MSc. Miroslav Andjelkovic’s report about a Short Term Scientific Mission at Jozef Stefan Institute in Ljubljana, TD1210-140716-078788
Large Structure of Phase-Space Manifolds Underlying Collective Dynamics of Knowledge Creation and Other Online Social Processes
As part of this STSM, in the period from 14.07.2016. to 24.07.2016., I worked at the Department of theoretical physics at the Jozef Stefan Institute in Ljubljana, under the supervision of Prof. Dr Bosiljaka Tadic. During this time, we managed to partially finish the work according to the proposed goals of the STSM.
As proposed, we have analysed time series of the empirical data sets representing the overall activity on the forum Q&A system Mathematics. The present focus was on the comparative analysis of networks, representing the time series of events that contain cognitive contents (mathematical tags). Different graphs are separated according to a structural parameter-weight of the links acquired by new mapping method. Then, we performed a systematic analysis of their dual graphs using the methods of algebraic topology.
By mapping the segments of long time series of the empirical data, we examined how the topology of the graphs, i.e., the phase space manifolds of the system, evolves over time. For this analysis, we have introduced a new mapping algorithm from time series to mathematical graphs, which involves weights of the links.
These weights are representing the impact of two points of the time series on each other. This algorithm is adjusted for time series with active cycles (due to human behaviour) and high trend (increasing activity in time).
I would like to thank for the hospitality at the Department of Theoretical Physics of The Jozef Stefan Institute, where I spent fantastic time and enjoyed working with Prof Tadic and her colleagues. I am sure that we will continue this research on our mutual benefit. Also, I thank the COST action KNOWeSCAPE for giving me this opportunity to come to Ljubljana once again and continue this collaboration, the experience that positively inspires my further work on PhD Thesis.