相关论文: Symmetry within Solutions
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
One common type of symmetry is when values are symmetric. For example, if we are assigning colours (values) to nodes (variables) in a graph colouring problem then we can uniformly interchange the colours throughout a colouring. For a…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
Without imposing restrictions on a weighted graph's arc lengths, symmetry structures cannot be expected. But, they exist. To find them, the graphs are decomposed into a component that dictates all closed path properties (e.g., shortest and…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…