Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.Comment: 165 pages, 40 figures, 16 tables; accepted for publication in Living Reviews in Relativit

The Snail repressor recruits EZH2 to specific genomic sites through the enrollment of the lncRNA HOTAIR in epithelial-to-mesenchymal transition

The transcription factor Snail is a master regulator of cellular identity and epithelial-to-mesenchymal transition (EMT) directly repressing a broad repertoire of epithelial genes. How chromatin modifiers instrumental to its activity are recruited to Snail-specific binding sites is unclear. Here we report that the long non-coding RNA (lncRNA) HOTAIR (for HOX Transcript Antisense Intergenic RNA) mediates a physical interaction between Snail and enhancer of zeste homolog 2 (EZH2), an enzymatic subunit of the polycomb-repressive complex 2 and the main writer of chromatin-repressive marks. The Snail-repressive activity, here monitored on genes with a pivotal function in epithelial and hepatic morphogenesis, differentiation and cell-type identity, depends on the formation of a tripartite Snail/HOTAIR/EZH2 complex. These results demonstrate an lncRNA-mediated mechanism by which a transcriptional factor conveys a general chromatin modifier to specific genes, thereby allowing the execution of hepatocyte transdifferentiation; moreover, they highlight HOTAIR as a crucial player in the Snail-mediated EMT.Oncogene advance online publication, 25 July 2016; doi:10.1038/onc.2016.260

Contribution of microscopy for understanding the mechanism of action against trypanosomatids

Transmission electron microscopy (TEM) has proved to be a useful tool to study the ultrastructural alterations and the target organelles of new antitrypanosomatid drugs. Thus, it has been observed that sesquiterpene lactones induce diverse ultrastructural alterations in both T. cruzi and Leishmania spp., such as cytoplasmic vacuolization, appearance of multilamellar structures, condensation of nuclear DNA, and, in some cases, an important accumulation of lipid vacuoles. This accumulation could be related to apoptotic events. Some of the sesquiterpene lactones (e.g., psilostachyin) have also been demonstrated to cause an intense mitochondrial swelling accompanied by a visible kinetoplast deformation as well as the appearance of multivesicular bodies. This mitochondrial swelling could be related to the generation of oxidative stress and associated to alterations in the ergosterol metabolism. The appearance of multilamellar structures and multiple kinetoplasts and flagella induced by the sesquiterpene lactone psilostachyin C indicates that this compound would act at the parasite cell cycle level, in an intermediate stage between kinetoplast segregation and nuclear division. In turn, the diterpene lactone icetexane has proved to induce the external membrane budding on T. cruzi together with an apparent disorganization of the pericellar cytoskeleton. Thus, ultrastructural TEM studies allow elucidating the possible mechanisms and the subsequent identification of molecular targets for the action of natural compounds on trypanosomatids.Fil: Lozano, Esteban Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Medicina y Biología Experimental de Cuyo; ArgentinaFil: Spina Zapata, Renata María. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos. Universidad Nacional de Cuyo. Facultad de Ciencias Médicas. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos; ArgentinaFil: Barrera, Patricia Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos. Universidad Nacional de Cuyo. Facultad de Ciencias Médicas. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos; ArgentinaFil: Tonn, Carlos Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Investigaciones en Tecnología Química. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Instituto de Investigaciones en Tecnología Química; ArgentinaFil: Sosa Escudero, Miguel Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos. Universidad Nacional de Cuyo. Facultad de Ciencias Médicas. Instituto de Histología y Embriología de Mendoza Dr. Mario H. Burgos; Argentin

Down-Regulation of GEP100 Causes Increase in E-Cadherin Levels and Inhibits Pancreatic Cancer Cell Invasion

AIMS: Invasion and metastasis are major reasons for pancreatic cancer death and identifying signaling molecules that are specifically used in tumor invasion is of great significance. The purpose of this study was to elucidate the role of GEP100 in pancreatic cancer cell invasion and metastasis and the corresponding molecular mechanism. METHODS: Stable cell lines with GEP100 knocked-down were established by transfecting GEP100 shRNA vector into PaTu8988 cells and selected by puromycin. qRT-PCR and Western blot were performed to detect gene expression. Matrigel-invasion assay was used to detect cancer cell invasion in vitro. Liver metastasis in vivo was determined by splenic injection of indicated cell lines followed by spleen resection. Immunofluorescence study was used to detect the intracellular localization of E-cadherin. RESULTS: We found that the expression level of GEP100 protein was closely related to the invasive ability of a panel of 6 different human pancreatic cancer cell lines. Down-regulation of GEP100 in PaTu8988 cells significantly decreased invasive activity by Matrigel invasion assay, without affecting migration, invasion and viability. The inhibited invasive activity was rescued by over-expression of GEP100 cDNA. In vivo study showed that liver metastasis was significantly decreased in the PaTu8988 cells with GEP100 stably knocked-down. In addition, an epithelial-like morphological change, mimicking a mesenchymal to epithelial transition (MET) was induced by GEP100 down-regulation. The expression of E-cadherin protein was increased 2-3 folds accompanied by its redistribution to the cell-cell contacts, while no obvious changes were observed for E-cadherin mRNA. Unexpectedly, the mRNA of Slug was increased by GEP100 knock-down. CONCLUSION: These findings provided important evidence that GEP100 plays a significant role in pancreatic cancer invasion through regulating the expression of E-cadherin and the process of MET, indicating the possibility of it becoming a potential therapeutic target against pancreatic cancer

Diminution of Voltage Threshold Plays a Key Role in Determining Recruitment of Oculomotor Nucleus Motoneurons during Postnatal Development

The size principle dictates the orderly recruitment of motoneurons (Mns). This principle assumes that Mns of different sizes have a similar voltage threshold, cell size being the crucial property in determining neuronal recruitment. Thus, smaller neurons have higher membrane resistance and require a lower depolarizing current to reach spike threshold. However, the cell size contribution to recruitment in Mns during postnatal development remains unknown. To investigate this subject, rat oculomotor nucleus Mns were intracellularly labeled and their electrophysiological properties recorded in a brain slice preparation. Mns were divided into 2 age groups: neonatal (1–7 postnatal days, n = 14) and adult (20–30 postnatal days, n = 10). The increase in size of Mns led to a decrease in input resistance with a strong linear relationship in both age groups. A well-fitted inverse correlation was also found between input resistance and rheobase in both age groups. However, input resistance versus rheobase did not correlate when data from neonatal and adult Mns were combined in a single group. This lack of correlation is due to the fact that decrease in input resistance of developing Mns did not lead to an increase in rheobase. Indeed, a diminution in rheobase was found, and it was accompanied by an unexpected decrease in voltage threshold. Additionally, the decrease in rheobase co-varied with decrease in voltage threshold in developing Mns. These data support that the size principle governs the recruitment order in neonatal Mns and is maintained in adult Mns of the oculomotor nucleus; but during postnatal development the crucial property in determining recruitment order in these Mns was not the modifications of cell size-input resistance but of voltage threshold

A new perspective of the climatological features of upper-level cut-off lows in the Southern Hemisphere

This study presents a detailed view of the seasonal variability of upper-level cut-off lows (COLs) in the Southern Hemisphere. The COLs are identified and tracked using data from a 36-year period of the European Centre for Medium Range Weather Forecast reanalysis (ERA-Interim). The objective identification of the COLs uses a new approach, which is based on 300 hPa relative vorticity minima, and three restrictive criteria of the presence of a cold-core, stratospheric potential vorticity intrusion, and cut-off cyclonic circulation. The highest COL activity is in agreement with previous studies, located near three main continental areas (Australia, South America, and Africa), with maximum frequencies usually observed in the austral autumn. The COL mean intensity values show a marked seasonal and spatial variation, with maximum (minimum) values during the austral winter (summer), a unique feature that has not been observed previously in studies based on the geopotential. The link between intensity and lysis is examined, and finds that weaker systems are more susceptible to lysis in the vicinity of the Andes Cordillera, associated with the topographic Rossby wave. Lysis and genesis regions are close to each other, confirming that COLs are quasi-stationary systems. Also, COLs tend to move eastward and are faster over the higher latitudes. The mean growth/decay rates coincide with the major genesis and lysis density regions, such as the significant decay values across the Andes all year. As a consequence of using vorticity for the tracking method a longer lifetime of COLs is detected than in other studies, but this does not affect the total frequency of occurrence. Comparisons with other studies suggest that the differences in seasonality are due to uncertainties in the reanalyses and the methods used to identify COLs

Extreme genomic erosion after recurrent demographic bottlenecks in the highly endangered Iberian lynx

Background: Genomic studies of endangered species provide insights into their evolution and demographic history, reveal patterns of genomic erosion that might limit their viability, and offer tools for their effective conservation. The Iberian lynx (Lynx pardinus) is the most endangered felid and a unique example of a species on the brink of extinction. Results: We generate the first annotated draft of the Iberian lynx genome and carry out genome-based analyses of lynx demography, evolution, and population genetics. We identify a series of severe population bottlenecks in the history of the Iberian lynx that predate its known demographic decline during the 20th century and have greatly impacted its genome evolution. We observe drastically reduced rates of weak-to-strong substitutions associated with GC-biased gene conversion and increased rates of fixation of transposable elements. We also find multiple signatures of genetic erosion in the two remnant Iberian lynx populations, including a high frequency of potentially deleterious variants and substitutions, as well as the lowest genome-wide genetic diversity reported so far in any species. Conclusions: The genomic features observed in the Iberian lynx genome may hamper short- and long-term viability through reduced fitness and adaptive potential. The knowledge and resources developed in this study will boost the research on felid evolution and conservation genomics and will benefit the ongoing conservation and management of this emblematic species