Related papers: Parabolic Molecules
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…
Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be…
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density {\sigma}g, the length ns the grafted side chains and their chemical nature fully determines the…
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…
We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We…
We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…
It remains a prime question of how to describe the optical properties of large molecular clusters accurately. Quantum chemical methods capture essential electronic details but are infeasible for entire clusters, while optical simulations…
We define distribution spaces of a sequence of convolutions of a set of distributions with smooth functions, the shearlet system. Then, we define associated sequence spaces and prove characterizations. We also show a reproducing identity in…
Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…
We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functions are used to characterize supplementary generalized…
Framelets (a.k.a. wavelet frames) are of interest in both theory and applications. Quite often, tight or dual framelets with high vanishing moments are constructed through the popular oblique extension principle (OEP). Though OEP can…
We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective)…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Duke, Imamo\=glu, and T\'oth have recently constructed a new geometric invariant, a hyperbolic orbifold, associated to each narrow ideal class of a real quadratic field. Furthermore, they have shown that the projection of these hyperbolic…
Recent SO(3)-equivariant models embedded a molecule as a set of single atoms fixed in the three-dimensional space, which is analogous to a ball-and-stick view. This perspective provides a concise view of atom arrangements, however, the…