Related papers: Dynamical Mean-Field Theory of Complex Systems on …
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
The statistical field theory of information dynamics on complex networks concerns the dynamical evolution of large classes of models of complex systems. Previous work has focused on networks where nodes carry an information field, which…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
Scalable load balancing algorithms are of great interest in cloud networks and data centers, necessitating the use of tractable techniques to compute optimal load balancing policies for good performance. However, most existing scalable…
Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random…
Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure,…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established.…
Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for…
Studies on social networks have proved that endogenous and exogenous factors influence dynamics. Two streams of modeling exist on explaining the dynamics of social networks: 1) models predicting links through network properties, and 2)…
Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…