I am a postdoc at the Korteweg-de Vries Institute for Mathematics at the University of Amsterdam in the Netherlands. I am part of the national research program NETWORKS which focuses on challenges posed by large-scale networks. Within this research program I am currently working on problems related to the routing of information in dynamic communication networks. The aim is to approach these problems from both an algorithmic and stochastic perspective.
Prior to starting my postdoc, I lived in Melbourne, Australia where I obtained my PhD from RMIT University. During my PhD I worked on random network models, in particular models based on Markov chains. From a practical perspective, one of the most important questions about these models is how quickly they converge to their stationary distribution. My interest in this question remains strong and I am continuing work in this area.
Other topics that I worked on throughout my PhD are the analysis of local network properties and the application of techniques from topological data analysis to network science. For the interested reader, my PhD thesis is available online and publications arising from this research can be found further down this page.
I enjoy working on problems that have practical applications, but require abstract mathematics to be analysed and solved.
I can be contacted at: c.j.carstens @ uva.nl
I have been working with scientific citation networks. Citation networks are roughly directed acyclic. A directed network is directed acyclic if it does not contain any directed cycles, or equivalently if its vertices can be ordered in such a way that edges only go from "new" to "old" vertices. This clearly makes sense for citation networks, since a paper should only cite papers that appeared before it.
I have been looking at different random network models for the class of directed acyclic network. You can find my implementations of several random network models and other code relating to directed acyclic networks here.
I built two JAVA applets that visualise persistent homology of 3D pointclouds. All homology computations in the applets are run using JavaPlex. The source code for the applets is available as part of the JavaPlex codebase. The applets can also be downloaded as runnable jars.
C. J. Carstens and K. J. Horadam, Switching edges to randomize networks: what goes wrong and how to fix it. Journal of Complex Networks, (2016).
C. J. Carstens, Topology of Complex Networks: Models and Analysis. PhD thesis, (2016).
C. J. Carstens, Proof of uniform sampling of binary matrices with fixed row sums and column sums for the fast Curveball algorithm. Physical Review E, (2015).
A. Hecker, C. J. Carstens and K. J. Horadam, Neighbourhood Distinctiveness: An Initial Study. Complex Networks VI, (2015).
C. J. Carstens, A uniform random graph model for directed acyclic networks and its effect on motif finding. Journal of Complex Networks, (2014).
C. J. Carstens, Motifs in Directed Acyclic Networks. International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2013).
J. Jeffers, K. J. Horadam, C. J. Carstens, A. Rao and S. Boztas, Influence Neighbourhoods in CiteSeer: A Case Study. International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), (2013).
C. J. Carstens and K. J. Horadam, Persistent Homology of Collaboration Networks. Mathematical Problems in Engineering, (2013).
C. J. Carstens, Twisted K-theory and T-duality. Master thesis. (2009).
C. J. Carstens, Homotopy Theory of Topological Spaces and Simplicial Sets. Bachelor thesis. (2007).
Algoritmes in ons dagelijks leven. Leve de Wiskunde!, Universiteit van Amsterdam (April 7, 2017).
The Curveball algorithm: A fast and flexible approach to sampling networks with fixed degree sequence. Science Park Informal Stochastic Meetings, University of Amsterdam (April 4, 2017).
Instructions on setting up a PaperCut client for printing at RMIT University from a Mac Book can be found here.