Related papers: Estimates of gradient perturbation series
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we…
This paper aims at achieving a "good" estimator for the gradient of a function on a high-dimensional space. Often such functions are not sensitive in all coordinates and the gradient of the function is almost sparse. We propose a method for…
We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper bounds on the exponential rates of enhanced dissipation.…
We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended…
We consider the problem of assigning a meaningful degree of belief to uncertainty estimates of perturbative series. We analyse the assumptions which are implicit in the conventional estimates made using renormalisation scale variations. We…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
We derive the matching conditions for cosmological perturbations in a Friedmann Universe where the equation of state undergoes a sharp jump, for instance as a result of a phase transition. The physics of the transition which is needed to…
The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite…
We give a brief overview of the theoretical status of the Transition Distribution Amplitudes and discuss their experimental near future.
The standard calculation of the spectrum of density perturbations produced during inflation assumes that there is only one real dynamical degree of freedom during inflation. However, there is no reason to believe that this is actually the…
We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
Previously defined covariant and gauge-invariant perturbation variables, representing, e.g., the fractional spatial energy density gradient on hypersurfaces of constant expansion, are used to simplify the linear perturbation analysis of a…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We obtain a limit theorem endowed with quantitative estimates for a general class of infinite dimensional hybrid processes with intrinsically two different time scales and including a population. As an application, we consider a large class…
Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…