Related papers: Symmetry within and between solutions
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…
Symmetry is an important factor in human perception in general, as well as in the visualization of graphs in particular. There are three main types of symmetry: reflective, translational, and rotational. We report the results of a human…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
The phenomenal success of physics in explaining nature and designing hardware is predicated on efficient computational models. A universal codebook of physical laws defines the computational rules and a physical system is an interacting…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object's shape and appearance in order to learn generalizable and…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
We call an objective function or algorithm symmetric with respect to an input if after swapping two parts of the input in any algorithm, the solution of the algorithm and the output remain the same. More formally, for a permutation $\pi$ of…
We consider symmetries and perturbed symmetries of canonical Hamiltonian equations of motion. Specifically we consider the case in which the Hamiltonian equations exhibit a Lambda symmetry under some Lie point vector field. After a brief…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…