Related papers: Spectral networks and higher web-like structures
Let M be the moduli space of irreducible flat PSL(2,R) connections on a punctured surface of finite type with parabolic holonomies around punctures. By using a notion of admissibility of an ideal arc, M is covered by dense open subsets…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
Predator-prey networks originating from different aqueous and terrestrial environments are compared to assess if the difference in environments of these networks produce any significant difference in the structure of such predator-prey…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…
The spectral gap of the graph Laplacian with Dirichlet boundary conditions is computed for the graphs of several communication networks at the IP-layer, which are subgraphs of the much larger global IP-layer network. We show that the…
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…
The study of network formation is pervasive in economics, sociology, and many other fields. In this paper, we model network formation as a `choice' that is made by nodes in a network to connect to other nodes. We study these `choices' using…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a…
We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…