We consider an application of power indices, which take into account preferences of agents for coalition formation proposed for an analysis of power distribution in elected bodies to reveal most powerful (central) nodes in networks. These indices take into account the parameters of the nodes in networks, a possibility of group influence from the subset of nodes to single nodes, and intensity of short and long interactions among the nodes. Some properties of the indices are discussed. Various applications are presented for the network of countries – those of religion, migration, foreign claims, conflicts, exchange of students, food export-import, etc.

This paper designs an allotment mechanism for a limited amount of an infinitely divisible good (resource) among a finite number of agents under transferable utility. The mechanism is efficient in the sense of total agents’ utility maximization. As a solution, we introduce an adaptation of the Groves–Ledyard “quadratic government” that was initially suggested for the problem of public good.

Dynamic quenching of the intensity of dual-band fluorescence pulses is modelled using numerical solutions of the equations for the population matrix of a model molecule with five states. The state with the highest energy is assumed to be resonantly excited by light and two other excited states that are populated by subsequent relaxation processes are assumed to be the initial states for molecular transitions with emission of dual-band fluorescence photons. The model parameters for the molecule are chosen to match the typical parameters of molecules with intramolecular proton phototransfer. Quenching is treated as a consequence of nonradiative decay of the excited states of the fluorescing molecule owing to collisions with quenchant molecules. Examples of different dual-band fl uorescence quenching mechanisms for the model molecule are given, depending on the decay of particular excited states of the molecule involving nonradiative intramolecular transitions or transitions into states of the quenchant molecules. Keywords mathematical modelling fluorescence quenching dual-band fluorescence pulses intramolecular hydrogen bond proton phototransfer

Probabilistic aspects of caching are considered. The caching serves to keep popular contents inside a memory unit called 'cache' to be able to access them quickly. Using extreme value theory we propose a caching strategy called Cluster Caching Rule driven by content popularity that may change in time. A non-Poisson request arrival process is used when requests are statistically correlated. The idea of the new approach is to locate in cache only contents whose popularity exceeds a sufficiently large threshold. Due to dependence and possible heavy-tailed distribution of inter-requests and inter-arrival times of documents, the popularity process builds clusters of exceedances. The cluster and inter-cluster sizes are geometrically distributed as derived in Markovich (2014). We use it to calculate means of the cache utilization and occupancy. We escape assumptions like a constant size of content and a Poisson request process that are typical in the literature.

Detection of abrupt changes in time series data structure is very useful in modeling and prediction in many application areas, where time series pattern recognition must be implemented. Despite of the wide amount of research in this area, the proposed methods require usually a long execution time and does not provide the possibility to estimate the real changes in variance and autocorrelation at certain points. Hence they cannot be efficiently applied to the large time series where only the change points with constraints must be detected. In the framework of the present paper we provide heuristic methods based on the moving variance ratio and moving median difference for identification of change points. The methods were applied for behavior analysis of farm animals using the data sets of 3D acceleration of an electronic ear tag obtained by means of the radio frequency identification (RFID).