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 proposes using geometric metrics, specifically eigenspace alignment, to monitor the structural integrity of large behavioral populations, demonstrating its effectiveness in detecting network…

The paper introduces Geodesic Flow Matching, a manifold-aware denoising technique that adapts Riemannian transport dynamics to accurately clean high-dimensional structured representations like Spatial…

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

The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

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 validates a specialized mathematical metric (the Burau-Lyapunov exponent) designed for detecting privilege escalation in cloud IAM graphs by applying it to an unrelated physical system: sola…

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.

The paper reformulates nonreversible perturbations of Fokker--Planck dynamics as gauge fields, providing a unified operator viewpoint to analyze relaxation processes and develop methods for learning o…

The paper proves the real-rootedness and ultra-log-concavity of the Poincaré polynomials for the moduli space $\overline{\mathcal M}_{0,n}$ and the Fulton--MacPherson space $\mathbb{P}^1[n]$ using a n…

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

The paper proposes a novel adversarial defense approach, TopFeaRe, by modeling graph adversarial attacks using complex dynamic system theory to locate the graph's critical state of resilience.

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…

The paper introduces Cellular Sheaf Neural Operators, a discretization-aware framework that models constrained PDEs by representing physical states on oriented cell complexes to enforce structure-pres…

This paper proposes a novel data-driven image encryption framework that learns the chaotic map dynamics directly from the image data, enhancing security beyond traditional fixed-map schemes.

The paper introduces the Black-Hole Attack, a poisoning vulnerability that exploits geometric defects in high-dimensional embedding spaces to force malicious vectors into the top-k results of vector d…