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We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
The classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal one-parameter deformation of a Lie algebra…
Light scattering and aberrations limit optical microscopy in biological tissue, which motivates the development of adaptive optics techniques. Here, we develop a method for adaptive optics with reflected light and deep neural networks…
Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.
This paper aims for set-to-hypergraph prediction, where the goal is to infer the set of relations for a given set of entities. This is a common abstraction for applications in particle physics, biological systems, and combinatorial…
This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…
We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems. The adaptation process is driven by a recovery-based a posteriori estimator for the $L^2(\Omega)$-norm of the…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from…
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…
The role of graded interfaces between materials in a cylindrical free-standing quantum wire with longitudinal heterostructures is theoretically investigated, by solving the Schr\"odinger equation within the effective mass approximation.…
Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is…
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
We define a differential graded algebra associated to Legendrian knots in Seifert fibered spaces with transverse contact structures. This construction is distinguished from other combinatorial realizations of contact homology invariants by…
We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
Supervised distributional methods are applied successfully in lexical entailment, but recent work questioned whether these methods actually learn a relation between two words. Specifically, Levy et al. (2015) claimed that linear classifiers…
Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…
We discuss the potential of multilayered plasmonic particles to tailor the optical scattering response. The interplay of plasmons localized in thin stacked shells realizes peculiar degenerate cloaking and resonant states occurring at…
We describe equivalence classes of exact indecomposable module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [S. Natale, On the equivalence of…