We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution of the KPZ equati ...
A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called 'basis rhombicity' which is the sum of the absolute val ...
In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that t ...
The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...
Far-field dot pattern generation is analyzed for a Gaussian beam source that illuminates a sinusoidal phase grating which is placed at a certain distance behind the beam waist. We obtain a bigger field of view with more numbers of points using a Gaussian b ...
Iterative real-time optimization schemes that employ modifier adaptation add bias and gradient correction terms to the model that is used for optimization. These affine corrections lead to meeting the first-order necessary conditions of optimality of the p ...
In this paper we demonstrate how, using the coset construction, a theory can be systematically made Weyl invariant by gauging the scale symmetry. We show that an analog of the inverse Higgs constraint allows the elimination of the Weyl vector (gauge) field ...
We study the problem of maximizing a monotone set function subject to a cardinality constraint k in the setting where some number of elements is deleted from the returned set. The focus of this work is on the worst-case adversarial setting. While there exi ...
In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. ...
In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY li ...
