Related papers: Evolution of networks with multiple junctions
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
We consider an evolving plane curve with two endpoints that can move freely on the $x$-axis with generating constant contact angles. We discuss the asymptotic behavior of global-in-time solutions when the evolution of this plane curve is…
In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…
Turbulent and vortical flows are ubiquitous and their characterization is crucial for the understanding of several natural and industrial processes. Among different techniques to study spatio-temporal flow fields, complex networks represent…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…
We consider the evolution of a network of strings in an expanding universe, allowing for the formation of junctions between strings of different tensions. By explicitly including, in the velocity-dependent evolution equations for the…
We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from an origin to a destination as quickly as possible. Flow patterns vary over…
A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical type equations.…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
We propose a weak formulation for the binormal curvature flow of curves in $\R^3.$ This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We investigate the laminar flow of two-fluid mixtures inside a simple network of inter-connected tubes. The fluid system is comprised of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct…
Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved…
We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak…
Investigating relation between various structural patterns found in real-world networks and stability of underlying systems is crucial to understand importance and evolutionary origin of such patterns. We evolve multiplex networks,…
The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…
We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…