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Topological Structure (topological + structure)
Selected AbstractsA study on two-stage self-organizing map and its application to clustering problemsELECTRICAL ENGINEERING IN JAPAN, Issue 1 2007Satoru Kato Abstract This paper presents a two-stage self-organizing map algorithm that we call two-stage SOM which combines Kohonen's basic SOM (BSOM) and Aoki's SOM with threshold operation (THSOM). In the first stage of two-stage SOM, we use BSOM algorithm in order to acquire topological structure of input data, and then we apply THSOM algorithm so that inactivated code vectors move to appropriate region reflecting the distribution of the input data. Furthermore, we show that two-stage SOM can be applied to clustering problems. Some experimental results reveal that two-stage SOM is effective for clustering problems in comparison with conventional methods. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(1): 46,53, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20268 [source] On morphometric properties of basins, scale effects and hydrological responseHYDROLOGICAL PROCESSES, Issue 1 2003Roger Moussa Abstract One of the important problems in hydrology is the quantitative description of river system structure and the identification of relationships between geomorphological properties and hydrological response. Digital elevation models (DEMs) generally are used to delineate the basin's limits and to extract the channel network considering pixels draining an area greater than a threshold area S. In this paper, new catchment shape descriptors, the geometric characteristics of an equivalent ellipse that has the same centre of gravity, the same principal inertia axes, the same area and the same ratio of minimal inertia moment to maximal inertia moment as the basin, are proposed. They are applied in order to compare and classify the structure of seven basins located in southern France. These descriptors were correlated to hydrological properties of the basins' responses such as the lag time and the maximum amplitude of a geomorphological unit hydrograph calculated at the basin outlet by routing an impulse function through the channel network using the diffusive wave model. Then, we analysed the effects of the threshold area S on the topological structure of the channel network and on the evolution of the source catchment's shape. Simple models based on empirical relationships between the threshold S and the morphometric properties were established and new catchment shape indexes, independent of the observation scale S, were defined. This methodology is useful for geomorphologists dealing with the shape of source basins and for hydrologists dealing with the problem of scale effects on basin topology and on relationships between the basin morphometric properties and the hydrological response. Copyright © 2002 John Wiley & Sons, Ltd. [source] Nanocarbon materials: probing the curvature and topology effects using phonon spectraJOURNAL OF RAMAN SPECTROSCOPY, Issue 9 2009Sanju Gupta Abstract Much has been learned from the use of resonance Raman spectroscopy and high-resolution transmission electron microscopy techniques about the micro-/nanoscopic structure of various nanostructured carbons. However, they still possess some features that are not entirely understood particularly in terms of topological characteristics, which go beyond making a distinction with just the geometrical structure at nanoscale. To effectively utilize the potential of these materials for technological needs, understanding both the geometrical and topological structure and perhaps relating these attributes to physical (optical/electronic, lattice vibrational) properties become indispensable. Here, we make an attempt to describe the differences between various nanostructures and provide geometrical and topological property assessment semiquantitatively by monitoring the phonon spectra using resonance Raman spectroscopy thereby also capturing the electronic spectra. We elucidate the notion of global topology and curvature for a range of technologically important nanoscale carbons including tubular (single-, double- and multiwalled nanotubes, peapod), spherical (hypo- and hyperfullerenes, onion-like carbon) and complex (nanocones, nanohorns, nanodisks and nanorings) geometries. To demonstrate the proof-of-concept, we determined the variation in the prominent Raman bands of the respective materials, represented as D, G and D* (the overtone of D) bands, as a possible topological or curvature trend due to their sensitivity toward structural modification. The latter arises from local topological defects such as pentagons giving rise to curved nanocarbons. In this study, we provide systematics of their variation with respect to their geometric forms and compare with highly oriented pyrolytic graphite and monolayer graphene since the nanocarbons discussed are their derivatives. Once established, this knowledge will provide a powerful machinery to understand newer nanocarbons and indeed point to an unprecedented emergent paradigm of global topology/curvature , property , functionality relationship. We emphasize that these concepts are applicable to other topologically distinct nanomaterials, which include boron-nitride (BN) nanotubes and nanotori, helical gold nanotubes and Möbius conjugated organics. Copyright © 2009 John Wiley & Sons, Ltd. [source] Exchange of conserved quantities, shock loci and Riemann problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2001Michael Sever Systems of conservation laws admitting extensions, such as entropy density/flux functions, generate related systems obtained by exchanging the extension with one of the constituent equations. Often if not always, the smooth solutions of the two systems coincide, and weak solutions of one system containing only small discontinuities are approximate weak solutions of the other. The adiabatic approximation for the Euler system illustrates the utility of this procedure. Such an exchange of conserved quantities preserves hyperbolicity and genuine non-linearity in the sense of Lax. On the other hand, the topological structure of the shock locus of a point in phase space and the solvability of Riemann problems in the large can be strongly affected. A discussion of when and how this occurs is given here. In this paper the exchange of conserved quantities is conveniently described by a simple homotopy in an extended version of the usual ,symmetric variables'. A dynamical system in phase space is constructed, the trajectories of which describe the Hugoniot locus of a fixed point in phase space at each state of the homotopy. The appearance of critical points for this dynamical system is identified with the alteration of the topological structure of the Hugoniot locus by the exchange of conserved quantities. Copyright © 2001 John Wiley & Sons, Ltd. [source] On topological properties of ultraproducts of finite setsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2005Gábor Sági Abstract In [3] a certain family of topological spaces was introduced on ultraproducts. These spaces have been called ultratopologies and their definition was motivated by model theory of higher order logics. Ultratopologies provide a natural extra topological structure for ultraproducts. Using this extra structure in [3] some preservation and characterization theorems were obtained for higher order logics. The purely topological properties of ultratopologies seem interesting on their own right. We started to study these properties in [2], where some questions remained open. Here we present the solutions of two such problems. More concretely we show 1. that there are sequences of finite sets of pairwise different cardinalities such that in their certain ultraproducts there are homeomorphic ultratopologies and 2. if A is an infinite ultraproduct of finite sets, then every ultratopology on A contains a dense subset D such that |D| < |A|. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Untangling intracellular DNA topologyMOLECULAR MICROBIOLOGY, Issue 4 2004Olivier Espeli Summary The biochemical steps by which bacterial topoisomerases alter the topology of DNA are well known. However, it has been a more vexing task to establish physiological roles and sites of action of the different topoisomerases within the context of the bacterial cell cycle. This difficulty can be attributed in part to the redundancy among the activities of the different enzymes. In this microreview, we will focus on recent progress in understanding the topological structure of the chromosome, analysis of topoisomerase mechanism in single-molecule assays and recent data on the regulation and integration of topoisomerase activity within the cell cycle that have all brought a new perspective to the action of topoisomerases in the bacterial cell. [source] Protein interaction networks of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster: Large-scale organization and robustnessPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 2 2006Dong Li Abstract High-throughput screens have begun to reveal protein interaction networks in several organisms. To understand the general properties of these protein interaction networks, a systematic analysis of topological structure and robustness was performed on the protein interaction networks of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster. It shows that the three protein interaction networks have a scale-free and high-degree clustering nature as the consequence of their hierarchical organization. It also shows that they have the small-world property with similar diameter at 4,5. Evaluation of the consequences of random removal of both proteins and interactions from the protein interaction networks suggests their high degree of robustness. Simulation of a protein's removal shows that the protein interaction network's error tolerance is accompanied by attack vulnerability. These fundamental analyses of the networks might serve as a starting point for further exploring complex biological networks and the coming research of "systems biology". [source] A new look at the quantum mechanics of the harmonic oscillatorANNALEN DER PHYSIK, Issue 7-8 2007H.A. Kastrup Abstract In classical mechanics the harmonic oscillator (HO) provides the generic example for the use of angle and action variables and I > 0 which played a prominent role in the "old" Bohr-Sommerfeld quantum theory. However, already classically there is a problem which has essential implications for the quantum mechanics of the (,,I)-model for the HO: the transformation is only locally symplectic and singular for (q,p) = (0,0). Globally the phase space {(q,p)} has the topological structure of the plane ,2, whereas the phase space {(,,I)} corresponds globally to the punctured plane ,2 -(0,0) or to a simple cone with the tip deleted. From the properties of the symplectic transformations on that phase space one can derive the functions h0 = I, h1 = Icos , and h2 = - Isin , as the basic coordinates on {(,,I)}, where their Poisson brackets obey the Lie algebra of the symplectic group of the plane. This implies a qualitative difference as to the quantum theory of the phase space {(,,I)} compared to the usual one for {(q,p)}: In the quantum mechanics for the (,,I)-model of the HO the three hj correspond to the self-adjoint generators Kj, j = 0,1,2, of certain irreducible unitary representations of the symplectic group or one of its infinitely many covering groups, the representations being parametrized by a (Bargmann) index k > 0. This index k determines the ground state energy of the (,,I)-Hamiltonian . For an m -fold covering the lowest possible value for k is k = 1/m, which can be made arbitrarily small by choosing m accordingly! This is not in contradiction to the usual approach in terms of the operators Q and P which are now expressed as functions of the Kj, but keep their usual properties. The richer structure of the Kj quantum model of the HO is "erased" when passing to the simpler (Q,P)-model! This more refined approach to the quantum theory of the HO implies many experimental tests: Mulliken-type experiments for isotopic diatomic molecules, experiments with harmonic traps for atoms, ions and BE-condensates, with charged HOs in external electric fields and the (Landau) levels of charged particles in external magnetic fields, with the propagation of light in vacuum, passing through strong external electric or magnetic fields. Finally it may lead to a new theoretical estimate for the quantum vacuum energy of fields and its relation to the cosmological constant. [source] A double-layered zinc(II) coordination polymer with the ligand 3,5-bis(carboxylatomethoxy)benzoateACTA CRYSTALLOGRAPHICA SECTION C, Issue 1 2009Zhong-Min Cen In the title compound, poly[hexaaquabis[,4 -3,5-bis(carboxylatomethoxy)benzoato]trizinc(II)], [Zn3(C11H7O8)2(H2O)6]n, there are two crystallographically distinct ZnII cations which are bridged by polycarboxylate ligands in a ,4 -bridging mode. A pair of ligands bridges adjacent Zn atoms to give centrosymmetric dimetal building blocks which act as four-connected nodes to be further interlinked into a two-dimensional double-layered framework with (4,4) topology. Other Zn atoms, lying on inversion centres, occupy the cavities of this topological structure. This submission shows a versatile polycarboxylate ligand with rigid and flexible functional groups, the co-operation and complementarity of which would meet the coordination requirements of a variety of topological structures. [source] Dirichlet duality and the nonlinear Dirichlet problemCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2009F. Reese Harvey We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F(Hess u) = 0 on a smoothly bounded domain , , ,n. In our approach the equation is replaced by a subset F , Sym2(,n) of the symmetric n × n matrices with ,F , {F = 0}. We establish the existence and uniqueness of continuous solutions under an explicit geometric "F -convexity" assumption on the boundary ,,. We also study the topological structure of F -convex domains and prove a theorem of Andreotti-Frankel type. Two key ingredients in the analysis are the use of "subaffine functions" and "Dirichlet duality." Associated to F is a Dirichlet dual set F, that gives a dual Dirichlet problem. This pairing is a true duality in that the dual of F, is F, and in the analysis the roles of F and F, are interchangeable. The duality also clarifies many features of the problem including the appropriate conditions on the boundary. Many interesting examples are covered by these results including: all branches of the homogeneous Monge-Ampčre equation over ,, ,, and ,; equations appearing naturally in calibrated geometry, Lagrangian geometry, and p -convex Riemannian geometry; and all branches of the special Lagrangian potential equation. © 2008 Wiley Periodicals, Inc. [source] Prediction of chromatographic relative retention time of polychlorinated biphenyls from the molecular electronegativity distance vectorJOURNAL OF SEPARATION SCIENCE, JSS, Issue 2 2006Shu-Shen Liu Abstract Using the molecular electronegativity distance vector (MEDV) descriptors derived directly from the molecular topological structures, the gas chromatographic relative retention times (RRTs) of 209 polychlorinated biphenyls (PCBs) on the SE-54 stationary phase were predicted. A five-variable regression equation with the correlation coefficient of 0.9964 and the root mean square errors of 0.0152 was developed. The descriptors included in the equation represent degree of chlorination (nCl), nonortho index (Ino), and interactions between three pairs of atom types, i. e., atom groups ,C= and ,C=, ,C= and >C=, ,C= and ,Cl. It has been proved that the retention times of all 209 PCB congeners can be accurately predicted as long as there are more than 50 calibration compounds. In the same way, the MEDV descriptors are also used to develop the five- or six-variable models of RRTs of PCBs on other 18 stationary phases and the correlation coefficients in both modeling stage and LOO cross-validation step are not lower than 0.99 except two models. [source] A double-layered zinc(II) coordination polymer with the ligand 3,5-bis(carboxylatomethoxy)benzoateACTA CRYSTALLOGRAPHICA SECTION C, Issue 1 2009Zhong-Min Cen In the title compound, poly[hexaaquabis[,4 -3,5-bis(carboxylatomethoxy)benzoato]trizinc(II)], [Zn3(C11H7O8)2(H2O)6]n, there are two crystallographically distinct ZnII cations which are bridged by polycarboxylate ligands in a ,4 -bridging mode. A pair of ligands bridges adjacent Zn atoms to give centrosymmetric dimetal building blocks which act as four-connected nodes to be further interlinked into a two-dimensional double-layered framework with (4,4) topology. Other Zn atoms, lying on inversion centres, occupy the cavities of this topological structure. This submission shows a versatile polycarboxylate ligand with rigid and flexible functional groups, the co-operation and complementarity of which would meet the coordination requirements of a variety of topological structures. [source] Two pseudo-polymorphic copper,benzene-1,2,4,5-tetracarboxylate complexesACTA CRYSTALLOGRAPHICA SECTION C, Issue 6 2007Jian-Hai Luo Two pseudo-polymorphic polymers, poly[ethylenediammonium [[aquacopper(II)]-,4 -benzene-1,2,4,5-tetracarboxylato] dihydrate], {(C2H10N2)[Cu(C10H2O8)(H2O)]·2H2O}n, (I), and poly[ethylenediammonium [copper(II)-,4 -benzene-1,2,4,5-tetracarboxylato] 2.5-hydrate], {(C2H10N2)[Cu(C10H2O8)]·2.5H2O}n, (II), contain two-dimensional anionic layers, ethylenediammonium (H2en) cations acting as counter-ions and free water molecules. Although the topological structures of the two anionic layers are homologous, the coordination environments of the CuII centres are different. In (I), the CuII centre, sitting on a general position, has a square-pyramidal environment. The two independent benzene-1,2,4,5-tetracarboxylate (btc) anions rest on centres of inversion. The CuII cation in (II) is located on a twofold axis in a square-planar coordination. The H2en cation is on an inversion centre and the btc ligand is split by a mirror plane. Extensive hydrogen-bonding interactions between the complexes, H2en cations and water molecules lead to the formation of three-dimensional supramolecular structures. [source] | ||||||||||||||||