Related papers: Kinetic Equations for Processes on Co-evolving Net…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
We study an opinion formation model by the means of a co-evolving complex network where the vertices represent the individuals, characterised by their evolving opinions, and the edges represent the interactions among them. The network…
Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted…
Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
It is shown how to explicitly coarse-grain the microscopic dynamics of the Vicsek model for self-propelled agents. The macroscopic transport equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
The parallel dynamics is given in the case of neural networks with separable coupling through starting from Coolen-Sherrington (CS) theory. It is shown that this retrieve dynamics as is the case of sequential evolution in the postulate of…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…