Detecting rich-club ordering in complex networks

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4-8]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure

Physical Activity Characteristics across GOLD Quadrants Depend on the Questionnaire Used

BACKGROUND:The GOLD multidimensional classification of COPD severity combines the exacerbation risk with the symptom experience, for which 3 different questionnaires are permitted. This study investigated differences in physical activity (PA) in the different GOLD quadrants and patient's distribution in relation to the questionnaire used. METHODS:136 COPD patients (58±21% FEV1 predicted, 34F/102M) completed COPD assessment test (CAT), clinical COPD questionnaire (CCQ) and modified Medical Research Council (mMRC) questionnaire. Exacerbation history, spirometry and 6MWD were collected. PA was objectively measured for 2 periods of 1 week, 6 months apart, in 5 European centres; to minimise seasonal and clinical variation the average of these two periods was used for analysis. RESULTS:GOLD quadrants C+D had reduced PA compared with A+B (3824 [2976] vs. 5508 [4671] steps.d-1, p<0.0001). The choice of questionnaire yielded different patient distributions (agreement mMRC-CAT κ = 0.57; CCQ-mMRC κ = 0.71; CCQ-CAT κ = 0.72) with different clinical characteristics. PA was notably lower in patients with an mMRC score ≥2 (3430 [2537] vs. 5443 [3776] steps.d-1, p <0.001) in both the low and high risk quadrants. CONCLUSIONS:Using different questionnaires changes the patient distribution and results in different clinical characteristics. Therefore, standardization of the questionnaire used for classification is critical to allow comparison of different studies using this as an entry criterion. CLINICAL TRIAL REGISTRATION:ClinicalTrials.gov NCT01388218

Coping religioso/espiritual em pessoas com doença renal crônica em tratamento hemodialítico

O estudo tem como objetivo investigar o uso do coping religioso/espiritual em pacientes com doença renal crônica em hemodiálise. A investigação ocorreu em uma clínica de hemodiálise, por meio de entrevista utilizando um questionário sociodemográfico e a escala de coping religioso/espiritual. Para análise dos dados, foram empregados a estatística descritiva e o teste coeficiente de correlação de Sperman, a análise de variância e o modelo de regressão linear múltipla. Foram entrevistados 123 indivíduos, dos quais 79,6% apresentaram escore alto para o coping religioso/espiritual e nenhum deles apresentou os escores baixos e irrisórios. As variáveis que influenciaram no comportamento do coping religioso/espiritual foram: sexo, faixa etária, tempo de tratamento, renda familiar e prática religiosa. Conclui-se que os pacientes em estudo utilizam de modo positivo o coping religioso/espiritual como estratégia de enfrentamento da doença, destacando-se as mulheres, com renda familiar maior e que frequentam semanalmente a igreja

Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between BN and general Boolean formulas are identified and common results to both system types are highlighted

Fractionation of cellulose nanocrystals : enhancing liquid crystal ordering without promoting gelation

Colloids of electrically charged nanorods can spontaneously develop a fluid yet ordered liquid crystal phase, but this ordering competes with a tendency to form a gel of percolating rods. The threshold for ordering is reduced by increasing the rod aspect ratio, but the percolation threshold is also reduced with this change; hence, prediction of the outcome is nontrivial. Here, we show that by establishing the phase behavior of suspensions of cellulose nanocrystals (CNCs) fractionated according to length, an increased aspect ratio can strongly favor liquid crystallinity without necessarily influencing gelation. Gelation is instead triggered by increasing the counterion concentration until the CNCs lose colloidal stability, triggering linear aggregation, which promotes percolation regardless of the original rod aspect ratio. Our results shine new light on the competition between liquid crystal formation and gelation in nanoparticle suspensions and provide a path for enhanced control of CNC self-organization for applications in photonic crystal paper or advanced composites

Impact of Single Links in Competitive Percolation -- How complex networks grow under competition

How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness upon gradual addition of links, was long believed to be continuous but recent numerical evidence on "explosive percolation" suggests that it might as well be discontinuous if links compete for addition. Here we analyze the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single link additions. We show that in generic competitive percolation processes, including those displaying explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce observable gaps because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, thus announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively.Comment: non-final version, for final see Nature Physics homepag