Related papers: Kinetic Theory of Random Graphs
In this letter, we analyze the evolution of physical quantities due to the interaction of strings with background fields. We will obtain the characteristic function for such a string theoretical process. This will be done by generalizing…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
Ranked data is commonly used in research across many fields of study including medicine, biology, psychology, and economics. One common statistic used for analyzing ranked data is Kendall's {\tau} coefficient, a non-parametric measure of…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We consider a model of a scalar field, with dispersion relation {\omega}(k), coupled to a random medium of two level atoms. We investigate the dynamics of states with at most one quanta of excitation in the system. In a high frequency…
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
Many aspects of graphs have been studied in depth. However, forecasting the structure of a graph at future time steps incorporating unseen, new nodes and edges has not gained much attention. In this paper, we present such an approach. Using…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…