Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams

Subgraph enumeration is a fundamental task in computer science. Since the number of subgraphs can be large, some enumeration algorithms exploit compressed representations for efficiency. One such representation is the Zero-suppressed Binary Decision Diagram (ZDD). ZDDs can represent the set of subgraphs compactly and support several poly-time queries, such as counting and random sampling. Researchers have proposed efficient algorithms to construct ZDDs representing the set of subgraphs under several constraints, which yield fruitful results in many applications. Recently, Zero-suppressed Sentential Decision Diagrams (ZSDDs) have been proposed as variants of ZDDs. ZSDDs can be smaller than ZDDs when representing the same set of subgraphs. However, efficient algorithms to construct ZSDDs are known only for specific types of subgraphs: matchings and paths. We propose a novel framework to construct ZSDDs representing sets of subgraphs under given constraints. Using our framework, we can construct ZSDDs representing several sets of subgraphs such as matchings, paths, cycles, and spanning trees. We show the bound of sizes of constructed ZSDDs by the branch-width of the input graph, which is smaller than that of ZDDs by the path-width. Experiments show that our methods can construct ZSDDs faster than ZDDs and that the constructed ZSDDs are smaller than ZDDs when representing the same set of subgraphs

Smearing Effect in Plane-Wave Matrix Model

Motivated by the usual D2-D0 system, we consider a configuration composed of flat membrane and fuzzy sphere membrane in plane-wave matrix model, and investigate the interaction between them. The configuration is shown to lead to a non-trivial interaction potential, which indicates that the fuzzy sphere membrane really behaves like a graviton, giant graviton. Interestingly, the interaction is of r^{-3} type rather than r^{-5} type. We interpret it as the interaction incorporating the smearing effect due to the fact that the considered supersymmetric flat membrane should span and spin in four dimensional subspace of plane-wave geometry.Comment: 26 pages; added referenc

Systematic Errors in the Hubble Constant Measurement from the Sunyaev-Zel'dovich effect

The Hubble constant estimated from the combined analysis of the Sunyaev-Zel'dovich effect and X-ray observations of galaxy clusters is systematically lower than those from other methods by 10-15 percent. We examine the origin of the systematic underestimate using an analytic model of the intracluster medium (ICM), and compare the prediction with idealistic triaxial models and with clusters extracted from cosmological hydrodynamical simulations. We identify three important sources for the systematic errors; density and temperature inhomogeneities in the ICM, departures from isothermality, and asphericity. In particular, the combination of the first two leads to the systematic underestimate of the ICM spectroscopic temperature relative to its emission-weighed one. We find that these three systematics well reproduce both the observed bias and the intrinsic dispersions of the Hubble constant estimated from the Sunyaev-Zel'dovich effect.Comment: 26 pages, 7 figures, accepted for publication in ApJ, Minor change

Magnetic coupling at interface of ultrathin Co film and antiferromagnetic Cr₂O₃ (0001) film

The magnetic coupling at the interface of Co and Cr has been investigated using ultrathin Co film on Cr₂O₃ (0001) film, which is expected to be a promising system to show the magnetoelectronic effect. We mainly examined the temperature dependence of magnetization, the exchange bias at different field directions relative to the Cr spin direction, and the temperature dependence of exchange bias. The temperature dependence of magnetization under 50 Oe indicates the collinear coupling of Co spin and Cr spin at the interface. Furthermore, the exchange bias effect is observed in the coupled direction of Co and Cr, namely, parallel to the Cr spin direction. However, the changes in the magnetic behavior with changing field directions and Co thicknesses imply the existence of biquadratic coupling of Co spin and Cr spin, as well. In agreement with the numerical calculation under the coexistence of collinear and biquadratic couplings, the exchange bias field decreases nonmonotonically with increasing temperature.Yu Shiratsuchia, Toshihiro Nakatani, Shin-ichi Kawahara, and Ryoichi Nakatani, Journal of Applied Physics 106, 033903 (2009); https://doi.org/10.1063/1.3182802

Identity Avoidance and Rendaku

One important observation that is made in the past phonological research is that constraints on output structures can both block and trigger phonological processes (i.e., conspiracy: Kisseberth 1970). This paper reports an experiment which shows that an Identity Avoidance constraint (a.k.a. the OCP) both blocks and triggers one phonological process in the same language, namely rendaku in Japanese. Our wug- experiment shows that rendaku is more likely to apply when the two CV moras across a morpheme boundary are identical; i.e. an Identity Avoidance constraint triggers rendaku. The experiment also shows that rendaku is less likely to apply when it would result in two adjacent identical CV moras across a morpheme boundary; i.e. the Identity Avoidance constraint blocks rendaku. These blocking and triggering effects of the general Identity Avoidance constraint on rendaku are a new discovery in Japanese phonology, despite the fact that rendaku has been studied extensively in the previous literature, suggesting the importance of experimentation in phonological research. Moreover, our case study offers experimental confirmation of the OCP conspiracy in natural languages

Extracting Galaxy Cluster Gas Inhomogeneity from X-ray Surface Brightness: A Statistical Approach and Application to Abell 3667

Our previous analysis indicates that small-scale fluctuations in the intracluster medium (ICM) from cosmological hydrodynamic simulations follow the lognormal distribution. In order to test the lognormal nature of the ICM directly against X-ray observations of galaxy clusters, we develop a method of extracting statistical information about the three-dimensional properties of the fluctuations from the two-dimensional X-ray surface brightness. We first create a set of synthetic clusters with lognormal fluctuations. Performing mock observations of these synthetic clusters, we find that the resulting X-ray surface brightness fluctuations also follow the lognormal distribution fairly well. Systematic analysis of the synthetic clusters provides an empirical relation between the density fluctuations and the X-ray surface brightness. We analyze \chandra observations of the galaxy cluster Abell 3667, and find that its X-ray surface brightness fluctuations follow the lognormal distribution. While the lognormal model was originally motivated by cosmological hydrodynamic simulations, this is the first observational confirmation of the lognormal signature in a real cluster. Finally we check the synthetic cluster results against clusters from cosmological hydrodynamic simulations. As a result of the complex structure exhibited by simulated clusters, the empirical relation shows large scatter. Nevertheless we are able to reproduce the true value of the fluctuation amplitude of simulated clusters within a factor of two from their X-ray surface brightness alone. Our current methodology combined with existing observational data is useful in describing and inferring the statistical properties of the three dimensional inhomogeneity in galaxy clusters.Comment: 34 pages, 17 figures, accepted for publication in Ap

Impact of Chandra calibration uncertainties on galaxy cluster temperatures: application to the Hubble Constant

We perform a uniform, systematic analysis of a sample of 38 X-ray galaxy clusters with three different Chandra calibrations. The temperatures change systematically between calibrations. Cluster temperatures change on average by roughly ~6% for the smallest changes and roughly ~13% for the more extreme changes between calibrations. We explore the effects of the changing cluster spectral properties on Sunyaev-Zel'dovich effect (SZE) and X-ray determinations of the Hubble constant. The Hubble parameter changes by +10% and -13% between the current calibration and two previous Chandra calibrations, indicating that changes in the cluster temperature basically explain the entire change in H_0. Although this work focuses on the difference in spectral properties and resultant Hubble parameters between the calibrations, it is intriguing to note that the newer calibrations favor a lower value of the Hubble constant, H_0 ~ 60 km s-1 Mpc-1, typical of results from SZE/X-ray distances. Both galaxy clusters themselves and the details of the instruments must be known precisely to enable reliable precision cosmology with clusters, which will be feasible with combined efforts from ongoing observations and planned missions and observatories covering a wide range of wavelengths.Comment: 18 pages, 5 figures; updated to match published versio

Soft X-ray Transmission Spectroscopy of Warm/Hot Intergalactic Medium with XEUS

We discuss the detectability of Warm/Hot Intergalactic medium (WHIM) via the absorption lines toward bright point sources with a future X-ray satellite mission, XEUS. While we consider bright QSOs as specific examples, the methodology can be applied to bright GRB afterglows. We create mock absorption spectra for bright QSOs (more than 20 QSOs over the all sky) using a light-cone output of a cosmological hydrodynamic simulation. We assume that WHIM is under collisional and photo-ionization equilibrium. If WHIM has a constant metallicity of $Z=0.1Z_\odot$, approximately 2 O{\sc vii} absorption line system with $>3\sigma$ will be detected on average along a random line-of-sight toward bright QSOs up to $z=0.3$ for 30 ksec exposure.Comment: 34 pages, 17 figures. Substantial revision. PASJ, in press (2006, vol.58, August 25 issue