Related papers: Estimation of Local Anisotropy Based on Level Sets

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

A set of locally finite perimeter $E \subset \mathbb{R}^{n}$ is called an anisotropic minimal surface in an open set $A$ if $\Phi(E;A) \le \Phi(F;A)$ for some surface energy $\Phi(E;A) = \int_{\partial^{*}E \cap A} \| \nu_{E}\| d…

The objective of active level set estimation for a black-box function is to precisely identify regions where the function values exceed or fall below a specified threshold by iteratively performing function evaluations to gather more…

We study the dynamical properties of spherical galaxies with surface luminosity profile described by the R^{1/m}-law, in which a variable degree of orbital anisotropy is allowed. The parameter m for the present models covers the range…

A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…

Surface grading, the process of leveling an uneven area containing pre-dumped sand piles, is an important task in the construction site pipeline. This labour-intensive process is often carried out by a dozer, a key machinery tool at any…

In recent years many procedures have been proposed to check the anisotropy of a dataset. We present a new simple procedure, based on a scale dependent approach, to detect anisotropy signatures in a given distribution with particular…

Let K be a self-similar or self-affine set in R^d, let \mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation…

A deterministic application $\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}^2$ deforms bijectively and regularly the plane and allows to build a deformed random field $X\circ\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}$ from a regular,…

We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks. We derive a closed-form expression for the expected generalization…

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both…

Let $G$ be a locally compact group. We examine the problem of determining when nonzero functions in $L^2(G)$ have linearly independent translations. In particular, we establish some results for the case when $G$ has an irreducible, square…

For a centered, homogeneous R^d-valued Gaussian random field X(t), t in R^k, with covariance matrix function R(s,t) = E[X(s) X(t)^T], we investigate the exact asymptotics of kappa_u(x) = P( theta(u) * integral over [0,T]^k of 1{X(t) > u b}…

We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether…

For a given l-adic sheaf F on a commutative algebraic group over a finite field k and an integer r we define the r-th local norm L-function of F at a point t in G(k) and prove its rationality. This function gives information on the sum of…

Let $\mathbb{A}$ be the adele ring of a totally real algebraic number field $F$. We push forward an explicit computation of a relative trace formula for periods of automorphic forms along a split torus in $GL(2)$ from a square free level…

Native ring structures within amorphous networks play a critical role in determining structural and optical properties, in part due to their ability to host dopants such as rare earth ions in silicate systems. In this work, we demonstrate…

(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our…

Let $\{X(t) : t \in [0, \infty) \}$ be a centered stationary Gaussian process. We study the exact asymptotics of $\pr (\sup_{s \in [0,T]} X(t) > u)$, as $u \to \infty$, where $T$ is an independent of \{X(t)\} nonnegative random variable. It…

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions,…