The article deals with the applied aspects of the preliminary vertices ranking for oriented weighted graph. In this paper, the authors observed the widespread use of this technique in developing heuristic discrete optimization algorithms. The ranking problem is directly related to the problem of social networks centrality and large real world data sets but as shown in the article ranking is explicitly or implicitly used in the development of algorithms as the initial stage of obtaining a solution for solving applied problems. Examples of such ranking application are given. The examples demonstrate the increase of efficiency for solving some optimization applied problems, which are widely used in mathematical methods of optimization, decision-making not only from the theoretical development point of view but also their applications. The article describes the structure of the first phase of the computational experiment, which is associated with the procedure of obtaining test data sets. The obtained data are presented by weighted graphs that correspond to several groups of the social network Vkontakte with the number of participants in the range from 9000 to 24 thousand. It is shown that the structural characteristics of the obtained graphs differ significantly in the number of connectivity components. Characteristics of centrality (degree's sequences), as shown, have exponential distribution. The main attention is given to the analysis of three approaches to graph vertices ranking. We propose analysis and comparison of the obtained set of ranks by the nature of their distribution. The definition of convergence for graph vertex ranking algorithms is introduced and the differences of their use in considering the data of large dimension and the need to build a solution in the presence of local changes are discussed.
We present the case of a 23-year-old male diagnosed with a complex congenital heart disease (with single ventricle physiology) which necessitated many surgical interventions including total cavopulmonary connection. The patient presents with recurrent (almost daily) highly symptomatic atrial tachycardia with rapid ventricular rate and poor haemodynamic tolerance. Due to failure of antiarrhythmic drug therapy the patient was referred for catheter ablation. Atrial access was provided following transconduit puncture with a standard transseptal set. Crossing to the atrium with the transseptal introducer was not successful due to resistance from the conduit and the atrial wall. Therefore, balloon dilation of the puncture using a cutting balloon was carried out which resulted in easy crossing to the atrium with a steerable transseptal introducer. Several atrial tachyarrhythmias were induced two of which allowed mapping demonstrating a macroreentrant tachycardia dependent on the cavoannular isthmus as well as a complex fi gure-of-eight circuit involving right pulmonary veins and the right atrial appendage. Linear lesions transecting the critical isthmuses of the two circuits were delivered which rendered the patient noninducible. During a 9-month follow-up period the patient remained arrhythmia free.
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