Juduicial Power & Illusion: The Republic of China\u27s Council of Grand Justices and Constitutional Interpretation

The Republic of China underwent a rapid political transformation from an authoritarian nation to a democratic state which required change at every level of the government. The ROC\u27s Council of Grand Justices has contributed to this period of reform through a number of constitutional interpretations which have resulted in greater individual liberties and further restrictions on government actions. This has been accomplished even though the Council operates against substantive and procedural limitations on its powers. A review of these Council interpretations from the past decade reveals that the Council has made steady inroads towards fulfilling its role as the supreme judicial body of the ROC. The Council, however, is not sufficiently protected from the influence of other government branches and still issues decisions carefully. The ROC government must ensure the Council is isolated from political influences before the Council will be able to impartially exercise the full range of its constitutionally mandated authority

Stellar mass functions of galaxies, disks and spheroids at z~0.1

We present the stellar mass functions (SMF) and mass densities of galaxies, and their spheroid and disk components in the local (z~0.1) universe over the range 8.9 <= log(M/M_solar) <= 12 from spheroid+disk decompositions and corresponding stellar masses of a sample of over 600,000 galaxies in the SDSS-DR7 spectroscopic sample. The galaxy SMF is well represented by a single Schechter function (M* = 11.116+/-0.011, alpha = -1.145+/-0.008), though with a hint of a steeper faint end slope. The corresponding stellar mass densities are (2.670+/-0.110), (1.687+/-0.063) and (0.910+/-0.029)x10^8 M_solar Mpc^-3 for galaxies, spheroids and disks respectively. We identify a crossover stellar mass of log(M/M_solar) = 10.3+/-0.030 at which the spheroid and disk SMFs are equal. Relative contributions of four distinct spheroid/disk dominated sub-populations to the overall galaxy SMF are also presented. The mean disk-to-spheroid stellar mass ratio shows a five fold disk dominance at the low mass end, decreasing monotonically with a corresponding increase in the spheroidal fraction till the two are equal at a galaxy stellar mass, log(M/M_solar)=10.479+/-0.013, the dominance of spheroids then grows with increasing stellar mass. The relative numbers of composite disk and spheroid dominated galaxies show peaks in their distributions, perhaps indicative of a preferred galaxy mass. Our characterization of the low redshift galaxy population provides stringent constraints for numerical simulations to reproduce.Comment: 30 pages, 18 figures, 5 tables (2 online), Accepted for publication in MNRA

Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford

A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$, $\operatorname{dist}(v, w, G) \leq \operatorname{dist}(v, w, T)$ and $operatorname{E}[\operatorname{dist}(v, w, T)] \leq \alpha \operatorname{dist}(v, w, G)$. Such embeddings are highly useful for designing fast approximation algorithms, as many hard problems are easy to solve on tree instances. However, to date the best parallel $(\operatorname{polylog} n)$-depth algorithm that achieves an asymptotically optimal expected stretch of $\alpha \in \operatorname{O}(\log n)$ requires $\operatorname{\Omega}(n^2)$ work and a metric as input. In this paper, we show how to achieve the same guarantees using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m^{1+\epsilon})$ work, where $m = |E|$ and $\epsilon > 0$ is an arbitrarily small constant. Moreover, one may further reduce the work to $\operatorname{\tilde{O}}(m + n^{1+\epsilon})$ at the expense of increasing the expected stretch to $\operatorname{O}(\epsilon^{-1} \log n)$. Our main tool in deriving these parallel algorithms is an algebraic characterization of a generalization of the classic Moore-Bellman-Ford algorithm. We consider this framework, which subsumes a variety of previous "Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss it in depth. In our tree embedding algorithm, we leverage it for providing efficient query access to an approximate metric that allows sampling the tree using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m)$ work. We illustrate the generality and versatility of our techniques by various examples and a number of additional results

Comments on: Interval Type-2 Fuzzy Sets are generalization of Interval-Valued Fuzzy Sets: Towards a Wider view on their relationship

This Letter makes some observations about [2] that further support the distinction between an interval type-2 fuzzy set (IT2 FS) and an interval-valued fuzzy set (IV FS), points out that all operations, methods and systems that have been developed and published about IT2 FSs are, so far, only valid in the special case when IT2 FS = IVFS, and suggests some research opportunities

Bulge mass is king: The dominant role of the bulge in determining the fraction of passive galaxies in the Sloan Digital Sky Survey

We investigate the origin of galaxy bimodality by quantifying the relative role of intrinsic and environmental drivers to the cessation (or `quenching') of star formation in over half a million local Sloan Digital Sky Survey (SDSS) galaxies. Our sample contains a wide variety of galaxies at z=0.02-0.2, with stellar masses of 8 < log(M*/M_sun) < 12, spanning the entire morphological range from pure disks to spheroids, and over four orders of magnitude in local galaxy density and halo mass. We utilise published star formation rates and add to this recent GIM2D photometric and stellar mass bulge + disk decompositions from our group. We find that the passive fraction of galaxies increases steeply with stellar mass, halo mass, and bulge mass, with a less steep dependence on local galaxy density and bulge-to-total stellar mass ratio (B/T). At fixed internal properties, we find that central and satellite galaxies have different passive fraction relationships. For centrals, we conclude that there is less variation in the passive fraction at a fixed bulge mass, than for any other variable, including total stellar mass, halo mass, and B/T. This implies that the quenching mechanism must be most tightly coupled to the bulge. We argue that radio-mode AGN feedback offers the most plausible explanation of the observed trends.Comment: Accepted to MNRAS. 32 pages, 27 figures. [This version is virtually identical to v1

Coarse and uniform embeddings between Orlicz sequence spaces

We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. On the other hand, we present examples which show that sometimes the embeddability is not determined by the values of these indices.Comment: 12 pages. This is the final version. To appear in Mediterr. J. Mat

Practical free-start collision attacks on 76-step SHA-1

In this paper we analyze the security of the compression function of SHA-1 against collision attacks, or equivalently free-start collisions on the hash function. While a lot of work has been dedicated to the analysis of SHA-1 in the past decade, this is the first time that free-start collisions have been considered for this function. We exploit the additional freedom provided by this model by using a new start-from-the-middle approach in combination with improvements on the cryptanalysis tools that have been developed for SHA-1 in the recent years. This results in particular in better differential paths than the ones used for hash function collisions so far. Overall, our attack requires about $2^{50}$ evaluations of the compression function in order to compute a one-block free-start collision for a 76-step reduced version, which is so far the highest number of steps reached for a collision on the SHA-1 compression function. We have developed an efficient GPU framework for the highly branching code typical of a cryptanalytic collision attack and used it in an optimized implementation of our attack on recent GTX 970 GPUs. We report that a single cheap US\$ 350 GTX 970 is sufficient to find the collision in less than 5 days. This showcases how recent mainstream GPUs seem to be a good platform for expensive and even highly-branching cryptanalysis computations. Finally, our work should be taken as a reminder that cryptanalysis on SHA-1 continues to improve. This is yet another proof that the industry should quickly move away from using this function