相关论文: Symmetry within Solutions
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…
We define a set inner product to be a function on pairs of convex bodies which is symmetric, Minkowski linear in each dimension, positive definite, and satisfies the natural analogue of the Cauchy-Schwartz inequality (which is not implied…
We define a new measure of network symmetry that is capable of capturing approximate global symmetries of networks. We apply this measure to different networks sampled from several classic network models, as well as several real-world…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as the…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
The status of internal symmetry breaking at high temperature in supersymmetric models is reviewed. This phenomenon could solve some well known cosmological problems, such as the domain wall, monopole and false vacuum problems.
Generalized symmetry integrability test for discrete equations on the square lattice is studied. Integrability conditions are discussed. A method for searching higher symmetries (including non-autonomous ones) for quad graph equations is…
We analyse symmetry breaking in general gauge theories paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: a Euclidean metric associated with the scalar…
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…
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
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…