This paper provides new upper bounds and algorithms for the shortest path map equivalence decomposition of a polygonal domain, leading to solutions for two-point shortest path queries, geodesic diamet…

This paper generalizes the Phoa principle in synthetic domain theory to transfinite cases, introduces sobriomorphisms, and proposes a hypothetical completeness theorem.

The paper investigates which quantum encodings can be applied directly to classical data point clouds while preserving the topological invariants necessary for topological data analysis (TDA).

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…

This paper studies the structural expressivity and parameterized complexity of counting homomorphisms from small temporal patterns to large temporal graphs, proving a temporal Lovász-style theorem, in…

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 introduces a local-to-global method for analyzing low influence functions on simplicial complexes and proves a local-to-global KKL-type Theorem.

This paper proves several properties about Extended Frege proof systems and circuit equivalence.

The paper shows that an oddomorphism between graphs does not imply graph minor containment and introduces a new structural relation called split-off minor.

This paper introduces normalized persistence, a version of persistent homology in topological data analysis, and proves its quantum hardness under the standard assumption that DQC1 is not in BPP.

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 proves that testing the equivalence of finite closure systems specified by implicational and intersection methods is coNP-complete.

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

The paper proposes using pseudo-sensitivities, derived from adjoint sensitivity fields, as an optimal conditioning signal in a Bernoulli flow-matching framework to significantly improve the out-of-dis…

This paper proves that counting quasi-trees in a connected ribbon graph is #P-complete.

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

The paper shows that every problem asking if a given graph has an edge-coloring without an edge-colored clique from a fixed family is poly-time equivalent to a Constraint Satisfaction Problem, resulti…

The paper introduces TopoTTA, a framework that uses persistent homology for topological data analysis to enhance the quality of anomaly segmentation in deep models, leading to an average 15% F1 improv…