Related papers: Nonasymptotic densities for shape reconstruction
This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the…
This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions…
In this paper we obtain density estimates for compact surfaces immersed in R^n with total boundary curvature less than 4pi and with sufficiently small L^p norm of the mean curvature, p>2. Our results generalize the main results in [2]. We…
The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about…
In this article we discuss density of products of biharmonic functions vanishing on an arbitrarily small part of the boundary. We prove that one can use three or more such biharmonic functions to construct a dense subset of smooth symmetric…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the…
We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
Let M be a compact, orientable, mean convex 3-manifold with boundary. We show that the set of all simple closed curves in the boundary of M which bound unique area minimizing disks in M is dense in the space of simple closed curves in the…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We show that intrinsic and extrinsic area density bounds are equivalent, with matching asymptotic values, for complete, connected, smooth minimal immersions $i:\Sigma^d\to\mathbb{R}^N$ of any dimension and codimension. Combining our results…
This paper outlines an exact analytic model for self-gravitating thin disc galaxies with flat rotation curves. It is shown that thin discs of matter alone can support perfectly flat rotation curves under Newtonian gravity, without needing…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…
We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous…