Related papers: Taut and Tense Networks
For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
Neural networks with rectified linear unit activations are essentially multivariate linear splines. As such, one of many ways to measure the "complexity" or "expressivity" of a neural network is to count the number of knots in the spline…
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…
Capsule networks are a type of neural network that have recently gained increased popularity. They consist of groups of neurons, called capsules, which encode properties of objects or object parts. The connections between capsules encrypt…
Artificial neural networks used for reinforcement learning are structurally rigid, meaning that each optimized parameter of the network is tied to its specific placement in the network structure. It also means that a network only works with…
Rooted phylogenetic networks are rooted acyclic digraphs. They are used to model complex evolution where hybridization, recombination and other reticulation events play important roles. A rigorous definition of network compression is…
AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We…
Message broadcasting in networks could be carried over spanning trees. A set of spanning trees in the same network is node independent if two conditions are satisfied. First, all trees are rooted at node $r$. Second, for every node $u$ in…
Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…
In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…
We describe a novel classifier with a tree structure, designed using information theory concepts. This Information Network is made of information nodes, that compress the input data, and multiplexers, that connect two or more input nodes to…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…