Related papers: Analytically solvable processes on networks
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
The possibility to identify the nature (e.g. random or scale free) of complex networks while performing respective random walks is investigated with respect to autonomous agents based on Bayesian decision theory and humans navigating…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…
The model of scientific paradigms spreading throughout the community of agents with memory is analyzed using the master equation. The case of two competing ideas is considered for various networks of interactions, including agents placed at…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the…
We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…
The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…
Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds.…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e. involving one connection at a time, or as complex contagion, in which multiple…
Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…