Related papers: Discrete Network Dynamics. Part 1: Operator Theory
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
This thesis aims to develop a compositional theory for the operational semantics of networks. The networks considered are described by either internal or enriched graphs. In the internal case we focus on $\mathsf{Q}$-nets, a generalization…
When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field…
Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We present two models of sparse dynamic networks that display transitivity - the tendency for vertices sharing a common neighbour to be neighbours of one another. Our first network is a continuous time Markov chain $G=\{G_t=(V,E_t), t\ge…
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data)…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
Latent stochastic block models are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between…
Latent space models are popular for analyzing dynamic network data. We propose a variational approach to estimate the model parameters as well as the latent positions of the nodes in the network. The variational approach is much faster than…
This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
In this paper we propose a continuous-time, dissipative Markov dynamics that asymptotically drives a network of n-dimensional quantum systems to the set of states that are invariant under the action of the subsystem permutation group. The…
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…
We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…