Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography

The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history

UV graviton scattering and positivity bounds from IR dispersion relations

Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, we find that infinite arc integrals, which are usually taken to vanish, can give a non-trivial contribution in the presence of gravity, unlike in the case of finite negative $t$. This implies that gravitational positivity bounds cannot be trusted unless the size of this contribution is estimated in some way, which implies assumptions on the UV completion of gravitational interactions. We discuss the relevance of these findings in the particular case of QED coupled to gravity.Comment: 20 pages, 2 figure

Post-inflationary GW production in generic higher (infinite) derivative gravity

Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the $R^2$, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher derivative operators which could potentially cause instabilities.Comment: We dedicate this paper to the memory of Valery Rubako

Positronium oscillations to Mirror World revisited

We present a calculation of the branching ratio of orthopositronium decay into an invisible mode, which is done in the context of Mirror World models, where ordinary positronium can disappear from our world due to oscillation into its mirror twin. In this revision we clarify some formulas and approximations used previously, correct them at some places, add new effects relevant for a feasible experiment and finally perform a combined analysis. We include into consideration various effects due to external magnetic and electric fields, collisions with cavity walls and scattering off gas atoms in the cavity. Oscillations of the Rydberg positroniums are also considered. To perform a numerical estimates in a realistic case we wrote computer code, which can be adopted in any experimental setup. Its work is illustrated with an example of a planned positronium experiment within the AEgIS project.Comment: 23 pages, 4 figures, typos corrected, references added, published versio

A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201

Markers of masculinity in Khanty, Russian, Kazakh and Chinese folklore: Pragma-Cognitive aspect

The article is devoted to the analysis of the psycholinguistic features of the male portrait in fairy tales in the different structural linguistic cultures: Khanty, Russian, Kazakh and Chinese. The choice is determined by the belonging of these peoples to traditional cultures with varying degrees of transformation of behavioral stereotypes. Traditional culture considers a man as the head of a large family, a protector, a breadwinner, a landowner with the competencies of a fisherman and a hunter, so a woman with children needs his help and care. In this regard, the purpose of this study is the need, based on the psycholinguistic features of personal characteristics, to reveal the masculine image in the tales of Khanty, Russians, Kazakhs and Chinese. The authors analyze the psycholinguistic and stylistic means of representing masculine traits in the fairy tales of these peoples. Kazakh, Khanty, Russian and Chinese fairy tales for the first time become the object of psycholinguistic characterization of personal characteristics on the example of the image of masculinity. The course of reasoning on the topic of the study leads the authors to the conclusion that the analyzed original texts of fairy tales contrast with a reliable representation of the ethnic group.  The traditional male portrait is shown from the position of describing the psycholinguistic features of personal characteristics, through the relationship of the main characters, through their external and internal speech. This approach makes it possible to identify a set of ethnic, social, historical and geographical factors inextricably linked with language, on the one hand, and on the other – caused by psychological manifestations

Crystal structure and synthesis of new trinuclear 3d-metal trifluoroacetates

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The Seventh International Olympiad in Cryptography: problems and solutions

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the first round and 49 teams in the second round from 32 countries. In this paper, problems and their solutions of NSUCRYPTO'2020 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, permutations, primality tests, etc. We discuss several open problems on JPEG encoding, Miller -- Rabin primality test, special bases in the vector space, AES-GCM. The problem of a modified Miller -- Rabin primality test was solved during the Olympiad. The problem for finding special bases was partially solved

University Employee Engagement Study Methodology

Представленная статья относится к категории исследовательских, в ней описывается проектирование и апробация исследования вовлеченности сотрудников российского университета. Вовлеченность сотрудников – один из важных HR-трендов XXI в, широко зарекомендовавший себя в бизнес-среде, однако мало популярный в академическом сообществе. Цель исследования заключалась в разработке доступного инструмента для управленцев университетов, с помощью которого можно было бы исследовать уровень вовлеченности сотрудников и в соответствии с полученными данными, выстраивать и корректировать кадровую политику образовательной организации. В рамках статьи были проанализированы ключевые модели вовлеченности (Aon Hewitt, Gallup Inc., Hay Group, ЭКОПСИ Консалтинг и др.), определены индикаторы и факторы вовлеченности. На основании полученных данных была спроектирована методика для университета, в ориентации на процессный и клиентоориентированный подход менеджмента была специфицирована типология должностей университета, проведено пилотное исследование. По результатам пилота были сформулированы частные выводы и рекомендации, касающиеся кадровой политики образовательной организации, проведена апробация методики. Дальнейшая задача – валидизация методики на большей выборке и на разных типах университетов. Настоящая статья может быть полезна как для HR-структур университетов, так и для управленческого штаба в целом, для тех, кто делает ставку на развитие сотрудников, на их потенциал, повышение лояльности к организации, вовлеченности в исполнение своих рабочих ролей. Оригинальность и новизна связаны с разработкой фокусированной методики для применения в организациях высшего профессионального образования.This research paper describes the design and approbation of the Russian university employees’ engagement study. Employees engagement is one of the most important HR-trends of the XXI century, widely established in the business environment, but little popular in the academic community. The purpose of the study was to develop a tool for university managers to help them build and adjust the personnel policy of the educational organization. The study analysed key models of employee engagement (Aon Hewitt, Gallup Inc., Hay Group etc.), defined indicators and factors of engagement. On the basis of the obtained data, there was designed a methodology to specify the typology of university positions as oriented to the process and customer-oriented management approaches. The methodology was tested, conclusions and recommendations concerning the personnel policy of the educational organization were formulated according to the results of the pilot study. The further research challenge is validating the methodology on a larger sample and on different types of universities. This article can be useful both for universities’ whole management staff within HR-structures and for those who rely upon the employees’ development, potential, loyalty towards the organization, role engagement. Original and new in the article does appear the development of focused methods to be used in higher education institutions