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We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm computes a stratification $\pi$ of the poset $P$ of simplices of a simplicial complex $K$, such that for each strata $P_{\pi=i} \subset P$, $P_{\pi=i}$ is maximal among all open subposets $U \subset \overline{P_{\pi=i}}$ in its closure such that the restriction of the local $\mathbb{Z}$-homology sheaf of $\overline{P_{\pi=i}}$ to $U$ is locally constant. Passage to the localization of $P$ dictated by $\pi$ then attaches a canonical stratified homotopy type to $K$. Using $\infty$-categorical methods, we first prove that the proposed algorithm correctly computes the canonical stratification of a simplicial complex; along the way, we prove a few general results about sheaves on posets and the homotopy types of links that may be of independent interest. We then present a pseudocode implementation of the algorithm, with special focus given to the case of dimension $\leq 3$, and show that it runs in polynomial time. In particular, an $n$-dimensional simplicial complex with size $s$ and $n\leq3$ can be processed in O($s^2$) time or O($s$) given one further assumption on the structure. Processing Delaunay triangulations of $2$-spheres and $3$-balls provides experimental confirmation of this linear running time., Comment: 36 pages. v3: added reference to Aoki's work on hypercomplete sheaves, otherwise minor changes in response to referee report

In this paper we demonstrate the methodology for parallelizing the computation of large one-dimensional discrete fast Fourier transforms (DFFTs) on multi-core Intel Xeon processors. DFFTs based on the recursive Cooley-Tukey method have to control cache utilization, memory bandwidth and vector hardware usage, and at the same time scale across multiple threads or compute nodes. Our method builds on single-threaded Intel Math Kernel Library (MKL) implementation of DFFT, and uses the Intel Cilk Plus framework for thread parallelism. We demonstrate the ability of Intel Cilk Plus to handle parallel recursion with nested loop-centric parallelism without tuning the code to the number of cores or cache metrics. The result of our work is a library called EFFT that performs 1D DFTs of size 2^N for N>=21 faster than the corresponding Intel MKL parallel DFT implementation by up to 1.5x, and faster than FFTW by up to 2.5x. The code of EFFT is available for free download under the GPLv3 license. This work provides a new efficient DFFT implementation, and at the same time demonstrates an educational example of how computer science problems with complex parallel patterns can be optimized for high performance using the Intel Cilk Plus framework., Comment: 17 pages. Submitted to Parallel Computing

We performed deep K'-band imaging observations of 2 massive clusters, MS 0451.6-0305 at z = 0.55 and MS 0440.5+0204 at z = 0.19, for searching counterparts of the faint sub-mm sources behind these clusters, which would provide one of the deepest extremely red object(ERO) samples. Comparing our near-infrared images with optical images taken by the Hubble Space Telescope and by the Subaru Telescope, we identified 13 EROs in these fields. The sky distributions of EROs are consistent with the previous results, that there is a sign of strong clustering among detected EROs. Also, the surface density with corrected lensing amplification factors in both clusters are in good agreement with that derived from previous surveys. We found 7 EROs and 3 additional very red objects in a small area (\sim 0.6 arcmin^2) of the MS 0451.6-0305 field around an extended SCUBA source. Many of their optical and near-infrared colors are consistent with dusty star-forming galaxies at high redshifts(z \sim 1.0-4.0), and they may be constituting a cluster of dusty starburst galaxies and/or lensed star-forming galaxies at high redshift. Their red J-K' colors and faint optical magnitudes suggest they are relatively old massive stellar systems with ages(>300 Mega years) suffering from dust obscuration. We also found a surface-density enhancement of EROs around the SCUBA source in the MS 0440.5+0204 field., Comment: 19 pages, 11 figures, Latex(using pasj00.cls). To be published in PASJ vol 55, No. 4(Aug 2003)

We present new optical images ($B$, $V$, and H$\alpha$) of the archetypical starburst/superwind galaxy M82 obtained with the 8.2 m Subaru Telescope to reveal new detailed structures of the superwind-driven nebula and the high-latitude dark lanes. The emission-line nebula is decomposed into (1) a ridge-dominated component comprising numerous filament/loop sub-structures whose overall morphology appears as a pair of narrow cylinders, and (2) a diffuse component extended over much wider opening angle from the nucleus. We suggest that these two components have different origins. The ridge-dominated component appears as a pair of cylinders rather than a pair of cones. Since this morphological property is similar to that of hot plasma probed by soft X-ray, this component seems to surround the hot plasma. On the other hand, the diffuse component may arise from dust grains which scatter stellar light from the galaxy. Since inner region of this component is seen over the prominent ^^ ^^ X"-shaped dark lanes streaming out from the nuclear region and they can be reproduced as a conical distribution of dust grains, there seems to be a dusty cold outflow as well as the hot one probed by soft X-ray and shock-excited optical emission lines. If this is the case, the presence of such high-latitude dust grains implies that neutral gaseous matter is also blown out during the course of the superwind activity., Comment: 12 pages, 6 figures. Accepted for publication in PASJ