This paper proposes HGeo-TopoMap, a method for topological mapping in autonomous driving using an explicit prior map and implicit spatial relations, achieving substantial improvements in accuracy and…

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

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 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 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…

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

This paper applies the MAP-Elites algorithm to procedurally generate diverse and high-quality First-Person Shooter maps using novel map representations.

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…

The paper proves XNLP-hardness of Directed Edge Geography and Undirected Edge Geography when parameterized by pathwidth, and shows their fixed-parameter tractability when parameterized by treewidth an…

This paper introduces PHINN-EEG, a topological time-series framework for dream mentation analysis using Dynamic Betti Curves and topology-conditioned flow matching, aiming for higher area under the re…

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

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.

The paper introduces an integrated computational toolbox using topological and fractal analysis to quantitatively track microstructural changes during casein gelation, correlating these subtle changes…

This paper introduces a new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.

The authors map the problem of finding the maximum cut of a planar graph with arbitrary weights to a minimum T-join problem in the absolute dual graph, enabling the use of shortest paths and adapting…

This paper presents a bidirectional perspective mapping between continuous integral R2 computation and integration over unions of anchored axis-aligned boxes, enabling the reuse of hypervolume algorit…

This paper presents a new modular architecture for NeoSLAM using modern frameworks, achieving real-time execution and minimal data discarding. It also compares NeoSLAM and RatSLAM across three dataset…