Related papers: Complexity of matrix problems
We prove $\textsf{NP-hardness}$ results for determining whether quivers are mutation equivalent to quivers with given properties. Specifically, determining whether a quiver is mutation-equivalent to a quiver with exactly $k$ arrows between…
Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…
For a pair of spaces $X$ and $Y$ such that $Y \subseteq X$, we define the relative topological complexity of the pair $(X,Y)$ as a new variant of relative topological complexity. Intuitively, this corresponds to counting the smallest number…
We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
We study a family of three-dimensional Lie algebras $L_\mu$ that depend on a continuous parameter $\mu$. We introduce certain quivers, which we denote by $Q_{m,n}$ $(m,n \in \mathbb{Z})$ and $Q_{\infty \times \infty}$, and prove that…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while…
Identifying the rank of species in a social or ecological network is a difficult task, since the rank of each species is invariably determined by complex interactions stipulated with other species. Simply put, the rank of a species is a…
We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all…
The goal of this article is to prove that every surface with a regular point in the three-dimensional projective space of degree at least four, is of wild representation type under the condition that either $X$ is integral or…
In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the…
We solve two problems in the theory of correspondences that have important implications in the theory of product systems. The first problem is the question whether every correspondence is the correspondence associated (by the representation…
Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…