強度変調放射線治療計画の線量体積制約に基づく最適化

We present a novel optimization method to handle dose-volume constraints (DVCs) directly in intensity-modulated radiation therapy (IMRT) treatment planning based on the idea of continuous dynamical methods. Most of the conventional methods are constructed for solving inconsistent inverse problems with, e.g., dose-volume based objective functions, and one expects to obtain a feasible solution that minimally violates the DVCs. We introduce the concept of ‘acceptable’, meaning that there exists a nonempty set of radiation beam weights satisfying the given DVCs, and we resolve the issue that the objective and evaluation are different in the conventional planning approach. We apply the initial-value problem of the proposed dynamical system to an acceptable and inconsistent inverse problem and prove that the convergence to an equilibrium in the acceptable set of solutions is theoretically guaranteed by using the Lyapunov theorem. Indeed, we confirmed that we can obtain acceptable beam weights through numerical experiments using phantom data simulating a clinical setup for an acceptable and inconsistent IMRT planning system

Production of the p-Process Nuclei in the Carbon-Deflagration Model for Type Ia Supernovae

We calculate nucleosynthesis of proton-rich isotopes in the carbon-deflagration model for Type Ia supernovae (SNe Ia). The seed abundances are obtained by calculating the s-process nucleosynthesis that is expected to occur in the repeating helium shell flashes on the carbon-oxygen (CO) white dwarf (WD) during mass accretion from a binary companion. When the deflagration wave passes through the outer layer of the CO WD, p-nuclei are produced by photodisintegration reactions on s-nuclei in a region with the peak temperature ranging from 1.9 to 3.6 x10^9 K. We confirm the sensitivity of the p-process on the initial distribution of s-nuclei. We show that the initial C/O ratio in the WD does not much affect the yield of p-nuclei. On the other hand, the abundance of 22Ne left after the s-processing has a large influence on the p-process via 22Ne(alpha,n) reaction. We find that about 50% of p-nuclides are co-produced when normalized to their solar abundances in all adopted cases of seed distribution. Mo and Ru, which are largely underproduced in Type II supernovae (SNe II), are produced more than in SNe II although they are underproduced with respect to the yield levels of other p-nuclides. The ratios between p-nuclei and iron in the ejecta are larger than the solar ratios by a factor of 1.2. We also compare the yields of oxygen, iron, and p-nuclides in SNe Ia and SNe II and suggest that SNe Ia could make a larger contribution than SNe II to the solar system content of p-nuclei.Comment: 18 pages, 9 figures, revised argument in section 3.2.2 and 3.5, results unchanged, Accepted for publication in the Astrophysical Journal, references adde

The r-Process in Supersonic Neutrino-Driven Winds: The Roll of Wind Termination Shock

Recent hydrodynamic studies of core-collapse supernovae imply that the neutrino-heated ejecta from a nascent neutron star develops to supersonic outflows. These supersonic winds are influenced by the reverse shock from the preceding supernova ejecta, forming the wind termination shock. We investigate the effects of the termination shock in neutrino-driven winds and its roll on the r-process. Supersonic outflows are calculated with a semi-analytic neutrino-driven wind model. Subsequent termination-shocked, subsonic outflows are obtained by applying the Rankine-Hugoniot relations. We find a couple of effects that can be relevant for the r-process. First is the sudden slowdown of the temperature decrease by the wind termination. Second is the entropy jump by termination-shock heating, up to several 100NAk. Nucleosynthesis calculations in the obtained winds are performed to examine these effects on the r-process. We find that 1) the slowdown of the temperature decrease plays a decisive roll to determine the r-process abundance curves. This is due to the strong dependences of the nucleosynthetic path on the temperature during the r-process freezeout phase. Our results suggest that only the termination-shocked winds with relatively small shock radii (~500km) are relevant for the bulk of the solar r-process abundances (A~100-180). The heaviest part in the solar r-process curve (A~180-200), however, can be reproduced both in shocked and unshocked winds. These results may help to constrain the mass range of supernova progenitors relevant for the r-process. We find, on the other hand, 2) negligible roles of the entropy jump on the r-process. This is a consequence that the sizable entropy increase takes place only at a large shock radius (~10,000km) where the r-process has already ceased.Comment: 11 pages, 7 figures, submitted to ApJ, revised following referee's comments,Accepted for publication in Ap

Control Technique of Maximum Local Lyapunov Exponent on Stable Periodic Solution in Continuous-Time Non-Autonomous Dynamical Systems

We previously proposed a parametric controller to avoid undesirable bifurcations of stable fixed and periodic points in discrete-time dynamical systems. The parameter regulation is derived from an optimization problem on the maximum local Lyapunov exponent and a method of steepest descent. In this paper, on the basis of the ideas and a stroboscopic mapping that transforms the trajectory of a continuous-time periodic solution into a sequence of points, we propose a technique to control the maximum local Lyapunov exponent on stable periodic oscillations in continuous-time non-autonomous dynamical systems

Supernova Nucleosynthesis and Extremely Metal-Poor Stars

We investigate hydrodynamical and nucleosynthetic properties of the jet-induced explosion of a population III $40M_\odot$ star and compare the abundance patterns of the yields with those of the metal-poor stars. We conclude that (1) the ejection of Fe-peak products and the fallback of unprocessed materials can account for the abundance patterns of the extremely metal-poor (EMP) stars and that (2) the jet-induced explosion with different energy deposition rates can explain the diversity of the abundance patterns of the metal-poor stars. Furthermore, the abundance distribution after the explosion and the angular dependence of the yield are shown for the models with high and low energy deposition rates $\dot{E}_{\rm dep}=120\times10^{51} {\rm ergs s^{-1}}$ and $1.5\times10^{51} {\rm ergs s^{-1}}$. We also find that the peculiar abundance pattern of a Si-deficient metal-poor star HE 1424--0241 can be reproduced by the angle-delimited yield for $\theta=30^\circ-35^\circ$ of the model with $\dot{E}_{\rm dep}=120\times10^{51} {\rm ergs s^{-1}}$.Comment: 6 pages, 3 figures. To appear in "ORIGIN OF MATTER AND EVOLUTION OF GALAXIES: From the Dawn of Universe to the Formation of Solar System", AIP Conf. Proc. 1016 (December 2007, Sapporo), eds. T. Suda, T. Nozawa, et al. (Melville: AIP

Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System

Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár's I-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize the I-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas

バイナリ・トモグラフィのための連続時間画像再構成

Binary tomography is the process of reconstructing a binary image from a finite number of projections. We present a novel method for solving binary tomographic inverse problems using a continuous-time image reconstruction (CIR) system described by nonlinear differential equations based on the minimization of a double Kullback- Leibler divergence. We prove theoretically that the divergence measure monotonically decreases in time. Moreover, we demonstrate numerically that the quality of the reconstructed images of the nonlinear CIR system is better than those from an iterative reconstruction method

FEASIBILITY STUDY ON THE FUSION OF PHITS SIMULATIONS AND THE DLNN ALGORITHM

We have recently have developed an in-situ multiple-channel depth distribution spectrometer (DDS) that can easily acquire on-site measurements of the depth distribution of specific radioactivities of Cs-134 and Cs-137 underground. Despite considerable improvements in the hardware developed for this device, the quantitative method for determining of radioactivities with this DDS device cannot yet achieve satisfactory performance for practical use. For example, this method cannot discriminate each γ-ray spectra of Cs-134 and Cs-137 acquired by the 20 thallium-doped caesium iodine CsI(Tl) scintillation crystal detectors of the DDS device from corresponding depth levels of underground soil. Therefore, we have applied deep learning neural network (DLNN) as a novel radiation measurement technique to discriminate the spectra and to determine the specific radioactivities of Cs-134 and Cs-137. We have developed model soil layers on a virtual space in Monte-Carlo based PHITS simulations and transported γ-ray radiation generated from a particular single soil layer or multiple layers as radiation sources; next, we performed PHITS calculations of those specific radioactivity measurements for each soil layer using DDS device based on machine learning via the DLNN algorithm. In this study, we obtained informative results regarding the feasibility of the proposal innovative radiation measurement method for further practical use in on-site applications

Multi-Dimensional Simulations of Radiative Transfer in Aspherical Core-Collapse Supernovae

We study optical radiation of aspherical supernovae (SNe) and present an approach to verify the asphericity of SNe with optical observations of extragalactic SNe. For this purpose, we have developed a multi-dimensional Monte-Carlo radiative transfer code, SAMURAI (SupernovA MUlti-dimensional RAdIative transfer code). The code can compute the optical light curve and spectra both at early phases (<~ 40 days after the explosion) and late phases (~ 1 year after the explosion), based on hydrodynamic and nucleosynthetic models. We show that all the optical observations of SN 1998bw (associated with GRB 980425) are consistent with polar-viewed radiation of the aspherical explosion model with kinetic energy 20 x 10^{51} ergs. Properties of off-axis hypernovae are also discussed briefly.Comment: 6 pages, 4 figures. Proceedings of "Origin of Matter and Evolution of Galaxies (OMEG07): From the Dawn of Universe to the Formation of Solar System", 4-7 Dec 2007, Sapporo, Japa