Number Of Divisions Research Articles

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study

The system matrix (SM) being a main part of statistical image reconstruction algorithms establishes relationship between the object and projection space. The aim was to determine it in a short duration time, towards obtaining the best quality of contrast images. In this study, a new analytical method based on Cavalieri's principle as subdividing common regions has been proposed in which the precision of the amounts of estimated areas was improved by increasing the number of divisions (NOD), and consequently the total SM's time was increased. An important issue is the tradeoff between the NODs and computational time. For this purpose, a Monte Carlo simulated Jaszczak phantom study was performed by the Monte Carlo N-Particle transport code version 5 (MCNP5) in which the tomographic images of resolution and contrast phantoms were reconstructed by maximum likelihood expectation maximization (MLEM) algorithm, and the influence of NODs variations was investigated. The results show that the lowest and best quality have been obtained at the NODs of 0 and 8, respectively and in the optimum case, the SM's total time at NOD of 8 was 925 s, which was much lower than those of the conventional Monte Carlo simulations and experimental test.

Optimal Divisionalization of Cable Television Operators Networks

In this article, a condition for the optimal division's number is presented, for a market with two cable operators who offer a network service. First, a reason is presented to justify a partial covering of the national market from the cable operators. Second, a problem of moral hazard is revealed, which is able to appear through the implementation of franchising schemes with independent divisions.

Structure of the exact wave function. III. Exponential ansatz

We continue to study exponential ansatz as a candidate of the structure of the exact wave function. We divide the Hamiltonian into ND (number of divisions) parts and extend the concept of the coupled cluster (CC) theory such that the cluster operator is made of the divided Hamiltonian. This is called extended coupled cluster (ECC) including ND variables (ECCND). It is shown that the S(simplest)ECC, including only one variable (ND=1), is exact in the sense that it gives an explicit solution of the Schrödinger equation when its single variable is optimized by the variational or H-nijou method. This fact further implies that the ECCND wave function with ND⩾2 should also have a freedom of the exact wave function. Therefore, by applying either the variational equation or the H-nijou equation, ECCND would give the exact wave function. Though these two methods give different expressions, the difference between them should vanish for the exact wave function. This fact solves the noncommuting problem raised in Paper I [H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000)]. Further, ECCND may give more rapidly converging solution than SECC because of its non-linear character, ECCND may give the exact wave function at the sets of variables different from SECC. Thus, ECCND is exact not only for ND=1, but also for ND⩾2. The operator of the ECC, exp(S), is an explicit expression of the wave operator that transforms a reference function into the exact wave function. The coupled cluster including general singles and doubles (CCGSD) proposed in Paper I is an important special case of the ECCND. We have summarized the method of solution for the SECC and ECCND truncated at order n. The performance of SECC and ECC2 is examined for a simple example of harmonic oscillator and the convergence to the exact wave function is confirmed for both cases. Quite a rapid convergence of ECC2 encourages an application of the ECCND to more general realistic cases.

Structure of the exact wave function. II. Iterative configuration interaction method

This is the second progress report on the study of the structure of the exact wave function. First, Theorem II of Paper I (H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000)) is generalized: when we divide the Hamiltonian of our system into ND (number of division) parts, we correspondingly have a set of ND equations that is equivalent to the Schrödinger equation in the necessary and sufficient sense. Based on this theorem, the iterative configuration interaction (ICI) method is generalized so that it gives the exact wave function with the ND number of variables in each iteration step. We call this the ICIND method. The ICIGSD (general singles and doubles) method is an important special case in which the GSD number of variables is involved. The ICI methods involving only one variable [ICION(one) or S(simplest)ICI] and only general singles (GS) number of variables (ICIGS) are also interesting. ICIGS may be related to the basis of the density functional theory. The convergence rate of the ICI calculations would be faster when ND is larger and when the quality of the initial guess function is better. We then study the structure of the ICI method by expanding its variable space. We also consider how to calculate the excited state by the ICIGSD method. One method is an ICI method aiming at only one exact excited state. The other is to use the higher solutions of the ICIGSD eigenvalues and vectors to compute approximate excited states. The latter method can be improved by extending the variable space outside of GSD. The underlying concept is similar to that of the symmetry-adapted-cluster configuration-interaction (SAC-CI) theory. A similar method of calculating the excited state is also described based on the ICIND method.