Related papers: Sur la lin\'earisation des tissus

We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.

We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.

We present a projectively invariant description of planar linear 3-webs. For a non-hexagonal 3-web, we introduce family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a…

We introduce an approach to training a given compact network. To this end, we leverage over-parameterization, which typically improves both neural network optimization and generalization. Specifically, we propose to expand each linear layer…

Convolutional neural networks (CNNs) learn abstract features to perform object classification, but understanding these features remains challenging due to difficult-to-interpret results or high computational costs. We propose an automatic…

As data-driven methods rise in popularity in materials science applications, a key question is how these machine learning models can be used to understand microstructure. Given the importance of process-structure-property relations…

A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…

We define the characteristic numbers of a holomorphic k-distribution of any dimension on $mathbb P^n$ and obtain relations between these numbers and the characteristic numbers of an invariant subvariety. As an application we bound the…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

In many application domains, networks are observed with node-level features. In such settings, a common problem is to assess whether or not nodal covariates are correlated with the network structure itself. Here, we present four novel…

We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…

Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can…

We study the linearization of line bundles and the local structure of actions of connected linear algebraic groups, in the setting of seminormal varieties. We show that several classical results about normal varieties extend to that…