PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.

Cladistic analysis of the suborder Conulariina Miller and Gurley, 1896 (Cnidaria, Scyphozoa; Vendian-Triassic)

Results of a cladistic analysis of the suborder Conulariina Miller and Gurley, 1896, a major extinct (Vendian-Triassic) group of scyphozoan cnidarians, are presented. The analysis sought to test whether the three conulariid subfamilies (Conulariinae Walcott, 1886, Paraconulariinae Sinclair, 1952 and Ctenoconulariinae Sinclair, 1952) recognized in the Treatise on Invertebrate Paleontology ( TIP) are monophyletic. A total of 17 morphological characters were scored for 16 ingroup taxa, namely the genera Archaeoconularia, Baccaconularia, Climacoconus, Conularia, Conulariella, Conularina, Ctenoconularia, Eoconularia, Glyptoconularia, Metaconularia, Notoconularia, Paraconularia, Pseudoconularia, Reticulaconularia, Teresconularia and Vendoconularia. The extant medusozoan taxa Cubozoa, Stauromedusae, Coronatae and Semaeostomeae served as outgroups. Unweighted analysisof the data matrix yielded 1057 trees, and successive weighting analysis resulted in one of the 1057 original trees. The ingroup is monophyletic with two autapomorphies: (1) the quadrate geometry of the oral region; and (2) the presence of a mineralized (phosphatic) periderm. Within the ingroup, the clade (Vendoconularia, Teresconularia, Conularina, Eoconularia) is supported by the sinusoidal longitudinal geometry of the transverse ridges, and the much larger clade (Baccaconularia, Glyptoconularia, Metaconularia, Pseudoconularia, Conularia, Ctenoconularia, Archaeoconularia, Notoconularia, Climacoconus, Paraconularia, Reticulaconularia) is supported by the presence of external tubercles, which, however, were lost in the clade (Notoconularia, Climacoconus, Paraconularia, Reticulaconularia). As proposed by Van Iten et al. (2000), the clade (Notoconularia, Climacoconus, Paraconularia, Reticulaconularia) is supported by the termination and alternation of the transverse ribs in the corner sulcus. The previously recognized subfamilies Conulariinae, Paraconulariinae and Ctenoconulariinae were not recovered from this analysis. The diagnostic features of Conulariinae (continuation of the transverse ornament across the corner sulcus and lack of carinae) and Ctenoconulariinae ( presence of carinae) are symplesiomorphic or homoplastic, and Paraconulariinae is polyphyletic. The families Conulariellidae Kiderlen, 1937 and Conulariopsidae Sugiyama, 1942, also recognized in the TIP, are monogeneric, and since they provide no additional phylogenetic information, should be abandoned.

Lead and aluminum bonding in Pb-Al metaphosphate glasses

The bonding properties of cations in phosphate glasses determine many short- and medium-range structural features in the glass network, hence influencing bulk properties. In this work, Pb-Al-metaphosphate glasses (1 - x)Pb-(PO(3))(2)center dot xAI(PO(3))(3) with 0 <= - x <= 1 were analyzed to determine the effect of the substitution of Pb by Al on the glass structure in the metaphosphate composition. The glass transition temperature and density were measured as a function of the Al concentration. The vibrational and structural properties were probed by Raman spectroscopy and nuclear magnetic resonance of (31)P, (27)Al, and (207)Pb. Aluminum incorporates homogeneously in the glass creating a stiffer and less packed network. The average coordination number for Al decreases from 5.9 to 5.0 as x increases from 0.1 to 1, indicating more covalent Al-O bonds. The coordination number of Pb in these glasses is greater than 8, showing an increasing ionic behavior for compositions richer in Al. A quantitative analysis of the phosphate speciation shows definite trends in the bonding of AlO(n) groups and phosphate tetrahedra. In glasses with x < 0.48, phosphate groups share preferentially only one nonbridging O corner with an AlO(n) coordination polyhedron. For x > 0.48 more than one nonbridging O can be linked to AlO(n) polyhedra. There is no corner sharing of O between AlO(n) and PbO(n) polyhedra nor between AlO(n) themselves throughout the compositional range. The PbO(n) coordination polyhedra show considerable nonbridging O sharing, with each O participating in the coordination sphere of at least two Pb. The bonding preferences determined for Al are consistent with the behavior observed in Na-Al and Ca-Al metaphosphates, indicating this may be a general behavior for ternary phosphate glasses.

A review of the tectonic evolution of the Sunsas belt, SW Amazonian Craton

The Sunsas-Aguapei province (1.20-0.95 Ga), SW Amazonian Craton, is a key area to study the heterogeneous effects of collisional events with Laurentia, which shows evidence of the Grenvillian and Sunsas orogens. The Sunsas orogen, characterized by an allochthonous collisional-type belt (1.11-1.00 Ga), is the youngest and southwestern most of the events recorded along the cratonic fringe. Its evolution occurred after a period of long quiescence and erosion of the already cratonized provinces (>1.30 Ga), that led to sedimentation of the Sunsas and Vibosi groups in a passive margin setting. The passive margin stage was roughly contemporary with intraplate tectonics that produced the Nova Brasilandia proto-oceanic basin (<1.21 Ga), the reactivation of the Ji-Parana shear zone network (1.18-1.12 Ga) and a system of aborted rifts that evolved to the Huanchaca-Aguapei basin (1.17-1.15 Ga). The Sunsas belt is comprised by the metamorphosed Sunsas and Vibosi sequences, the Rincon del Tigre mafic-ultramafic sill and granitic intrusive suites. The latter rocks yield epsilon(Nd(t)) signatures (-0.5 to -4.5) and geochemistry (S,1, A-types) suggesting their origin associated with a continental arc setting. The Sunsas belt evolution is marked by ""tectonic fronts"" with sinistral offsets that was active from c. 1.08 to 1.05 Ga, along the southern edge of the Paragua microcontinent where K/Ar ages (1.27-1.34 Ga) and the Huanchaca-Aguapei flat-lying cover attest to the earliest tectonic stability at the time of the orogen. The Sunsas dynamics is coeval with inboard crustal shortening, transpression and magmatism in the Nova Brasilandia belt (1.13-1.00 Ga). Conversely, the Aguapei aulacogen (0.96-0.91 Ga) and nearby shear zones (0.93-0.91 Ga) are the late tectonic offshoots over the cratonic margin. The post-tectonic to anorogenic stages took place after ca. 1.00 Ga, evidenced by the occurrences of intra-plate A-type granites, pegmatites, mafic dikes and sills, as well as of graben basins. Integrated interpretation of the available data related to the Sunsas orogen supports the idea that the main nucleus of Rodinia incorporated the terrains forming the SW corner of Amazonia and most of the Grenvillian margin, as a result of two independent collisional events, as indicated in the Amazon region by the Ji-Parana shear zone event and the Sunsas belt, respectively. (C) 2009 Elsevier Ltd. All rights reserved.

THE RIO APA CRATON IN MATO GROSSO DO SUL (BRAZIL) AND NORTHERN PARAGUAY: GEOCHRONOLOGICAL EVOLUTION, CORRELATIONS AND TECTONIC IMPLICATIONS FOR RODINIA AND GONDWANA

The Rio Apa cratonic fragment crops out in Mato Grosso do Sul State of Brazil and in northeastern Paraguay. It comprises Paleo-Mesoproterozoic medium grade metamorphic rocks, intruded by granitic rocks, and is covered by the Neoproterozoic deposits of the Corumbi and Itapocurni Groups. Eastward it is bound by the southern portion of the Paraguay belt. In this work, more than 100 isotopic determinations, including U-Pb SHRIMP zircon ages, Rb-Sr and Sm-Nd whole-rock determinations, as well as K-Ar and Ar-Ar mineral ages, were reassessed in order to obtain a complete picture of its regional geological history. The tectonic evolution of the Rio Apa Craton starts with the formation of a series of magmatic arc complexes. The oldest U-Pb SHRIMP zircon age comes from a banded gneiss collected in the northern part of the region, with an age of 1950 +/- 23 Ma. The large granitic intrusion of the Alumiador Batholith yielded a U-Pb zircon age of 1839 +/- 33 Ma, and from the southeastern part of the area two orthogneisses gave zircon U-Pb ages of 1774 +/- 26 Ma and 1721 +/- 25 Ma. These may be coeval with the Alto Terere metamorphic rocks of the northeastern corner, intruded in their turn by the Baia das Garcas granitic rocks, one of them yielding a zircon U-Pb age of 1754 +/- 49 Ma. The original magmatic protoliths of these rocks involved some crustal component, as indicated by the Sm-Nd TDm model ages, between 1.9 and 2.5 Ga. Regional Sr isotopic homogenization, associated with tectonic deformation and medium-grade metamorphism occurred at approximately 1670 Ma, as suggested by Rb-Sr whole rock reference isochrons. Finally, at 1300 Ma ago, the Ar work indicates that the Rio Apa Craton was affected by widespread regional heating, when the temperature probably exceeded 350 degrees C. Geographic distribution, age and isotopic signature of the fithotectonic units suggest the existence of a major suture separating two different tectonic domains, juxtaposed at about 1670 Ma. From that time on, the unified Rio Apa continental block behaved as one coherent and stable tectonic unit. It correlates well with the SW corner of the Amazonian Craton, where the medium-grade rocks of the Juruena-Rio Negro tectonic province, with ages between 1600 and 1780 Ma, were reworked at about 1300 Ma. Looking at the largest scale, the Rio Apa Craton is probably attached to the larger Amazonian Craton, and the actual configuration of southwestern South America is possibly due to a complex arrangement of allochthonous blocks such as the Arequipa, Antofalla and Pampia, with different sizes, that may have originated as disrupted parts of either Laurentia or Amazonia, and were trapped during later collisions of these continental masses.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.