相关论文: Natural differential operators and graph complexes

We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…

We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural…

Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…

In this paper, we first develop a new family of conjugate prior distributions for the cell parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G.…

Graph-based procedural materials are ubiquitous in content production industries. Procedural models allow the creation of photorealistic materials with parametric control for flexible editing of appearance. However, designing a specific…

We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete…

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…

Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order $k\ge 2$ on a smooth manifold of dimension $n\ge 2$ and show their application to the equivalence…

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…

In two seminal papers Kontsevich used a construction called_graph homology_ as a bridge between certain infinite dimensional Lie algebras and various topological objects, including moduli spaces of curves, the group of outer automorphisms…

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…

We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…

In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…

We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…

We study cone differential operators on the half-axis and edge-degenerate differential operators on a half-space. We construct subspaces of edge Sobolev spaces that can be considered as natural domains for edge-degenerate operators and…

For a smooth algebraic variety $X$, we study the category of finitely generated modules over the ring of function of $X$ that has a compatible action of the Lie algebra $\mathcal{V}$ of polynomials vector fields on $X$. We show that the…

In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…

We prove that the inclusion from oriented graph complex into graph complex with at least one source is a quasi-isomorphism, showing that homology of the "sourced" graph complex is also equal to the homology of standard Kontsevich's graph…