Related papers: Analytic Deformations of Minimal Networks
In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…
We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Most complex networks are not static, but evolve along time. Given a specific configuration of one such changing network, it becomes a particularly interesting issue to quantify the diversity of possible unfoldings of its topology. In this…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands,…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…
Network dynamics offers critical insights into the behavior and evolution of complex systems. Here, we focus on the topological dynamics of networks to explore a unique process for reducing the average distance: topological compression. The…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
Traditional landscape analysis of deep neural networks aims to show that no sub-optimal local minima exist in some appropriate sense. From this, one may be tempted to conclude that descent algorithms which escape saddle points will reach a…
Dynamic Spectrum Access systems exploit temporarily available spectrum (`white spaces') and can spread transmissions over a number of non-contiguous sub-channels. Such methods are highly beneficial in terms of spectrum utilization. However,…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…