In order to prolong the lifetime of sensor nodes, wireless sensor networks are partitioned into clusters. The most of the proposed Equal Clustering algorithms do not consider location of the base station. This situation causes hot spots or energy hole problem in multi-hop data forwarding. Unequal clustering mechanisms, which are designed by considering the location of the base station to solve ...

We consider the problem of how societies should be partitioned into classes if individuals express their views about who should be put with whom in the same class. A non-bossy social aggregator depends only on those cells of the individual partitions the society members classify themselves in. This fact allows us to concentrate on a corresponding “opinion graph” for each pro…le of views. By mea...

The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the domatic number is almost surely equal to 3. We also give a lower bound on the domatic number of a graph in terms of order, minimum degree and m...

On a finite metric graph with standard vertex conditions and equal edge lengths, the large magnitude eigenvalues of the Schrödinger operator ∆ + q cluster near the eigenvalues of the Laplace operator ∆. Based on the spectral ’periodicity’ of ∆, the clusters can be partitioned into a finite collection of classes. There is a class dependent formula for the cluster trace (or average eigenvalue shi...

This paper studies the core of combined games, obtained by summing two coalitional games. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games whose core is equal to the core of the combined game. On the other hand, for non balanced games, the binary relation associating two component games whose combination has an empty ...

Objective: Measurements of heart rate variability (HRV) during sleep have become increasingly popular as sleep could provide an optimal state for HRV assessments. While sleep stages have been reported to affect HRV, the effect of sleep stages on the variance of HRV parameters were hardly investigated. We aimed to assess the variance of HRV parameters during the different sleep stages. Further, ...