Related papers: Weighted Epsilon-Nets
This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
Network backbones provide useful sparse representations of weighted networks by keeping only their most important links, permitting a range of computational speedups and simplifying network visualizations. A key limitation of existing…
Graphons are analytic objects representing limits of convergent sequences of graphs. Lov\'asz and Szegedy conjectured that every finitely forcible graphon, i.e. any graphon determined by finitely many graph densities, has a simple…
Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership…
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted…
This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength…
We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can…
This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…
Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…