Related papers: Symmetries in Images on Ancient Seals
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the…
A rectangular dual of a plane graph $G$ is a contact representation of $G$ by interior-disjoint rectangles such that (i) no four rectangles share a point, and (ii) the union of all rectangles is a rectangle. In this paper, we study…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Given a quandle, we can construct a symmetric quandle called the symmetric double of the quandle. We show that the (co)homology groups of a given quandle are isomorphic to those of its symmetric double. Moreover, quandle coloring numbers…
Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how…
Classical shadows (CS) have emerged as a powerful way to estimate many properties of quantum states based on random measurements and classical post-processing. In their original formulation, they come with optimal (or close to) sampling…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume…
Seals are extremely useful devices to prevent fluid leakage. However, the exact mechanism of roughness induced leakage is not well understood. We present a theory of the leak-rate of seals, which is based on percolation theory and a…
With the development and widespread application of digital image processing technology, image splicing has become a common method of image manipulation, raising numerous security and legal issues. This paper introduces a new splicing image…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
The computational cost of micromechanics for heterogeneous materials can be reduced in certain cases where symmetric boundary conditions are applicable. We derived an eighth symmetric formulation of the Generalized Method of Cells for…
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…
State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
Voltage operations extend traditional geometric and combinatorial operations (such as medial, truncation, prism, and pyramid over a polytope) to operations on maniplexes, maps, polytopes, and hypertopes. In classical operations, the…
Image segmentation and image recognition are well established computational techniques in the broader discipline of image processing. Segmentation allows to locate areas in an image, while recognition identifies specific objects within an…