473 research outputs found

    Non-intersecting squared Bessel paths at a hard-edge tacnode

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    The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of nn non-intersecting squared Bessel paths, with all paths starting at the same point a>0a>0 at time t=0t=0 and ending at the same point b>0b>0 at time t=1t=1. Our interest lies in the critical regime ab=1/4ab=1/4, for which the paths are tangent to the hard edge at the origin at a critical time t∗∈(0,1)t^*\in (0,1). The critical behavior of the paths for n→∞n\to\infty is studied in a scaling limit with time t=t∗+O(n−1/3)t=t^*+O(n^{-1/3}) and temperature T=1+O(n−2/3)T=1+O(n^{-2/3}). This leads to a critical correlation kernel that is defined via a new Riemann-Hilbert problem of size 4×44\times 4. The Riemann-Hilbert problem gives rise to a new Lax pair representation for the Hastings-McLeod solution to the inhomogeneous Painlev\'e II equation q"(x)=xq(x)+2q3(x)−ν,q"(x) = xq(x)+2q^3(x)-\nu, where ν=α+1/2\nu=\alpha+1/2 with α>−1\alpha>-1 the parameter of the squared Bessel process. These results extend our recent work with Kuijlaars and Zhang \cite{DKZ} for the homogeneous case ν=0\nu = 0.Comment: 54 pages, 13 figures. Corrected error in Theorem 2.

    Super-solar metallicity at the position of the ultra-long GRB130925A

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    Over the last decade there has been immense progress in the follow-up of short and long GRBs, resulting in a significant rise in the detection rate of X-ray and optical afterglows, in the determination of GRB redshifts, and of the identification of the underlying host galaxies. Nevertheless, our theoretical understanding on the progenitors and central engines powering these vast explosions is lagging behind, and a newly identified class of `ultra-long' GRBs has fuelled speculation on the existence of a new channel of GRB formation. In this paper we present high signal-to-noise X-shooter observations of the host galaxy of GRB130925A, which is the fourth unambiguously identified ultra-long GRB, with prompt gamma-ray emission detected for ~20ks. The GRB line of sight was close to the host galaxy nucleus, and our spectroscopic observations cover both this region along the bulge/disk of the galaxy, in addition to a bright star-forming region within the outskirts of the galaxy. From our broad wavelength coverage we obtain accurate metallicity and dust-extinction measurements at both the galaxy nucleus, and an outer star-forming region, and measure a super-solar metallicity at both locations, placing this galaxy within the 10-20% most metal-rich GRB host galaxies. Such a high metal enrichment has implications on the progenitor models of both long and ultra-long GRBs, although the edge-on orientation of the host galaxy does not allow us to rule out a large metallicity variation along our line of sight. The spatially resolved spectroscopic data presented in this paper offer important insight into variations in the metal and dust abundance within GRB host galaxies. They also illustrate the need for IFU observations on a larger sample of GRB host galaxies at varies metallicities to provide a more quantitative view on the relation between the GRB circumburst and the galaxy-whole properties.Comment: 9 pages, 3 figures, A&A in press, matches published versio

    Intussusception of the Small Intestine Caused by a Primary Melanoma?

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    Although the gastrointestinal tract is a fairly frequent site of melanoma metastases, reports of small bowel intussusception caused by melanoma are very rare. We report the case of a 77-year-old man who was admitted to our hospital with epigastric pain, melena and anaemia. After clinical examination, laboratory evaluation and radiological work-up the diagnosis of a jejunal intussusception was made. Exploratory laparoscopy revealed a large tumour arising from the jejunum, approximately 20 cm distal to the angle of Treitz. Small bowel resection with an end-to-end anastomosis was performed. Histological examination showed an intestinal melanoma. There are different theories concerning the origin of malignant melanoma in the small bowel. Although the small and large intestines normally contain no melanocytes, these cells have occasionally been found in the alimentary and respiratory tracts and even in lymph nodes, which supports the theory of a primary origin of melanoma at these sites. Since this was a solitary intestinal lesion and there was no history of cutaneous melanoma, we conclude that this could be an example of a very rare primary melanoma of the small intestine

    Surface ruptures associated to the July-August 2007 Gelai volcano-tectonic event, North Tanzania

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    A seismic crisis with a series of moderate earthquakes started on July 12th 2007 in the Natron area in North Tanzania. According to the USGS-NEIC earthquake catalogue, it lasted up to the 8th of September and 80 teleseismic earthquakes were recorded, with the strongest one on July 17th (Mw 5.9). Soon after the main event of July 17th, the presence of open surface fissures was reported on the ground, on the southern flank of the recent (th event shows the presence of two surface fracture systems delimiting a NNE-trending narrow graben in the southern flank of the Gelai volcano. These features were subsequently mapped in relative detail in the field in October 2007 before the following rain season. They turn to be subvertical open fissures, arranged in en-échelon way and displaying horizontal dilation as well as vertical offset. They are interpreted to evolve at depth into 60-75° dipping normal fault systems. According to their calculated dip, these fault systems converge at depth where they should either merge or intersect. Assuming a 50 m high vertical portion for the open fracture, the depth and horizontal coordinates of the fault intersection point are calculated for a series of profiles drawn across the graben structure.It is suspected that the July-August moderate-magnitude earthquake swam crisis might correspond to a volcano-tectonic event during which a magmatic dyke was injected at depth under the southern flank of the Gelai volcano. In this scenario, the observed graben structure bounded by the open fracture network and the inferred normal faults at depth are similar to the volcano-extensional structures that commonly form in the upper crust above a thin subvertical dyke injection. The top of this inferred dyke should correspond approximately to the intersection of the lines prolonging the two normal faults (even if physically the faults did not join the top of dyke), with an average depth of 4000m under the topographic surface

    PCSK9 inhibitors and ezetimibe with or without statin therapy for cardiovascular risk reduction: a systematic review and network meta-analysis.

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    OBJECTIVE To compare the impact of ezetimibe and proprotein convertase subtilisin/kexin type 9 (PCSK9) inhibitors on cardiovascular outcomes in adults taking maximally tolerated statin therapy or who are statin intolerant. DESIGN Network meta-analysis. DATA SOURCES Medline, EMBASE, and Cochrane Library up to 31 December 2020. ELIGIBILITY CRITERIA FOR SELECTING STUDIES Randomised controlled trials of ezetimibe and PCSK9 inhibitors with ≥500 patients and follow-up of ≥6 months. MAIN OUTCOME MEASURES We performed frequentist fixed-effects network meta-analysis and GRADE (grading of recommendations, assessment, development, and evaluation) to assess certainty of evidence. Results included relative risks (RR) and absolute risks per 1000 patients treated for five years for non-fatal myocardial infarction (MI), non-fatal stroke, all-cause mortality, and cardiovascular mortality. We estimated absolute risk differences assuming constant RR (estimated from network meta-analysis) across different baseline therapies and cardiovascular risk thresholds; the PREDICT risk calculator estimated cardiovascular risk in primary and secondary prevention. Patients were categorised at low to very high cardiovascular risk. A guideline panel and systematic review authors established the minimal important differences (MID) of 12 per 1000 for MI and 10 per 1000 for stroke. RESULTS We identified 14 trials assessing ezetimibe and PCSK9 inhibitors among 83 660 adults using statins. Adding ezetimibe to statins reduced MI (RR 0.87 (95% confidence interval 0.80 to 0.94)) and stroke (RR 0.82 (0.71 to 0.96)) but not all-cause mortality (RR 0.99 (0.92 to 1.06)) or cardiovascular mortality (RR 0.97 (0.87 to 1.09)). Similarly, adding PCSK9 inhibitor to statins reduced MI (0.81 (0.76 to 0.87)) and stroke (0.74 (0.64 to 0.85)) but not all-cause (0.95 (0.87 to 1.03)) or cardiovascular mortality (0.95 (0.87 to 1.03)). Among adults with very high cardiovascular risk, adding PCSK9 inhibitor was likely to reduce MI (16 per 1000) and stroke (21 per 1000) (moderate to high certainty); whereas adding ezetimibe was likely to reduce stroke (14 per 1000), but the reduction of MI (11 per 1000) (moderate certainty) did not reach MID. Adding ezetimibe to PCSK9 inhibitor and statin may reduce stroke (11 per 1000), but the reduction of MI (9 per 1000) (low certainty) did not reach MID. Adding PCSK9 inhibitors to statins and ezetimibe may reduce MI (14 per 1000) and stroke (17 per 1000) (low certainty). Among adults with high cardiovascular risk, adding PCSK9 inhibitor probably reduced MI (12 per 1000) and stroke (16 per 1000) (moderate certainty); adding ezetimibe probably reduced stroke (11 per 1000), but the reduction in MI did not achieve MID (8 per 1000) (moderate certainty). Adding ezetimibe to PCSK9 inhibitor and statins did not reduce outcomes beyond MID, while adding PCSK9 inhibitor to ezetimibe and statins may reduce stroke (13 per 1000). These effects were consistent in statin-intolerant patients. Among moderate and low cardiovascular risk groups, adding PCSK9 inhibitor or ezetimibe to statins yielded little or no benefit for MI and stroke. CONCLUSIONS Ezetimibe or PCSK9 inhibitors may reduce non-fatal MI and stroke in adults at very high or high cardiovascular risk who are receiving maximally tolerated statin therapy or are statin-intolerant, but not in those with moderate and low cardiovascular risk
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