Vectorial Ribaucour Transformations for the Lame Equations

The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package

A high-pressure hydrogen time projection chamber for the MuCap experiment

The MuCap experiment at the Paul Scherrer Institute performed a high-precision measurement of the rate of the basic electroweak process of nuclear muon capture by the proton, $\mu^- + p \rightarrow n + \nu_\mu$. The experimental approach was based on the use of a time projection chamber (TPC) that operated in pure hydrogen gas at a pressure of 10 bar and functioned as an active muon stopping target. The TPC detected the tracks of individual muon arrivals in three dimensions, while the trajectories of outgoing decay (Michel) electrons were measured by two surrounding wire chambers and a plastic scintillation hodoscope. The muon and electron detectors together enabled a precise measurement of the $\mu p$ atom's lifetime, from which the nuclear muon capture rate was deduced. The TPC was also used to monitor the purity of the hydrogen gas by detecting the nuclear recoils that follow muon capture by elemental impurities. This paper describes the TPC design and performance in detail.Comment: 15 pages, 13 figures, to be submitted to Eur. Phys. J. A; clarified section 3.1.2 and made minor stylistic corrections for Eur. Phys. J. A requirement

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

Measurement of the Rate of Muon Capture in Hydrogen Gas and Determination of the Proton's Pseudoscalar Coupling gPg_P

The rate of nuclear muon capture by the proton has been measured using a new experimental technique based on a time projection chamber operating in ultra-clean, deuterium-depleted hydrogen gas at 1 MPa pressure. The capture rate was obtained from the difference between the measured $\mu^-$ disappearance rate in hydrogen and the world average for the $\mu^+$ decay rate. The target's low gas density of 1% compared to liquid hydrogen is key to avoiding uncertainties that arise from the formation of muonic molecules. The capture rate from the hyperfine singlet ground state of the $\mu p$ atom is measured to be $\Lambda_S=725.0 \pm 17.4 s^{-1}$, from which the induced pseudoscalar coupling of the nucleon, $g_P(q^2=-0.88 m_\mu^2)=7.3 \pm 1.1$, is extracted. This result is consistent with theoretical predictions for $g_P$ that are based on the approximate chiral symmetry of QCD.Comment: submitted to Phys.Rev.Let

Two-dimensional rational solitons and their blow-up via the Moutard transformation

By using the Moutard transformation of two-dimensional Schroedinger operators we derive a procedure for constructing explicit examples of such operators with rational fast decaying potentials and degenerate $L_2$-kernels (this construction was sketched in arXiv:0706.3595) and show that if we take some of these potentials as the Cauchy data for the Novikov-Veselov equation (a two-dimensional version of the Korteweg-de Vries equation), then the corresponding solutions blow up in a finite timeComment: 22 pages, PDFLatex, 9 figures. v2: some computations correcte

АНАЛИЗ ОТНОСИТЕЛЬНОЙ ЭКСПРЕССИИ ГЕНА HMGA2 И ОНКОГЕННОЙ МИКРОРНК-221 В ЦИТОЛОГИЧЕСКИХ ПРЕПАРАТАХ, ПОЛУЧЕННЫХ ПРИ ТОНКОИГОЛЬНОЙ АСПИРАЦИОННОЙ БИОПСИИ УЗЛОВ ЩИТОВИДНОЙ ЖЕЛЕЗЫ

Background. Fine-needle aspiration biopsy is recognized as the “gold standard” in the preoperative diagnosis of thyroid cancer. However, this method does not always allow reliable differentiation between benign and malignant thyroid nodules. Thus, the cytological report of a “follicular neoplasm or suspicious for a follicular neoplasm” suggests surgical lobectomy. However, in most cases, this conclusion does not point to follicular cancer but to benign neoplasm, follicular adenoma, where the surgical intervention is excessive. This implies the great relevance of finding biological markers capable of enhancing the specificity of detecting malignant neoplasms. Such markers may include an increase in the level of expression of oncogenes or a change in the expression of microRNA, since it is known that the content of a number of microRNAs changes significantly during the development of thyroid tumors.Materials and methods. The expression level of the HMGA2 gene, normally active at the embryonic stage, and oncogenic miRNA-221 microRNA was analyzed using real-time reverse transcription polymerase chain reaction in 713 cytological preparations of the thyroid gland (stained material dried on glasses) obtained by standard fine-needle aspiration biopsy. The sample included preparations corresponding to different cytological diagnoses: benign (n = 375), follicular neoplasm or suspicious for a follicular neoplasm (n = 143), medullary carcinoma (n = 7), papillary carcinoma (n = 186) and anaplastic carcinoma (n = 2).Results. The content of messenger RNA (mRNA) HMGA2 (P = 1.6 × 10–66, area under curve ROC 0.946) and miR-221 (P = 6.3 × 10–61, area under curve ROC 0.927) proved to be significantly elevated in papillary carcinoma compared to benign tumors. Follicular neoplasms showed significant heterogeneity in the quantity of both molecular markers. At the same time, an elevated level of miR-221 (3 times on average) was also characteristic of samples from this group with an increased level of expression of the HMGA2 gene (an average of 85 times). With regard to the quantity of these markers, the group of follicular neoplasms, in which no increase in the HMGA2 mRNA level was detected, did not differ from the group of benign nodules.Conclusions. The obtained results show that assessing the expression of HMGA2 mRNA and oncogenic miR-221 makes it possible to differentiate the papillary thyroid carcinoma from goiter at the preoperative stage, and based on the content of the HMGA2 mRNA, the group of follicular neoplasms can be divided into subgroups presumably differing in the risk of malignancy.Введение. Цитологический анализ препаратов тонкоигольной аспирационной пункционной биопсии является «золотым стандартом» дооперационной диагностики рака щитовидной железы (ЩЖ). Однако этот метод не всегда позволяет надежно дифференцировать доброкачественные и злокачественные узлы ЩЖ. Так, цитологическое заключение «фолликулярная опухоль или подозрение на фолликулярную опухоль» предполагает оперативное вмешательство. Однако в большинстве случаев это заключение соответствует не фолликулярному раку, а доброкачественной фолликулярной аденоме, в отношении которой хирургическое вмешательство оказывается избыточным. В связи с этим актуален поиск биологических маркеров, анализ содержания которых мог бы повысить специфичность определения злокачественных опухолей. К таким маркерам может относиться повышение уровня экспрессии онкогенов или изменение экспрессии микроРНК, поскольку известно, что при развитии опухолей ЩЖ существенно меняется содержание целого ряда микроРНК.Материалы и методы. С помощью полимеразной цепной реакции с обратной транскрипцией с детекцией в реальном времени проведен анализ уровня экспрессии гена HMGA2, в норме активного на эмбриональной стадии, и онкогенной микроРНК миРНК-221 в 713 цитологических препаратах ЩЖ (окрашенный материал, высушенный на стеклах), полученных при выполнении стандартной тонкоигольной аспирационной пункционной биопсии. Выборка включала препараты, соответствующие разным цитологическим заключениям: доброкачественные образования (n = 375), фолликулярные опухоли или подозрение на фолликулярную опухоль (n = 143), медуллярный рак (n = 7), папиллярный рак (n = 186), анапластический рак (n = 2).Результаты. Содержание матричной РНК (мРНК) HMGA2 (P = 1,6 ×10–66; площадь под ROC-кривой 0,946) и миРНК-221 (P = 6,3 × 10–61; площадь под ROC-кривой 0,927) оказалось достоверно повышенным при папиллярном раке по сравнению с доброкачественными опухолями. Фолликулярные опухоли продемонстрировали существенную неоднородность по содержанию обоих молекулярных маркеров. При этом для образцов из этой группы с повышенным (в среднем в 85 раз) уровнем экспрессии гена HMGA2 был характерен также повышенный (в среднем в 3 раза) уровень миРНК-221. Группа фолликулярных опухолей, в которых не выявлены повышенные уровни мРНК гена HMGA2, по содержанию перечисленных маркеров не отличалась от группы доброкачественных образований.Заключение. Полученные результаты показывают, что оценка экспрессии мРНК HMGA2 и онкогенной миРНК-221 позволяет дифференцировать на дооперационной стадии папиллярный рак ЩЖ и доброкачественные неопухолевые образования, а по содержанию мРНК HMGA2 можно разделить группу фолликулярных опухолей на подгруппы, предположительно различающиеся по риску злокачественности