The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\partial f/\partial w, \partial f/\partial z)$ on ${\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.Comment: 6 page

Connected components of spaces of Morse functions with fixed critical points

Let $M$ be a smooth closed orientable surface and $F=F_{p,q,r}$ be the space of Morse functions on $M$ having exactly $p$ critical points of local minima, $q\ge1$ saddle critical points, and $r$ critical points of local maxima, moreover all the points are fixed. Let $F_f$ be the connected component of a function $f\in F$ in $F$. By means of the winding number introduced by Reinhart (1960), a surjection $\pi_0(F)\to{\mathbb Z}^{p+r-1}$ is constructed. In particular, $|\pi_0(F)|=\infty$, and the Dehn twist about the boundary of any disk containing exactly two critical points, exactly one of which is a saddle point, does not preserve $F_f$. Let $\mathscr D$ be the group of orientation preserving diffeomorphisms of $M$ leaving fixed the critical points, ${\mathscr D}^0$ be the connected component of ${\rm id}_M$ in $\mathscr D$, and ${\mathscr D}_f\subset{\mathscr D}$ the set of diffeomorphisms preserving $F_f$. Let ${\mathscr H}_f$ be the subgroup of ${\mathscr D}_f$ generated by ${\mathscr D}^0$ and all diffeomorphisms $h\in{\mathscr D}$ which preserve some functions $f_1\in F_f$, and let ${\mathscr H}_f^{\rm abs}$ be its subgroup generated ${\mathscr D}^0$ and the Dehn twists about the components of level curves of functions $f_1\in F_f$. We prove that ${\mathscr H}_f^{\rm abs}\subsetneq{\mathscr D}_f$ if $q\ge2$, and construct an epimorphism ${\mathscr D}_f/{\mathscr H}_f^{\rm abs}\to{\mathbb Z}_2^{q-1}$, by means of the winding number. A finite polyhedral complex $K=K_{p,q,r}$ associated to the space $F$ is defined. An epimorphism $\mu:\pi_1(K)\to{\mathscr D}_f/{\mathscr H}_f$ and finite generating sets for the groups ${\mathscr D}_f/{\mathscr D}^0$ and ${\mathscr D}_f/{\mathscr H}_f$ in terms of the 2-skeleton of the complex $K$ are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik Moskov. Univ., a typo in theorem 1 is correcte

Aggregation in a mixture of cetyltrimethylammonium bromide and polyoxyethylene 600 monolaurate solutions

Micellization in the cetyltrimethylammonium bromide (CTAB)-polyoxyethylene 600 monolaurate (PL)-chloroform system is studied with dielcometric titration, NMR self-diffusion (2D DOSY), 13C NMR spectroscopy, and light scattering methods. The formation of mixed aggregates of surfactants is established. It is shown that CTAB and PL polar moieties interact in the inverse micelle core in the vicinity of PL carbonyl group. © Pleiadas Publishing, Inc., 2006

Method for non-invasive assessment of the structure of a heart valve bioprosthesis

Background. The study of explanted heart valve bioprostheses is a valuable source of information about the destructive processes in their components that develop as a result of prolonged contact with the recipient’s body. An analysis of the morphology, staging and degree of involvement of various valve prosthesis materials in the prevalence of pathological processes – calcification, mechanical damage, growth of the connective tissue capsule, is the basis for developing potential methods for increasing the service life of these products and reducing the risk of re-interventions. The aim of the study was to evaluate the potential of computed microtomography to analyze the internal structure of a biological prosthetic heart valve explanted due to dysfunction. Material and methods. In this work, we investigated the prevalence of pathological mineralization of the PeriCor bioprosthesis, explanted as a result of the developed dysfunction of the leaflet apparatus with a clinical picture of grade 2B prosthetic insufficiency. The material was described macroscopically, after which it was subjected to high-resolution computed microtomography. In the structure of the sample, X-ray dense areas of pathological mineralization were identified and described, and the volume of the material involved in calcification was assessed. Results. It was shown that the main pathological changes that led to prosthetic dysfunction were degenerative changes in the biomaterial with signs of calcification, thickening and rupture of the leaflets. It was quantitatively determined that the areas of radiologically dense inclusions (calcifications) occupy 11.1 % of the volume of the material. It has been established that the described areas are associated with the sheathing of the frame and with the elements of the suture material used in the production of this bioprosthesis. Conclusion. The method of non-destructive analysis of the internal structure of altered materials of a biological prosthesis studied in this work has demonstrated the possibility of а qualitative and quantitative assessment of areas of pathological mineralization, their distribution and connection with other processes leading to the development of prosthetic dysfunction. The method makes it possible to visualize macro- and microsites of calcification and can become a valuable tool to complement existing approaches to the study of explanted bioprostheses

The cinnamyl alcohol dehydrogenase gene family is involved in the response to Fusarium oxysporum in resistant and susceptible flax genotypes

Flax (Linum usitatissimum L.) is used for the production of textile, oils, pharmaceuticals, and composite materials. Fusarium wilt, caused by the fungus Fusarium oxysporum f. sp. lini, is a very harmful disease that reduces flax production. Flax cultivars that are resistant to Fusarium wilt have been developed, and the genes that are involved in the host response to F. oxysporum have been identified. However, the mechanisms underlying resistance to this pathogen remain unclear. In the present study, we used transcriptome sequencing data obtained from susceptible and resistant flax genotypes grown under control conditions or F. oxysporum infection. Approximately 250 million reads, generated with an Illumina NextSeq instrument, were analyzed. After filtering to exclude the F. oxysporum transcriptome, the remaining reads were mapped to the L. usitatissimum genome and quantified. Then, the expression levels of cinnamyl alcohol dehydrogenase (CAD) family genes, which are known to be involved in the response to F. oxysporum, were evaluated in resistant and susceptible flax genotypes. Expression alterations in response to the pathogen were detected for all 13 examined CAD genes. The most significant differences in expression between control and infected plants were observed for CAD1B, CAD4A, CAD5A, and CAD5B, with strong upregulation of CAD1B, CAD5A, and CAD5B and strong downregulation of CAD4A. When plants were grown under the same conditions, the expression levels were similar in all studied flax genotypes for most CAD genes, and statistically significant differences in expression between resistant and susceptible genotypes were only observed for CAD1A. Our study indicates the strong involvement of CAD genes in flax response to F. oxysporum but brings no evidence of their role as resistance gene candidates. These findings contribute to the understanding of the mechanisms underlying the response of flax to F. oxysporum infection and the role of CAD genes in stress resistance

The Murchison Widefield Array: the Square Kilometre Array Precursor at low radio frequencies

The Murchison Widefield Array (MWA) is one of three Square Kilometre Array Precursor telescopes and is located at the Murchison Radio-astronomy Observatory in the Murchison Shire of the mid-west of Western Australia, a location chosen for its extremely low levels of radio frequency interference. The MWA operates at low radio frequencies, 80-300 MHz, with a processed bandwidth of 30.72 MHz for both linear polarisations, and consists of 128 aperture arrays (known as tiles) distributed over a ~3 km diameter area. Novel hybrid hardware/software correlation and a real-time imaging and calibration systems comprise the MWA signal processing backend. In this paper the as-built MWA is described both at a system and sub-system level, the expected performance of the array is presented, and the science goals of the instrument are summarised.Comment: Submitted to PASA. 11 figures, 2 table

Multi-frequency polarization properties of ten quasars on deca-parsec scales at z > 3

Global VLBI (EVN+VLBA) polarization observations at 5 and 8.4 GHz of ten high redshift (z > 3) quasars are presented. The core and jet brightness temperatures are found through modelling the self-calibrated uv-data with Gaussian components, which provide reliable estimates of the flux density and size of individual components. The observed high core brightness temperatures (median $T_{\rm b,\,core}=4\times10^{11}$ K) are consistent with Doppler boosted emission from a relativistic jet orientated close to the line-of-sight. This can also explain the dramatic jet bends observed for some of our sources since small intrinsic bends can be significantly amplified due to projection effects in a highly beamed relativistic jet. We also model-fit the polarized emission and, by taking the minimum angle separation between the model-fitted polarization angles at 5 and 8.4 GHz, we calculate the minimum inferred Faraday rotation measure (RM$_{\rm min}$) for each component. We also calculate the minimum intrinsic RM in the rest frame of the AGN (RM$_{\rm min}^{\rm intr}$ = RM$_{\rm min} (1+z)^2$), first subtracting the integrated (presumed foreground) RM in those cases where we felt we could do this reliably. The resulting mean core $|$RM$_{\rm min}^{\rm intr}|$ is 5580 rad m$^{-2}$, with a standard deviation of 3390 rad m$^{-2}$, for four high-z quasars for which we believe we could reliably remove the foreground RM. We find relatively steep core and jet spectral index values, with a median core spectral index of -0.3 and a median jet spectral index of -1.0. Comparing our results with RM observations of more nearby Active Galactic Nuclei at similar emitted frequencies does not provide any significant evidence for dependence of the quasar nuclear environment with redshift.Comment: Published in MNRAS. 18 pages, 7 figures, 5 table

High-energy sources at low radio frequency : the Murchison Widefield Array view of Fermi blazars

This is the accepted version of the following article: Giroletti, M. et al., A&A, 588 (2016) A141, which has been published in final form at DOI: http://dx.doi.org/10.1051/0004-6361/201527817. This article may be used for non-commercial purposes in accordance with the EDP Sciences self-archiving policies.Low-frequency radio arrays are opening a new window for the study of the sky, both to study new phenomena and to better characterize known source classes. Being flat-spectrum sources, blazars are so far poorly studied at low radio frequencies. We characterize the spectral properties of the blazar population at low radio frequency compare the radio and high-energy properties of the gamma-ray blazar population, and search for radio counterparts of unidentified gamma-ray sources. We cross-correlated the 6,100 deg^2 Murchison Widefield Array Commissioning Survey catalogue with the Roma blazar catalogue, the third catalogue of active galactic nuclei detected by Fermi-LAT, and the unidentified members of the entire third catalogue of gamma-ray sources detected by \fermilat. When available, we also added high-frequency radio data from the Australia Telescope 20 GHz catalogue. We find low-frequency counterparts for 186 out of 517 (36%) blazars, 79 out of 174 (45%) gamma-ray blazars, and 8 out of 73 (11%) gamma-ray blazar candidates. The mean low-frequency (120--180 MHz) blazar spectral index is $\langle \alpha_\mathrm{low} \rangle=0.57\pm0.02$: blazar spectra are flatter than the rest of the population of low-frequency sources, but are steeper than at $\sim$GHz frequencies. Low-frequency radio flux density and gamma-ray energy flux display a mildly significant and broadly scattered correlation. Ten unidentified gamma-ray sources have a (probably fortuitous) positional match with low radio frequency sources. Low-frequency radio astronomy provides important information about sources with a flat radio spectrum and high energy. However, the relatively low sensitivity of the present surveys still misses a significant fraction of these objects. Upcoming deeper surveys, such as the GaLactic and Extragalactic All-Sky MWA (GLEAM) survey, will provide further insight into this population.Peer reviewedFinal Published versio

A search for periodicity in the light curves of selected blazars

We present an analysis of multifrequency light curves of the sources 2223-052 (3C 446), 2230+114 (CTA 102), and 2251+158 (3C 454.3), which had shown evidence of quasi-periodic activity. The analysis made use of data from the University of Michican Radio Astronomy Observatory (USA) at 4.8, 8, and 14.5 GHz, as well as the Metsahovi Radio Astronomy Observatory (Finland) at 22 and 37 GHz. Application of two different methods (the discrete autocorrelation function and the method of Jurkevich) both revealed evidence for periodicity in the flux variations of these sources at essentially all frequencies. The periods derived for at least two of the sources -- 2223-052 and 2251+158-- are in good agreement with the time interval between the appearance of successive VLBI components. The derived periods for 2251+158 (P = 12.4 yr and 2223-052 (P = 5.8 yr) coincide with the periods found earlier by other authors based on optical light curves.Comment: 27 pages, 11 figures, accepted for publication in Astronomy Report

SDHx mutations are associated with the PI3K-Akt signaling pathway in vagal paragangliomas

Background: Vagal paraganglioma (VPGL) is a very rare neuroendocrine tumor arising from the paraganglion associated with the vagus nerve. VPGL is mainly characterized by an asymptomatic course and slow growth. However, up to 19% of tumors can metastasize. Due to the rarity of this tumor, information about VPGL is limited to single cases and small sample sets; the data on molecular genetic features is extremely scarce. Methods: For the first time we have analyzed the enrichment of biological pathways associated with mutations in the SDHx genes in VPGLs. Bioinformatics analysis was performed based on the results of high-throughput transcriptome sequencing on an Illumina platform for 33 tumor tissues obtained from patients with vagal paragangliomas. Results: Eight pathways of the Kyoto Encyclopedia of Genes and Genomes (KEGG) database with gene overrepresentation (top-40 mode) have been identified. Significant changes were shown for the cancer-associated PI3K-Akt signaling pathway and interconnected pathways of focal adhesion and interaction of receptors with the extracellular matrix enriched by overexpressed genes. Conclusion: Our result indicates the association of SDHx mutations with changes in the PI3K-Akt signaling pathway in vagal paraganglioma. The potential mechanism of deregulation in this pathway could be linked with a state of pseudohypoxia induced by the dysfunction of succinate dehydrogenase due to mutations in the SDHx genes