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 simplifies the proof of the bound on the target dimension for reducing the dimension of high-dimensional polygonal curves using random projections, extending it to various distance measures…

This paper proves that single-vector embeddings require a larger representation size than multi-vector embeddings to approximate certain similarities.

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.

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

This paper presents multiword arithmetic, a type of multiprecision arithmetic that uses parallel computing to improve efficiency and accuracy, and provides code implementation in PHCpack.

The paper investigates applying Riemannian optimization techniques to low-rank matrix parameters for deep learning, but finds that the proposed methods do not conclusively outperform the AdamW baselin…

This paper investigates the closeness of singularity for $n imes n$ unimodular matrices, specifically for $(2k+1)$-ary and $(k+1)$-ary cases of $4 imes 4$ nonnegative unimodular matrices.

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…

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 Grid Programs, a novel, Turing-complete model of computation where programs are two-dimensional arrangements of instructions, fundamentally departing from linear code structures.

This paper studies the decidability and complexity properties of unary three-way and two-way deterministic and nondeterministic two-dimensional automata.

The paper introduces a theoretically grounded evaluation framework for watermarking generative models, proposing a novel method (SSB) that allows for systematic design across all security-robustness-f…

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 authors prove that two-dimensional ray tracing with thin lenses and plane mirrors using the ABCD model is Turing-complete.