Graph Annotations in Modeling Complex Network Topologies

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs

Hyperbolic Geometry of Complex Networks

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

Shell Model for Drag Reduction with Polymer Additive in Homogeneous Turbulence

Recent direct numerical simulations of the FENE-P model of non-Newtonian hydrodynamics revealed that the phenomenon of drag reduction by polymer additives exists (albeit in reduced form) also in homogeneous turbulence. We introduce here a simple shell model for homogeneous viscoelastic flows that recaptures the essential observations of the full simulations. The simplicity of the shell model allows us to offer a transparent explanation of the main observations. It is shown that the mechanism for drag reduction operates mainly on the large scales. Understanding the mechanism allows us to predict how the amount of drag reduction depends of the various parameters in the model. The main conclusion is that drag reduction is not a universal phenomenon, it peaks in a window of parameters like Reynolds number and the relaxation rate of the polymer

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

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

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.

Evaluation of Colour Pre-processing on Patch-Based Classification of H&E-Stained Images

This paper compares the effects of colour pre-processing on the classification performance of H&E-stained images. Variations in the tissue preparation procedures, acquisition systems, stain conditions and reagents are all source of artifacts that can affect negatively computer-based classification. Pre-processing methods such as colour constancy, transfer and deconvolution have been proposed to compensate the artifacts. In this paper we compare quantitatively the combined effect of six colour pre-processing procedures and 12 colour texture descriptors on patch-based classification of H&E-stained images. We found that colour pre-processing had negative effects on accuracy in most cases – particularly when used with colour descriptors. However, some pre-processing procedures proved beneficial when employed in conjunction with classic texture descriptors such as co-occurrence matrices, Gabor filters and Local Binary Patterns

Structural efficiency of percolation landscapes in flow networks

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

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

Quintessence and Gravitational Waves

We investigate some aspects of quintessence models with a non-minimally coupled scalar field and in particular we show that it can behave as a component of matter with $-3 \lesssim P/\rho \lesssim 0$. We study the properties of gravitational waves in this class of models and discuss their energy spectrum and the cosmic microwave background anisotropies they induce. We also show that gravitational waves are damped by the anisotropic stress of the radiation and that their energy spectrum may help to distinguish between inverse power law potential and supergravity motivated potential. We finish by a discussion on the constraints arising from their density parameter \Omega_\GW.Comment: 21 pages, 18 figures, fianl version, accepted for publication in PR