Multiplexity and multireciprocity in directed multiplexes

Real-world multi-layer networks feature nontrivial dependencies among links of different layers. Here we argue that, if links are directed, dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of `multiplexity', there is also a tendency to anti-align as the result of what we call `multireciprocity', i.e. the fact that links in one layer can be reciprocated by \emph{opposite} links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the World Trade Multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is however largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness/complexity metrics.Comment: 20 pages, 8 figure

Spatial effects in real networks: measures, null models, and applications

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two factors can be varied arbitrarily, it is much more difficult to disentangle these two architectural effects in real networks. Here we propose a solution to the problem by introducing global and local measures of spatial effects that, through a comparison with adequate null models, effectively filter out the spurious contribution of non-spatial constraints. Our filtering allows us to consistently compare different embedded networks or different historical snapshots of the same network. As a challenging application we analyse the World Trade Web, whose topology is expected to depend on geographic distances but is also strongly determined by non-spatial constraints (degree sequence or GDP). Remarkably, we are able to detect weak but significant spatial effects both locally and globally in the network, showing that our method succeeds in retrieving spatial information even when non-spatial factors dominate. We finally relate our results to the economic literature on gravity models and trade globalization

The role of distances in the World Trade Web

In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. However, it has been recently shown that gravity models fail to reproduce the binary topology of the World Trade Web. In this paper a different approach is presented: the formalism of exponential random graphs is used and the distances are treated as constraints, to be imposed on a previously chosen ensemble of graphs. Then, the information encoded in the geographical distances is used to explain the binary structure of the World Trade Web, by testing it on the degree-degree correlations and the reciprocity structure. This leads to the definition of a novel null model that combines spatial and non-spatial effects. The effectiveness of spatial constraints is compared to that of nonspatial ones by means of the Akaike Information Criterion and the Bayesian Information Criterion. Even if it is commonly believed that the World Trade Web is strongly dependent on the distances, what emerges from our analysis is that distances do not play a crucial role in shaping the World Trade Web binary structure and that the information encoded into the reciprocity is far more useful in explaining the observed patterns.Comment: Preprint, accepted for SITIS 2012 (http://www.sitis-conf.org/). Final version to be published by IEEE Computer Society as conference proceeding

Reciprocity of weighted networks

In directed networks, reciprocal links have dramatic effects on dynamical processes, network growth, and higher-order structures such as motifs and communities. While the reciprocity of binary networks has been extensively studied, that of weighted networks is still poorly understood, implying an ever-increasing gap between the availability of weighted network data and our understanding of their dyadic properties. Here we introduce a general approach to the reciprocity of weighted networks, and define quantities and null models that consistently capture empirical reciprocity patterns at different structural levels. We show that, counter-intuitively, previous reciprocity measures based on the similarity of mutual weights are uninformative. By contrast, our measures allow to consistently classify different weighted networks according to their reciprocity, track the evolution of a network's reciprocity over time, identify patterns at the level of dyads and vertices, and distinguish the effects of flux (im)balances or other (a)symmetries from a true tendency towards (anti-)reciprocation

Anti-obesity drug therapy in clinical practice: Evidence of a poor prescriptive attitude

Obesity is a worldwide growing problem for the health care systems and its treatment is strongly recommended. Orlistat, naltrexone/bupropion, and liraglutide are approved for weight loss in Italy in patients with a Body Mass Index (BMI) ≥ 30 kg/m2 or ≥ 27 kg/m2 with concomitant diseases. However, the prescription of these drugs is significantly low worldwide. General practitioners (GPs) play a key role in the early diagnosis and appropriate management of obesity. The aim of the study was to investigate the management of obesity and the prescriptive attitude of anti-obesity drugs in a general practice setting.All patients registered in lists of 8 GPs with a recorded diagnosis of obesity or BMI values ≥ 30 kg/m2 in the period 2017–2018, were recruited. A descriptive analysis of demographic and clinical characteristic was carried out. The Spearman's correlation rank test was applied to identify correlations between BMI and all the variables of interest.Among 1301 obese patients, only 66.1 % had been diagnosed and 29.4 % had no registered BMI value. Patients with recorded BMI, were overweight (7.8 %) or in the obesity class I (38.8 %), class II (14.1 %), and class III (7.1 %), respectively.The obese patients (class 1–3) were older [66 (55–76) vs 49 (32–59); p < 0.01], and had more concurrent diseases [5 (3−8) vs 4 (2–6); p < 0.01] than patients who reached a BMI < 30 Kg/m2. Moreover, most of obese were high cardiovascular risk (HCVr) patients (67.0 % vs 31.9 %; p < 0.01). The BMI was directly related to age (rs 0.14; p < 0.01), diabetes (rs 0.19; p < 0.01), hypertension (rs 0.14; p < 0.01), heart failure (rs 0.09; p < 0.01), HCVr (rs 0. 12; p < 0.01) and number of comorbidities (rs 0.08; p = 0.01). No prescriptions of orlistat or naltrexone/bupropion were found. Liraglutide was prescribed only in 7 patients because of the concomitant presence of diabetes.Our results suggest a low adherence to guide line recommendations for obesity management and confirm an under-prescription of anti-obesity drugs in Italy