Local modularity measure for network clusterizations

Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity $Q$ has been introduced as a measure to assess the quality of clusterizations. $Q$ has a global view, while in many real-world networks clusters are linked mainly \emph{locally} among each other (\emph{local cluster-connectivity}). Here, we introduce a new measure, localized modularity $LQ$, which reflects local cluster structure. Optimization of $Q$ and $LQ$ on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.Comment: 5 pages, 4 figures, RevTex4; Changed conten

Finding local community structure in networks

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(d*k^2) for general graphs when $d$ is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time-consuming, the running time is linear, O(k). We show that on computer-generated graphs this technique compares favorably to algorithms that require global knowledge. We also use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer and show the existence of mesoscopic structure.Comment: 7 pages, 6 figure

Spectral centrality measures in complex networks

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.Comment: 11 pages, 10 figures, 5 tables. Final version published in Physical Review

Finding community structure in very large networks

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers

A Phase 3 Study of Evolocumab (AMG 145) in Statin-Treated Japanese Patients at High Cardiovascular Risk

Evolocumab (AMG 145), a fully human monoclonal antibody against PCSK9, significantly reduced low-density lipoprotein cholesterol (LDL-C) levels in phase 2 and 3 studies. This phase 3 study evaluated the efficacy and safety of evolocumab plus atorvastatin in Japanese patients with hyperlipidemia or mixed dyslipidemia and high cardiovascular risk. Patients were randomized to atorvastatin 5 or 20 mg/day for 4 weeks. Subsequently, patients underwent second randomization to evolocumab 140 mg biweekly (Q2W) or 420 mg monthly (QM) or placebo Q2W or QM. Coprimary end points were % change from baseline in LDL-C at week 12 and mean of weeks 10 and 12. Secondary end points included change and % change in other lipids and proportion of patients reaching LDL-C <70 mg/dl. Adverse events and laboratory values were recorded. Four hundred four patients were randomized to study drug. At baseline, the mean (SD) age was 61 (10) years (placebo) and 62 (11) years (evolocumab); 39% and 40% were women; 14% and 12% had cerebrovascular or peripheral arterial disease; and 51% and 47% had diabetes. At entry, mean (SD) calculated LDL-C was 128 (23) mg/dL; after stabilization on atorvastatin 5 and 20 mg/day, baseline LDL-C levels were 118 (35) and 94 (24) mg/dL, respectively. Mean LDL-C reductions at week 12 for evolocumab versus placebo ranged from 67% to 76%. No imbalances were observed in adverse events between treatment groups. Efficacy and safety for Q2W or QM evolocumab dosing were similar. In conclusion, in high-risk Japanese patients receiving stable statin therapy, evolocumab markedly reduced LDL-C and was well tolerated

How to project a bipartite network?

The one-mode projecting is extensively used to compress the bipartite networks. Since the one-mode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the network-based resource-allocation dynamics, we raise a weighting method, which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method in compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do personal recommendation?Comment: 7 pages, 4 figure

A Method to Find Community Structures Based on Information Centrality

Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using centrality measures to define the community boundaries (M. Girvan and M. E. J. Newman, Community structure in social and biological networks Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality. We test the algorithm on computer generated and real-world networks whose community structure is already known or has been studied by means of other methods. We show that our algorithm, although it runs to completion in a time O(n^4), is very effective especially when the communities are very mixed and hardly detectable by the other methods.Comment: 13 pages, 13 figures. Final version accepted for publication in Physical Review

The macro-behavior of agents' opinion under the influence of an external field

In this paper, a model about the evolution of opinion on small world networks is proposed. We studied the macro-behavior of the agents' opinion and the relative change rate as time elapses. The external field was found to play an important role in making the opinion $s(t)$ balance or increase, and without the influence of the external field, the relative change rate $\gamma(t)$ shows a nonlinear increasing behavior as time runs. What's more, this nonlinear increasing behavior is independent of the initial condition, the strength of the external field and the time that we cancel the external field. Maybe the results can reflect some phenomenon in our society, such as the function of the macro-control in China or the Mass Media in our society.Comment: 8 pages, 3 figure

Acute treatment with omecamtiv mecarbil to increase contractility in acute heart failure

Background: Omecamtiv mecarbil (OM) is a selective cardiac myosin activator that increases myocardial function in healthy volunteers and in patients with chronic heart failure. Objectives: This study evaluated the pharmacokinetics, pharmacodynamics, tolerability, safety, and efficacy of OM in patients with acute heart failure (AHF). Methods: Patients admitted for AHF with left ventricular ejection fraction ≤40%, dyspnea, and elevated plasma concentrations of natriuretic peptides were randomized to receive a double-blind, 48-h intravenous infusion of placebo or OM in 3 sequential, escalating-dose cohorts. Results: In 606 patients, OM did not improve the primary endpoint of dyspnea relief (3 OM dose groups and pooled placebo: placebo, 41%; OM cohort 1, 42%; cohort 2, 47%; cohort 3, 51%; p = 0.33) or any of the secondary outcomes studied. In supplemental, pre-specified analyses, OM resulted in greater dyspnea relief at 48 h (placebo, 37% vs. OM, 51%; p = 0.034) and through 5 days (p = 0.038) in the high-dose cohort. OM exerted plasma concentration-related increases in left ventricular systolic ejection time (p &lt; 0.0001) and decreases in end-systolic dimension (p &lt; 0.05). The adverse event profile and tolerability of OM were similar to those of placebo, without increases in ventricular or supraventricular tachyarrhythmias. Plasma troponin concentrations were higher in OM-treated patients compared with placebo (median difference at 48 h, 0.004 ng/ml), but with no obvious relationship with OM concentration (p = 0.95). Conclusions: In patients with AHF, intravenous OM did not meet the primary endpoint of dyspnea improvement, but it was generally well tolerated, it increased systolic ejection time, and it may have improved dyspnea in the high-dose group. (Acute Treatment with Omecamtiv Mecarbil to Increase Contractility in Acute Heart Failure [ATOMIC-AHF]; NCT01300013)

Efficacy and Safety of Evolocumab in Reducing Lipids and Cardiovascular Events

BACKGROUND: Evolocumab, a monoclonal antibody that inhibits proprotein convertase subtilisin-kexin type 9 (PCSK9), significantly reduced low-density lipoprotein (LDL) cholesterol levels in short-term studies. We conducted two extension studies to obtain longer-term data. METHODS: In two open-label, randomized trials, we enrolled 4465 patients who had completed 1 of 12 phase 2 or 3 studies ("parent trials") of evolocumab. Regardless of study-group assignments in the parent trials, eligible patients were randomly assigned in a 2:1 ratio to receive either evolocumab (140 mg every 2 weeks or 420 mg monthly) plus standard therapy or standard therapy alone. Patients were followed for a median of 11.1 months with assessment of lipid levels, safety, and (as a prespecified exploratory analysis) adjudicated cardiovascular events including death, myocardial infarction, unstable angina, coronary revascularization, stroke, transient ischemic attack, and heart failure. Data from the two trials were combined. RESULTS: As compared with standard therapy alone, evolocumab reduced the level of LDL cholesterol by 61%, from a median of 120 mg per deciliter to 48 mg per deciliter (P<0.001). Most adverse events occurred with similar frequency in the two groups, although neurocognitive events were reported more frequently in the evolocumab group. The risk of adverse events, including neurocognitive events, did not vary significantly according to the achieved level of LDL cholesterol. The rate of cardiovascular events at 1 year was reduced from 2.18% in the standard-therapy group to 0.95% in the evolocumab group (hazard ratio in the evolocumab group, 0.47; 95% confidence interval, 0.28 to 0.78; P=0.003). CONCLUSIONS: During approximately 1 year of therapy, the use of evolocumab plus standard therapy, as compared with standard therapy alone, significantly reduced LDL cholesterol levels and reduced the incidence of cardiovascular events in a prespecified but exploratory analysis. (Funded by Amgen; OSLER-1 and OSLER-2 ClinicalTrials.gov numbers, NCT01439880 and NCT01854918.)