No abstract

Transmission and betweenness centrality are key concepts in communication networks theory. Based on this concept, new concepts of networkness and network surplus have recently been defined. However, all these four concepts include unrealistic assumption about equal communication between vertices. Here, we propose more realistic assumption that the amount of communication of vertices decreases as their distance increases. We assume that amount of communication between vertices u and v is proportional to d (u, v) λ where λ < 0. Taking this into account generalised versions of these four descriptors are defined. Extremal values of these descriptors are analysed.

The effect of biomass dynamics on the estimation of watercolumn primary production is analyzed, by coupling a primary production model to a simple growth equation for phytoplankton. The production model is formulated with depth-and time-resolved biomass, and placed in the context of earlier models, with emphasis on the canonical solution for watercolumn production. A relation between the canonical solution and the general solution for the case of an arbitrary depth-dependent biomass profile was derived, together with an analytical solution for watercolumn production in case of a depth dependent biomass profile described with the shifted Gaussian function. The analysis was further extended to the case of a time-dependent, mixed-layer biomass, and two additional analytical solutions to this problem were derived, the first in case of increasing mixed-layer biomass and the second in case of declining biomass. The solutions were tested with Hawaii Ocean Time-series data. The canonical solution for mixed-layer production has proven to be a good model for this data set. The shifted Gaussian function was demonstrated to be an accurate model for the measured biomass profiles and the shifted Gaussian parameters extracted from the measured profiles were further used in the analytical solution for watercolumn production and results compared with data. The influence of time-dependent biomass on mixed-layer production was studied through analytical solutions. Re-examining the Critical Depth Hypothesis we derived an expression for the daily increase in mixed-layer biomass. Finally, the work was placed in a remote sensing context and the time-dependent model for biomass related to the remotely sensed-biomass.

In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices. Generalised versions of these four descriptors were presented, taking into account that communication between vertices u and v is decreasing as the distance between them is increasing. Therefore, we weight the quantity of communication by λ d (u,v) where λ ∈ 0, 1 . Extremal values of these descriptors are analysed.

Networks (or graphs) appear as dominant structures in different domains, including sociology, biology, neuroscience and computing. In most cases, these graphs are directed which changes the semantics of the edges that are no longer symmetrical in the sense that the beginning vertex transfers some property or value to the end vertex, but not vice versa. Detecting community structure in complex networks is an interdisciplinary topic with many relevant areas of application. In order to detect communities in directed acyclic networks, apart from the direction of the edge, the requirement for topological ordering of the vertices should be taken into account. In other words, if the vertices are topologically order is such a way that xWe present an algorithm derived from LPA algorithms which are commonly used in network detection, mostly because of their quick computational time and fairly good results. They were originally developed for undirected networks, but have been modified for this purpose.