Integration on complex Grassmannians, deformed monotone Hurwitz numbers, and interlacing phenomena

We introduce a family of polynomials, which arise in three distinct ways: in the large $N$ expansion of a matrix integral, as a weighted enumeration of factorisations of permutations, and via the topological recursion. More explicitly, we interpret the complex Grassmannian $\mathrm{Gr}(M,N)$ as the space of $N \times N$ idempotent Hermitian matrices of rank $M$ and develop a Weingarten calculus to integrate products of matrix elements over it. In the regime of large $N$ and fixed ratio $\frac{M}{N}$, such integrals have expansions whose coefficients count factorisations of permutations into monotone sequences of transpositions, with each sequence weighted by a monomial in $t = 1 - \frac{N}{M}$. This gives rise to the desired polynomials, which specialise to the monotone Hurwitz numbers when $t = 1$. These so-called deformed monotone Hurwitz numbers satisfy a cut-and-join recursion, a one-point recursion, and the topological recursion. Furthermore, we conjecture on the basis of overwhelming empirical evidence that the deformed monotone Hurwitz numbers are real-rooted polynomials whose roots satisfy remarkable interlacing phenomena. An outcome of our work is the viewpoint that the topological recursion can be used to "topologise" sequences of polynomials, and we claim that the resulting families of polynomials may possess interesting properties. As a further case study, we consider a weighted enumeration of dessins d'enfant and conjecture that the resulting polynomials are also real-rooted and satisfy analogous interlacing properties.Comment: 30 pages, 3 figures. Comments welcome

Properties and Design Characteristics of the Fiber Concrete

AbstractUnder the contemporary conditions of permanent construction complication, the volume of reinforce-concrete structures that are in the process of exploitation of building function in the conditions of difficult loading is growing: they are exposed to the slanting bend, twisting and dynamic influences. These structures include foundations and ceilings of productive buildings installed with the use of vibrating equipment (flatting mills, press, metal-working machine-tools), beams for a faucet, highway coverage, bridge elements, air strips of the air fields, body elements of hydro energetic objects. The complex loaded structures shall meet the stringent requirements not only in terms of bending and compression resistance but also in terms of structural integrity maintenance (crack resistance). In case of the technological process change or formation of defects and damages, repair of these elements is not possible – they can be only replaced, and this will demand to stop the production, sort out a high-cube of reinforced-concrete structures and, consequently, lead to material expenses comparable with a new building construction. An increase of the exploitation term of the complex loaded reinforce-concrete structures is a topical and economically demanded research

An efficient MPI/OpenMP parallelization of the Hartree-Fock method for the second generation of Intel Xeon Phi processor

Modern OpenMP threading techniques are used to convert the MPI-only Hartree-Fock code in the GAMESS program to a hybrid MPI/OpenMP algorithm. Two separate implementations that differ by the sharing or replication of key data structures among threads are considered, density and Fock matrices. All implementations are benchmarked on a super-computer of 3,000 Intel Xeon Phi processors. With 64 cores per processor, scaling numbers are reported on up to 192,000 cores. The hybrid MPI/OpenMP implementation reduces the memory footprint by approximately 200 times compared to the legacy code. The MPI/OpenMP code was shown to run up to six times faster than the original for a range of molecular system sizes.Comment: SC17 conference paper, 12 pages, 7 figure

COMPARATIVE ANALYSIS OF RADIOLOGIC ASPECTS OF FACET JOINTS IN SURGICAL TREATMENT OF PATIENTS WITH DEGENERATIVE DISEASES OF THE LUMBAR SPINE

Objective To study the radiologic characteristics of facet joints at different stages of the degenerative process in the lumbar spine to determine the indications for various methods of fixing the affected segment and to evaluate the results of treatment.Material and Methods To determine the radiologic aspects of facet joints in the affected area and in  adjacent segments of the lumbar spine, two groups were formed, including 136 patients who underwent multispiral computed tomography in two-energy mode before surgery and 12 months after surgery. Group I included patients who underwent rigid fixation of the spine (360°), and group II included patients who underwent dynamic fixation using nitinol rods (180°).Results Based on a comprehensive instrumental study, it was found that the degeneration of the intervertebral disc according to Pfirrmann II and III revealed an increase in the density of the cartilaginous plate in facet joints (HU). These digital indicators confirm the preservation of joint functionality, both in the affected area and in adjacent segments. With severe degrees of disk degeneration in Pfirrmann IV and V and facet joints, deep pathological changes occurred, directed towards the loss of facet joints functionality.Conclusion The obtained digital indicators of dual-energy computed tomography for the state of facet joints  in combination with the results of magnetic resonance imaging can be used as criteria in a complex of patient studies to assess the degree of degeneration of the vertebral motion segment in the affected area and adjacent segments. We recommend using these criteria as a diagnostic component for finding optimal methods of surgical treatment

Managing virtual rapport on Tripadvisor: discourse in hotel responses to negative online reviews

Digital technology has immensely transformed communication, and social media facilitates online feedback mechanisms, empowering consumers’ voices via online reviews. This has led to the pervasively growing influence of electronic word of mouth (eWOM) on customers’ purchase intentions, as negative online reviews can be detrimental to business performance. Therefore, digital business engagement on online platforms is essential to ensure customer satisfaction and manage online reputation. Building on Spencer-Oatey’s (2008) Rapport Management Model (RMM), this qualitative study explores the rapport management strategies used by eighteen Malaysian five-, four- and three-star hotels to respond to negative online reviews, from the perspective of the RMM discourse domain. The hotel responses were collected from TripAdvisor, using purposeful sampling and analysed with Computer-Mediated Discourse Analysis. The findings show that the five- and four-star hotels employed higher frequencies of moves in their responses to complaints in negative reviews. Some four- and three-star hotels took a more confrontational approach by using the sub-move ‘denying problems’. In terms of RMM rapport orientation, this sub-move can be rapport-challenging in customer relationships. This study highlights that managing negative reviews more efficiently for service recovery on online platforms is essential to maintain customer relationships and establish a positive online corporate reputation. More generally, the findings provide insights on cultural rapport management strategies used in one Southeast Asian country—Malaysia

Temperament and self-based correlates of cooperative, competitive and individualistic learning preferences

People vary in the extent to which they prefer cooperative, competitive or individualistic achievement tasks. In the present research, we conducted two studies designed to investigate correlates and possible roots of these social interdependence orientations, namely approach and avoidance temperament, general self-efficacy, implicit theories of intelligence, and contingencies of self-worth based in others’ approval, competition, and academic competence. The results indicated that approach temperament, general self-efficacy, and incremental theory were positively, and entity theory was negatively related to cooperative preferences (|r| range from .11 to .41); approach temperament, general self-efficacy, competition contingencies, and academic competence contingencies were positively related to competitive preferences (|r| range from .16 to .46); and avoidance temperament, entity theory, competitive contingencies, and academic competence contingencies were positively related, and incremental theory was negatively related to individualistic preferences (|r| range from .09 to .15). The findings are discussed with regard to the meaning of each of the three social interdependence orientations, cultural differences among the observed relations, and implications for practicioners

From Bengali to English: sequential bilingualism of a second-generation British Bangladeshi

The paper discusses sequential language acquisition of the researcher's daughter Safa who transformed from a monolingual Bengali speaker to an almost monolingual English speaker in a few months after moving to the UK. Safa was born in Bangladesh and was a monolingual Bengali speaker until she was three years and nine months when the family moved to the UK. Unlike most research on sequential bilingualism, Safa's transition from Bengali to English went through a period of an invented language, which she developed and used for a few months. Safa then underwent language shift as Bengali became her passive language. Safa's loss of fluency in Bengali was mainly due to the absence of Bengali linguistic environment, because her family lived outside the community. Safa's mother's indifference to Bangladeshi ethnicity and her parents’ positive attitude towards Britishness meant that her decline in Bengali did not cause them much concern. Despite the lack of proficiency in Bengali, Safa still retains a strong ethnic Bangladeshi identity. Tabors and Snow’s four-stage developmental process of sequential second-language acquisition has been applied to find the similarities and differences in Safa's case, while language maintenance and shift theories have contributed to the analysis of the process of her language shift

Nanostructure of teeth enamel in norm and at dysplasia of connecting Tissue

According to the results of the study of the tooth enamel ultrastructure by atomic force microscopy, it is possible to speak about the violation of mineralization and the organization of enamel prisms of persons with the signs of DCT. Atomic force microscopy method makes it possible to study in detail the internal structures of the enamel of teeth with and without DCT. This method allows us to study in detail the distinctive features of the shape and structure of the enamel prisms, the size of the enamel prisms in the vertical and horizontal planes, the number of enamel prisms per unit volume, the distance between the enamel prisms, the size of the cover of the enamel prism, the height of the inter-prism interval that have a specific content and certain principles of their individual characteristics shaping.По результатам исследования ультраструктуры эмали зубов методом атомно - силовой микроскопии можно говорить о нарушении минерализации и организации эмалевых призм улице признаками дисплазии соединительной ткани (ДСТ). Метод атомно-силовой микроскопии позволяет детально изучить внутренние структуры эмали зубов при ДСТ и без нее. Названный метод позволяет детально изучить отличительные признаки по форме и строению эмалевых призм, размеру эмалевых призм в вертикальной и горизонтальной плоскостях, количеству эмалевых призм в единице объема, расстоянию между эмалевыми призмами, величине оболочки эмалевой призмы, высоте межпризменного промежутка, которые имеют конкретное содержание и определенные принципы формообразования их индивидуальных особенностей

Neurolinguistic aspects of attrition

International audienceThe aim of this paper is to provide the reader with a general overview of the field of attrition. Having situated this relatively new research domain with respect to related fields and approaches, a brief summary of the most important research questions and preliminary findings is given. The discussion then focuses on two issues that are of particular interest with respect to neurolinguistics: the role of the subject's age and of the influence of L2. Concerning the former, a summary of research on the critical period hypothesis is given and discussed in the light of findings from attrition research. Another issue concerns the principal mechanisms involved in L1 attrition, i.e. whether attrition occurs because of lack of L1 use or because of its replacement by the competing L2 structures. Research issues of such scope need integrative approaches and greatly benefit from comparisons with related fields such as normal aging, acquisition and aphasia