相关论文: The Scenery Flow for Self-Affine Measures

The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms, which yield information about the "fractal" structure of these measures. The…

Conical density theorems are used in the geometric measure theory to derive geometric information from given metric information. The idea is to examine how a measure is distributed in small balls. Finding conditions that guarantee the…

We report results on the scaling properties of changes in contrast of natural images in different visual environments. This study confirms the existence, in a vast class of images, of a multiplicative process relating the variations in…

We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent…

In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…

Finite-size scaling expressions for the current near the continuous phase transition, and for the local density near the first-order transition, are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process…

Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu is a Bernoulli measure on E with dim_H mu = dim_L mu, where dim_H and dim_L denote Hausdorff…

We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and…

A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly…

We give a condition for absolute continuity of self-similar measures in arbitrary dimensions. This allows us to construct the first explicit absolutely continuous examples of inhomogeneous self-similar measures in dimension one and two. In…

We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…

If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…

We describe a family $\phi_{\lambda}$ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli…

Bernoulli pads generate locally large wall shear stresses on workpieces, which can be used for cleaning, but may also damage delicate surfaces. This work presents direct measurements of the wall shear stress using constant temperature…

In the domain of supervised scene flow estimation, the process of manual labeling is both time-intensive and financially demanding. This paper introduces SSFlowNet, a semi-supervised approach for scene flow estimation, that utilizes a blend…

Imposing consistency through proxy tasks has been shown to enhance data-driven learning and enable self-supervision in various tasks. This paper introduces novel and effective consistency strategies for optical flow estimation, a problem…

We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have…

We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…

We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.