Average characteristic polynomials in the two-matrix model

The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2,$$ where $V$ and $W$ are given potential functions and \tau\in\er. We study averages of products and ratios of characteristic polynomials in the two-matrix model, where both matrices $M_1$ and $M_2$ may appear in a combined way in both numerator and denominator. We obtain determinantal expressions for such averages. The determinants are constructed from several building blocks: the biorthogonal polynomials $p_n(x)$ and $q_n(y)$ associated to the two-matrix model; certain transformed functions $\P_n(w)$ and \Q_n(v); and finally Cauchy-type transforms of the four Eynard-Mehta kernels $K_{1,1}$, $K_{1,2}$, $K_{2,1}$ and $K_{2,2}$. In this way we generalize known results for the $1$-matrix model. Our results also imply a new proof of the Eynard-Mehta theorem for correlation functions in the two-matrix model, and they lead to a generating function for averages of products of traces.Comment: 28 pages, references adde

Non-colliding Brownian Motions and the extended tacnode process

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded and many typos correcte

Possible coupling between climatically induced lake level change, volcanic eruptions and seismotectonic activation in the Rukwa-Rungwe-Nyasa rift, SW Tanzania

The Rukwa rift basin is presently a closed hydrogeological depression containing a shallow lake (max 20 me deep) with its surface at an altitude around 810 m above sea level. Lacustrine terraces and paleo-shorelines are known up to 980 m above sea level, an altitude at which it reach the overflow sill towards Lake Tanganyika. Both Lakes Tanganyika and Nyasa (Malawi) are presently overflowing, but as their lake level fluctuates, they have been disconnected from their outlet in the recent past. High resolution seismic profiling in both Lakes Rukwa and Malawi has show the presence of active fault systems underneath the lake floor. Some of these fault systems appear to have had a cyclic activity, with alternating periods of high tectonic activity/sedimentation and periods of tectonic quiescence. The accommodation zone between Lake Rukwa and Nyasa is occupied by the Rungwe volcanic Province, with the Ngozi, Rungwe and Kiejo volcanoes presenting signs of recent volcanic activity. The Rungwe Province is cross-cut by several directions of faults, which clearly control the location of the volcanic vents.In our work, we reviewed the available data on recent (Late Pleistocene – Holocene) volcanic eruptions, in the Rungwe area itself, in the drill cores from the surrounding lakes and from aerial observations up to 300 km away from the Rungwe Province. We performed morphotectonic and paleoseismic investigations of the Kanda fault, a major normal fault between lakes Rukwa and Tanganyika. We investigated lacustrine deposits of the Rukwa basin corresponding to the two last cycles of high lake level. The chronological framework was established using 30 new radiocarbon dating and the most prominent volcanic tephra layers were used as a reference in the correlations. The results are still preliminary, but a good correlation already appear between climatically induced lake level change (in Lake Rukwa), seismo-tectonic activation of the regional fault network (underneath Lake Rukwa and the Kanda fault between Lakes Rukwa and Tanganyika) and the timing of the recent strong volcanic eruptions in the Rungwe Volcanic Province since the last 40.000 years. This relation is explained taking into account that Lake Rukwa is very sensitive to climate change as it occupies a flat depression and its overflow outlet is 180 m above its present-day level. Its lake level rises rapidly when the climate becomes more humid as it was the case during the Last Glacial Maximum and during the Younger Dryas event. Increase in lake level means increasing of the load in the basin and perturbation of the ambient tectonic stresses. In most of the Rukwa rift, the tectonic stress is of extensional (normal faulting) regime, with the maximum principal stress axis (sigma 1) subvertical. In these conditions, increasing the vertical load will increase the shear stress on the existing normal faults, triggering (seismogenic) normal faulting deformation. As the architecture of the active volcanoes in the Rungwe Province is tectonically controlled, activation of the faults, together with a greater pressure of water in the tectonic discontinuities are likely to trigger large volcanic eruptions, strongly explosive

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

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

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

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?

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

Flexural deformation and basin-mountain coupling in the northern Kyrgyz Tien Shan: transition from the Issyk-Kul basin to the Kumtor plateau

During the late stage of the India-Asia collision, deformation propagated northwards into the Asian foreland. North of the stable Tarim plate, the Tien Shan range – an old Palaeozoic fold belt – was strongly reactivated. It now accommodates more than one third of the total shortening rate between Stable Eurasia and the Indian continent.In the northern part of the Kyrgyz Tien-Shan Range, the 600 m deep Lake Issyk-Kul occupies a lense-shaped tectonic depression elongated in an E-W direction and bordered on its northern and southern sides by high mountain ranges (> 4000 m high). To the north, the Kungey Alatau range has the structure of an active positive flower structure with the Chon-Kemin – Chilik fault in its middle (location of several Ms > 8.0 historic earthquakes). To the south, the Terskey range forms the frontal scarp of the high and relatively flat Kumtor Plateau whose surface is undulating between 3800 and 5200 m high.Multidisciplinary investigation was performed during several summer campaigns, involving structural geology, paleostress reconstructions, tectono-stratigraphy and paleoseismology in the mountain ranges and lake shore, as well as high-resolution seismic profiling and heat flow measurements in Lake Issyk-Kul. Investigations included also the seismotectonics analysis of a large number of earthquake focal mechanisms determined from the local seismic network.All the results are best integrated in a model of lithospheric deformation by flexural folding and basin-mountain coupling. The Issyk-Kul basin probably formed as a flexural downwarp of the lithosphere rather than as a symmetric ramp basin, as once proposed. South of the Issyk-Kul depression, the Kumtor plateau still show large remains of the pre-Cainozoic flat erosion surface that is widespread in the Central Asia, now strongly uplifted and slightly undulating. Deformation at mountain-basin interface occurs mainly by tilting around a horizontal axis of the pre-Cainozoic basement (up to 60°from the horizontal), and top-to-the south reverse faulting at the southern margin of the basin (basin towards the range), in an opposite sense to what could be expected in the case of a ramp basin. The focal mechanism of a recent earthquake along the southern mountain-basin interface confirms this interpretation (25 December 2006 Ms 5.8)

До питання підготовки музейної експозиції з історії культури первісного суспільства

In Europe, water management is moving from flood defense to a risk management approach, which takes both the probability and the potential consequences of flooding into account. In this report, we will look at Directives and (non-)EU- initiatives in place to deal with flood risk in Europe indirectly and directly. Emphasis will lie on the two Directives most specifically aimed at floods: the Water Framework Directive (WFD) and the Floods Directive (FD) – how are they related and how they have been or are implemented in the Member States (MSs)? In February 1995, the Netherlands and France took the initiative for a discussion on streamlining the water legislation of the European Union (EU) which resulted in the creation of the WFD in 2000. The WFD provided a new system for the protection and improvement of Europe’s water environment – its rivers, lakes, estuaries, coastal waters and groundwaters. Its main innovation is the requirement that water be managed in an integrated way, with river basin management as leading managing unit. Since flood protection is not explicitly addressed in the WFD, the need to clarify the role of the WFD in flood protection was put on the European agenda as early as 2003, and in 2007, the FD became a fact. The FD is to be implemented in coordination with the WFD, notably by coordinating Flood Risk Management Plans (FRMPs) and River Basin Management Plans (RBMPs). Both the WFD and the FD reflect a shift in EU-governance. Instead of the more traditional top-down legalistic approach they emphasise the importance of more bottom up initiatives from the actors who have to implement the Directives. Combined with the expanded freedom and flexibility for national and local governments, with this new approach, the FD is the first Water Directive in EU law that does not offer an equal minimum level of protection for EU citizens. While both Directives are meant to harmonise European legislation, much flexibility on objectives and measures in the FD is left to the MSs, justified by the nature of flooding and the subsidiarity principle. This creates multi-actor, multi-level and multi-sector challenges addressed in report D1.1.2 (Hegger et al. 2013). For instance, the FD sets out general obligations for transboundary cooperation, but at the national level, the scope and distributions of duties, rights and powers of the various organizations involved should be set out in law. Other challenges identified in the literature are concrete issues related to mandatory flood risks assessments, flood risk maps, and Flood Risk Management plans, but also the involvement of the public and stakeholders, the science-policy interface, uncertainties related to climate change predictions and effects, the coordination with the WFD, the lack of safety standards, the lack of possibilities for EU citizens to rely on substantive provisions before the administrative courts and finally, transboundary aspects such as issues of scale, mismatches between national policies, the assessment of transboundary effects and division of costs related to this. In sum, this report has clarified the development, content and implementation of the current European flood risk governance policies, possible synergies between the two most important Directives linked to floods, and identified topics and questions for more in-depth questions relevant for the next work packages, pertaining to, in no particular order, a) the level of implementation and level of ambition as well as the competent authorities in the case study countries; b) the transboundary nature of floods; c) synergies and conflicts between FD and WFD and other issues not mentioned in these Directives; d) the degree of harmonization, for instance when it comes to flood safety standards and e) the subsidiarity principle – is this conform the requirements set out in the FD? Because while current European flood regulation specified in the WFD and FD provides several potential opportunities for improving flood risk governance, it is not self-evident that all of these opportunities will materialise in all MSs

Earthquake geology of the Kanda fault system (Tanganyika-Rukwa rift, SW highlands of Tanzania)

The 160 km-long Kanda normal fault system is running longitudinally across the Ufipa tilted horst between the Tanganyika and Rukwa rift basins in the western branch of the East African Rift System. It is likely to have been affected the Ms 7.4 earthquake in 1910 whose instrumental epicentre was located approximately near Sumbawanga town, along the northern portion of the fault. Remote sensing, morphotectonic, and palaeoseismological investigations together with structural geology and electric resistivity profiling allow to characterise the main seismological parameters of this major active fault.In order to reconstruct the along-trend displacement profile and fault segmentation, topographic profiles were made across the fault scarp using data from differential GPS, Hand GPS and the 90 m resolution STRM DEM. Comparison of topographic profiles from the same site using the different topographic data provides some insight on the methodology and validity of topographic profiles extraction. Due to the large dimensions of the fault scarp (10-30 m high) the strong magnitude of the potential earthquakes (Ms. 7.5) and the large associated co-seismic slip (2-4 m), classical paleoseismic trenching is difficult to apply. Instead, we used existing exposures such as natural trenches, road cuts and outcrops, supplemented by a dense topographic survey (5000 points on differential GPS over less than 1 km2) to produce a 2 m resolution digital elevation model, performed detailed geological mapping, airphoto interpretation, electric resistivity profiling, small drillings, and C14 dating. Efforts were concentrated on a promising site where river sediments and peat deposits are interbedded with volcanic tephra layers and largely exposed on the footwall. Results show that the Kanda fault had different cycles of activity, separated by tectonically quite periods. The last period of activity probably started by 11 cal Ka BP, soon after the deposition of a marked tephra layer, but sedimentation on the footwall continued up to 5 Ka cal BP. Since then, the minimum offset is estimated at 17.9 m, which gives a minimum slip rate of 3.58 mm/year, of an equivalent of one earthquakes generating 3.58 m slip per 1000 years (Ms in the range of 7.0 - 7.5)

The development and application of a new tool to assess the adequacy of the content and timing of antenatal care

Abstract Background: Current measures of antenatal care use are limited to initiation of care and number of visits. This study aimed to describe the development and application of a tool to assess the adequacy of the content and timing of antenatal care. Methods: The Content and Timing of care in Pregnancy (CTP) tool was developed based on clinical relevance for ongoing antenatal care and recommendations in national and international guidelines. The tool reflects minimal care recommended in every pregnancy, regardless of parity or risk status. CTP measures timing of initiation of care, content of care (number of blood pressure readings, blood tests and ultrasound scans) and whether the interventions were received at an appropriate time. Antenatal care trajectories for 333 pregnant women were then described using a standard tool (the APNCU index), that measures the quantity of care only, and the new CTP tool. Both tools categorise care into 4 categories, from ‘Inadequate’ (both tools) to ‘Adequate plus’ (APNCU) or ‘Appropriate’ (CTP). Participants recorded the timing and content of their antenatal care prospectively using diaries. Analysis included an examination of similarities and differences in categorisation of care episodes between the tools. Results: According to the CTP tool, the care trajectory of 10,2% of the women was classified as inadequate, 8,4% as intermediate, 36% as sufficient and 45,3% as appropriate. The assessment of quality of care differed significantly between the two tools. Seventeen care trajectories classified as ‘Adequate’ or ‘Adequate plus’ by the APNCU were deemed ‘Inadequate’ by the CTP. This suggests that, despite a high number of visits, these women did not receive the minimal recommended content and timing of care. Conclusions: The CTP tool provides a more detailed assessment of the adequacy of antenatal care than the current standard index. However, guidelines for the content of antenatal care vary, and the tool does not at the moment grade over-use of interventions as ‘Inappropriate’. Further work needs to be done to refine the content items prior to larger scale testing of the impact of the new measure