Stellar Evolution Constraints on the Triple-Alpha Reaction Rate

We investigate the quantitative constraint on the triple-alpha reaction rate based on stellar evolution theory, motivated by the recent significant revision of the rate proposed by nuclear physics calculations. Targeted stellar models were computed in order to investigate the impact of that rate in the mass range of 0.8 < M / Msun < 25 and in the metallicity range between Z = 0 and Z = 0.02. The revised rate has a significant impact on the evolution of low- and intermediate-mass stars, while its influence on the evolution of massive stars (M >~ 10 Msun) is minimal. We find that employing the revised rate suppresses helium shell flashes on AGB phase for stars in the initial mass range 0.8 < M / Msun < 6, which is contradictory to what is observed. The absence of helium shell flashes is due to the weak temperature dependence of the revised triple-alpha reaction cross section at the temperature involved. In our models, it is suggested that the temperature dependence of the cross section should have at least nu > 10 at T = 1 - 1.2 x 10^8 K where the cross section is proportional to T^{nu}. We also derive the helium ignition curve to estimate the maximum cross section to retain the low-mass first red giants. The semi-analytically derived ignition curves suggest that the reaction rate should be less than ~ 10^{-29} cm^6 s^{-1} mole^{-2} at ~ 10^{7.8} K, which corresponds to about three orders of magnitude larger than that of the NACRE compilation. In an effort to compromise with the revised rates, we calculate and analyze models with enhanced CNO cycle reaction rates to increase the maximum luminosity of the first giant branch. However, it is impossible to reach the typical RGB tip luminosity even if all the reaction rates related to CNO cycles are enhanced by more than ten orders of magnitude.Comment: 14 pages, 8 figures, accepted by the Ap

SAGA: Stellar Abundances for Galactic Archaeology

A tutorial for the Stellar Abundances for Galactic Archaeology (SAGA) database is presented. This paper describes the outline of the database, reports the current status of the data compilation and known problems, and presents plans for future updates and extensions.Comment: Proceedings of the conference, "Nuclei in the Cosmos XII", invited talk at Online Support sessio

Triggered Clause Pushing for IC3

We propose an improvement of the famous IC3 algorithm for model checking safety properties of finite state systems. We collect models computed by the SAT-solver during the clause propagation phase of the algorithm and use them as witnesses for why the respective clauses could not be pushed forward. It only makes sense to recheck a particular clause for pushing when its witnessing model falsifies a newly added clause. Since this trigger test is both computationally cheap and sufficiently precise, we can afford to keep clauses pushed as far as possible at all times. Experiments indicate that this strategy considerably improves IC3's performance.Comment: 4 page

Issues in multi-media information networks

In an integrated service environment, where users exchange various types of aural and visual information, networks should appear friendly to its users providing tools for management of multi-media information. Networks should also efficiently satisfy diverse performance requirements of different information being exchanged.In this paper we present new architecture for integrated service networks being investigated and developed by the Distributed Computation and Communication Group at the Department of Computer Science in the Columbia University. Research efforts are devoted to developing both (1) document management software to allow users to manipulate and relate text/graphics/voice information in a dynamic way, and (2) a tree network architecture for reliable and efficient exchange of multi-media information

Coherent configurations and triply regular association schemes obtained from spherical designs

Delsarte-Goethals-Seidel showed that if $X$ is a spherical $t$-design with degree $s$ satisfying $t\geq 2s-2$, $X$ carries the structure of an association scheme. Also Bannai-Bannai showed that the same conclusion holds if $X$ is an antipodal spherical $t$-design with degree $s$ satisfying $t=2s-3$. As a generalization of these results, we prove that a union of spherical designs with a certain property carries the structure of a coherent configuration. We derive triple regularity of tight spherical $4,5,7$-designs, mutually unbiased bases, linked symmetric designs with certain parameters.Comment: 17page