相关论文: A Class of Non Invertible Matrices in GF (2) for P…

It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…

In many applications one wants to identify identical subtrees of a program syntax tree. This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good…

We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…

Cancelable biometric techniques have been used to prevent the compromise of biometric data by generating and using their corresponding cancelable templates for user authentication. However, the non-invertible distance preserving…

A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially-4 uniform function called…

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This…

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…

Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, the…

We prove that the basis and the generating function of a geometric grid class of permutations Geom$(M)$ are computable from the matrix $M$, as well as some variations on this result. Our main tool is monadic second-order logic on…

In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…

A square matrix of order n with $n\geq 2$ is called permutative matrix when all its rows (up to the frst one) are permutations of precisely its frst row. In this paper recalling spectral results for partitioned into $2$-by-$2$ symmetric…

We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…

The enumeration of Hamiltonian cycles on 2n*2n grids of nodes is a longstanding problem in combinatorics. Previous work has concentrated on counting all cycles. The current work enumerates nonisomorphic cycles -- that is, the number of…

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…

Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…