Effect of assortative mixing in the second-order Kuramoto model

In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases movement.Comment: 7 pages, 6 figures. In press in Physical Review

Low-dimensional behavior of Kuramoto model with inertia in complex networks

Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.Comment: 6 figure

Spectra of random networks in the weak clustering regime

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics

Validation of a contemporary prostate cancer grading system using prostate cancer death as outcome

BACKGROUND: Gleason scoring (GS) has major deficiencies and a novel system of five grade groups (GS⩽6; 3+4; 4+3; 8; ⩾9) has been recently agreed and included in the WHO 2016 classification. Although verified in radical prostatectomies using PSA relapse for outcome, it has not been validated using prostate cancer death as an outcome in biopsy series. There is debate whether an ‘overall' or ‘worst' GS in biopsies series should be used. METHODS: Nine hundred and eighty-eight prostate cancer biopsy cases were identified between 1990 and 2003, and treated conservatively. Diagnosis and grade was assigned to each core as well as an overall grade. Follow-up for prostate cancer death was until 31 December 2012. A log-rank test assessed univariable differences between the five grade groups based on overall and worst grade seen, and using univariable and multivariable Cox proportional hazards. Regression was used to quantify differences in outcome. RESULTS: Using both ‘worst' and ‘overall' GS yielded highly significant results on univariate and multivariate analysis with overall GS slightly but insignificantly outperforming worst GS. There was a strong correlation with the five grade groups and prostate cancer death. CONCLUSIONS: This is the largest conservatively treated prostate cancer cohort with long-term follow-up and contemporary assessment of grade. It validates the formation of five grade groups and suggests that the ‘worst' grade is a valid prognostic measure

Lignin biomarkers as tracers of mercury sources in lakes water column

This study presents the role of specific terrigenous organic compounds as important vectors of mercury (Hg) transported from watersheds to lakes of the Canadian boreal forest. In order to differentiate the autochthonous from the allochthonous organic matter (OM), lignin derived biomarker signatures [Lambda, S/V, C/V, P/(V ? S), 3,5-Bd/V and (Ad/Al)v] were used. Since lignin is exclusively produced by terrigenous plants, this approach can give a non equivocal picture of the watershed inputs to the lakes. Moreover, it allows a characterization of the source of OM and its state of degradation. The water column of six lakes from the Canadian Shield was sampled monthly between June and September 2005. Lake total dissolved Hg concentrations and Lambda were positively correlated, meaning that Hg and ligneous inputs are linked (dissolved OM r2 = 0.62, p\0.0001; particulate OM r2 = 0.76, p\0.0001). Ratios of P/(V ? S) and 3,5-Bd/V from both dissolved OM and particulate OM of the water column suggest an inverse relationship between the progressive state of pedogenesis and maturation of the OM in soil before entering the lake, and the Hg concentrations in the water column. No relation was found between Hg levels in the lakes and the watershed flora composition—angiosperm versus gymnosperm or woody versus non-woody compounds. This study has significant implications for watershed management of ecosystems since limiting fresh terrestrial OM inputs should reduce Hg inputs to the aquatic systems. This is particularly the case for largescale land-use impacts, such as deforestation, agriculture and urbanization, associated to large quantities of soil OM being transferred to aquatic systems

Systematic variation in food web body-size structure linked to external subsidies.

The relationship between body mass (M) and size class abundance (N) depicts patterns of community structure and energy flow through food webs. While the general assumption is that M and N scale linearly (on log-log axes), nonlinearity is regularly observed in natural systems, and is theorized to be driven by nonlinear scaling of trophic level (TL) with M resulting in the rapid transfer of energy to consumers in certain size classes. We tested this hypothesis with data from 31 stream food webs. We predicted that allochthonous subsidies higher in the web results in nonlinear M-TL relationships and systematic abundance peaks in macroinvertebrate and fish size classes (latter containing salmonids), that exploit terrestrial plant material and terrestrial invertebrates, respectively. Indeed, both M-N and M-TL significantly deviated from linear relationships and the observed curvature in M-TL scaling was inversely related to that observed in M-N relationships. Systemic peaks in M-N, and troughs in M-TL occurred in size classes dominated by generalist invertebrates, and brown trout. Our study reveals how allochthonous resources entering high in the web systematically shape community size structure and demonstrates the relevance of a generalized metabolic scaling model for understanding patterns of energy transfer in energetically 'open' food webs