The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices

Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic (geometric) mean of weight vectors, calculated from all spanning trees, is proved to be optimal to the (logarithmic) least squares problem, not only for complete, as it was recently shown in Lundy, M., Siraj, S., Greco, S. (2017): The mathematical equivalence of the "spanning tree" and row geometric mean preference vectors and its implications for preference analysis, European Journal of Operational Research 257(1) 197-208, but for incomplete matrices as well. Unlike the complete case, where an explicit formula, namely the row arithmetic/geometric mean of matrix elements, exists for the (logarithmic) least squares problem, the incomplete case requires a completely different and new proof. Finally, Kirchhoff's laws for the calculation of potentials in electric circuits is connected to our results.Comment: 21 pages, 6 figure

Random to chaotic temperature transition in low-field Fano-Feshbach resonances of cold thulium atoms

Here, we report on the observation of a random to chaotic temperature transition in the spacing of Fano-Feshbach resonances in the ultracold polarized gas of thulium atoms. This transition is due to the appearance of so-called d-resonances, which are not accessible at low temperatures, in the spectra at high temperatures, which drastically changes thulium's overall resonance statistic. In addition to this statistical change, it has been observed that s- and d-resonances experience quite different temperature shifts: s-resonances experience almost no shift with the temperature, while d-resonances experience an obvious positive shift. In addition, careful analysis of the broad Fano-Feshbach resonances enabled the determination of the sign of thulium's background scattering length. A rethermalization experiment made it possible to estimate a length value of a=144+-38a.u.. This proves that thulium atoms are suitable for achieving Bose-Einstein Condensation

REOPERATIONS IN CHILDREN WITH ANORECTAL MALFORMATIONS

The aim of the study was to assess the possibility of using a surgical approach – anterior sagittal anoproctoplasty in children who had previously been operated with various techniques for anorectal malformations. Material and methods. The analysis of postoperative results was performed using a scale for assessing the long-term results of treatment of anorectal malformations before and after surgery. A retrospective study of the patients who was previously operated for various forms of anorectal malformations for the period from 2016 to 2019 in pediatric surgery department of State Novosibirsk district hospital was performed. The early and long-term outcomes were assessed. Results. The criteria for repeated surgical treatment were: rectal mislocated outside of the sphincter mechanism, low social adaptation, secondary changes from the perineum and external genital organs. After investigation (identification of the sphincter mechanism using a myostimulator, irrigoscopy, MRI or MSCT of the pelvic organs), all patients underwent surgical correction – the anterior sagittal anoproctoplasty. Postoperative results were assessed using Holschneider score. The results obtained in the course of this study indicate the possibility of using this method of surgical treatment. Discussion. Children previously underwent surgery for anorectal malformations but having severe functional disorders in the anorectal region, are a complex group of patients who must be determined specific criteria for the reoperations need. The efficiency of surgical treatment depends on the presence of associated congenital malformations (myelodysplasia, pathology of the sacrum and tailbone), as well as the severity of cicatricial changes in the sphincter mechanism. Surgical intervention in 33.3 % of cases led to satisfactory and in 66.7 % of cases to good results