Related papers: Row completion of polynomial and rational matrices…
The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this…
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…
The aim in packing problems is to decide if a given set of pieces can be placed inside a given container. A packing problem is defined by the types of pieces and containers to be handled, and the motions that are allowed to move the pieces.…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…
The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…
This paper studies generic and perturbation properties inside the linear space of $m\times (m+n)$ polynomial matrices whose rows have degrees bounded by a given list $d_1, \ldots, d_m$ of natural numbers, which in the particular case $d_1 =…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
We consider the following problem: given $d \times d$ rational matrices $A_1, \ldots, A_k$ and a polyhedral cone $\mathcal{C} \subset \mathbb{R}^d$, decide whether there exists a non-zero vector whose orbit under multiplication by $A_1,…
We establish necessary and sufficient conditions for the existence of an LU factorization $A=LU$ for an arbitrary square matrix $A$, including singular and rank-deficient cases, without the use of row or column permutations. We prove that…
In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…
Indexing a set of strings for prefix search or membership queries is a fundamental task with many applications such as information retrieval or database systems. A classic abstract data type for modelling such an index is a trie. Due to the…
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces…
Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete.…
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq…
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…
The National Health and Nutrition Examination Survey (NHANES) studies the nutritional and health status over the whole U.S. population with comprehensive physical examinations and questionnaires. However, survey data analyses become…