Related papers: Large order fluctuations, switching, and control i…
The aim of this paper is to investigate complex dynamic networks which can model high-voltage power grids with renewable, fluctuating energy sources. For this purpose we use the Kuramoto model with inertia to model the network of power…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
We consider two optimization problems in which a planner aims to influence the average transient opinion in the Friedkin-Johnsen dynamics on a network by intervening on the agents' innate opinions. Solving these problems requires full…
Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
The analysis of network data has gained considerable interest in recent years. This also includes the analysis of large, high-dimensional networks with hundreds and thousands of nodes. While exponential random graph models serve as…
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…
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…
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
Fluctuation-dominated phase ordering refers to a steady state in which the magnitude of long-range order varies strongly owing to fluctuations, and to the associated coarsening phenomena during the approach to steady state. Strong…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms…
Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…