Optimization of the collimator mask for the rotational modulation collimator-based gamma-ray/neutron dual-particle imager

The purpose of this study is to optimize the collimator mask design for the rotational modulation collimator (RMC) imaging system. First, we optimized the slat and slit width of the collimator mask which affects the number of particles entering the detector and, thus, alters the morphology of modulation patterns. However, the conventional collimator mask design with bilateral symmetry posed an inherent ambiguity issue in the estimation of the source location in the reconstructed image. Therefore, we propose a new asymmetric collimator mask design which can solve the ambiguity problem for the development of the dual-particle imaging system. Modulation patterns for various types of asymmetric mask designs were calculated with Monte Carlo simulations, and modulation and transmission efficiencies were compared with ones for the conventional RMC mask design to evaluate the nominal performance of the new mask designs. The proposed asymmetric collimator mask removed the ambiguous artifact from the reconstructed image without compromising transmission and modulation efficiencies. In addition, one can even expect to achieve better spatial resolution in the reconstructed image with the proposed new asymmetric mask design, as compared with the asymmetric mask design suggested from the previous study.     

Degree and wealth distribution in a network induced by wealth

A network induced by wealth is a social network model in which wealth induces individuals to participate as nodes, and every node in the network produces and accumulates wealth utilizing its links. More specifically, at every time step a new node is added to the network, and a link is created between one of the existing nodes and the new node. Innate wealth-producing ability is randomly assigned to every new node, and the node to be connected to the new node is chosen randomly, with odds proportional to the accumulated wealth of each existing node. Analyzing this network using the mean value and continuous flow approaches, we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node. From this relation, we show that the degree distribution of the network induced by wealth is scale-free. We also show that the wealth distribution has a power-law tail and satisfies the 80/20 rule. We also show that, over the whole range, the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the Bouchaud-Mèzard model, even though the mechanism for producing wealth is quite different in our model. Further, we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log-normal distribution, while for the richest, the cumulative wealth distribution has a power-law behavior.     

A new approach to an N/G/1 queue

We propose a new approach that gives a one-step computational algorithm to directly obtain the queue length distribution of an N/G/1 queueing system. The new approach is based on the supplementary variable method and the matrix–analytic method. We shall show that this approach enables us to derive the joint distribution of the queue length and the elapsed service time. This revised version was published online in June 2006 with corrections to the Cover Date.