Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Extension of geodesic acoustic mode theory to helical systems

The present paper extends the theory of geodesic acoustic mode (GAM) oscillation, which so far has been applied to tokamaks, to helical systems. By using drift kinetic equations for three-dimensional equilibriums, a generalized dispersion relation is obtained including Landau damping. The oscillation frequency is obtained in terms of the squared sum of Fourier components of the magnetic field intensity expressed by means of magnetic flux coordinates. An analytic form of the collisionless damping rate of GAM is obtained by solving the dispersion relation perturbatively. It is found that the GAM frequency is higher in helical systems than in tokamaks and that damping rate is enhanced in multi-helicity magnetic configurations. However, damping rates are predicted to be small if the temperature of electrons is higher than that of ions

Euclidean versus hyperbolic congestion in idealized versus experimental networks

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure

What did HERA teach us about the structure of the proton?

Starting in 2008 the H1 and ZEUS experiments have been combining their data in order to provide the most complete and accurate set of deep-inelastic data as the legacy of HERA. The present review presents these combinations, both published and preliminary, and explores how they have been used to give information on the structure of the proton. The HERAPDF parton distribution functions (PDFs) are presented and compared with other current PDFs and with data from the Tevatron and LHC colliders.Comment: 49 pages, 49 figures, to be published in J.Phys.

Initial data for stationary space-times near space-like infinity

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the proof found in the literature of the statement that all asymptotically flat, vacuum stationary space-times admit an analytic compactification at null infinity. Stationary initial data are physical important and highly non-trivial examples of a large class of data with similar regularity properties at space-like infinity, namely, initial data for which the metric and the extrinsic curvature have asymptotic expansion in terms of powers of a radial coordinate. We isolate the property of the stationary data which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page

A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT

We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega = v_0 k + a + b/k + ..., where the limiting velocity v_0 is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m_q. We compute a and b in terms of the meson quantum numbers and T/m_q. The limiting meson velocity v_0 becomes much smaller than the speed of light at temperatures below but close to T_diss, the temperature above which no meson bound states at rest in the plasma are found. From our result for v_0, we find that the temperature above which no meson bound states with velocity v exist is T_diss(v) \simeq (1-v^2)^(1/4) T_diss, up to few percent corrections.We thus confirm by direct calculation of meson dispersion relations a result inferred indirectly in previous work via analysis of the screening length between a static quark and antiquark in a moving plasma. Although we do not do our calculations in QCD, we argue that the qualitative features of the dispersion relation we compute, including in particular the relation between dissociation temperature and meson velocity, may apply to bottomonium and charmonium mesons propagating in the strongly coupled plasma of QCD. We discuss how our results can contribute to understanding quarkonium physics in heavy ion collisions.Comment: 57 pages, 12 figures; references adde

IEA EBC Annex 57 ‘Evaluation of Embodied Energy and CO_2eq for Building Construction'

The current regulations to reduce energy consumption and greenhouse gas emissions (GHG) from buildings have focused on operational energy consumption. Thus legislation excludes measurement and reduction of the embodied energy and embodied GHG emissions over the building life cycle. Embodied impacts are a significant and growing proportion and it is increasingly recognized that the focus on reducing operational energy consumption needs to be accompanied by a parallel focus on reducing embodied impacts. Over the last six years the Annex 57 has addressed this issue, with researchers from 15 countries working together to develop a detailed understanding of the multiple calculation methods and the interpretation of their results. Based on an analysis of 80 case studies, Annex 57 showed various inconsistencies in current methodological approaches, which inhibit comparisons of results and difficult development of robust reduction strategies. Reinterpreting the studies through an understanding of the methodological differences enabled the cases to be used to demonstrate a number of important strategies for the reduction of embodied impacts. Annex 57 has also produced clear recommendations for uniform definitions and templates which improve the description of system boundaries, completeness of inventory and quality of data, and consequently the transparency of embodied impact assessments