~ similar to 2606.13161· 18 results
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 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…
Xinjiang Yu, Junyi Han, Zhuofan Chen, Chi Zhang +6 more
DiagramRAG is a lightweight retrieval-augmented framework that uses reference diagrams to guide the completion of scientific diagrams from incomplete user sketches, achieving high performance on stand…
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…
PlanarBench introduces a novel benchmark to test LLM spatial reasoning by requiring them to draw planar graphs as ASCII art from an edge list, finding that edge count is a stronger difficulty predicto…
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 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 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 Grid Programs, a novel, Turing-complete model of computation where programs are two-dimensional arrangements of instructions, fundamentally departing from linear code structures.
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 develops a parameterized algorithm for the NP-complete Tree Containment problem, showing it can be solved efficiently based on a structural parameter called scanwidth.
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 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…
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 the base-m length codec, a canonical and robust encoding scheme that maps byte strings to lists of residues modulo m, essential for finite-ring cryptosystems.
Xiangyu Gao, Winston Li, Jiakang Li, Zirui Li +3 more
The paper introduces Accordion, an end-to-end framework that significantly improves the efficiency of compiling fermionic Hamiltonians into quantum circuits for simulation on constrained quantum hardw…
This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.