Complex networks: topology, spectrum and linear processes

The concept of a network, defined as a collection of interconnected nodes or entities, has become a foundation for a new field of inquiry, namely network science. Despite the apparent simplicity of the concept, the pairwise representation of interconnecting nodes has enabled a plethora of insights into the structure of networks and the effects...

Linear Clustering Process on Networks

Community detection and graph partitioning have seamlessly integrated themselves into the fabric of network science by providing valuable insights into the structure, function, and dynamics of complex networks. In this thesis, a comprehensive performance comparison of the recently introduced Linear Clustering Process (LCP) is carried out against...

Linear Clustering Process on Networks

We propose a linear clustering process on a network consisting of two opposite forces: attraction and repulsion between adjacent nodes. Each node is mapped to a position on a one-dimensional line. The attraction and repulsion forces move the nodal position on the line, depending on how similar or different the neighbourhoods of two adjacent...

Guided proposals for simulating multi-dimensional diffusion bridges

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the...

Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals

Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing data problem where the diffusion bridges in between discrete-time observations are missing. The...