Due to the healthcare burden associated with migraines, prompt and effective treatment is vital to improve patient outcomes and ED workflow. This was a prospective, randomized, double-blind trial. Adults who presented to the ED with a diagnosis of migraine from August of 2019 to March of 2020 were included. Pregnant patients, or with renal impairment were excluded. Patients were randomized to receive intravenous magnesium, prochlorperazine, or metoclopramide. The primary outcome was change in pain from baseline on a numeric rating scale (NRS) evaluated at 30 min after initiation of infusion of study drug. Secondary outcomes included NRS at 60 and 120 min, ED length of stay, necessity for rescue analgesia, and adverse effects. A total of 157 patients were analyzed in this study. Sixty-one patients received magnesium, 52 received prochlorperazine, and 44 received metoclopramide. Most patients were white females, and the median age was 36 years. Hypertension and migraines were the most common comorbidities, with a third of the patients reporting an aura. There was a median decrease in NRS at 30 min of three points across all three treatment arms. The median decrease in NRS (IQR) at 60 min was −4 (2–6) in the magnesium group, −3 (2–5) in the metoclopramide group, and − 4.5 (2–7) in the prochlorperazine group (
p
= 0.27). There were no statistically significant differences in ED length of stay, rescue analgesia, or adverse effects. Reported adverse effects were dizziness, anxiety, and akathisia. No significant difference was observed in NRS at 30 min between magnesium, metoclopramide and prochlorperazine.
The main objective of this research article is to classify different types of m-polar fuzzy edges in an m-polar fuzzy graph by using the strength of connectedness between pairs of vertices. The identification of types of m-polar fuzzy edges, including α-strong m-polar fuzzy edges, β-strong m-polar fuzzy edges and δ-weak m-polar fuzzy edges proved to be very useful to completely determine the basic structure of m-polar fuzzy graph. We analyze types of m-polar fuzzy edges in strongest m-polar fuzzy path and m-polar fuzzy cycle. Further, we define various terms, including m-polar fuzzy cut-vertex, m-polar fuzzy bridge, strength reducing set of vertices and strength reducing set of edges. We highlight the difference between edge disjoint m-polar fuzzy path and internally disjoint m-polar fuzzy path from one vertex to another vertex in an m-polar fuzzy graph. We define strong size of an m-polar fuzzy graph. We then present the most celebrated result due to Karl Menger for m-polar fuzzy graphs and illustrate the vertex version of Menger’s theorem to find out the strongest m-polar fuzzy paths between affected and non-affected cities of a country due to an earthquake. Moreover, we discuss an application of types of m-polar fuzzy edges to determine traffic-accidental zones in a road network. Finally, a comparative analysis of our research work with existing techniques is presented to prove its applicability and effectiveness.
In this paper, we introduced Wiener index ( WI ) and average Wiener index ( AWI ) of directed rough fuzzy graph (DRFG). WI is the most extensively used index in graph theory. This index is based on the geodesic distance between two vertices. If there is no directed path from vertex x to vertex y in DRFG, we assume that the weight of geodesic from vertex x to vertex y is zero. In this paper, we investigate the connection between WI and connectivity index ( CI ), which is one of the most prominent index, by presenting several examples and results. We introduced the concept of complete directed rough fuzzy graph (CDRFG) along with some useful results like CDRFG have no weak edges. We also compute the WI for CDRFG. Moreover, we discussed three types of vertices: Wiener enhancing vertex (WEV), Wiener reducing vertex (WRV), and Wiener neutral vertex (WNV). The proposed study of DRFG is suitable for modeling uncertainties and unclear data information in the real life circumstances. In the end, we proposed an application of the WI in the human trafficking network. We also presented a detailed comparative analysis and comparison table by comparing our result for both CI and WI for the same human trafficking network.
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