Spherical principal series of quantum Harish-Chandra modules

The non-degenerate spherical principal series of quantum Harish-Chandra modules is constructed. These modules appear in the theory of quantum bounded symmertic domains.Comment: 14 page

On a q-analog of the Wallach-Okounkov formula

We obtain a $q$-analog of the well known Wallach-Okounkov result on a joint spectrum of invariant differential operators with polynomial coefficients on a prehomogeneous vector space of complex $n \times n$-matrices. We are motivated by applications to the problems of harmonic analysis in the quantum matrix ball: our main theorem can be used while proving the Plancherel formula (to be published). This paper is dedicated to our friend and colleague Dmitry Shklyarov who celebrates his 30-th birthday on April 8, 2006.Comment: 10 pages, corrected minor misprint

Low-energy vibrational density of states of plasticized poly(methyl methacrylate)

The low-energy vibrational density of states (VDOS)of hydrogenated or deuterated poly(methyl methacrylate)(PMMA)plasticized by dibutyl phtalate (DBP) is determined by inelastic neutron scattering.From experiment, it is equal to the sum of the ones of the PMMA and DBP components.However, a partition of the total low-energy VDOS among PMMA and DBP was observed.Contrary to Raman scattering, neutron scattering does not show enhancement of the boson peak due to plasticization.Comment: 9 pages, 2 figures (Workshop on Disordered Systems, Andalo

Spherical Principal Series of Quantum Harish-Chandra Modules

The nondegenerate spherical principal series of quantum Harish-Chandra modules is constructed. These modules appear in the theory of quantum bounded symmetric domains

Optimum Treatment Strategy in Chronic Coronary Syndromes: the New Trials vs the Current Guidelines

Coronary revascularization is one of the most studied types of interventions in cardiology, but there is no consensus among specialists about the indications for its implementation in patients with chronic coronary syndromes (CCS). The data of recently completed clinical trials on the role of revascularization in CCS clearly contradict the current Guidelines, emphasizing the high effectiveness of modern conservative therapy. This paper discusses the main recommendations of the most significant American and European Guidelines on myocardial revascularization, and also analyzes the appropriateness of revascularization to improve the prognosis and symptoms in chronic coronary syndromes in view of the new research data, primarily the ISCHEMIA study (NCT01471522). Its strengths and limitations are discussed in detail. The data on the expediency of revacularization in CCS, obtained after the completion of ISCHEMIA and its potential significance, as well as subgroup analyses of ISCHEMIA, including in the most important ‘problem’ subgroups (3-vessel disease, proximal LAD disease, severe ischemia on stress test, etc.) are discussed. The paper also discusses the important achievements in modern drug therapy of chronic coronary syndromes, primarily antithrombotic therapy. The data of the COMPASS study (NCT01776424) are discussed, based on which the addition of a second antithrombotic drug – rivaroxaban in a small dose (2.5 mg BID) – is recommended for patients with CCS without atrial fibrillation who have high-risk characteristics. Indications the administration of dual antithrombotic therapy to patients with CCS, comparative results of its various regimens in relation to the prevention of cardiovascular complications, the risk of bleeding and the net clinical effect are given

Degenerate principal series of quantum Harish-Chandra modules

In this paper we study a quantum analogue of a degenerate principal series of $U_q \mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \times n$-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable and investigate their equivalence. These results are q-analogues of known classical results on reducibility and unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and Tan.Comment: 33 pages, 4 figure

Inelastic light, neutron, and X-ray scatterings related to the heterogeneous elasticity of glasses

The effects of plasticization of poly(methyl methacrylate) glass on the boson peaks observed by Raman and neutron scattering are compared. In plasticized glass the cohesion heterogeneities are responsible for the neutron boson peak and partially for the Raman one, which is enhanced by the composition heterogeneities. Because the composition heterogeneities have a size similar to that of the cohesion ones and form quasiperiodic clusters, as observed by small angle X-ray scattering, it is inferred that the cohesion heterogeneities in a normal glass form nearly periodic arrangements too. Such structure at the nanometric scale explains the linear dispersion of the vibrational frequency versus the transfer momentum observed by inelastic X-ray scattering.Comment: 9 pages, 2 figures, to be published in J. Non-Cryst. Solids (Proceedings of the 4th IDMRCS

МикроРНК: половые гормоны, гормональный канцерогенез, гормоночувствительность опухолевой ткани

Sex hormones, regulating normal physiological processes of most tissues and organs, are considered to be one of the key factors in the development and progression of the reproductive system cancer. Recently, the importance of the system for post-transcriptional control of gene expression mediated by short single-stranded RNA molecules (microRNA) became evident. This system is involved in regulation of normal physiological processes and in the pathogenesis of many diseases, including cancer. In review we discuss the relationship between the two regulatory systems – sex hormones and microRNAs. The relationship of these systems is considered in the context of two tumors – breast and prostate cancer. In particular, the history of research on the role of sex hormones in the pathogenesis of breast cancer and prostate cancer is briefly covered. Additionally, modern scientific data on the biogenesis and biological role of microRNAs are presented in more detail. In the cells of the hormone-sensitive tissues, sex hormones regulate the microRNA-mediated machinery of gene expression control by two known ways: specifically, affecting the activity of individual microRNA molecules and non-specifically by altering the efficiency of microRNA biogenesis and activity of RNA-induced silencing complex. This downstream regulatory network substantially enhances biological effects of sex hormones at physiological conditions. Malignant transformation leads to a distortion of the regulatory effects of sex hormones that crucially influence the system of microRNA-regulated post-transcriptional control of gene expression. The most established and clinically significant example of such phenomenon is the loss of sensitivity of cells to the regulatory action of these hormones. As a consequence, cancer cells acquire the ability to active proliferation without stimulation with sex hormones. This effect is partly mediated by microRNAs. Also, relevant experimental data indicating the involvement of microRNAs in the phenomenon of breast cancer and prostate cancer cells hormone resistance are discussed in the review.Conception of the possible primary role of microRNAs in the process of malignant transformation and distortion of hormonal regulation is based on a smaller number of scientific reports. In general, in accordance with the main biological role of microRNAs, latter may affect sex hormones function via interaction with the mRNAs of hormone receptors and inhibition of their synthesis. As a result, the effect of many microRNA is converging on the single mRNA, results in suppression of corresponding protein function and, in the end, leads to inhibition of regulatory cascade downstream of sex steroids.Finally, the analysis of the fundamental aspects of sex hormones – microRNA interplay is supplemented by brief overview of clinically significant problems. The prospects for development and introduction into clinical practice innovative methods of diagnosis, prediction and optimization of therapy of breast and prostate cancers are discussed as well.Половые гормоны, регулируя нормальные физиологические процессы большинства тканей и органов, традиционно считаются одним из ключевых факторов развития и прогрессии опухолей органов репродуктивной системы. В течение последних лет стала очевидной значимость системы посттранскрипционного контроля генной экспрессии, опосредуемой короткими одноцепочечными молекулами РНК, так называемыми микроРНК, в регуляции нормальных физиологических процессов и в патогенезе многих заболеваний, включая онкологические. В представленном обзоре обсуждается взаимосвязь между двумя в определенном смысле самостоятельными регуляторными системами – половыми гормонами и микроРНК. Взаимоотношения этих систем рассматриваются в контексте двух онкологических заболеваний – рака молочной железы (РМЖ) и рака предстательной железы (РПЖ).Кратко освещается история исследований роли половых гормонов в патогенезе РМЖ и РПЖ, более подробно представлены современные данные о биогенезе и биологической роли микроРНК. В клетках гормоночувствительных тканей половые гормоны регулируют работу микроРНК-аппарата регуляции генной экспрессии двумя известными путями: специфично, влияя на активность отдельных молекул микроРНК, и неспецифично, изменяя эффективность биогенеза микроРНК и активность цитоплазматического РНК-белкового комплекса. С учетом работы такой регуляторной сети существенно расширяются представления о биологических эффектах половых гормонов в физиологических условиях. Злокачественная трансформация приводит к искажению регуляторных эффектов половых гормонов, что отражается и усиливается регулируемой ими системой посттранскрипционного контроля генной экспрессии, опосредуемой микроРНК. К числу наиболее исследованных и клинически значимых примеров этого феномена относится утрата чувствительности к влиянию половых гормонов, на фоне чего клетки приобретают способность к активной пролиферации безгормональной стимуляции за счет подключения коллатеральных сигнальных путей и ростовых факторов. Этот феномен отчасти опосредуется микроРНК, и как следствие, к обсуждению привлекаются современные экспериментальные данные, указывающие на причастность микроРНК к формированию феномена гормональной резистентности клеток РМЖ и РПЖ. Представления о возможной первичной роли нарушений функций микроРНК в процессе опухолевой трансформации и искажения механизмов гормональной регуляции основаны на меньшем количестве проведенных и опубликованных исследований. В целом, в соответствии с основной биологической ролью микроРНК, их таргетное воздействие на функции половых гормонов в основном опосредуется взаимодействием с различными участками матричной РНК (мРНК) соответствующих гормональных рецепторов и ведет к угнетению синтеза последних. В итоге действие многих микроРНК конвергируется на одной молекуле мРНК, что в большинстве случаев приводит к подавлению сигнальных каскадов, индуцируемых половыми гормонами.Анализ фундаментальных аспектов дополнен обзором клинически значимых проблем, в решении которых должна учитываться взаимосвязь половых гормонов и микроРНК. Коротко обсуждаются перспективы развития и внедрения в клиническую практику методов диагностики, прогнозирования и оптимизации терапии опухолевых заболеваний гормоночувствительных тканей на основе сведений о микроРНК и их связях с обсуждаемыми проблемами

Experimental library screening demonstrates the successful application of computational protein design to large structural ensembles

The stability, activity, and solubility of a protein sequence are determined by a delicate balance of molecular interactions in a variety of conformational states. Even so, most computational protein design methods model sequences in the context of a single native conformation. Simulations that model the native state as an ensemble have been mostly neglected due to the lack of sufficiently powerful optimization algorithms for multistate design. Here, we have applied our multistate design algorithm to study the potential utility of various forms of input structural data for design. To facilitate a more thorough analysis, we developed new methods for the design and high-throughput stability determination of combinatorial mutation libraries based on protein design calculations. The application of these methods to the core design of a small model system produced many variants with improved thermodynamic stability and showed that multistate design methods can be readily applied to large structural ensembles. We found that exhaustive screening of our designed libraries helped to clarify several sources of simulation error that would have otherwise been difficult to ascertain. Interestingly, the lack of correlation between our simulated and experimentally measured stability values shows clearly that a design procedure need not reproduce experimental data exactly to achieve success. This surprising result suggests potentially fruitful directions for the improvement of computational protein design technology

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE