Related papers: A Commentary on "Breaking Row and Column Symmetrie…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…
Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
The paper studies the set of all square binary matrices containing an exact number of 1's in each rows and in each column. A connection is established between the cardinal number of this set and the cardinal number of its subset of matrices…
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the…
The model of the neutrino mass matrix which we proposed in 2000 is revisited in the light of the recent T2K experiments. This model has the special property that it predicts the maximal 2-3 mixing and CP violation under the some simple…
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as…
Molecular simulations provide a powerful means to unravel the complex relationships between network architecture and the mechanical response of polymer networks, with a particular emphasis on rupture and fracture phenomena. Although…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
This article presents new enumerative results related to symmetric planar maps. In the first part a new way of enumerating rooted simple quadrangulations and rooted simple triangulations is presented, based on the description of two…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column…