Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for a partition of a network into modules. Recently some authors [1,2] have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows to find the exact splits reported in the literature, as well as the substructure beyond the actual split.

Aims To assess tolerability and optimal time point for initiation of sacubitril/valsartan in patients stabilised after acute heart failure (AHF). Methods and results TRANSITION was a randomised, multicentre, open‐label study comparing two treatment initiation modalities of sacubitril/valsartan. Patients aged ≥ 18 years, hospitalised for AHF were stratified according to pre‐admission use of renin–angiotensin–aldosterone system inhibitors and randomised (n = 1002) after stabilisation to initiate sacubitril/valsartan either ≥ 12‐h pre‐discharge or between Days 1–14 post‐discharge. Starting dose (as per label) was 24/26 mg or 49/51 mg bid with up‐ or down‐titration based on tolerability. The primary endpoint was the proportion of patients attaining 97/103 mg bid target dose after 10 weeks. Median time of first dose of sacubitril/valsartan from the day of discharge was Day –1 and Day +1 in the pre‐discharge group and the post‐discharge group, respectively. Comparable proportions of patients in the pre‐ and post‐discharge initiation groups met the primary endpoint [45.4% vs. 50.7%; risk ratio (RR) 0.90; 95% confidence interval (CI) 0.79–1.02]. The proportion of patients who achieved and maintained for ≥ 2 weeks leading to Week 10, either 49/51 or 97/103 mg bid was 62.1% vs. 68.5% (RR 0.91; 95% CI 0.83–0.99); or any dose was 86.0% vs. 89.6% (RR 0.96; 95% CI 0.92–1.01). Discontinuation due to adverse events occurred in 7.3% vs. 4.9% of patients (RR 1.49; 95% CI 0.90–2.46). Conclusions Initiation of sacubitril/valsartan in a wide range of heart failure with reduced ejection fraction patients stabilised after an AHF event, either in hospital or shortly after discharge, is feasible with about half of the patients achieving target dose within 10 weeks. Clinical Trial Registration: http://ClinicalTrials.gov ID: NCT02661217

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.

No abstract

In this paper we apply a heuristic method based on artificial neural networks in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the neural network heuristic and we compare them to those obtained with three previous heuristic methods.Comment: 12 pages; submitted to "Computers & Operations Research

AimsThe aim of this study was to evaluate the haemodynamic effects of serelaxin (30 µg/kg/day 20-h infusion and 4-h post-infusion period) in patients with acute heart failure (AHF).Methods and resultsThis double-blind, multicentre study randomized 71 AHF patients with pulmonary capillary wedge pressure (PCWP) ≥18 mmHg, systolic blood pressure (BP) ≥115 mmHg, and estimated glomerular filtration rate ≥30 mL/min/1.73 m2 to serelaxin (n = 34) or placebo (n = 37) within 48 h of hospitalization. Co-primary endpoints were peak change from baseline in PCWP and cardiac index (CI) during the first 8 h of infusion. Among 63 patients eligible for haemodynamic analysis (serelaxin, n = 32; placebo, n = 31), those treated with serelaxin had a significantly higher decrease in peak PCWP during the first 8 h of infusion (difference vs. placebo: −2.44 mmHg, P = 0.004). Serelaxin showed no significant effect on the peak change in CI vs. placebo. Among secondary haemodynamic endpoints, a highly significant reduction in pulmonary artery pressure (PAP) was observed throughout the serelaxin infusion (largest difference in mean PAP vs. placebo: −5.17 mmHg at 4 h, P < 0.0001). Right atrial pressure, systemic/pulmonary vascular resistance, and systolic/diastolic BP decreased from baseline with serelaxin vs. placebo and treatment differences reached statistical significance at some time points. Serelaxin administration improved renal function and decreased N-terminal pro-brain natriuretic peptide levels vs. placebo. Treatment with serelaxin was well tolerated with no apparent safety concerns.ConclusionThe haemodynamic effects of serelaxin observed in the present study provide plausible mechanistic support for improvement in signs and symptoms of congestion observed with this agent in AHF patients.ClinicalTrials.gov identifier NCT01543854.

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance and Williams' formula which enables the implementation of the algorithm in a recursive way.

Abstract. Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of NewmanGirvan modularity. We construct then a general framework and apply it to some synthetic and real networks.PACS number: 89.75