Related papers: Spectral networks and higher web-like structures
Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e. over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove that, under…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…
The structure of the Internet at the Autonomous System (AS) level has been studied by both the Physics and Computer Science communities. We extend this work to include features of the core and the periphery, taking a radial perspective on…
Air pollution can be studied in the urban structure regulated by transport networks. Transport networks can be studied as geometric and topological graph characteristics through designed models. Current studies do not offer a comprehensive…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
We study cubic differentials and their spectral networks on Riemann surfaces, focusing on the polynomial case on the Riemann sphere. We introduce the notion of spectral core as the primary tool for our study, refining the classical notion…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It…
Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…