Belief Propagation Algorithm for Portfolio Optimization Problems

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.Comment: 5 pages, 2 figures, to submit to EP

Dust formation and mass loss around intermediate-mass AGB stars with initial metallicity Zini≤10−4Z_{\rm ini} \leq 10^{-4} in the early Universe I: Effect of surface opacity on the stellar evolution and dust-driven wind

Dust formation and resulting mass loss around Asymptotic Giant Branch (AGB) stars with initial metallicity in the range of $0 \leq Z_{\rm ini} \leq 10^{-4}$ and initial mass $2\leq M_{\rm ini}/M_{\odot} \leq 5$ are explored by the hydrodynamical calculations of dust-driven wind (DDW) along the AGB evolutionary tracks. We employ the MESA code to simulate the evolution of stars, assuming an empirical mass-loss rate in the post-main sequence phase, and considering the three types of low-temperature opacities (scaled-solar, CO-enhanced, and CNO-enhanced opacities) to elucidate the effect on the stellar evolution and the DDW. We find that the treatment of low-temperature opacity strongly affects the dust formation and resulting DDW; in the carbon-rich AGB phase, the maximum $\dot{M}$ of $M_{\rm ini} \geq$ 3 $M_{\odot}$ star with the CO-enhanced opacity is at least one order of magnitude smaller than that with the CNO-enhanced opacity. A wide range of stellar parameters being covered, a necessary condition for driving efficient DDW with $\dot{M} \ge 10^{-6}$ $M_{\odot}$ yr$^{-1}$ is expressed as the effective temperature $T_{\rm eff} \lesssim 3850$ K and $\log(\delta_{\rm C}L/\kappa_{\rm R} M) \gtrsim 10.43\log T_{\rm eff}-32.33$ with the carbon excess $\delta_{\rm C}$ defined as $\epsilon_{\rm C} - \epsilon_{\rm O}$ and the Rosseland mean opacity $\kappa_{\rm R}$ in units of cm$^2$g$^{-1}$ in the surface layer, and the stellar mass (luminosity) $M$ $(L)$ in solar units. The derived fitting formulae of gas and dust mass-loss rates in terms of input stellar parameters could be useful for investigating the dust yield from AGB stars in the early Universe being consistent with the stellar evolution calculations.Comment: 26 pages, 7 figures, 4 tables, accepted for publication in MNRA

Changes in S100β protein levels in cerebrospinal fluid after thoracoabdominal aortic operations

AbstractJ Thorac Cardiovasc Surg 2001;122:1019-2

Semidilute Principle for Gels

Polymer gels such as jellies and soft contact lenses are soft solids consisting of three-dimensional polymer networks swollen with a large amount of solvent. For approximately 80 years, the swelling of polymer gels has been described using the Flory--Huggins mean-field theory. However, this theory is problematic when applied to polymer gels with large solvent contents owing to the significant fluctuations in polymer concentration. In this study, we experimentally demonstrate the superiority of the semidilute scaling law over the mean-field theory for predicting the swelling of polymer gels. Using the semidilute scaling law, we experimentally determine the universal critical exponent $\nu$ of the self-avoiding walk via swelling experiments on polymer gels. The experimentally obtained value $\nu\simeq 0.589$ is consistent with the previously reported value of $\nu\simeq 0.588$, which was obtained by precise numerical calculations. Furthermore, we theoretically derive and experimentally demonstrate a scaling law that governs the equilibrium concentrations. This scaling law contradicts the predictions made by de Gennes' $c^{*}$ theorem. A major deficiency of the $c^*$ theorem is that the network elasticity, which depends on the as-prepared state, is neglected. These findings reveal that the semidilute scaling law is a fundamental principle for accurately predicting and controlling the equilibrium swelling of polymer gels.Comment: 12 pages, 11 figure

A Detailed Study on the Liquefaction-Induced Settlement of Timber Houses During the 2000 Tottoriken-Seibu Earthquake

More than 100 timber houses settled and tilted due to liquefaction at a housing development during the 2000 Tottoriken-seibu earthquake in Japan. Among the damaged houses, 47 houses tilted more than 15/1000. Heavily tilted houses were necessary to restore to become horizontal after the earthquake, though several houses, that tilted slightly, were not necessary to restore. The authors studied the boundary of the angle of the restored and non-restored houses. According to the study by the authors, the critical angle of tilting to restore houses was about 10/1000. The authors studied soil conditions also, and found that groundwater level was shallower than about 1.7 m in the damaged zone. This implies that small structures such as timber houses have no damage due to liquefaction if the groundwater level or the bottom of surface non-liquefiable layer is deeper that about 1.7 m

Arterio-jugular Differences in Serum S-100β Proteins in Patients Receiving Selective Cerebral Perfusion

Purpose The early increase in serum S100β after cardiopulmonary bypass (CPB) seems to be derived from an extracerebral source. To exclude contamination, we investigated the arterio-jugular differences in S100β levels in patients receiving selective cerebral perfusion (SCP). We also evaluated the brain-protective effect of SCP by comparing the arterial S100β levels with those in patients undergoing coronary artery bypass grafting (CABG). Methods We measured arterial and jugular venous levels of S100β in ten patients undergoing aortic arch repair with SCP for up to 12h postoperatively (SCP group). We also measured arterial levels of S100β in nine patients undergoing CABG (CPB group). Results There was no incidence of hospital death or stroke. The arterial levels of S100β in both groups were comparable and peaked just after the conclusion of CPB. The arterial and jugular venous levels of S100β were almost equivalent. The arterio-jugular differences in S100β levels were negligible, even in our SCP-group patient with postoperative delirium, who had a peak value three times higher than the other patients. Conclusions The arterio-jugular differences in S100β did not clarify the origin of their increase. Thus, measuring the jugular venous levels of S100β in patients without postoperative clinical neurological deterioration would be of little benefit. However, SCP seems to protect the brain against S100β release as effectively as conventional CPB