We present a new approximation scheme that allows us to increase the accuracy of analytical predictions of the power spectra of inflationary perturbations for two specific classes of inflationary models. Among these models are chaotic inflation with a monomial potential, power-law inflation and natural inflation (inflation at a maximum). After reviewing the established first order results we ca...

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide system...

The power spectra of the scalarand tensor-type structures generated in an inflation model based on nonminimally coupled scalar field are derived. The contributions of these structures to the anisotropy of the cosmic microwave background radiation are derived, and are compared with the four year COBE DMR data. The constraints on the ratio of the self-coupling and nonmimimal coupling constants, t...

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that ∑n i=1 d s i (s = 1, . . . , k) is determined by the Laplacian spectrum of H, where d1, . . . , dn is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spec...

We present a new approximation scheme that allows us to increase the accuracy of analytical predictions of the power spectra of inflationary perturbations for two specific classes of inflationary models. Among these models are chaotic inflation with a monomial potential, power-law inflation and natural inflation (inflation at a maximum). After reviewing the established first order results we ca...

In the machine learning fields, Recurrent Neural Network (RNN) has become a popular algorithm for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and inference. In this paper, we are trying to reduce the number of parameters and maintain the expressive power from RNN simultaneously. We utilize several tensor decom...

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latentvariable model. Our approach relies on a lowrank linear regression to recover a symmetric t...

We give a proof of concept for efficiently modeling tensor configuration distributions with Markov random fields (MRFs) and inferring the most likely tensor configurations with maximum a posteriori (MAP) estimations. We demonstrate the plausibility of our method by resolving fiber crossings in a synthetic dataset, experimenting with three different MAP estimation methods on a grid MRF model. Th...