Topological multi-contour decomposition for image analysis and image retrieval

Successful classification, information retrieval and image analysis tools are intimately related with the quality of the features employed in the process. Pixel intensities, color, texture and shape are, generally, the basis from which most of the features are Computed and used in such fields. This papers presents a novel shape-based feature extraction approach where an image is decomposed into multiple contours, and further characterized by Fourier descriptors. Unlike traditional approaches we make use of topological knowledge to generate well-defined closed contours, which are efficient signatures for image retrieval. The method has been evaluated in the CBIR context and image analysis. The results have shown that the multi-contour decomposition, as opposed to a single shape information, introduced a significant improvement in the discrimination power. (c) 2008 Elsevier B.V. All rights reserved,

Topological interactions in warped extra dimensions

Topological interactions will be generated in theories with compact extra dimensions where fermionic chiral zero modes have different localizations. This is the case in many warped extra dimension models where the right-handed top quark is typically localized away from the left-handed one. Using deconstruction techniques, we study the topological interactions in these models. These interactions appear as trilinear and quadrilinear gauge boson couplings in low energy effective theories with three or more sites, as well as in the continuum limit. We derive the form of these interactions for various cases, including examples of Abelian, non-Abelian and product gauge groups of phenomenological interest. The topological interactions provide a window into the more fundamental aspects of these theories and could result in unique signatures at the Large Hadron Collider, some of which we explore.

Topological invariants of isolated complete intersection curve singularities

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Topological triangle characterization with application to object detection from images

A novel mathematical framework inspired on Morse Theory for topological triangle characterization in 2D meshes is introduced that is useful for applications involving the creation of mesh models of objects whose geometry is not known a priori. The framework guarantees a precise control of topological changes introduced as a result of triangle insertion/removal operations and enables the definition of intuitive high-level operators for managing the mesh while keeping its topological integrity. An application is described in the implementation of an innovative approach for the detection of 2D objects from images that integrates the topological control enabled by geometric modeling with traditional image processing techniques. (C) 2008 Published by Elsevier B.V.

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l; l) = (2; 5); (4; 7); and (6; 8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l; l) = (10; 8) and (2; 9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l; l) = (10; 5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy`s plane, which may be an indication of residual contaminations in the full-and cut-sky maps.

Weak antilocalization in HgTe quantum wells near a topological transition

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.

Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly Influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network Sampling Therefore, it becomes critical to devise effective means for sound estimation of net work topological and dynamical properties will le avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential IS Illustrated with respect to two real-world networks. namely bone canals and air transportation (C) 2009 Elsevier B.V. All rights reserved.

Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

Contrasting magmatic signatures in the Rairakhol and Koraput alkaline complexes, Eastern Ghats belt, India

The relation between alkaline magmatism and tectonism has been a contentious issue, particularly for the Precambrian continental regions. Alkaline complexes at the southwestern margin of Eastern Ghats belt, India, have been interpreted as rift-valley magmatism. However, those complexes occurring in granulite ensemble in the interior segments of the Eastern Ghats belt could not possibly be related to the rift-system, assumed for the western margin of the Eastern Ghats belt. Koraput complex was emplaced in a pull-apart structure, dominated by magmatic fabrics and geochemically similar to a fractionated alkaline complex, compatible with an alkalibasalt series. Rairakhol complex, on the other hand, shows dominantly solid-state deformation fabrics and geochemically similar to a fractionated calc-alkaline suite. Isotopic data for the Koraput complex indicate ca. 917 Ma alkaline magmatism from a depleted mantle source and postcrystalline thermal overprint at ca. 745 Ma, also recorded from sheared metapelitic country rocks. The calc-alkaline magmatism of the Rairakhol complex occurred around 938 Ma, from an enriched mantle source, closely following Grenvillian granulite facies imprint in the charnockitic country rocks.

The Guarguaraz Complex and the Neoproterozoic-Cambrian evolution of southwestern Gondwana: Geochemical signatures and geochronological constraints

The Guarguaraz Complex, in western Argentina, comprises a metasedimentary assemblage, associated with mafic sills and ultramafic bodies intruded by basaltic dikes, which are interpreted as Ordovician dismembered ophiolites. Two kinds of dikes are recognized, a group associated with the metasediments and the other ophiolite-related. Both have N-MORB signatures, with epsilon(Nd) between +3.5 and +8.2, indicating a depleted source, and Grenville model ages between 0.99 and 1.62 Ga. A whole-rock Sm-Nd isochron yielded an age of 655 +/- 76 Ma for these mafic rocks, which is compatible with cianobacteria and acritarchae recognized in the clastic metasedimentary platform sequences, that indicate a Neoproterozoic (Vendian)-Cambrian age of deposition. The Guarguaraz metasedimentary-ophiolitic complex represents, therefore, a remnant of an oceanic basin developed to the west of the Grenville-aged Cuyania terrane during the Neoproterozoic. The southernmost extension of these metasedimentary sequences in Cordon del Portillo might represent part of this platform and not fragments of the Chilenia terrane. An extensional event related to the fragmentation of Rodinia is represented by the mafic and ultramafic rocks. The Devonian docking of Chilenia emplaced remnants of ocean floor and slices of the Cuyania terrane (Las Yaretas Gneisses) in tectonic contact with the Neoproterozoic metasediments, marking the Devonian western border of Gondwana. (C) 2009 Elsevier Ltd. All rights reserved.

Nd and Pb isotope signatures on the Southeastern South American upper margin: Implications for sediment transport and source rocks

Neodymium and lead isotope values in sediment samples were used to interpret sediment transport and source rocks on the Southeastern South American upper margin. The sediments of the Argentinian margin exhibit an average epsilon(Nd) value of -1.9, indicating the influence of the Andean rocks as sediment sources. Sediments from the Rio de La Plata estuary show an average epsilon(Nd) value of -9.6 which is similar to that of the Southern Brazilian Upper Margin. Finally, sediments of Southeastern Brazil, which are associated with the transport of the Brazil Current exhibit an average epsilon(Nd) of -13.0. The Pb isotope signatures also confirm the differentiation of source rocks in the sedimentation of the study area. In addition, Pb isotopes helped to establish the extent of the influence of the Rio de La Plata on the sedimentation of the Southern Brazilian margin. In terms of Pb isotopes the sediments from the Rio de La Plata estuary and Southern Brazil are more radiogenic than those of Southeastem Brazil and the Argentinian margin. (c) 2007 Elsevier B.V. All rights reserved.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Conserved tissue expression signatures of intronic noncoding RNAs transcribed from human and mouse loci

It has been postulated that noncoding RNAs (ncRNAs) are involved in the posttranscriptional control of gene expression, and may have contributed to the emergence of the complex attributes observed in mammalians. We show here that the complement of ncRNAs expressed from intronic regions of the human and mouse genomes comprises at least 78,147 and 39,660 transcriptional units, respectively. To identify conserved intronic sequences expressed in both humans and mice, we used custom-designed human cDNA microarrays to separately interrogate RNA from mouse and human liver, kidney, and prostate tissues. An overlapping tissue expression signature was detected for both species, comprising 198 transcripts; among these, 22 RNAs map to intronic regions with evidence of evolutionary conservation in humans and mice. Transcription of selected human-mouse intronic ncRNAs was confirmed using strand-specific RT-PCR. Altogether, these results support an evolutionarily conserved role of intronic ncRNAs in human and mouse, which are likely to be involved in the fine tuning of gene expression regulation in different mammalian tissues. (C) 2008 Elsevier Inc. All rights reserved.