An algorithm for the fuzzy maximum flow problem

The problem of finding the maximum flow between a source and a destination node in a network with uncertainties in its capacities is an important problem of network flows, since it has a wide range of applications in different areas (telecommunications, transportations, manufacturing, etc) and therefore deserves special attention. However, due to complexity in working with this kind of problems, there are a few algorithms in literature, which demand that the user informs the desirable maximum flow, which is difficult when the network is the large scale. In this paper, an algorithm based on the classic algorithm of Ford-Fulkerson is proposed. The algorithm uses the technique of the incremental graph and it does not request that the decision-maker informs the desirable flow, in contrast of the main works of literature. The uncertainties of the parameters are resolved using the fuzzy sets theory

Distribution of myocardial work in arterial hypertension: insights from non-invasive left ventricular pressure-strain relations

A index of non-invasive myocardial work (MWI) can account for pressure during the assessment of cardiac function, potentially separating the influence of loading conditions from the influence of the underlying tissue remodelling. The aim is to assess LV function accounted for loading and explore hypertensive MWI distribution by comparing healthy individuals to hypertensive patients without and with localized basal septal hypertrophy (BSH). An echocardiogram was performed in 170 hypertensive patients and 20 healthy individuals. BSH was defined by a basal-to-mid septal wall thickness ratio ≥ 1.4. LV speckle-tracking was performed, and the MWI calculated globally and regionally for the apical, mid and basal regions. An apex-to-base gradient, seen in regional strain values, was preserved in the distribution of myocardial work, with the apical region compensating for the impairment of the basal segments. This functional redistribution was further pronounced in patients with localized BSH. In these patients, segmental MWI analysis revealed underlying impairment of regional work unrelated to acute loading conditions. Non-invasive MWI analysis offers the possibility to compare LV function regardless of blood pressure at the time of observation. Changes in MWI distribution can be seen in hypertension unrelated to the load-dependency of strain. Accentuated functional changes affirm the role of BSH as an echocardiographic marker in hypertension.This work was supported by Horizon 2020 European Commission Project H2020-MSCA-ITN-2016 (764738), Grant from Fundacio La Marató de TV3 (040310, Exp 2015.40.30), and from Fondo de Investigaciones Sanitarias - Instituto de Salud Carlos III (PI17/01131). PL holds a Wellcome Trust Senior Research Fellowship (209450/Z/17/Z)