176 research outputs found

    Hyperbolic Geometry of Complex Networks

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    We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

    Spin-polarized oxygen hole states in cation deficient La(1-x)CaxMnO(3+delta)

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    When holes are doped into a Mott-Hubbard type insulator, like lightly doped manganites of the La(1-x)CaxMnO3 family, the cooperative Jahn-Teller distortions and the appearance of orbital ordering require an arrangement of Mn(3+)/Mn(4+) for the establishment of the insulating canted antiferromagnetic (for x<=0.1), or of the insulating ferromagnetic (for 0.1<x<= 0.2) ground state. In the present work we provide NMR evidence about a novel and at the same time puzzling effect in La(1-x)CaxMnO(3+delta) systems with cation deficience. We show that in the low Ca-doping regime, these systems exhibit a very strong hyperfine field at certain La nuclear sites, which is not present in the stoichiometric compounds. Comparison of our NMR results with recent x-ray absorption data at the Mn K edge, suggests the formation of a spin-polarized hole arrangement on the 2p oxygen orbitals as the origin of this effect.Comment: 10 pages, 4 Figures, submitted to PR

    On the observational determination of squeezing in relic gravitational waves and primordial density perturbations

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    We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavior of the higher order multipoles C_l of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum l(l+1)C_l as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion 1:3:5:..., whereas at the dips they are ordered as 1:2:3:.... We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum, that may be detected by the advanced observational missions, such as MAP and PLANCK. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.Comment: 34 pages, 3 figures; to appear in Phys. Rev. D66, 0435XX (2002); includes Note Added in Proofs: "The latest CBI observations (T.J.Pearson et al., astro-ph/0205388) have detected four peaks, at l ~ 550, 800, 1150, 1500, and four dips, at l ~ 400, 700, 1050, 1400. These positions are in a very good agreement with the theoretical formula (6.35) of the present paper. We interpret this data as confirmation of our conclusion that it is gravity, and not acoustics, that is responsible for the observed structure.

    Structural efficiency of percolation landscapes in flow networks

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    Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures in the framework of percolation theory, and in particular the key role of edge interfaces bridging the communication between core and periphery, allow us to shed light on the structural properties of real and theoretical flow networks, and to define criteria and quantities to characterize their efficiency at the interplay between structure and functionality. In particular, it is possible to assess that an optimal flow network should look like a "hairy ball", so to minimize bottleneck effects and the sensitivity to failures. Moreover, the thorough analysis of two real networks, the Internet customer-provider set of relationships at the autonomous system level and the nervous system of the worm Caenorhabditis elegans --that have been shaped by very different dynamics and in very different time-scales--, reveals that whereas biological evolution has selected a structure close to the optimal layout, market competition does not necessarily tend toward the most customer efficient architecture.Comment: 8 pages, 5 figure

    Quality assurance for the query and distribution systems of the RCSB Protein Data Bank

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    The RCSB Protein Data Bank (RCSB PDB, www.pdb.org) is a key online resource for structural biology and related scientific disciplines. The website is used on average by 165 000 unique visitors per month, and more than 2000 other websites link to it. The amount and complexity of PDB data as well as the expectations on its usage are growing rapidly. Therefore, ensuring the reliability and robustness of the RCSB PDB query and distribution systems are crucially important and increasingly challenging. This article describes quality assurance for the RCSB PDB website at several distinct levels, including: (i) hardware redundancy and failover, (ii) testing protocols for weekly database updates, (iii) testing and release procedures for major software updates and (iv) miscellaneous monitoring and troubleshooting tools and practices. As such it provides suggestions for how other websites might be operated

    The RCSB Protein Data Bank: redesigned web site and web services

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    The RCSB Protein Data Bank (RCSB PDB) web site (http://www.pdb.org) has been redesigned to increase usability and to cater to a larger and more diverse user base. This article describes key enhancements and new features that fall into the following categories: (i) query and analysis tools for chemical structure searching, query refinement, tabulation and export of query results; (ii) web site customization and new structure alerts; (iii) pair-wise and representative protein structure alignments; (iv) visualization of large assemblies; (v) integration of structural data with the open access literature and binding affinity data; and (vi) web services and web widgets to facilitate integration of PDB data and tools with other resources. These improvements enable a range of new possibilities to analyze and understand structure data. The next generation of the RCSB PDB web site, as described here, provides a rich resource for research and education
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