Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

A p53-independent role for the MDM2 antagonist Nutlin-3 in DNA damage response initiation.

BACKGROUND: The mammalian DNA-damage response (DDR) has evolved to protect genome stability and maximize cell survival following DNA-damage. One of the key regulators of the DDR is p53, itself tightly regulated by MDM2. Following double-strand DNA breaks (DSBs), mediators including ATM are recruited to the site of DNA-damage. Subsequent phosphorylation of p53 by ATM and ATM-induced CHK2 results in p53 stabilization, ultimately intensifying transcription of p53-responsive genes involved in DNA repair, cell-cycle checkpoint control and apoptosis. METHODS: In the current study, we investigated the stabilization and activation of p53 and associated DDR proteins in response to treatment of human colorectal cancer cells (HCT116p53+/+) with the MDM2 antagonist, Nutlin-3. RESULTS: Using immunoblotting, Nutlin-3 was observed to stabilize p53, and activate p53 target proteins. Unexpectedly, Nutlin-3 also mediated phosphorylation of p53 at key DNA-damage-specific serine residues (Ser15, 20 and 37). Furthermore, Nutlin-3 induced activation of CHK2 and ATM - proteins required for DNA-damage-dependent phosphorylation and activation of p53, and the phosphorylation of BRCA1 and H2AX - proteins known to be activated specifically in response to DNA damage. Indeed, using immunofluorescent labeling, Nutlin-3 was seen to induce formation of γH2AX foci, an early hallmark of the DDR. Moreover, Nutlin-3 induced phosphorylation of key DDR proteins, initiated cell cycle arrest and led to formation of γH2AX foci in cells lacking p53, whilst γH2AX foci were also noted in MDM2-deficient cells. CONCLUSION: To our knowledge, this is the first solid evidence showing a secondary role for Nutlin-3 as a DDR triggering agent, independent of p53 status, and unrelated to its role as an MDM2 antagonist

Seamounts

Definition: Seamounts are literally mountains rising from the seafloor. More specifically, they are “any geographically isolated topographic feature on the seafloor taller than 100 m, including ones whose summit regions may temporarily emerge above sea level, but not including features that are located on continental shelves or that are part of other major landmasses” (Staudigel et al., 2010). The term “guyot” can be used for seamounts having a truncated cone shape with a flat summit produced by erosion at sea level (Hess, 1946), development of carbonate reefs (e.g., Flood, 1999), or partial collapse due to caldera formation (e.g., Batiza et al., 1984). Seamounts <1,000 m tall are sometimes referred to as “knolls” (e.g., Hirano et al., 2008). “Petit spots” are a newly discovered subset of sea knolls confined to the bulge of subducting oceanic plates of oceanic plates seaward of deep-sea trenches (Hirano et al., 2006)

Semidiurnal temperature changes caused by tidal front movements in the warm season in seabed habitats on the Georges Bank northern margin and their ecological implications

This article is distributed under the terms of the Creative Commons Public Domain. The definitive version was published in PLoS ONE 8 (2013): e55273, doi:10.1371/journal.pone.0055273.Georges Bank is a large, shallow feature separating the Gulf of Maine from the Atlantic Ocean. Previous studies demonstrated a strong tidal-mixing front during the warm season on the northern bank margin between thermally stratified water in the Gulf of Maine and mixed water on the bank. Tides transport warm water off the bank during flood tide and cool gulf water onto the bank during ebb tide. During 10 days in August 2009, we mapped frontal temperatures in five study areas along ~100 km of the bank margin. The seabed “frontal zone”, where temperature changed with frontal movment, experienced semidiurnal temperature maxima and minima. The tidal excursion of the frontal boundary between stratified and mixed water ranged 6 to 10 km. This “frontal boundary zone” was narrower than the frontal zone. Along transects perpendicular to the bank margin, seabed temperature change at individual sites ranged from 7.0°C in the frontal zone to 0.0°C in mixed bank water. At time series in frontal zone stations, changes during tidal cycles ranged from 1.2 to 6.1°C. The greatest rate of change (−2.48°C hr−1) occurred at mid-ebb. Geographic plots of seabed temperature change allowed the mapping of up to 8 subareas in each study area. The magnitude of temperature change in a subarea depended on its location in the frontal zone. Frontal movement had the greatest effect on seabed temperature in the 40 to 80 m depth interval. Subareas experiencing maximum temperature change in the frontal zone were not in the frontal boundary zone, but rather several km gulfward (off-bank) of the frontal boundary zone. These results provide a new ecological framework for examining the effect of tidally-driven temperature variability on the distribution, food resources, and reproductive success of benthic invertebrate and demersal fish species living in tidal front habitats.This study was supported by salary funds from the regular annual salary budget from Northeast Fisheries Science Center (NEFSC) and United States Geological Survey Woods Hole Coastal and Marine Science Center (USGS WH C&MSC), respectively; ship time funds from the NEFSC annual budget for days-at-sea ship operations; equipment from the NEFSC and USGS WH C&MSC annual equipment budgets

Experimental study of dense pyroclastic density currents using sustained, gas-fluidized granular flows

© 2014, Springer-Verlag Berlin Heidelberg. We present the results of laboratory experiments on the behaviour of sustained, dense granular flows in a horizontal flume, in which high-gas pore pressure was maintained throughout the flow duration by continuous injection of gas through the flume base. The flows were fed by a sustained (0.5–30 s) supply of fine (75 ± 15 μm) particles from a hopper; the falling particles impacted an impingement surface at concentrations of ~3 to 45 %, where they densified rapidly to generate horizontally moving, dense granular flows. When the gas supplied through the flume base was below the minimum fluidization velocity of the particles (i.e. aerated flow conditions), three flow phases were identified: (i) an initial dilute spray of particles travelling at 1–2 m s−1, followed by (ii) a dense granular flow travelling at 0.5–1 m s−1, then by (iii) sustained aggradation of the deposit by a prolonged succession of thin flow pulses. The maximum runout of the phase 2 flow was linearly dependent on the initial mass flux, and the frontal velocity had a square-root dependence on mass flux. The frontal propagation speed during phase 3 had a linear relationship with mass flux. The total mass of particles released had no significant control on either flow velocity or runout in any of the phases. High-frequency flow unsteadiness during phase 3 generated deposit architectures with progradational and retrogradational packages and multiple internal erosive contacts. When the gas supplied through the flume base was equal to the minimum fluidization velocity of the particles (i.e. fluidized flow conditions), the flows remained within phase 2 for their entire runout, no deposit formed and the particles ran off the end of the flume. Sustained granular flows differ significantly from instantaneous flows generated by lock-exchange mechanisms, in that the sustained flows generate (by prolonged progressive aggradation) deposits that are much thicker than the flowing layer of particles at any given moment. The experiments offer a first attempt to investigate the physics of the sustained pyroclastic flows that generate thick, voluminous ignimbrites

The influence of cultivation methods on Shewanella oneidensis physiology and proteome expression

High-throughput analyses that are central to microbial systems biology and ecophysiology research benefit from highly homogeneous and physiologically well-defined cell cultures. While attention has focused on the technical variation associated with high-throughput technologies, biological variation introduced as a function of cell cultivation methods has been largely overlooked. This study evaluated the impact of cultivation methods, controlled batch or continuous culture in bioreactors versus shake flasks, on the reproducibility of global proteome measurements in Shewanellaoneidensis MR-1. Variability in dissolved oxygen concentration and consumption rate, metabolite profiles, and proteome was greater in shake flask than controlled batch or chemostat cultures. Proteins indicative of suboxic and anaerobic growth (e.g., fumarate reductase and decaheme c-type cytochromes) were more abundant in cells from shake flasks compared to bioreactor cultures, a finding consistent with data demonstrating that “aerobic” flask cultures were O2 deficient due to poor mass transfer kinetics. The work described herein establishes the necessity of controlled cultivation for ensuring highly reproducible and homogenous microbial cultures. By decreasing cell to cell variability, higher quality samples will allow for the interpretive accuracy necessary for drawing conclusions relevant to microbial systems biology research

Phenome-wide association analysis of LDL-cholesterol lowering genetic variants in PCSK9

BACKGROUND: We characterised the phenotypic consequence of genetic variation at the PCSK9 locus and compared findings with recent trials of pharmacological inhibitors of PCSK9. METHODS: Published and individual participant level data (300,000+ participants) were combined to construct a weighted PCSK9 gene-centric score (GS). Seventeen randomized placebo controlled PCSK9 inhibitor trials were included, providing data on 79,578 participants. Results were scaled to a one mmol/L lower LDL-C concentration. RESULTS: The PCSK9 GS (comprising 4 SNPs) associations with plasma lipid and apolipoprotein levels were consistent in direction with treatment effects. The GS odds ratio (OR) for myocardial infarction (MI) was 0.53 (95% CI 0.42; 0.68), compared to a PCSK9 inhibitor effect of 0.90 (95% CI 0.86; 0.93). For ischemic stroke ORs were 0.84 (95% CI 0.57; 1.22) for the GS, compared to 0.85 (95% CI 0.78; 0.93) in the drug trials. ORs with type 2 diabetes mellitus (T2DM) were 1.29 (95% CI 1.11; 1.50) for the GS, as compared to 1.00 (95% CI 0.96; 1.04) for incident T2DM in PCSK9 inhibitor trials. No genetic associations were observed for cancer, heart failure, atrial fibrillation, chronic obstructive pulmonary disease, or Alzheimer's disease - outcomes for which large-scale trial data were unavailable. CONCLUSIONS: Genetic variation at the PCSK9 locus recapitulates the effects of therapeutic inhibition of PCSK9 on major blood lipid fractions and MI. While indicating an increased risk of T2DM, no other possible safety concerns were shown; although precision was moderate

ICAR: endoscopic skull‐base surgery

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