Counting Homomorphisms to Trees Modulo a Prime

Many important graph-theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article, we study the complexity of # p H OMS T O H , the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p . Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies. Our main result states that for every tree H and every prime p the problem # p H OMS T O H is either polynomial time computable or # p P-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of # p H OMS T O H are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p . These results are the first suggesting that such dichotomies hold not only for the modulo 2 case but also for the modular counting functions of all primes p .

Serological prevalence of SARS-CoV-2 antibody among children and young age (between age 2-17 years) group in India: An interim result from a large multi-centric population-based seroepidemiological study

Background: Concern has been raised in India regarding the probable third wave of COVID-19 where children and young age group is thought to get affected the most. There is a lack of serological prevalence data in this age group. We have some interim data from our research for WHO unity protocol, which might help policymakers and the research community to answer such questions based on evidence. Hence, we conducted a study to compare the COVID -19 sero-positivity rate between children and adults Methods/Materials: This is part of an ongoing large multi-centric population-based sero-surveillance study. The study is being conducted in five selected states with a proposed total sample size of 10,000. We have data of 4,500 participants at the time of midterm analysis from four states of India. Total serum antibody against SARS-CoV-2 virus was assessed qualitatively by using a standard ELISA kit. Here we are reporting the interim data of serological prevalence among children aged between 2 to 17 years along with a comparison with ≥18-year old participants. Results: The data collection period was from 15th March 2021 to 10th June 2021. Total available data was of 4,509 participants out of which <18 years were 700 and ≥18 years was 3,809. The site-wise number of available data among the 2-17 year age group were 92, 189, 165, 146 and 108 for the site of Delhi urban resettlement colony, Delhi rural (Villages in Faridabad district under Delhi NCR), Bhubaneswar rural, Gorakhpur rural and Agartala rural area respectively. The seroprevalence was 55.7% in the <18 years age group and 63.5% in the ≥ 18 year age group. There was no statistically significant difference in prevalence between adult and children. Conclusion: SARS-CoV-2 sero-positivity rate among children was high and were comparable to the adult population. Hence, it is unlikely that any future third wave by prevailing COVID-19 variant would disproportionately affect children two years or older.

Personality Classification Experiment by Applying k-Means Clustering

This paper describes personality classification experiment by applying k-means clustering machine learning algorithms. Several previous studies have been attempted to predict personality types of human beings automatically by using various machine learning algorithms. However, only few of them have obtained good accuracy results. To classify a person into personality types, we used Jungian Type Inventory. Our method consists of three parts: data collection, data preparation, and hyper-parameter tuning. Our testing results showed that the k-means model has 107 inertia value, which is a good number for an unsupervised learning model as an interim result. With the result, we divided the data into 16 clusters, which can be considered as personality types. We continue this research with analysis of large data to be collected in the future.

COLLECTION OF BOOKS OF THE CYRILLIC FONT OF THE XVII – EARLY XX CENTURE IN THE IRKUTSK REGIONAL STATE UNIVERSAL SCIENTIFIC LIBRARY NAMED AFTER I. I. MOLCHANOV-SIBIRSKY: THE EXPERIENCE OF STUDYING AND CATALOGIZATION

The article is devoted to the thematic collection of books of the Cyrillic font of the XVII – early XX century, stored in the Department of Historical and Cultural Heritage of the Irkutsk Regional Library named after I. I. MolchanovSibirsky. The library staff formed this collection by means of identifying books from the general book storage, donations and purchases from private individuals in the period from 1976 to 2018. It presents data about the history of the collection formation, the main sources and stages of books receipt, the characteristic of its current state: number, analysis by year, place and type of publication. Particular attention is paid to books acquired at the end of XIX – early XX century. Circumstances of the pre-revolutionary library stock formation (until 1920 – the Irkutsk City Public Library) and books of the Cyrillic font purchased during this period are considered. Books accepted according to the Decree of the Council of People's Commissars of 1918 «On the order of requisition of libraries, book warehouse and books in general» are analyzed. On the example of books belonging to the library of the Irkutsk Ascension Monastery, the role of preserved ownership and dedicatory inscriptions in the study of the history of this library and the history of the individual specimens is considered. Descriptions of the four versions of the monastery library bookplates and some inscriptions with notes about the receipt history of books are provided. Inscriptions on four editions of the XVIII century are examined in detail as examples of books with the unique history. Texts of inscriptions are reproduced in the original orthography (excepting obsolete letters). All books are associated with famous personalities in the history of the region and Russia as a whole. Among them: the Bishop of Irkutsk and Nerchinsk, Saint Sophronius (Kristalevsky; 1703–1771), Hieromonk Herman, etc. The article is an interim result of a two-year study and description of the collection. The result of the work will be the release of a printed catalog.

Family entrepreneurship in the countryside: Some details of the portrait

The article is an interim result of many years of studies focused on the wide range of issues related to the development of farmers’ movement, to the interaction of contemporary rural entrepreneurs with government, rural population and colleagues in production activities. This project (field expeditions of 2018-2019) aims at assessing the challenges and prospects of the two key social institutions of the Russian village - local authorities and entrepreneurs - in terms of the dominant scenarios of their interaction and their role in stabilizing the situation in rural areas. This two-year field studies repeat the expeditions of a decade ago combining quantitative and qualitative approaches in the study of specific cases - settlements that represent the features of the Non-Black Earth regions of Russia. The author focuses on the issue actually ignored by researchers of agricultural problems - family entrepreneurship in the countryside. In the introduction, the author provides a brief overview of the specifics of the rural lifestyle in pre-revolutionary Russia. The first part of the article considers social-economic processes in the countryside during the Soviet period, which laid the foundation for the problems that determined the paths of the post-Soviet rural development. The second part of the article presents the features of the post-Soviet period in the life of the village, mainly based on the data of field expeditions to the Russian Non-Black Earth regions in 2004-2008. And, finally, the third part of the article summarizes the author’s first impressions and some results of the 2019 field expeditions and identifies permanent challenges for rural entrepreneurs. For instance, in almost every rural area of the Russian Non-Black Earth regions, one can meet farmers who strive to create a family business but are forced to take numerous tricks to achieve their goal, as if proving M. Certeau theory of resistance of the “weak” to the “strong”.

Lord’s Equity Theorem Revisited

Lord’s (1980) equity theorem claims observed-score equating to be possible only when two test forms are perfectly reliable or strictly parallel. An analysis of its proof reveals use of an incorrect statistical assumption. The assumption does not invalidate the theorem itself though, which can be shown to follow directly from the discrete nature of the equating problem it addresses. But, surprisingly, an obvious relaxation of the problem is enough to obtain exactly the opposite result: As long as two test forms measure the same ability, they can always be equated, no matter their reliability, degree of parallelness, or even difference in length. Also, in spite of its lack of validity, the original proof of Lord’s theorem has an important interim result directly applicable to the problem of assembling a new test form pre-equated to an old form.

Yezidis and Christianity: Shaping of a New Identity

For the last decades, the Yezidi identity whose main marker was for centuries based on a unique religion, the Sharfadin, has undergone specific transformations. One of the most stable trends playing a crucial role in the mentioned process, is the spread of Orthodox Christianity, particularly among the Yezidis of Georgia and Russia. This phenomenon is especially interesting regarding the fact that, unlike neo-Protestant missions, Orthodox Church has never been active in proselytism particularly among the Yezidis; no Orthodox mission has ever focused its activities on this group. Yet, the number of the Yezidis converting to the Orthodox Christianity gradually grows. The paper is an interim result of a project on the modern transformations of the Yezidi identity. Compiled on the materials collected by the author through interviews and questionnaires among the converted Yezidis of Georgia and Russia, it focuses on several particular cases reflecting the shaping of a principally new identity, when Christian mentality replaces the Yezidi eclectic religious outlook.