Related papers: Symmetries in Images on Ancient Seals
TEM images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion…
In this paper, we show that symmetries, which are known in the theory of integrable systems, naturally appeared in the classical linear theory of deformations of thin shells. Our result shows that if the middle surface of a shell becomes…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
We review the stamp folding problem, the number of ways to fold a strip of $n$ stamps, and the related problem of enumerating meander configurations. The study of equivalence classes of foldings and meanders under symmetries allows to…
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
Magnetic skyrmions are two-dimensional non-collinear spin textures characterised by an integer topological number. They commonly crystallise at low temperatures in bulk noncentrosymmetric ferromagnets where the lack of inversion symmetry…
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects…
Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used…
For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and…
In this paper we study different kinds of symmetries related to the domino tilings of chessboards.
How were surfaces evaluated before the invention of the sexagesimal place value notation in Mesopotamia? This chapter examines a group of five tablets containing tables for surfaces of squares and rectangles dated to the Early Dynastic…
We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which the $v_i$ are the rows. We characterize properties of $v$ in…
Image splicing is a common form of image forgery. Such alterations may leave no visual clues of tampering. In recent works camera characteristics consistency across the image has been used to establish the authenticity and integrity of…