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This paper presents the East Central European late medieval and early sixteenth century classroom commentaries as a source material which is still relatively unexplored and little researched, and has a great potential for understanding the communal experience of reading at the threshold of the early modern times. A large number of early prints survive from the years 1480–1550 with manuscript annotations which show clear signs of having been read in a university environment. After a survey of the typical characteristics of such prints, I will particularly focus on sources coming from the university of Cracow and Vienna from the years 1490–1535, and examine this material from several aspects, including the reading procedure, the purposes of reading, the commenting practice, the main type of commentaries, and the individual reading experience. I will try to show that the change in the format of media that the appearance of print, and particularly this type of prints brought along was also able to involve new readers and change the way in which the interpretation of the text was carried out.

AbstractIt is often claimed that humanity has stopped evolving because modern medicine erased all selection on survival. Even if that would be true, and it is not, there would be other mechanisms of evolution which could still led to changes in allelic frequencies. Here I show, by applying basic evolutionary genetics knowledge, that we expect humanity to evolve. The results from genome sequencing projects have repeatedly affirmed that there are still recent signs of selection in our genomes. I give some examples of such adaptation. Then I briefly discuss what our evolutionary future has in store for us.

Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In this paper we start to study level sets of generic $1$-H\"older-$\alpha$ functions defined on fractals. This is related to some sort of "thickness", "conductivity" properties of fractals. The main concept of our paper is $D_{*}(\alpha, F)$ which is the essential supremum of the Hausdorff dimensions of the level sets of a generic $1$-H\"older-$\alpha$ function defined on the fractal $F$. We prove some basic properties of $D_{*}(\alpha, F)$, we calculate its value for an example of a "thick fractal sponge", we show that for connected self similar sets $D_{*}(\alpha, F)$ it equals the Hausdorff dimension of almost every level in the range of a generic $1$-H\"older-$\alpha$ function. Comment: Revised version after referee's report. A new example was added, introduction was modified, a Main results section was also added

AbstractThe present study offers a re-evaluation of literary production in Hungary under the Jagiellonian kings Wladislas II and Louis II. Traditionally, the literary works produced in this period have been contrasted to the blossoming of humanist literature under King Matthias, and disregarded in many respects. The aim of this study is to make a survey of the main authors and other agents of the literary culture of this period and to stress that this age experienced an unseen growth and expansion in late medieval and humanist scholarly and lay culture. While János Horváth called the authors of this period “humanists with party allegiances”, I argue that their stronger “party allegiance” is, in fact, the direct result of the steady growth in the number of intellectuals with a modern, humanistic educational outlook, and of a less centralized state.

AbstractDue to the constantly increasing number of mutations in the SARS-CoV-2 genome, concerns have emerged over the possibility of decreased diagnostic accuracy of reverse transcription-polymerase chain reaction (RT-PCR), the gold standard diagnostic test for SARS-CoV-2. We propose an analysis pipeline to discover genomic variations overlapping the target regions of commonly used PCR primer sets. We provide the list of these mutations in a publicly available format based on a dataset of more than 1.2 million SARS-CoV-2 samples. Our approach distinguishes among mutations possibly having a damaging impact on PCR efficiency and ones anticipated to be neutral in this sense. Samples are categorized as “prone to misclassification” vs. “likely to be correctly detected” by a given PCR primer set based on the estimated effect of mutations present. Samples susceptible to misclassification are generally present at a daily rate of 2% or lower, although particular primer sets seem to have compromised performance when detecting Omicron samples. As different variant strains may temporarily gain dominance in the worldwide SARS-CoV-2 viral population, the efficiency of a particular PCR primer set may change over time, therefore constant monitoring of variations in primer target regions is highly recommended.

A necklace can be considered as a cyclic list of n red and n blue beads in an arbitrary order. In the necklace folding problem the goal is to find a large crossing-free matching of pairs of beads of different colors in such a way that there exists a “folding” of the necklace, that is a partition into two contiguous arcs, which splits the beads of any matching edge into different arcs. We give counterexamples for some conjectures about the necklace folding problem, also known as the separated matching problem. The main conjecture (given independently by three sets of authors) states that [Formula presented], where μ is the ratio of the maximum number of matched beads to the total number of beads. We refute this conjecture by giving a construction which proves that μ≤2−2<0.5858≪0.66. Our construction also applies to the homogeneous model when we match beads of the same color. Moreover, we also consider the problem where the two color classes do not necessarily have the same size. © 2022 Elsevier Inc.

Hausdorff dimensions of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections'' of a "network" corresponding to a fractal set, $F$. This lead to the definition of the topological Hausdorff dimension of fractals. In this paper we continue our study of the level sets of generic $1$-H\"older-$\alpha$ functions. While in a previous paper we gave the initial definitions and established some properties of these generic level sets, in this paper we provide numerical estimates in the case of the Sierpi\'nski triangle. These calculations give better insight and illustrate why can one think of these generic $1$-H\"older-$\alpha$ level sets as something measuring "thickness/narrow cross-sections/conductivity'' of a fractal "network". We also give an example for the phenomenon which we call phase transition for $D_{*}(\alpha, F)$. This roughly means that for a certain lower range { of $\alpha$s } only the geometry of $F$ determines $D_{*}(\alpha, F)$ while for larger values the H\"older exponent, $\alpha$ also matters. Comment: Updated version after referee's suggestions

AbstractCsikós and Horváth proved in J Geom Anal 28(4): 3458-3476, (2018) that if a connected Riemannian manifold of dimension at least 4 is harmonic, then the total scalar curvatures of tubes of small radius about an arbitrary regular curve depend only on the length of the curve and the radius of the tube, and conversely, if the latter condition holds for cylinders, i.e., for tubes about geodesic segments, then the manifold is harmonic. In the present paper, we show that in contrast to the higher dimensional case, a connected 3-dimensional Riemannian manifold has the above mentioned property of tubes if and only if the manifold is a D’Atri space, furthermore, if the space has bounded sectional curvature, then it is enough to require the total scalar curvature condition just for cylinders to imply that the space is D’Atri. This result gives a negative answer to a question posed by Gheysens and Vanhecke. To prove these statements, we give a characterization of D’Atri spaces in terms of the total scalar curvature of geodesic hemispheres in any dimension.