Related papers: On Rank Problems for Planar Webs and Projective St…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking…
In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-universal practice of assuming that a function, matrix, or tensor…
A framework consists of an undirected graph $G$ and a matroid $M$ whose elements correspond to the vertices of $G$. Recently, Fomin et al. [SODA 2023] and Eiben et al. [ArXiV 2023] developed parameterized algorithms for computing paths of…
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
We classify noninvertible, holomorphic selfmaps of the projective plane that preserve an algebraic web. In doing so, we obtain interesting examples of critically finite maps.
Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.
We generalize methods to compute various kinds of rank to the case of a toric variety $X$ embedded into projective space using a very ample line bundle $\mathcal{L}$. We find an upper bound on the cactus rank. We use this to compute rank,…
In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of…
Link directions are essential to the functionality of networks and their prediction is helpful towards a better knowledge of directed networks from incomplete real-world data. We study the problem of predicting the directions of some links…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
We study three classical graph problems - Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the…
The edge geodesic cover problem of a graph $G$ is to find a smallest number of geodesics that cover the edge set of $G$. The edge $k$-general position problem is introduced as the problem to find a largest set $S$ of edges of $G$ such that…
A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…
We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.