Related papers: Detecting self-similarity in surface microstructur…

Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle…

We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpi\'nski carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…

This is a survey paper on the dimension theory of self-similar measures on the real line focusing on the role of entropy rates.

We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting…

We examine the growth of eccentricities of a population of particles with initially circular orbits around a central massive body. Successive encounters between pairs of particles increase the eccentricities in the disk on average. As long…

We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated…

We study the density of specular reflection points in the geometrical optics limit when light scatters off fluctuating interfaces and membranes in thermodynamic equilibrium. We focus on the statistical mechanics of both capillary-gravity…

Many systems of both theoretical and applied interest display multi-affine scaling at small length scales. We demonstrate analytically and numerically that when vertical discontinuities are introduced into a self-affine surface, the surface…

Our goal in this paper is to discover near duplicate patterns in large collections of artworks. This is harder than standard instance mining due to differences in the artistic media (oil, pastel, drawing, etc), and imperfections inherent in…

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a…

For $0< \rho < 1/3$ and $\rho \le \lambda \le 1-2\rho$, let $E$ be the self-similar set generated by the iterated function system $$\Phi = \big\{ \varphi_1(x) = \rho x ,\; \varphi_2(x) = \rho x + \lambda, \; \varphi_3(x) = \rho x + 1- \rho…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…

The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. In particular, on a variety of lattices and initial…

We study two-dimensional eigenvalue ensembles close to certain types of singular points in the bulk of the droplet. We prove existence of a microscopic density which quickly approaches the classical equilibrium density, as the distance from…

While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…