Related papers: Gradient-prolongation commutativity and graph theo…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…

Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in inverse problems, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel…

In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…

A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…

Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain…

We extend path analysis by giving sufficient conditions for computing the partial covariance of two random variables from their covariance. This is specifically done by correcting the covariance with the product of some partial variance…

Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commutator. Then we use the topological structure of the minimal…

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…