I am a grad student in the School of Mathematics at the University of Manchester. My research interest is model-theoretic and proof-theoretic methods in Group Theory. Previously, I used Persistent Homology to analyze the behavior of random number generators. I also have a few papers on metaheuristics with applications to various open-source software projects. See below for my papers.
Which one of these three point clouds can we get by sampling the unit cube using a pseudorandom number generator? Surprisingly, the answer is any one of them, depending on the generator we use. All three generators sample the same manifold: the unit cube, which has one connected component and no holes. However, the first two generators are faulty. In the first case, the RANDU generator of IBM, the resulting point cloud consists of 15 separate connected components (parallel planes). In the second case, there is only one component, but it contains many holes.
My honours thesis involved classifying pseudorandom number generators based on their ability to reflect the topological properties of the manifolds they sample. Using persistent homology, it is possible to rigorously define the Betti numbers of a point set, and investigate their relationship to the Betti numbers of the sampled manifold.
I have a strong interest in logic, including proof theory and linear logic as well as computer-verified mathematics and type theory.
I work on Proofbox, a Dependency Injection framework based on Proof Search in the LJT Sequent Calculus.
In 2013, I started formalizing parts of the theory of Synthetic Differential Geometry in the Agda proof assistant. The project is on indefinite hiatus due to other pursuits, but drop me an email if you're interested in taking it up. I still maintain the FAQ on Smooth Infinitesimal Analysis .
My executable Agda formulation of Yablo's paradox is here. Fun exercise: figure out what happens when the paradox term is evaluated.
I used various metaheuristics to kill nasty hash container bugs in Hadoop (a distributed computing platform), optimize popular Java libraries for power consumption, and to do DAASE-style improvement programming. I also participated in database query optimization research for Keysight/Agilent.
|Repairing and Optimizing Hadoop Hash Code Implementations. Z. A. Kocsis, G. Neumann, J. Swan, M. G. Epitropakis, A. E. I. Brownlee, S. O. Haraldsson and E. Bowles||SSBSE||2014||bib|
|The Representative Metaheuristic Design Pattern. J. Swan, Z. A. Kocsis, and A. Lisitsa||GECCO||2014||bib|
|Object-Oriented Genetic Improvement for Improved Energy Consumption in Google Guava. N. Burles, E. Bowles, A. E. I. Brownlee, Z. A. Kocsis, J. Swan, and N. Veerapen||SSBSE||2015||bib|
|Haiku - a Scala Combinator Toolkit. Z. A. Kocsis, A. E. I. Brownlee, J. Swan, and R. Senington||SSBSE||2015||bib|
|Embedded Dynamic Improvement. N. Burles, J. Swan, E. Bowles, A. E. I. Brownlee, Z. A. Kocsis, and N. Veerapen||GECCO||2015||bib|