Related papers: Labels of real projective varieties

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

Varieties of minimal degree and del Pezzo varieties are basic objects in projective algebraic geometry. Those varieties have been characterized and classified for a long time in many aspects. Motivated by the question "which varieties are…

We consider graph labelings with an assignment of odd prime numbers to the vertices. Similarly to graceful graphs, a labeling is said to be elegant if the absolute differences between the labels of adjacent vertices describe exactly the…

We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its…

We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…

We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to the case where the systems are complex C*-algebras. We…

Sommese has conjectured a classification of smooth projective varieties X containing, as an ample divisor, a P^d-bundle Y over a smooth variety Z. This conjecture is known if d>1, if dim(X)<5, or if Z admits a finite morphism to an Abelian…

Let $X$ be a normal projective variety admitting a polarized or int-amplified endomorphism $f$. We list up characteristic properties of such an endomorphism and classify such a variety from the aspects of its singularity, anti-canonical…

Let q be a power of a prime integer p, and let X be a Hermitian variety of degree q+1 in the n-dimensional projective space. We count the number of rational normal curves that are tangent to X at distinct q+1 points with intersection…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

The notion of denominator vectors can be extended to all generic basis elements of upper cluster algebras in a natural way. Under a weakened version of generic pairing assumption, we provide a representation-theoretic interpretation for…

Extreme multi-label classification aims to learn a classifier that annotates an instance with a relevant subset of labels from an extremely large label set. Many existing solutions embed the label matrix to a low-dimensional linear…

Let $E$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors $K_X+(t-r)det(E)$ when $t>=dim(X)$ and $t>r$. As a corollary, we classify pairs…

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…

Let $(X,c_X)$ be a convex projective surface equipped with a real structure. The space of stable maps $\bar{\mathcal{M}}_{0,k}(X,d)$ carries different real structures induced by $c_X$ and any order two element $\tau$ of permutation group…

A simple and connected $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$, such that adjacent vertices have relatively prime labels. We will present previously…

Competitive methods for multi-label classification typically invest in learning labels together. To do so in a beneficial way, analysis of label dependence is often seen as a fundamental step, separate and prior to constructing a…

In this paper, we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and the arguments rely on the apolarity lemma. In the special…