~ similar to 2606.00245· 18 results
This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.
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).
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…
This paper develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.
The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…
This paper characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…
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…
The paper formally models structure-informed multiple sequence alignment (MSA-S) as an NP-complete optimization problem, establishing a strong computational complexity baseline for the field.
This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.
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 paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…
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…
This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.
Yuming Zhao, Junhui Hou, Qijian Zhang, Jia Qin +1 more
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 proposes a two-stage method to improve the efficiency and robustness of the Locally Aligned Ant Technique (LAAT) for detecting cosmic structures in noisy, high-dimensional point clouds.
This paper proposes a scalable topological learning framework for higher-order graph representation by introducing simplified and factored cellular Weisfeiler Leman tests and a novel random walk metho…
This paper presents a quantum attack on Module-LWE based lattice schemes like ML-KEM, demonstrating a polynomial-time quantum algorithm with a high success probability.