相关论文: Symmetry within Solutions
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
It is made the attempt to explain why there exists a division between internal symmetries referring to quantum numbers and external symmetries referring to space-time within the description of relativistic quantum field theories. It is hold…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
Symmetry problems in harmonic analysis are formulated and solved. One of these problems is equivalent to the refined Schiffer's conjecture which was recently proved by the author. Let $k=const>0$ be fixed, $S^2$ be the unit sphere in…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
Color symmetry implies that the colors of geometrical objects are assigned according to their symmetry properties. It is defined by associating the elements of the symmetry group with a color permutation. I use this concept for generative…
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\em and} the (physical) states. For infinitely extended systems the states fall into physically…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
Virtually all network analyses involve structural measures between pairs of vertices, or of the vertices themselves, and the large amount of symmetry present in real-world complex networks is inherited by such measures. This has practical…
Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a…
What does it mean for a boundary condition to be symmetric with respect to a non-invertible global symmetry? We discuss two possible definitions in 1+1d. On the one hand, we call a boundary weakly symmetric if the symmetry defects can…
An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the…
An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study…
We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional.
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
Motivated by phase transitions in combinatorial optimization problems, we define two kinds of geometry-preserving reductions between constraint satisfaction problems and other NP-search problems. We give a couple of examples and…
We review the {\it Noether Symmetry Approach} as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact…