Related papers: Energy returns in global AdS_4
Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
This work considers positive energy theorems in asymptotically, locally AdS spacetimes. Particular attention is given to spacetimes where conformal infinity has compact, Einstein cross-sections admitting Killing or parallel spinors; a…
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of…
We study the gravitational field of a spinning radiation beam-pulse (a gyraton) in a D-dimensional asymptotically AdS spacetime. It is shown that the Einstein equations for such a system reduce to a set of two linear equations in a…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics,…
We argued in arXiv:1408.0624 that the quartic scalar field in AdS has features that could be instructive for answering the gravitational stability question of AdS. Indeed, the conserved charges identified there have recently been observed…
In this paper, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on $\mathbb T^2$, based on a new approximate system which is different from the classical Ginzburg-Landau approximation.…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
In this paper, we propose a weak approximation of the reflection coupling (RC) for stochastic differential equations (SDEs), and prove it converges weakly to the desired coupling. In contrast to the RC, the proposed approximate reflection…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact non-linearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred towards small scales by a direct cascade, whereas the number…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…
We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some energy function. We show that this simple…
The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell's RG equations for massless QED in curved space, we determine the gravitational counterterms and the…
We present a numerical study of turbulence in Bose-Einstein condensates within the 3D Gross-Pitaevskii equation. We concentrate on the direct energy cascade in forced-dissipated systems. We show that behavior of the system is very sensitive…