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Topological Properties (topological + property)
Selected AbstractsTopological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM)ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Jeanette Netzel Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T, 20,K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (lmax = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C,C, C,N and C,O bonds, and for hydrogen bonds together with covalent C,H and N,H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. [source] Topological properties and evolution of granules and porulesASTRONOMISCHE NACHRICHTEN, Issue 4 2003L. Pravdjuk No abstract is available for this article. [source] Brain networks: Graph theoretical analysis and development modelsINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 2 2010Myoung Won Cho Abstract A trendy method to understand the brain is to make a map representing the structural network of the brain, also known as the connectome, on the scale of a brain region. Indeed analysis based on graph theory provides quantitative insights into general topological principles of brain network organization. In particular, it is disclosed that typical brain networks share the topological properties, such as small-world and scale-free, with many other complex networks encountered in nature. Such topological properties are regarded as characteristics of the optimal neural connectivity to implement efficient computation and communication; brains with disease or abnormality show distinguishable deviations in the graph theoretical analysis. Considering that conventional models in graph theory are, however, not adequate for direct application to the neural system, we also discuss a model for explaining how the neural connectivity is organized. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 108,116, 2010 [source] On open-set lattices and some of their applications in semanticsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 12 2003Mouw-Ching Tjiok In this article, we present the theory of Kripke semantics, along with the mathematical framework and applications of Kripke semantics. We take the Kripke-Sato approach to define the knowledge operator in relation to Hintikka's possible worlds model, which is an application of the semantics of intuitionistic logic and modal logic. The applications are interesting from the viewpoint of agent interactives and process interaction. We propose (i) an application of possible worlds semantics, which enables the evaluation of the truth value of a conditional sentence without explicitly defining the operator "," (implication), through clustering on the space of events (worlds) using the notion of neighborhood; and (ii) a semantical approach to treat discrete dynamic process using Kripke-Beth semantics. Starting from the topological approach, we define the measure-theoretical machinery, in particular, we adopt the methods developed in stochastic process,mainly the martingale,to our semantics; this involves some Boolean algebraic (BA) manipulations. The clustering on the space of events (worlds), using the notion of neighborhood, enables us to define an accessibility relation that is necessary for the evaluation of the conditional sentence. Our approach is by taking the neighborhood as an open set and looking at topological properties using metric space, in particular, the so-called ,-ball; then, we can perform the implication by computing Euclidean distance, whenever we introduce a certain enumerative scheme to transform the semantic objects into mathematical objects. Thus, this method provides an approach to quantify semantic notions. Combining with modal operators Ki operating on E set, it provides a more-computable way to recognize the "indistinguishability" in some applications, e.g., electronic catalogue. Because semantics used in this context is a local matter, we also propose the application of sheaf theory for passing local information to global information. By looking at Kripke interpretation as a function with values in an open-set lattice ,,U, which is formed by stepwise verification process, we obtain a topological space structure. Now, using the measure-theoretical approach by taking the Borel set and Borel function in defining measurable functions, this can be extended to treat the dynamical aspect of processes; from the stochastic process, considered as a family of random variables over a measure space (the probability space triple), we draw two strong parallels between Kripke semantics and stochastic process (mainly martingales): first, the strong affinity of Kripke-Beth path semantics and time path of the process; and second, the treatment of time as parametrization to the dynamic process using the technique of filtration, adapted process, and progressive process. The technique provides very effective manipulation of BA in the form of random variables and ,-subalgebra under the cover of measurable functions. This enables us to adopt the computational algorithms obtained for stochastic processes to path semantics. Besides, using the technique of measurable functions, we indeed obtain an intrinsic way to introduce the notion of time sequence. © 2003 Wiley Periodicals, Inc. [source] Intramolecular hydrogen bond in 3-imino-propenylamine isomers: AIM and NBO studiesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2010H. Raissi Abstract The molecular structure and intramolecular hydrogen bond energy of 18 conformers of 3-imino-propenyl-amine were investigated at MP2 and B3LYP levels of theory using the standard 6-311++G** basis set. The atom in molecules or AIM theory of Bader, which is based on the topological properties of the electron density (,), was used additionally and the natural bond orbital (NBO) analysis was also carried out. Furthermore calculations for all possible conformations of 3-imino-propenyl-amin in water solution were also carried out at B3LYP/6-311++G** and MP2/6-311++G** levels of theory. The calculated geometrical parameters and conformational analyses in gas phase and water solution show that the imine,amine conformers of this compound are more stable than the other conformers. B3LYP method predicts the IMA-1 as global minimum. This stability is mainly due to the formation of a strong NH···N intramolecular hydrogen bond, which is assisted by ,-electrons resonance, and this ,-electrons are established by NH2 functional group. Hydrogen bond energies for all conformers of 3-imino-propenyl-amine were obtained from the related rotamers methods. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Synthesis and vibrational analysis of N-(2,-Furyl)-ImidazoleJOURNAL OF RAMAN SPECTROSCOPY, Issue 8 2009A. E. Ledesma Abstract The N-(2,-furyl)-imidazole (1) has been prepared and characterized using infrared, Raman and multidimensional nuclear magnetic resonance spectroscopies. Theoretical calculations have been carried out by employing the Density Functional Theory (DFT) method, in order to optimize the geometry of their two conformers in the gas phase and to support the assignments of the vibrational bands of 1 to their normal modes. For a complete assignment of the compound, DFT calculations were combined with Scaled Quamtum Mecanic Force Field (SQMFF) methodology in order to fit the theoretical wavenumber values to the experimental one. Furthermore, Natural Bond Orbital (NBO) and topological properties by Atoms In Molecules (AIM) calculations were performed to analyze the nature and magnitude of the intramolecular interactions. The result reveals that two conformers are expected in liquid phase. Copyright © 2009 John Wiley & Sons, Ltd. [source] On some geometric and topological properties of generalized Orlicz,Lorentz sequence spacesMATHEMATISCHE NACHRICHTEN, Issue 2 2008Foralewski Abstract Generalized Orlicz,Lorentz sequence spaces ,, generated by Musielak-Orlicz functions , satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition ,,2 for , is defined in such a way that it guarantees many positive topological and geometric properties of ,,. The problems of the Fatou property, the order continuity and the Kadec,Klee property with respect to the uniform convergence of the space ,, are considered. Moreover, some embeddings between ,, and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of ,,, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [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] The order of the ring: assembly of Escherichia coli cell division componentsMOLECULAR MICROBIOLOGY, Issue 1 2006Miguel Vicente Summary Topological cues appear to override temporal events in the assembly of the Escherichia coli cell division ring. When a procedure that allows the recruitment of ring components based on their topological properties is used, a concerted mode of assembly of several components of the divisome, rather than a strict linear mode, is revealed. Three multimolecular complexes, the proto-ring, the periplasmic connector and the peptidoglycan factory, show some degree of concertation for their assembly. In addition, back-recruitment of all late proteins except FtsN into the division ring occurs even in the absence of proteins incorporated at earlier stages, i.e. FtsA or FtsQ. [source] Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficientsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2002N. S. Bakhvalov Abstract We prove extension theorems in the norms described by Stokes and Lamé operators for the three-dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well-known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two-dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd. [source] Discovering functions and revealing mechanisms at molecular level from biological networksPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 16 2007Shihua Zhang Abstract With the increasingly accumulated data from high-throughput technologies, study on biomolecular networks has become one of key focuses in systems biology and bioinformatics. In particular, various types of molecular networks (e.g., protein,protein interaction (PPI) network; gene regulatory network (GRN); metabolic network (MN); gene coexpression network (GCEN)) have been extensively investigated, and those studies demonstrate great potentials to discover basic functions and to reveal essential mechanisms for various biological phenomena, by understanding biological systems not at individual component level but at a system-wide level. Recent studies on networks have created very prolific researches on many aspects of living organisms. In this paper, we aim to review the recent developments on topics related to molecular networks in a comprehensive manner, with the special emphasis on the computational aspect. The contents of the survey cover global topological properties and local structural characteristics, network motifs, network comparison and query, detection of functional modules and network motifs, function prediction from network analysis, inferring molecular networks from biological data as well as representative databases and software tools. [source] The interplay between experiment and theory in charge-density analysisACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2004Philip Coppens The comparison of theory and experiment remains a cornerstone of scientific inquiry. Various levels of such comparison applicable to charge-density analysis are discussed, including static and dynamic electron densities, topological properties, d -orbital occupancies and electrostatic moments. The advantages and drawbacks of the pseudoatom multipole are discussed, as are the experimentally constrained wavefunctions introduced by Jayatilaka and co-workers, which combine energy minimization with the requirement to provide a reasonable fit to the X-ray structure factors. The transferability of atomic densities can be exploited through construction of a pseudoatom databank, which may be based on analysis of ab initio molecular electron densities, and can be used to evaluate a host of physical properties. Partitioning of theoretical energies with the Morokuma,Ziegler energy decomposition scheme allows direct comparison with electrostatic interaction energies obtained from electron densities represented by the pseudoatom formalism. Compared with the Buckingham expression for the interaction between non-overlapping densities, the agreement with theory is much improved when a newly developed hybrid EP/MM (exact potential/multipole model) method is employed. [source] Weak intra- and intermolecular interactions in a binaphthol imine: an experimental charge-density study on (±)-8,-benzhydrylideneamino-1,1,-binaphthyl-2-olACTA CRYSTALLOGRAPHICA SECTION B, Issue 6 2009Louis J. Farrugia The charge density in (±)-8,-benzhydrylideneamino-1,1,-binaphthyl-2-ol (1) has been studied experimentally using Mo,K, X-ray diffraction at 100,K, and by theory using density-functional thoery (DFT) calculations at the B3LYP/6-311++G** level. The nature of the weak intramolecular peri -C...N, CH...,, H...H and C(,)...C(,) interactions has been examined by topological analysis using the Quantum Theory of Atoms in Molecules (QTAIM) approach. An analysis of the density ,(r), the Laplacian of the density ,2,(rb) and other topological properties at the bond-critical points were used to classify these interactions. The study confirms the presence of the intramolecular CH..., interaction in (1), which was previously suspected on geometrical grounds. An analysis of the ellipticity profiles along the bond paths unambiguously shows the ,-delocalization between the imine unit and one N -phenyl group. The weak intermolecular interactions in the crystal of (1) were examined experimentally and theoretically through the pairwise interactions of the seven independent dimeric pairs of (1) responsible for the set of unique intermolecular interactions, and also through examination of the Hirshfeld surface dnorm property. The theoretical dimeric-pair calculations used the BLYP-D functional which supplements the exchange-correlational functional with an empirical dispersion term to provide a more accurate determination of the energies for the weak intermolecular interactions. [source] Charge-density study on cyclosporine AACTA CRYSTALLOGRAPHICA SECTION D, Issue 3 2009S. K. J. Johnas Two single-crystal X-ray diffraction data sets of cyclosporine A were measured to high resolution using synchrotron radiation at temperatures of 5 and 90,K. They allowed an accurate determination of its molecular and electronic structure. Three electron-density models based on pseudoatom scattering factors were compared in terms of derived bond topological properties and in terms of electron-density differences on a grid. In one model multipole parameters were freely refined, whereas in the other two models the density was built up from fixed database parameters from the invariom database and University at Buffalo Databank. The data quality not only allowed benchmarking of the quality of both databases with the refined density, but also judgement of the feasibility of a multipole refinement of a larger oligopeptide structure such as cyclosporine A. Both databases performed equally well and reproduced the experimentally determined charge density satisfactorily. [source] DNA topology and topoisomerasesBIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION, Issue 1 2009Teaching a "knotty" subject Abstract DNA is essentially an extremely long double-stranded rope in which the two strands are wound about one another. As a result, topological properties of the genetic material, including DNA underwinding and overwinding, knotting, and tangling profoundly influence virtually every major nucleic acid process. Despite the importance of DNA topology, it is a conceptionally difficult subject to teach because it requires students to visualize three-dimensional relationships. This article will familiarize the reader with the concept of DNA topology and offer practical approaches and demonstrations to teaching this "knotty" subject in the classroom. Furthermore, it will discuss topoisomerases, the enzymes that regulate the topological state of DNA in the cell. These ubiquitous enzymes perform a number of critical cellular functions by generating transient breaks in the double helix. During this catalytic event, topoisomerases maintain genomic stability by forming covalent phosphotyrosyl bonds between active site residues and the newly generated DNA termini. Topoisomerases are essential for cell survival. However, because they cleave the genetic material, these enzymes also have the potential to fragment the genome. This latter feature of topoisomerases is exploited by some of the most widely prescribed anticancer and antibacterial drugs currently in clinical use. Finally, in addition to curing cancer, topoisomerase action also has been linked to the induction of specific types of leukemia. [source] | ||||||||||||||||