This paper defines and investigates ample sets of Cartesian products using minor-subproducts and provides characterizations of ampleness, including equivalence to ampleness of complement, superisometr…

This paper shows that any boolean matrix with bounded factorization norm can be expressed as a signed sum of blow-up identity matrices, and this result has applications to matrix sequences and complex…

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

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.

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…

The paper explains a method for finding the number of solutions to a system of multivariate polynomial inequalities over a finite field and applies it to find formulas for the number of contiguous sup…

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 proposes methods to optimally permute the rows and columns of a sparse matrix to minimize the number of cyclic diagonals required for homomorphic sparse-matrix vector multiplication, signif…

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

This paper improves the bound on the treewidth of the product of two graphs and proves similar results for pathwidth, Cartesian products, and strict bramble number.

This paper presents a local computation algorithm to approximate the top eigenvector of a symmetric matrix with entries between -1 and 1, building on Swartworth and Woodruff's work.

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 product coding scheme that converts bit-level reliability into block-level reliability, achieving the same asymptotic rate.

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

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 introduces $g$MAGNUS, a new algorithm for sparse matrix-matrix multiplication on GPUs that addresses heavy rows by reordering intermediate products and achieves significant speedups.

This paper investigates how the extremality of fixed-volume spanning trees changes based on product-grid boundary factors in two and arbitrary dimensions.