相关论文: Matrix Construction Using Cyclic Shifts of a Colum…
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
The concept of a fully interlacing matrix of formal power series with real coefficients is introduced. This concept extends and strengthens that of an interlacing sequence of real-rooted polynomials with nonnegative coefficients, in the…
Given a matrix over a skew field fixing the column (1,...,1)^t, we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes.
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…
In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…
In this paper, we investigate the importance of column scaling in relating two signed-graphic representations of the same matroid. We used the Sage Mathematics software to generate many examples of signed-graphic matroids and their…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
We study the use of effective transfer matrices for the numerical computation of masses (or correlation lengths) in lattice spin models. The effective transfer matrix has a strongly reduced number of components. Its definition is motivated…
A mutation cycle is a cycle in a graph whose vertices are labeled by the quivers in a given mutation class and whose edges correspond to single mutations. For any fixed $n\ge 4$, we describe arbitrarily long mutation cycles involving…
Let $X$ be a $n\times p$ matrix with coherence $\mu(X)=\max_{j\neq j'} |X_j^tX_{j'}|$. We present a simplified and improved study of the quasi-isometry property for most submatrices of $X$ obtained by uniform column sampling. Our results…
An arbitrary $m\times n$ Boolean matrix $M$ can be decomposed {\em exactly} as $M =U\circ V$, where $U$ (resp. $V$) is an $m\times k$ (resp. $k\times n$) Boolean matrix and $\circ$ denotes the Boolean matrix multiplication operator. We…
The crystallography of displacive phase transformations can be described with three types of matrices: the lattice distortion matrix, the orientation relationship matrix, and the correspondence matrix. The paper gives some formula to…
There is a digraph corresponding to every square matrix over $\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence…