Related papers: Matrix Theory for Minimal Trellises
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from…
Recently a notion of self-duality for differential equations of maximal cuts was introduced, which states that there should be a basis in which the matrix for an {\epsilon}-factorised differential equation is persymmetric. It was observed…
In this paper we study some new theories of characteristic homology classes for singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformation mC_{*}: K_{0}(var/X)-> G_{0}(X)[y], which…
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular…
In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…
We continue developing the theory around the twin-width of totally ordered binary structures, initiated in the previous paper of the series. We first introduce the notion of parity and linear minors of a matrix, which consists of…
We investigate topology change in (1+1) dimensions by analyzing the scalar-curvature action $1/2 \int R dV$ at the points of metric-degeneration that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily possesses. In two…
The Thurston spine consists of the subset of Teichm\"uller space at which the set of shortest curves, the systoles, cuts the surface into polygons. The systole function is a topological Morse function on Teichm\"uller space. This paper…
The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories…
We settle an open problem of several years standing by showing that the least-squares mean for positive definite matrices is monotone for the usual (Loewner) order. Indeed we show this is a special case of its appropriate generalization to…
The Johnson--Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be flattened to lower dimensions while…
In this note, we show how to provide sharp control on the least singular value of a certain translated linearization matrix arising in the study of the local universality of products of independent random matrices. This problem was first…
We study a variety of questions centered around the computation of cohomology of line bundles on the incidence correspondence (the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane…
We define a Weil-\'etale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex $\mathbb{Z}^c$) of a large class of $\mathbb{Z}$-constructible sheaves on an integral $1$-dimensional proper arithmetic…
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
We introduce trim resolutions of complex algebraic varieties, a strengthening of the notion of small resolution. We prove that the characteristic cycle of the intersection cohomology sheaf of a variety admitting a trim resolution is…
We establish the eigenvalue interlacing property (i.e. the smallest real eigenvalue of a matrix is less than the smallest real eigenvalue of any its principal submatrix) for the class of matrices, introduced by Kotelyansky (all principal…