Related papers: Linear pencils on graphs and on real curves
In this paper, flows of a viscid fluids on curves are considered. Symmetry algebras and the corresponding fields of differential invariants are found. We study their dependence on thermodynamic states of media, and provide classification of…
In the previous paper by Pereira and the author, it was proved that any pencil of plane curves of degree greater than one with irreducible generic fiber can have at most five completely reducible fibers although no examples with five such…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
We consider the problem of placing arrow heads in directed graph drawings without them overlapping other drawn objects. This gives drawings where edge directions can be deduced unambiguously. We show hardness of the problem, present exact…
We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…
The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
We introduce the notion of microlocal versal deformation of a plane curve. We construct equisingular versal deformations of Legendrian curves that are the conormal of a semi-quasi-homogeneous branch.
In this paper, we introduce the concept of up-color kernel, which is a generalization of a kernel for vertex-colored digraphs. We give sufficient and necessary conditions for several families of digraphs to have an up-color kernel, as well…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…
In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology \cite{Civan}, and the framework through which it was studied, we introduce the linear coloring on graphs. We…