Network analysis of the Kyiv bylyny cycle -- east Slavic epic narratives

Abstract

Since the pioneering work of Joseph Campbell in the 1960's, universality emerged as an important qualitative notion in the field of comparative mythology. In recent times, the advent of network science permitted new quantitative approaches to literary studies. Here we bring the Kyiv bylyny cycle into the field East Slavic epic narratives originating in modern-day Ukraine. By comparing them to other prominent European epics, we identify universal and distinguishing properties of the social networks in bylyny.

Phase transitions above the upper critical dimension

“…The approach of Luijten and Blöte provides a more complete mechanism, and almost closes the question concerning finite-size-scaling above the upper critical dimension at least for the free energy sector. In their original paper, they considered the O(N ) φ 4 model and here we extend the results to the φ n model of equation (63). The study is based on RG equations for the scaling fields which, limited to linear order, are of the form 3…”

“…The associated amplitudes are Γ − = (n − 2) −1 and Γ + = 1. The specific heat exponent from equation ( 25) requires the second derivative of the free energy wrt t. The homogeneous system has a free energy given by inserting the equilibrium order parameter (65) and (66) in the expansion (63), leading to…”

“…Although this is not done in the original BNPY paper, we believe it is instructive to explicitly state the complete agreement with Fisher's scenario. Here we do this in the context of the φ n model of equation (63). Using the appropriate derivatives of the free energy density wrt t, and to h, we get the first four "classical" exponents in the BNPY approach…”

“…We refer the reader to Ref. [63] for an analysis of medieval Ukrainian literature which refutes that view and concludes: "Thus the Kyiv cycle of east Slavic epic narratives falls nicely within the European tradition in network terms -it is in many ways like Ireland's heroic tradition and Iceland's social ones." Finally, express our solidarity with the Ukrainian people and people the world over who actively strive to uphold the most noble principles of academia and of humanity.…”