Related papers: Shape Theory Via SV Decomposition II
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Exclusive non-leptonic two-body decays are discussed on the basis of a generalized factorization approach which also includes non-factorizeable contributions. Numerous decay processes can be described satisfactorily. The success of the…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be…
Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
Through the use of wavelet based Besov norms, we compute nontrivial multiscale nonlinear features of a given data set so as to enhance the standard Dynamic-Mode Decomposition algorithm. Thus we are able to build sophisticated observables…
A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is considered. Two major difficulties, collapsed cells and an…
In this paper we provide an alternative reduction theory for real, binary forms with no real roots. Our approach is completely geometric, making use of the notion of hyperbolic center of mass in the upper half-plane. It appears that our…
{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical…
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend…
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs)…
We classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of…
Nonparametric statistics for distribution functions F or densities f=F' under qualitative shape constraints provides an interesting alternative to classical parametric or entirely nonparametric approaches. We contribute to this area by…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
A classification of SL$(n)$ invariant valuations on the space of convex polytopes in $R^n$ without any continuity assumptions is established. A corresponding result is obtained on the space of convex polytopes in $R^n$ that contain the…