Related papers: An edge-based formulation of elastic network model…
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…
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit. We focus on a bounded region $M$ with a co-dimension…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and…
This paper develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks modeled as linear time-invariant systems. We consider Gramian-based performance metrics and propose a novel…
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…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…
Networks - collections of interacting elements or nodes - abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions,…
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge…
Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a…
Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast time scales. Several empirical statistical properties of these networks have been shown to be robust across a…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…