Related papers: Relative Resolution: A Multipole Approximation at …
Given that the physical properties of polymeric liquids extend on a wide range of lengthscales, it is computationally convenient to represent them by coarse-grained (CG) descriptions at various granularities to investigate local and global…
Super-resolution (SR) is a severely ill-posed problem with inherent ambiguity, as widely recognized in both empirical and theoretical studies. Although recent semantic-guided and multi-modal SR methods exploit large models or external…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We present an introduction to the derived and relative resolutions of the moduli of stable maps. We discuss one application and mention a few problems.
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit,…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which address this problem by keeping the…
Satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena. One important feature of satellite images is the trade-off between spatial/spectral resolution and their revisiting time, a…
The surface of a molecule determines much of its chemical and physical property, and is of great interest and importance. In this Letter, we introduce the concept of molecular multiresolution surfaces as a new paradigm of multiscale…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…