Clustering and the hyperbolic geometry of complex networks

Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was proposed recently by Krioukov et al. as a mathematical model of complex networks, under the fundamental assumption that hyperbolic geometry underlies the structure of these networks. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show how the global clustering coefficient can be tuned by these parameters and we give an explicit formula for this function.Comment: 51 pages, 1 figur

Metabolic Imaging Detects Low Levels of Glycolytic Activity That Vary with Levels of c-Myc Expression in Patient-Derived Xenograft Models of Glioblastoma.

13C MRI of hyperpolarized [1-13C]pyruvate metabolism has been used in oncology to detect disease, investigate disease progression, and monitor response to treatment with a view to guiding treatment in individual patients. This technique has translated to the clinic with initial studies in prostate cancer. Here, we use the technique to investigate its potential uses in patients with glioblastoma (GB). We assessed the metabolism of hyperpolarized [1-13C]pyruvate in an orthotopically implanted cell line model (U87) of GB and in patient-derived tumors, where these were produced by orthotopic implantation of cells derived from different patients. Lactate labeling was higher in the U87 tumor when compared with patient-derived tumors, which displayed intertumoral heterogeneity, reflecting the intra- and intertumoral heterogeneity in the patients' tumors from which they were derived. Labeling in some patient-derived tumors could be observed before their appearance in morphologic images, whereas in other tumors it was not significantly greater than the surrounding brain. Increased lactate labeling in tumors correlated with c-Myc-driven expression of hexokinase 2, lactate dehydrogenase A, and the monocarboxylate transporters and was accompanied by increased radioresistance. Because c-Myc expression correlates with glioma grade, this study demonstrates that imaging with hyperpolarized [1-13C]pyruvate could be used clinically with patients with GB to determine disease prognosis, to detect early responses to drugs that modulate c-Myc expression, and to select tumors, and regions of tumors for increased radiotherapy dose.Significance: Metabolic imaging with hyperpolarized [1-13C]pyruvate detects low levels of c-Myc-driven glycolysis in patient-derived glioblastoma models, which, when translated to the clinic, could be used to detect occult disease, determine disease prognosis, and target radiotherapy. Cancer Res; 78(18); 5408-18. ©2018 AACR.The work was supported by a Cancer Research UK Programme grant (17242) and by the CRUK-EPSRC Imaging Centre in Cambridge and Manchester (16465) awarded to K. M. Brindle. F. Kreis was supported by a Marie Curie ITN studentship (EUROPOL) and R. Mair by Addenbrooke's Charitable Trust and a CRUK Cambridge Centre Fellowship

Volume-Targeted Ventilation and Arterial Carbon Dioxide in Neonates

Objectives: To review the arterial carbon dioxide tensions (PaCO2) in newborn infants ventilated using synchronized intermittent mandatory ventilation (SIMV) in volume guarantee mode (using the Drager Babylog 8000+) with a unit policy targeting tidal volumes of approximately 4 mL/kg. Methods: Data on ventilator settings and arterial (PaCO2 levels were collected on all arterial blood gases (ABG; n = 288) from 50 neonates ( 65 mmHg) were determined. Results: The mean (SD) (PaCO2 during the first 48 h was 46.6 (9.0) mmHg. The mean (SD) (PaCO2 on the first blood gas of those infants commenced on volume guarantee from admission was 45.1 (12.5) mmHg. Severe hypo- or hypercapnoea occurred in 8% of infants at the time of their first blood gas measurement, and i

Characterizing the community structure of complex networks

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as ``fingerprints'' of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Our findings are verified by the use of two fundamentally different community detection methods.Comment: 15 pages, 20 figures, 4 table

Anatomical Network Comparison of Human Upper and Lower, Newborn and Adult, and Normal and Abnormal Limbs, with Notes on Development, Pathology and Limb Serial Homology vs. Homoplasy

How do the various anatomical parts (modules) of the animal body evolve into very different integrated forms (integration) yet still function properly without decreasing the individual's survival? This long-standing question remains unanswered for multiple reasons, including lack of consensus about conceptual definitions and approaches, as well as a reasonable bias toward the study of hard tissues over soft tissues. A major difficulty concerns the non-trivial technical hurdles of addressing this problem, specifically the lack of quantitative tools to quantify and compare variation across multiple disparate anatomical parts and tissue types. In this paper we apply for the first time a powerful new quantitative tool, Anatomical Network Analysis (AnNA), to examine and compare in detail the musculoskeletal modularity and integration of normal and abnormal human upper and lower limbs. In contrast to other morphological methods, the strength of AnNA is that it allows efficient and direct empirical comparisons among body parts with even vastly different architectures (e.g. upper and lower limbs) and diverse or complex tissue composition (e.g. bones, cartilages and muscles), by quantifying the spatial organization of these parts-their topological patterns relative to each other-using tools borrowed from network theory. Our results reveal similarities between the skeletal networks of the normal newborn/adult upper limb vs. lower limb, with exception to the shoulder vs. pelvis. However, when muscles are included, the overall musculoskeletal network organization of the upper limb is strikingly different from that of the lower limb, particularly that of the more proximal structures of each limb. Importantly, the obtained data provide further evidence to be added to the vast amount of paleontological, gross anatomical, developmental, molecular and embryological data recently obtained that contradicts the long-standing dogma that the upper and lower limbs are serial homologues. In addition, the AnNA of the limbs of a trisomy 18 human fetus strongly supports Pere Alberch's ill-named "logic of monsters" hypothesis, and contradicts the commonly accepted idea that birth defects often lead to lower integration (i.e. more parcellation) of anatomical structures

Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks

Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To understand the joint effects of these two network properties on epidemic dynamics, the effective degree model of Lindquist et al. [28] is reformulated with a new moment closure to apply to highly clustered networks. A simulation study comparing alternative ODE models and stochastic simulations is performed for SIR (Susceptible–Infected–Removed) epidemic dynamics, including a test for the conjectured error behaviour in [40], providing evidence that this novel model can be a more accurate approximation to epidemic dynamics on complex networks than existing approaches

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at √s = 7 TeV with the ATLAS detector

This paper presents a measurement of the cross-section for high transverse momentum W and Z bosons produced in pp collisions and decaying to all-hadronic final states. The data used in the analysis were recorded by the ATLAS detector at the CERN Large Hadron Collider at a centre-of-mass energy of √s = 7 TeV;{\rm Te}{\rm V}$and correspond to an integrated luminosity of$4.6\;{\rm f}{{{\rm b}}^{-1}}$. The measurement is performed by reconstructing the boosted W or Z bosons in single jets. The reconstructed jet mass is used to identify the W and Z bosons, and a jet substructure method based on energy cluster information in the jet centre-of-mass frame is used to suppress the large multi-jet background. The cross-section for events with a hadronically decaying W or Z boson, with transverse momentum${{p}_{{\rm T}}}\gt 320\;{\rm Ge}{\rm V}$and pseudorapidity$|\eta |\lt 1.9$, is measured to be${{\sigma }_{W+Z}}=8.5\pm 1.7$ pb and is compared to next-to-leading-order calculations. The selected events are further used to study jet grooming techniques