Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Isothermal seed germination of Adenanthera pavonina

(Isothermal seed germination of Adenanthera pavonina). This work reports aspects of seed germination at different temperatures of Adenanthera pavonina L., a woody Southeast Asian Leguminosae. Germination was studied by measuring the final percentages, the rate, the rate variance and the synchronisation of the individual seeds calculated by the minimal informational entropy of frequencies distribution of seed germination. Overlapping the germinability range with the range for the highest values of germination rates and the minimal informational entropy of frequencies distribution of seed germination, we found that the best temperature for the germination of A. pavonina seeds is 35 degrees C. The slope mu of the Arrhenius plot of the germination rates is positive for T < 35 degrees C and negative for T > 35 degrees C. The activation enthalpies, estimated from closely-spaced points, shows that vertical bar Delta H-vertical bar < 12 Cal mol(-1) occur for temperatures in the range between 25 degrees C and 40 degrees C. The ecological implication of these results are that this species may germinate very fast in tropical areas during the summer season. This may be an advantage to the establishment of this species under the climatic conditions in those areas.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Isothermal seed germination of Adenanthera pavonina

This work reports aspects of seed germination at different temperatures of Adenanthera pavonina L., a woody Southeast Asian Leguminosae. Germination was studied by measuring the final percentages, the rate, the rate variance and the synchronisation of the individual seeds calculated by the minimal informational entropy of frequencies distribution of seed germination. Overlapping the germinability range with the range for the highest values of germination rates and the minimal informational entropy of frequencies distribution of seed germination, we found that the best temperature for the germination of A. pavonina seeds is 35 ºC. The slope µ of the Arrhenius plot of the germination rates is positive for T < 35 ºC and negative for T > 35 ºC. The activation enthalpies, estimated from closely-spaced points, shows that |ΔH-| < 12 Cal mol-1 occur for temperatures in the range between 25 ºC and 40 ºC. The ecological implication of these results are that this species may germinate very fast in tropical areas during the summer season. This may be an advantage to the establishment of this species under the climatic conditions in those areas.