Spectral solver for Cauchy problems in polar coordinates using discrete Hankel transforms

We introduce a Fourier-Bessel-based spectral solver for Cauchy problems featuring Laplacians in polar coordinates under homogeneous Dirichlet boundary conditions. We use FFTs in the azimuthal direction to isolate angular modes, then perform discrete Hankel transform (DHT) on each mode along the radial direction to obtain spectral coefficients. The two transforms are connected via numerical and cardinal interpolations. We analyze the boundary-dependent error bound of DHT; the worst case is $\sim N^{-3/2}$, which governs the method, and the best $\sim e^{-N}$, which then the numerical interpolation governs. The complexity is $O[N^3]$. Taking advantage of Bessel functions being the eigenfunctions of the Laplacian operator, we solve linear equations for all times. For non-linear equations, we use a time-splitting method to integrate the solutions. We show examples and validate the method on the two-dimensional wave equation, which is linear, and on two non-linear problems: a time-dependent Poiseuille flow and the flow of a Bose-Einstein condensate on a disk

Internal tide generation from isolated seamounts and continental shelves

We model linear, inviscid non-hydrostatic internal tides generated by the interaction of a barotropic tide with variable topography in two dimensions. We first derive an asymptotic solution for the nonuniform barotropic flow over the topography that serves as forcing for the baroclinic equations. The resulting internal-tide generation problem is reformulated as a Coupled-Mode System (CMS) by means of a series decomposition of the baroclinic stream function in terms of vertical basis functions. We solve this CMS numerically and also provide a method for estimating the sea-surface signature of internal tides. We consider several seamounts and shelf profiles and perform calculations for a wide range of (topographic) heights and slopes. For subcritical topographies, the energy flux as a function of height exhibits local maxima, separated by cases of weakly- or even non-radiating topographies. For supercritical topographies, the energy flux generally increases with height and criticality. Our calculations agree with the Weak Topography Approximation only for very small heights. Perhaps more surprisingly, they agree with the Knife Edge model only for moderately supercritical topographies. We also compare the effect of the adjusted barotropic tide on the energy flux and the local properties of the baroclinic field with other semi-analytical methods based on a uniform barotropic tide. We observe significant differences in the flow field near the topographies only

Interaction between Glycogen Synthase Kinase-3 and Estrogen Receptor-alpha in ligand-dependent activation of the receptor

Glycogen synthase kinase-3 (GSK-3), a serine/threonine kinase with docking properties, regulates numerous cellular processes. Two isoforms, GSK-3alpha and GSK-3beta have been described. In vivo, GSK-3beta is the major isoform and plays a key role in the regulation of transcription factors including steroid receptors. The aim of the present work, mainly performed on the estrogen receptor-alpha (ERalpha)-positive MCF-7 human breast cancer cell line, was to unravel the role of GSK-3 regarding ERalpha function. After silencing of GSK-3alpha and/or GSK-3beta isoforms using specific siRNA sequences, increased proteasomal degradation of ERalpha was observed. The use of the proteasome inhibitor MG132 restored ERalpha protein levels in GSK-3 silenced cells, showing that GSK-3 stabilizes ERalpha and protects it from proteasomal degradation. In another approach, specific silencing of the endogenous GSK-3beta of MCF-7 cells using microRNA constructs was accompanied by down-regulation of ERalpha protein content. In these cells, ERalpha protein was rescued after overexpression of wild-type or kinase-inactive xenopus GSK-3beta, which suggests that the docking properties of GSK-3 and not the kinase activity are important for ERalpha stabilization. Then, we found that 17beta-estradiol (E2) -treatment resulted in rapid phosphorylation and consequent inactivation of cytoplasmic GSK-3. This GSK-3 phosphorylation may lead to ERalpha release from the GSK-3/ERalpha complex and ERalpha translocation into the nucleus, where it is phosphorylated at Ser-118 leading to its full activation. Upon E2 stimulation, treatment of the cells with the GSK-3 inhibitor LiCl resulted in a decrease of ERalpha phosphorylation at Ser-118. This decrease was confirmed upon silencing of GSK-3 in the nucleus and show that a nuclear active pool of GSK-3 is required for E2-induced phosphorylation of ERalpha at Ser-118. As a consequence, in GSK-3 silenced cells, E2-induced ERalpha transcriptional activity, studied by ERE-dependent luciferase reporter assays and by measuring transcription of the ERalpha-dependent target genes, pS2 and progesterone receptor, by quantitative real-time PCR, was significantly reduced. In GSK-3 silenced cells, neither Ser-118 phosphorylation nor luciferase activity was restored by use of MG132. Furthermore, overexpression of human GSK-3beta wild-type and mutants inactive towards primed substrate of the kinase in MCF-7 cells stably transfected with an ERE-controlled luciferase reporter confirmed that GSK-3 triggers E2-induced ERalpha activation and suggests that ERalpha is a non-primed substrate of GSK-3 kinase. Taken together, this newly signalling pathway depicted a dual function of GSK-3 regarding ERalpha, GSK-3 stabilises ERalpha in the cytoplasm of unstimulated cells and phosphorylates/activates the receptor in the nucleus upon E2 treatment. This permits the conclusion that GSK-3 represents a link between the rapid cytoplasmic non-genomic and the nuclear genomic actions of E2-liganded ERalpha. Finally, ERalpha signalling pathway plays a crucial role in breast cancer initiation and progression. Therefore, the regulation of ERalpha function and activity by GSK-3 may have an impact on breast cancer progression. Preliminary data from GSK-3beta immunostaining of formalin-fixed human tissue sections suggests a tendency toward an increase of GSK-3beta expression in grade 3 tumors in comparison with grade 1/2 tumors

The Impact of Finite-Amplitude Bottom Topography on Internal Wave Generation in the Southern Ocean

Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in a kilometer-thick layer above rough bottom topography collocated with the deep-reaching fronts of the Antarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, two-dimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levels of turbulent energy dissipation. This study presents two- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at three-dimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarily associated with finite-amplitude bottom topography effects that suppress vertical motions and thus reduce the amplitude of the internal waves radiated from topography. The implication of these results for the global lee-wave generation is discussed.National Science Foundation (U.S.) (Award CMG-1024198

Glucose-Dependent Insulinotropic Polypeptide (GIP) Induces Calcitonin Gene-Related Peptide (CGRP)-I and Procalcitonin (Pro-CT) Production in Human Adipocytes

Context: Increased plasma levels of glucose-dependent insulinotropic polypeptide (GIP), calcitonin CT gene-related peptide (CGRP)-I, and procalcitonin (Pro-CT) are associated with obesity. Adipocytes express functional GIP receptors and the CT peptides Pro-CT and CGRP-I. However, a link between GIP and CT peptides has not been studied yet. Objective: The objective of the study was the assessment of the GIP effect on the expression and secretion of CGRP-I and Pro-CT in human adipocytes, CGRP-I and CT gene expression in adipose tissue (AT) from obese vs. lean subjects, and plasma levels of CGRP-I and Pro-CT after a high-fat meal in obese patients. Design and Participants: Human preadipocyte-derived adipocytes, differentiated in vitro, were treated with GIP. mRNA expression and protein secretion of CGRP-I and Pro-CT were measured. Human CGRP-I and CT mRNA expression in AT and CGRP-I and Pro-CT plasma concentrations were assessed. Results: Treatment with 1 nm GIP induced CGRP-I mRNA expression 6.9 ± 1.0-fold (P > 0.001 vs. control) after 2 h and CT gene expression 14.0 ± 1.7-fold (P > 0.001 vs. control) after 6 h. GIP stimulated CGRP-I secretion 1.7 ± 0.2-fold (P > 0.05 vs. control) after 1 h. In AT samples of obese subjects, CGRP-I mRNA expression was higher in sc AT (P > 0.05 vs. lean subjects), whereas CT expression was higher in visceral AT (P > 0.05 vs. lean subjects). CGRP-I plasma levels increased after a high-fat meal in obese patients. Conclusion: GIP induces CGRP-I and CT expression in human adipocytes. Therefore, elevated Pro-CT and CGRP-I levels in obesity might result from GIP-induced Pro-CT and CGRP-I release in AT and might be triggered by a high-fat diet. How these findings relate to the metabolic complications of obesity warrants further investigations

Convective quenching of stellar pulsations

Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of the convection-pulsation coupling, in which the oscillations are sustained by a continuous physical process: the kappa-mechanism. Thanks to both a frequential analysis and a projection of the physical fields onto an acoustic subspace, we study how the convective motions affect the unstable radial oscillations. Results: depending on the initial physical conditions, two main behaviours are obtained: (i) either the unstable fundamental acoustic mode has a large amplitude, carries the bulk of the kinetic energy and shows a nonlinear saturation similar to the purely radiative case; (ii) or the convective motions affect significantly the mode amplitude that remains very weak. In this second case, convection is quenching the acoustic oscillations. We interpret these discrepancies in terms of the difference in density contrast: larger stratification leads to smaller convective plumes that do not affect much the purely radial modes, while large-scale vortices may quench the oscillations.Comment: 15 pages, 17 figures, 3 tables, accepted for publication in A&

Improved Internal Wave Spectral Continuum in a Regional Ocean Model

Recent work demonstrates that high‐resolution global models forced simultaneously by atmospheric fields and the astronomical tidal potential contain a partial internal (gravity) wave (IW) spectral continuum. Regional simulations of the MITgcm forced at the horizontal boundaries by a global run that carries a partial IW continuum spectrum are performed at the same grid spacing as the global run and at finer grid spacings in an attempt to fill out more of the IW spectral continuum. Decreasing only the horizontal grid spacing from 2 to 0.25 km greatly improves the frequency spectra and slightly improves the vertical wavenumber spectra of the horizontal velocity. Decreasing only the vertical grid spacing by a factor of 3 does not yield any significant improvements. Decreasing both horizontal and vertical grid spacings yields the greatest degree of improvement, filling the frequency spectrum out to 72 cpd. Our results suggest that improved IW spectra in regional models are possible if they are run at finer grid spacings and are forced at their lateral boundaries by remotely generated IWs. Additionally, consistency relations demonstrate that improvements in the spectra are indeed due to the existence of IWs at higher frequencies and vertical wavenumbers when remote IW forcing is included and model grid spacings decrease. By being able to simulate an IW spectral continuum to 0.25 km scales, these simulations demonstrate that one may be able to track the energy pathways of IWs from generation to dissipation and improve the understanding of processes such as IW‐driven mixing.Plain Language SummaryModels of internal waves (IWs) may help us to better understand the spatial geography of mixing in the ocean and are playing an increasingly important role in the planning of satellite missions. Following recent work showing that high‐resolution global models contain a partial IW spectrum, this paper describes further improvements in the spectrum seen in a high‐resolution regional model forced at the boundaries by a previously performed global IW simulation. Decreasing only the horizontal grid spacing greatly improves the frequency spectra and slightly improves the vertical wavenumber spectra of velocity. Increasing only the number of vertical levels does not yield any significant improvements. Decreasing both horizontal and vertical grid spacings yields the greatest improvement in both spectra. Our results suggest that regional models can exhibit improved IW spectra over global models if two conditions are met—they must have higher horizontal and vertical resolutions, and they must have remotely generated IWs at their boundaries. Application of the so‐called consistency relations demonstrates that the model is indeed carrying a field of high‐frequency IWs. Being able to simulate a fuller IW spectrum demonstrates that one may be able to use these models to improve the understanding of IW‐driven processes and energy pathways.Key PointsInternal gravity wave spectra in regional models are more realistic as model grid spacing decreasesThe vertical wavenumber spectra improve less dramatically than the frequency spectraInternal gravity wave consistency relations are applied to modeled spectraPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154917/1/jgrc23947_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154917/2/jgrc23947.pd

On Applying Formal Techniques to the Development of Hybrid Services: Challenges and Directions

We are primarily interested in formal techniques and how they are applied to the development of hybrid services in particular. We analyze the peculiarities of such services, we look at the use of formal techniques for communication services in the industry and highlight some of the major concerns for the application of formality in an industrial environment. It is argued that with the introduction of hybrid services, more pragmatism is required in applying formal techniques. We briefly describe an ongoing joint collaboration with Alcatel, Swisscom and the Swiss Federal Institute of Technology in which formal techniques are applied to the specification and testing of hybrid services

Glycogen Synthase Kinase (GSK) 3β phosphorylates and protects nuclear myosin 1c from proteasome-mediated degradation to activate rDNA transcription in early G1 cells

Nuclear myosin 1c (NM1) mediates RNA polymerase I (pol I) transcription activation and cell cycle progression by facilitating PCAF-mediated H3K9 acetylation, but the molecular mechanism by which NM1 is regulated remains unclear. Here, we report that at early G1 the glycogen synthase kinase (GSK) 3β phosphorylates and stabilizes NM1, allowing for NM1 association with the chromatin. Genomic analysis by ChIP-Seq showed that this mechanism occurs on the rDNA as active GSK3β selectively occupies the gene. ChIP assays and transmission electron microscopy in GSK3β-/- mouse embryonic fibroblasts indicated that at G1 rRNA synthesis is suppressed due to decreased H3K9 acetylation leading to a chromatin state incompatible with transcription. We found that GSK3β directly phosphorylates the endogenous NM1 on a single serine residue (Ser-1020) located within the NM1 C-terminus. In G1 this phosphorylation event stabilizes NM1 and prevents NM1 polyubiquitination by the E3 ligase UBR5 and proteasome-mediated degradation. We conclude that GSK3β-mediated phosphorylation of NM1 is required for pol I transcription activation

IL-6 stimulation of DNA replication is JAK1/2 mediated in cross-talk with hyperactivated ERK1/2 signaling

Myeloproliferative neoplasms (MPNs) are developing resistance to therapy by JAK1/2 inhibitor ruxolitinib. To explore the mechanism of ruxolitinib's limited effect, we examined the JAK1/2 mediated induction of proliferation related ERK1/2 and AKT signaling by proinflammatory interleukin-6 (IL-6) in MPN granulocytes and JAK2V617F mutated human erythroleukemia (HEL) cells. We found that JAK1/2 or JAK2 inhibition prevented the IL-6 activation of STAT3 and AKT pathways in polycythemia vera and HEL cells. Further, we showed that these inhibitors also blocked the IL-6 activation of the AKT pathway in primary myelofibrosis (PMF). Only JAK1/2 inhibitor ruxolitinib largely activated ERK1/2 signaling in essential thrombocythemia and PMF (up to 4.6 fold), with a more prominent activation in JAK2V617F positive granulocytes. Regarding a cell cycle, we found that IL-6 reduction of HEL cells percentage in G2M phase was reversed by ruxolitinib (2.6 fold). Moreover, ruxolitinib potentiated apoptosis of PMF granulocytes (1.6 fold). Regarding DNA replication, we found that ruxolitinib prevented the IL-6 augmentation of MPN granulocytes frequency in the S phase of the cell cycle (up to 2.9 fold). The inflammatory stimulation induces a cross-talk between the proliferation linked pathways, where JAK1/2 inhibition is compensated by the activation of the ERK1/2 pathway during IL-6 stimulation of DNA replication