| The performance of a neural network based edge detector for high-contrast images has been investigated both quantitatively and qualitatively. We have compared it's performance for both synthetic and natural images with those of four existing edge detection methods namely, Sobel's operator, Johnson proposed Contrast based Sobel operator, MarrHildreth's Laplacian-of-Gaussian (LoG) operator, and...

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. Barriers to transport, which mitigate mixing, describe a skeleton about which possibly turbulent flow evolves. We propose a novel, direct geometric method to identify subsets of phase space that remain strongly coherent over a finite time durati...

The goal of this paper is to study a nonlinear elliptic equation in which the divergence form operator −div(a(x,∇u)) is involved. Such operators appear in many nonlinear diffusion problems, in particular in the mathematical modeling of non-Newtonian fluids (see [5] for a discussion of some physical background). Particularly, the p-Laplacian operator −div(|∇u|p−2∇u) is a special case of the oper...

Random billiards are billiard dynamical systems for which the reflection law giving the postcollision direction of a billiard particle as a function of the pre-collision direction is specified by a Markov (scattering) operator P . Billiards with microstructure are random billiards whose Markov operator is derived from a “microscopic surface structure” on the boundary of the billiard table. The ...

Bony and Häfner have recently obtained positive commutator estimates on the Laplacian in the low-energy limit on asymptotically Euclidean spaces; these estimates can be used to prove local energy decay estimates if the metric is non-trapping. We simplify the proof of the estimates of Bony-Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), b...

The positive-definiteness of the Hamiltonian operator for Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. It was indeed well known that the Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from infinitely many inverse powers of the Laplacian. If space-time is replaced by a compact Riemannian four-manifold without boundary, on w...

We consider the random Schrödinger operator−ε−2∆(d) +ξ (ε)(x), with ∆(d) the discrete Laplacian on Zd and ξ (ε)(x) are bounded and independent random variables, on sets of the form Dε := {x ∈ Zd : xε ∈ D} for D bounded, open and with a smooth boundary, and study the statistics of the Dirichlet eigenvalues in the limit ε ↓ 0. Assuming Eξ (ε)(x) = U(xε) holds for some bounded and continuous funct...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...

We consider the Dirichlet Laplacian in the half-plane with constant magnetic field. Due to the translational invariance this operator admits a fiber decomposition and a family of dispersion curves, that are real analytic functions. Each of them is simple and monotonically decreasing from positive infinity to a finite value, which is the corresponding Landau level. These finite limits are thresh...

This paper presents a novel approach for non-iterative surface smoothing with feature preservation on arbitrary meshes. Laplacian operator is performed in a global way over the mesh. The surface smoothing is formulated as a quadratic optimization problem, which is easily solved by a sparse linear system. The cost function to be optimized penalizes deviations from the global Laplacian operator w...