Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Expression of tumour-specific antigens underlies cancer immunoediting

Cancer immunoediting is a process by which immune cells, particularly lymphocytes of the adaptive immune system, protect the host from the development of cancer and alter tumour progression by driving the outgrowth of tumour cells with decreased sensitivity to immune attack1, 2. Carcinogen-induced mouse models of cancer have shown that primary tumour susceptibility is thereby enhanced in immune-compromised mice, whereas the capacity for such tumours to grow after transplantation into wild-type mice is reduced2, 3. However, many questions about the process of cancer immunoediting remain unanswered, in part because of the known antigenic complexity and heterogeneity of carcinogen-induced tumours4. Here we adapted a genetically engineered, autochthonous mouse model of sarcomagenesis to investigate the process of cancer immunoediting. This system allows us to monitor the onset and growth of immunogenic and non-immunogenic tumours induced in situ that harbour identical genetic and histopathological characteristics. By comparing the development of such tumours in immune-competent mice with their development in mice with broad immunodeficiency or specific antigenic tolerance, we show that recognition of tumour-specific antigens by lymphocytes is critical for immunoediting against sarcomas. Furthermore, primary sarcomas were edited to become less immunogenic through the selective outgrowth of cells that were able to escape T lymphocyte attack. Loss of tumour antigen expression or presentation on major histocompatibility complex I was necessary and sufficient for this immunoediting process to occur. These results highlight the importance of tumour-specific-antigen expression in immune surveillance, and potentially, immunotherapy.National Institutes of Health (U.S.) (Grant 1 U54 CA126515-01)National Cancer Institute (U.S.) (Cancer Center Support Grant P30-CA14051)Margaret A. Cunningham Immune Mechanisms in Cancer Research Fellowship AwardJohnD. Proctor FoundationDaniel K. Ludwig Schola

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Molecular phylogeny and timing of diversification in Alpine Rhithrogena (Ephemeroptera: Heptageniidae).

BACKGROUND: Larvae of the Holarctic mayfly genus Rhithrogena Eaton, 1881 (Ephemeroptera, Heptageniidae) are a diverse and abundant member of stream and river communities and are routinely used as bio-indicators of water quality. Rhithrogena is well diversified in the European Alps, with a number of locally endemic species, and several cryptic species have been recently detected. While several informal species groups are morphologically well defined, a lack of reliable characters for species identification considerably hampers their study. Their relationships, origin, timing of speciation and mechanisms promoting their diversification in the Alps are unknown. RESULTS: Here we present a species-level phylogeny of Rhithrogena in Europe using two mitochondrial and three nuclear gene regions. To improve sampling in a genus with many cryptic species, individuals were selected for analysis according to a recent DNA-based taxonomy rather than traditional nomenclature. A coalescent-based species tree and a reconstruction based on a supermatrix approach supported five of the species groups as monophyletic. A molecular clock, mapped on the most resolved phylogeny and calibrated using published mitochondrial evolution rates for insects, suggested an origin of Alpine Rhithrogena in the Oligocene/Miocene boundary. A diversification analysis that included simulation of missing species indicated a constant speciation rate over time, rather than any pronounced periods of rapid speciation. Ancestral state reconstructions provided evidence for downstream diversification in at least two species groups. CONCLUSIONS: Our species-level analyses of five gene regions provide clearer definitions of species groups within European Rhithrogena. A constant speciation rate over time suggests that the paleoclimatic fluctuations, including the Pleistocene glaciations, did not significantly influence the tempo of diversification of Alpine species. A downstream diversification trend in the hybrida and alpestris species groups supports a previously proposed headwater origin hypothesis for aquatic insects

Cancer immunotherapy by immunosuppression

We have previously suggested that the stimulatory effect of a weak immune reaction on tumor growth may be necessary for the growth of incipient tumors. In the present paper, we enlarge upon and extend that idea by collecting evidence in the literature bearing upon this new hypothesis that a growing cancer, whether in man or mouse, is throughout its lifespan, probably growing and progressing because of continued immune stimulation by a weak immune reaction. We also suggest that prolonged immunosuppression might interfere with progression and thus be an aid to therapy. While most of the considerable evidence that supports the hypothesis comes from observations of experimental mouse tumors, there is suggestive evidence that human tumors may behave in much the same way, and as far as we can ascertain, there is no present evidence that necessarily refutes the hypothesis

Understanding the rapid summer warming and changes in temperature extremes since the mid-1990s over Western Europe

Analysis of observations indicates that there was a rapid increase in summer (June-August, JJA) mean surface air temperature (SAT) since the mid-1990s over Western Europe. Accompanying this rapid warming are significant increases in summer mean daily maximum temperature, daily minimum temperature, annual hottest day temperature and warmest night temperature, and an increase in frequency of summer days and tropical nights, while the change in the diurnal temperature range (DTR) is small. This study focuses on understanding causes of the rapid summer warming and associated temperature extreme changes. A set of experiments using the atmospheric component of the state-of-the-art HadGEM3 global climate model have been carried out to quantify relative roles of changes in sea surface temperature (SST)/sea ice extent (SIE), anthropogenic greenhouse gases (GHGs), and anthropogenic aerosols (AAer). Results indicate that the model forced by changes in all forcings reproduces many of the observed changes since the mid-1990s over Western Europe. Changes in SST/SIE explain 62.2% ± 13.0% of the area averaged seasonal mean warming signal over Western Europe, with the remaining 37.8% ± 13.6% of the warming explained by the direct impact of changes in GHGs and AAer. Results further indicate that the direct impact of the reduction of AAer precursor emissions over Europe, mainly through aerosol-radiation interaction with additional contributions from aerosol-cloud interaction and coupled atmosphere-land surface feedbacks, is a key factor for increases in annual hottest day temperature and in frequency of summer days. It explains 45.5% ± 17.6% and 40.9% ± 18.4% of area averaged signals for these temperature extremes. The direct impact of the reduction of AAer precursor emissions over Europe acts to increase DTR locally, but the change in DTR is countered by the direct impact of GHGs forcing. In the next few decades, greenhouse gas concentrations will continue to rise and AAer precursor emissions over Europe and North America will continue to decline. Our results suggest that the changes in summer seasonal mean SAT and temperature extremes over Western Europe since the mid-1990s are most likely to be sustained or amplified in the near term, unless other factors intervene

Localization and Broadband Follow-Up of the Gravitational-Wave Transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser InterferometerGravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimatesof the time, significance, and sky location of the event were shared with 63 teams of observers covering radio,optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter wedescribe the low-latency analysis of the GW data and present the sky localization of the first observed compactbinary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-rayCoordinates Network circulars, giving an overview of the participating facilities, the GW sky localizationcoverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger,there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadbandcampaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broadcapabilities of the transient astronomy community and the observing strategies that have been developed to pursueneutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-upcampaign are being disseminated in papers by the individual teams

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Genetic differentiation and admixture between sibling allopolyploids in the Dactylorhiza majalis complex

Allopolyploidization often happens recurrently, but the evolutionary significance of its iterative nature is not yet fully understood. Of particular interest are the gene flow dynamics and the mechanisms that allow young sibling polyploids to remain distinct while sharing the same ploidy, heritage and overlapping distribution areas. By using eight highly variable nuclear microsatellites, newly reported here, we investigate the patterns of divergence and gene flow between 386 polyploid and 42 diploid individuals, representing the sibling allopolyploids Dactylorhiza majalis s.s. and D. traunsteineri s.l. and their parents at localities across Europe. We make use in our inference of the distinct distribution ranges of the polyploids, including areas in which they are sympatric (that is, the Alps) or allopatric (for example, Pyrenees with D. majalis only and Britain with D. traunsteineri only). Our results show a phylogeographic signal, but no clear genetic differentiation between the allopolyploids, despite the visible phenotypic divergence between them. The results indicate that gene flow between sibling Dactylorhiza allopolyploids is frequent in sympatry, with potential implications for the genetic patterns across their entire distribution range. Limited interploidal introgression is also evidenced, in particular between D. incarnata and D. traunsteineri. Altogether the allopolyploid genomes appear to be porous for introgression from related diploids and polyploids. We conclude that the observed phenotypic divergence between D. majalis and D. traunsteineri is maintained by strong divergent selection on specific genomic areas with strong penetrance, but which are short enough to remain undetected by genotyping dispersed neutral markers.UE FWF; P22260UE: Y66

Antimicrobial activity and brine shrimp toxicity of extracts of Terminalia brownii roots and stem

BACKGROUND: Ternimalia brownii Fresen (Combretaceae) is widely used in traditional medicine to treat bacterial, fungal and viral infections. There is a need to evaluate extracts of this plant in order to provide scientific proof for it's wide application in traditional medicine system. METHODS: Extraction of stem bark, wood and whole roots of T. brownii using solvents of increasing polarity, namely, Pet ether, dichloromethane, dichloromethane: methanol (1:1), methanol and aqua, respectively, afforded dry extracts. The extracts were tested for antifungal and antibacterial activity and for brine shrimp toxicity test. RESULTS: Extracts of the stem bark, wood and whole roots of T. brownii exhibited antibacterial activity against standard strains of Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa, Klebsiella pneumoniae, Salmonella typhi, and Bacillus anthracis and the fungi, Candida albicans and Cryptococcus neoformans. Aqueous extracts exhibited the strongest activity against both bacteria and fungi. Extracts of the roots and stem bark exhibited relatively mild cytotoxic activity against brine shrimp larvae with LC(50 )values ranging from 113.75–4356.76 and 36.12–1458.81 μg/ml, respectively. The stem wood extracts exhibited the highest toxicity against the shrimps (LC(50 )values 2.58–14.88 μg/ml), while that of cyclophosphamide, a standard anticancer drug, was 16.33 (10.60–25.15) μg/ml. CONCLUSION: These test results support traditional medicinal use of, especially, aqueous extracts for the treatment of conditions such as diarrhea, and gonorrhea. The brine shrimp results depict the general trend among plants of the genus Terminalia, which are known to contain cytotoxic compounds such as hydrolysable tannins. These results warrant follow-up through bioassay-directed isolation of the active principles