… We define two domains to be exactly symmetric with respect to scalar field topology if the
percentage of overlap of their branch decompositions is 100%. This corresponds to the branch …

… Thomas and Natarajan [TN13] focused on detecting symmetry in scalar fields using
augmented extremum graphs. They used the geodesic distances between extrema, and the earth …

… , spin structures, etc.—while others are more geometric—Riemannian metrics, connections
for a fixed gauge group, scalar fields, spinor fields, etc., More precisely, a field F is …

… scalar field models with topological and non-topological … The classical field theory of the
scalar field in various spatial … In what follows we use the properties of symmetry of the sine-…

… While the former task can be addressed using topological analysis of scalar fields, the latter
requires geometry based solutions. Our approach combines the two by utilizing the contour …

… III we examine scalar fields with a Xp self-interaction in space-times which are flat, but which
… with a topology of g ~S' admits a twisted scalar field' "in addition to an untwisted field. For …

… algorithms for the topological analysis of scalar data. Our … that have no impact on the topological
description of the data and … lifetime of minima is estimated with the symmetric procedure. …

… topological field theories is based on the concept of equivariant cohomology. Since we are
interested in models with extended topological symmetry, … -algebra valued scalar field φ on a …

… We define two domains to be exactly symmetric with respect to scalar field topology if the
percentage of overlap of their branch decompositions is 100%. This corresponds to the branch …

… Both vector and tensor fields are multivariate; they involve … and symmetric tensor fields in
N dimensional space embody as much information as N and iN(N + 1) independent scalar fields…