相关论文: Symmetry within Solutions
We address the problem of finding harmonic colors, this problem has many applications, from fashion to industrial design. In order to solve this problem we consider that colors follow normal distributions in tone (chroma and lightness) and…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration,…
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…
The manuscript presents a theoretical proof in conglomeration with new definitions on Inaccessibility and Inside for a point S related to a simple or self intersecting polygon P. The proposed analytical solution depicts a novel way of…
A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
The degree of symmetry of a combinatorial object, such as a lattice path, is a measure of how symmetric the object is. It typically ranges from zero, if the object is completely asymmetric, to its size, if it is completely symmetric. We…
Indistinguishable objects often occur when modelling problems in constraint programming, as well as in other related paradigms. They occur when objects can be viewed as being drawn from a set of unlabelled objects, and the only operation…
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…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…
We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…
A symmetry of a dynamical system is a map that transforms one trajectory to another trajectory. We introduce a new type of abstraction for hybrid automata based on symmetries. The abstraction combines different modes in a concrete automaton…
The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…
We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature.…
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…
In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or…