Related papers: Dynamical processes on metric networks
This study presents a dynamic Bayesian network framework that facilitates intuitive gradual edge changes. We use two conditional dynamics to model the edge addition and deletion, and edge selection separately. Unlike previous research that…
Pathophysiolpgical modelling of brain systems from microscale to macroscale remains difficult in group comparisons partly because of the infeasibility of modelling the interactions of thousands of neurons at the scales involved. Here, to…
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…
The dynamics of decisions in complex networks is studied within a Markov process framework using numerical simulations combined with mathematical insight into the process mechanisms. A mathematical discrete-time model is derived based on a…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
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…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
Using neural networks to solve partial differential equations (PDEs) is gaining popularity as an alternative approach in the scientific computing community. Neural networks can integrate different types of information into the loss…
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…
Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…
Background: Controlling global epidemics in the real world and accelerating information propagation in the artificial world are of great significance, which have activated an upsurge in the studies on networked spreading dynamics. Lots of…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…
Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…
In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…