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Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines,…
Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…
The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to a \textit{scalar product}, which we used to define \textit{orthogonals} in these…
Scientific Machine Learning (SciML) faces unique challenges for extreme-resolution data, with mitigations that often fail to scale or degrade the accuracy of trained models. While some specialized methods have achieved remarkable results in…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
Recent developments have created differentiable physics simulators designed for machine learning pipelines that can be accelerated on a GPU. While these can simulate biomechanical models, these opportunities have not been exploited for…
The past few years have witnessed growth in the computational requirements for training deep convolutional neural networks. Current approaches parallelize training onto multiple devices by applying a single parallelization strategy (e.g.,…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding…
We use topological techniques to do a workspace analysis of the Canfield Joint, a mechanical linkage constructed with two plates connected by three legs. The Canfield Joint has three degrees of freedom and can be controlled using three…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the…
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfunctions in the kernel of GJMS operators.…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…