相关论文: Fano schemes of generic intersections and machine …

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

Recently, the coupling of two different modes of a homogeneous plasmonic particle and their sharply varying spectra were elucidated as Fano resonances; an 'interference' of two spatially orthogonal modes driving each other. On the other…

Interactions between several features sometimes play an important role in prediction tasks. But taking all the interactions into consideration will lead to an extremely heavy computational burden. For categorical features, the situation is…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

We show that the Debarre-de Jong conjecture that the Fano scheme of lines on a smooth hypersurface of degree at most n in n-dimensional projective space must have its expected dimension, and the Beheshti-Starr conjecture that bounds the…

Most physical or social phenomena can be represented by ontologies where the constituent entities are interacting in various ways with each other and with their environment. Furthermore, those entities are likely heterogeneous and…

To every local complete intersection ring one may associate a so-called generic hypersurface. In this paper we introduce rank varieties for modules and complexes over the generic hypersurface. The definition uses extension of scalars,…

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may…

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This enables us to define some new invariants of smooth projective…

We study the virtual intersection theory of Hyperquot schemes parameterizing sequences of quotient sheaves of a vector bundle on a smooth projective curve. Our results generalize the Vafa--Intriligator formula for Quot schemes and provide a…

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

We find a relation between a cubic hypersurface $Y$ and its Fano variety of lines $F(Y)$ in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then…

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…

Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…

A Pfaff field on a projective space is a map from the sheaf of differential s-forms, for a certain s, to an invertible sheaf. The interesting ones are those arising from a Pfaff system, as they give rise to a distribution away from their…

We show that Fano lattice polygons define a class of balanced quivers with interesting properties. The combinatorics of these quivers is related to singularities of the underlying toric Fano surface. This allows us to show that every Fano…

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…

We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted…

Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from…