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We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the…
We study surface and bulk properties of porous films produced by a model in which particles incide perpendicularly to a substrate, interact with deposited neighbors in its trajectory, and aggregate laterally with probability of order $a$ at…
This paper presents an end-to-end differentiable algorithm for robust and detail-preserving surface normal estimation on unstructured point-clouds. We utilize graph neural networks to iteratively parameterize an adaptive anisotropic kernel…
An important aspect of modeling spatially-referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the…
This paper presents a technique, combining the integral equations (IE) and the Generalized Sheet Transition Conditions (GSTCs) with bianisotropic susceptibility tensors, to compute electromagnetic wave scattering by cylindrical metasurfaces…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
Two-dimensional (2D) tin(II) sulfide (SnS) crystals belong to a class of orthorhombic semiconducting materials that are lately attracting significant interest, given their remarkable properties, such as in-plane anisotropic optical and…
We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences…
3D Gaussian Splatting has emerged as a powerful scene representation for real-time novel-view synthesis. However, its standard adaptive density control relies on screen-space positional gradients, which do not distinguish between geometric…
Faceted grain boundaries can migrate in interesting and unexpected ways. For example, faceted {\Sigma}11 <110> tilt grain boundaries were observed to exhibit mobility values that could be strongly dependent on the direction of migration. In…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
We develop a general continuum mechanics framework for active anisotropic plates within the F\"oppl-von K\'arm\'an limit, incorporating a preferential direction and inelastic active contractions in geometrically nonlinear plate theory.…
Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often…
We study surfaces with constant anisotropic mean curvature which are invariant under a helicoidal motion. For functionals with axially symmetric Wulff shapes, we generalize the recently developed twizzler representation of Perdomo to the…
Upon using fundamental electromagnetic properties of metasurfaces we build a platform to classify reciprocal bianisotropic metasurfaces from typical experimental measurements and determine isotropic, anisotropic, bi-isotropic (chiral), and…
In this paper we propose a measure of anisotropy as a quality parameter to estimate the amount of noise in noisy images. The anisotropy of an image can be determined through a directional measure, using an appropriate statistical…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…
We synthesize geometrically tailorable anisotropic plates by combining button shaped fish-scale like features on soft substrates, then lacing them with high-stiffness strings. This creates a new type of biomimetic architectured structure…