be the eigenvalues corresponding to the semigroup of the Cauchy process killed upon exiting D. We obtain the following estimate on the spectral gap: λ2 − λ1 ≥ Cb a2 , wh...

Models with dark energy decaying into dark matter have been proposed to solve the coincidence problem in cosmology. We study the effect of such coupling in the matter power spectrum. Due to the interaction, the growth of matter density perturbations during the radiation dominated regime is slower compared to non-interacting models with the same ratio of dark matter to dark energy today. This ef...

The lower spectral radius, or joint spectral subradius, of a set of real d× d matrices is defined to be the smallest possible exponential growth rate of long products of matrices drawn from that set. The lower spectral radius arises naturally in connection with a number of topics including combinatorics on words, the stability of linear inclusions in control theory, and the study of random Cant...

By analyzing the connection between complex Hadamard matrices and spectral sets we prove the direction “spectral ⇒ tile” of the Sectral Set Conjecture for all sets A of size |A| ≤ 5 in any finite Abelian group. This result is then extended to the infinite grid Z for any dimension d, and finally to R. It was pointed out recently in [16] that the corresponding statement fails for |A| = 6 in the g...