Related papers: Open problems in Costas arrays
Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
The Catalan triangle, as well as a Fuss-Catalan triangle, enter a problem of counting particular tied arc diagrams. This setting allows us to prove some combinatorial properties of these triangles.
After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.
We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than…
We address the problem of fusing array operations based on criteria such as shape compatibility, data reusability, and communication. We formulate the problem as a graph partition problem that is general enough to handle loop fusion,…
A class $\mathfrak{M}$ of coarse spaces is called a variety if $\mathfrak{M}$ is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety…
In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
Young open clusters are our laboratories for studying high-mass star formation and evolution. Unfortunately, the information that they provide is difficult to interpret, and sometimes contradictory. In this contribution, I present a few…
The contextuality problem connected with existence of joint probability distribution creating all the given marginals is studied. It is shown for several examples considered previously in literature that there exist some new solutions for…
Lower bounds for some explicit decision problems over the complex numbers are given.
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then…
Clusters of galaxies are often embedded in larger-scale superclusters with dimensions of tens or perhaps even hundreds of Mpc. Observational and theoretical evidence suggest an important connection between cluster properties and their…
We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…