Alignment Theory of Parallel-beam CT Image Reconstruction for Elastic-type Objects using Virtual Focusing Method

X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of projected images from an object showing elastic motion. Here, we present a mathematical solution to reconstruct the projection image set obtained from an object with specific elastic motions: periodically, regularly, and elliptically expanded or contracted specimens. To reconstruct the projection image set from expanded or contracted specimens, we introduce new methods; detection of sample's motion modes, mathematical re-scaling pixel values and converting projection angle for a common layerComment: 30 pages, 11 figure

Network Marketing on a Small-World Network

We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability $\alpha$ is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price $p$ of the product and the referral fee $r$ are used as free parameters to maximize the profit of the manufacturer. It is observed that at $\alpha=0$ the maximized profit is constant independent of the network size $N$ while at $\alpha \neq 0$, it increases linearly with $N$. This is in parallel to the small-world transition. It is also revealed that while the optimal value of $p$ stays at an almost constant level in a broad range of $\alpha$, that of $r$ is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.Comment: 12 pages, to appear in Physica

Thermodynamic arrow of time of quantum projective measurements

We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, finite survival probability of the ground state limits the time asymmetry to be less than $\ln 2$. We illustrate our results for a concrete system and discuss the fixed point of the time asymmetry in the limit of infinitely repeated projections.Comment: 6 pages in two columns, 1 figure, to appear in EP