Beyond the tree of texts: Building an empirical model of scribal variation through graph analysis of texts and stemmata

Stemmatology, or the reconstruction of the transmission history of texts, is a field that stands particularly to gain from digital methods. Many scholars already take stemmatic approaches that rely heavily on computational analysis of the collated text (e.g. Robinson and O’Hara 1996; Salemans 2000; Heikkilä 2005; Windram et al. 2008 among many others). Although there is great value in computationally assisted stemmatology, providing as it does a reproducible result and allowing access to the relevant methodological process in related fields such as evolutionary biology, computational stemmatics is not without its critics. The current state-of-the-art effectively forces scholars to choose between a preconceived judgment of the significance of textual differences (the Lachmannian or neo-Lachmannian approach, and the weighted phylogenetic approach) or to make no judgment at all (the unweighted phylogenetic approach). Some basis for judgment of the significance of variation is sorely needed for medieval text criticism in particular. By this, we mean that there is a need for a statistical empirical profile of the text-genealogical significance of the different sorts of variation in different sorts of medieval texts. The rules that apply to copies of Greek and Latin classics may not apply to copies of medieval Dutch story collections; the practices of copying authoritative texts such as the Bible will most likely have been different from the practices of copying the Lives of local saints and other commonly adapted texts. It is nevertheless imperative that we have a consistent, flexible, and analytically tractable model for capturing these phenomena of transmission. In this article, we present a computational model that captures most of the phenomena of text variation, and a method for analysis of one or more stemma hypotheses against the variation model. We apply this method to three ‘artificial traditions’ (i.e. texts copied under laboratory conditions by scholars to study the properties of text variation) and four genuine medieval traditions whose transmission history is known or deduced in varying degrees. Although our findings are necessarily limited by the small number of texts at our disposal, we demonstrate here some of the wide variety of calculations that can be made using our model. Certain of our results call sharply into question the utility of excluding ‘trivial’ variation such as orthographic and spelling changes from stemmatic analysis.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Adolescents' value of children and their intentions to have children: A cross-cultural and multilevel analysis

This study contributes to research regarding the value of children (VOC) by comparing adolescents' VOC and their intentions to have children across 12 cultures and by exploring the relations between these constructs at the individual and cultural levels using multilevel modeling. A total of 3,348 adolescents from 12 cultures participated in this study. On average, adolescents reported that they intended to have about two children and also reported emotional VOC as being highly important. Adolescents from cultures with a low as compared to a high level of economic development reported a higher importance of the utilitarian-normative VOC. Results of the multilevel analyses showed that the reported emotional VOC was positively related to the number of children adolescents intended to have at the individual level, whereas the utilitarian-normative VOC was not related to adolescents' intention to have children. At the cultural level, the VOC dimensions were only partly related to adolescents' intention to have children. The results are discussed with regard to adolescents' future family orientation and in relation to the VOC approach.