Participation and performance trends in 6-hour ultra-marathoners – a retrospective data analysis of worldwide participation from 1991-2010

Participation trends in 6-hour ultra-marathons held word-wide were investigated to gain basic demographic data on 6-hour ultra-marathoners and where these races took place. Participation trends and the association between nationality and race performance were investigated in all 6-hour races held worldwide between 1991 and 2010. Participation increased linearly in both women and men across years. The annual number of finishes was significantly higher in men than in women (P=0.013). The male-to-female ratio remained stable at ~4 since 1991. Runners in age group 45-49 years showed the largest increase in participation for both men (800 participants in 18 years) and women (208 participants in 16 years). Europe attracted most of the runners from other continents (166 runners), more than all other continents combined (55 runners). European runners also showed the best top ten performances (73±3 km for women and 77±11 km for men), while African (with 65±9 km for men) and South American (54±4 km for women and 65±2 km for men) runners showed the weakest. To summarize, participation in 6-hour ultra-marathons increased across years. Most of the development took place in Europe and in athletes in the age group 45-49 years. Europe also attracted the most diverse field of athletes with runners from all other continents. European runners accounted for the most runners and achieved the best top ten performances.

Data analysis using circular causality in networks

Complex systems in causal relationships are known to be circular rather than linear; this means that a particular result is not produced by a single cause, but rather that both positive and negative feedback processes are involved. However, although interpreting systemic interrelationships requires a language formed by circles, this has only been developed at the diagram level, and not from an axiomatic point of view. The first difficulty encountered when analysing any complex system is that usually the only data available relate to the various variables, so the first objective was to transform these data into cause-and-effect relationships. Once this initial step was taken, our discrete chaos theory could be applied by finding the causal circles that will form part of the system attractor and allow their behavior to be interpreted. As an application of the technique presented, we analyzed the system associated with the transcription factors of inflammatory diseases.

A Sociocybernetics Data Analysis Using Causality in Tourism Networks

The aim of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on a pre-designed algorithm and applying our interpretation of chaos theory developed in the context of General Systems Theory. This article sets out the causal relationships associated with tourist flows in order to enable the formulation of appropriate strategies. Our results can be applied to numerous cases. For example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups and to analyse tourist behaviour in terms of the most relevant variables. Unlike statistical analyses that merely provide information on current data, our method uses orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.