This paper presents a polynomial-time Monte Carlo algorithm to determine the symmetry Lie algebra of a parametrized variety directly from the parametrization.

The paper introduces PRISM, a novel representation learning framework that learns isometric embeddings by explicitly modeling the intrinsic geodesic metric of 3D surfaces, achieving superior performan…

This paper simplifies the proof of the bound on the target dimension for reducing the dimension of high-dimensional polygonal curves using random projections, extending it to various distance measures…

The paper introduces a subgrid marching tetrahedra scheme that accurately recovers complex, intersection-free manifold meshes from tetrahedral grids, overcoming limitations of classic marching methods…

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

The paper presents a novel and significantly faster algorithm for computing the second discrete homology group of a graph by identifying five basic quotient shapes of the 3-cube.

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.

This paper constructs a cubic graph with a polyhedral map whose automorphism groups are isomorphic to a given finite group.

The paper introduces a new term expansion for a calculus with explicit substitutions, allowing the relation of a lambda-calculus with explicit substitutions to Boudol's resource aware lambda-calculus.

Ramos and White's theorem on multiplicity stability of rational homology for configuration spaces of certain graphs is extended and computed for various families of graphs using computer algebra.

This paper introduces a new way to represent finite posets as subwords of finite words in categories, and characterizes the monic categories that admit this representation.

This paper establishes a Coding Theorem in the context of symmetry groups and develops a connection between subgroups of a group and subsets of binary strings.

This paper introduces and implements variants of the symmetric lexicographic symmetric-subset reverse search framework for enumerating symmetric feasible subsets of a finite set, applying it to cocirc…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

This paper proves conditions for efficiently approximating expectations of certain functions with respect to standard Gaussian or symmetric exponential probability measures.

This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…

The paper proposes GIM-World, a geometry-aware implicit memory framework that significantly improves long-horizon video world models by explicitly encoding 3D scene geometry into a compact memory stat…