Related papers: Computing Path Signature Varieties in Macaulay2
Identifying and characterizing mutational paths is an important issue in evolutionary biology and in bioengineering. We here introduce a generic description of mutational paths in terms of the goodness of sequences and of the mutational…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
There are very few explicit evaluations of path integrals for topological gauge theories in more than 3 dimensions. Here we provide such a calculation for the path integral representation of the Ray-Singer Torsion of a flat connection on a…
I discuss possible consequences of A. D. Sakharov's hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical…
In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on…
Two signed graphs are called switching isomorphic if one of them is isomorphic to a switching equivalent of the other. To determine the number of switching non-isomorphic signed graphs on a specific graph, we will establish a method based…
We study rectangles inscribed in lines in the plane by parametrizing these rectangles in two ways, one involving slope and the other aspect ratio. This produces two paths, one that finds rectangles with specified slope and the other…
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for…
Recently, Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of…
In this article, we discuss a probabilistic interpretation of McShane's identity as describing a finite measure on the space of embedded paths though a point.
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
Signature verification has been one of the major researched areas in the field of computer vision. Many financial and legal organizations use signature verification as access control and authentication. Signature images are not rich in…
We describe the computer algebra software package SpectralSequences for the computer algebra system Macaulay2. This package implements many data types, objects and algorithms which pertain to, among other things, filtered complexes,…
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 formulate path integrals on any Riemannian manifold which admits the action of a compact Lie group by isometric transformations. We consider a path integral on a Riemannian manifold M on which a Lie group G acts isometrically. Then we…
The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…
A spline is an assignment of polynomials to the vertices of a graph, where the difference of two polynomials along an edge must belong to the ideal labeling that edge. We consider a ring of splines $\mathcal{M}_{H}$ constructed on a graph…
This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…