Related papers: Estimates of gradient perturbation series

We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…

We introduce new measures of decoherence appropriate for evaluation of quantum computing designs. Environment-induced deviation of a quantum system's evolution from controlled dynamics is quantified by a single numerical measure. This…

Recent experimental determinations of the spectral index describing the scalar mode spectrum of density perturbations encourage comparison with predictions from models of the very early universe. Unlike extended inflation, Induced-gravity…

Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary…

We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous…

We present a new, exact scalar field cosmology for which the spectrum of scalar (density) perturbations can be calculated exactly. We use this exact result to the probe the accuracy of approximate calculations of the perturbation spectrum.

We study density perturbations, including their non-Gaussianity, in models in which the decay rate of the curvaton depends on another light scalar field, denoted the modulaton. Although this model shares some similarities with the standard…

We study perturbations of random dynamical systems whose associated transfer operators admit a uniform spectral gap. We provide a $k^{\text{th}}$-order approximation for the invariant density of the associated random dynamical system. We…

We prove an optimal 4G Theorem for the Gaussian kernel. We also propose a new general method of estimating Schroedinger perturbations of transition densities, and give applications to the Gaussian kernel.

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time series, they offer limited insights, as semantically…

We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.

The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second…

Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…

We compute the spectral index for scalar perturbations generated in a primordial inflationary model. In this model, the transition of the inflationary phase to the radiative era is achieved through the decay of the cosmological term leading…

The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…

We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.

We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. While much is known about the limits of…

This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very…

Spectrum of density perturbations in the Universe generated from quantum-gravitational fluctuations in slow-roll-over inflationary scenarios with the Brans-Dicke gravity is calculated. It is shown that after inflation the isocurvature mode…