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

Understanding Root Uptake of Nutrients, Toxic and Polluting Elements in Hydroponic Culture

peer reviewe

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.

Tracing the origin of dissolved silicon transferred from various soil-plant systems towards rivers: a review

Silicon (Si) released as H4SiO4 by weathering of Si-containing solid phases is partly recycled through vegetation before its land-to-rivers transfer. By accumulating in terrestrial plants to a similar extent as some major macronutrients (0.1–10% Si dry weight), Si becomes largely mobile in the soil-plant system. Litter-fall leads to a substantial reactive biogenic silica pool in soil, which contributes to the release of dissolved Si (DSi) in soil solution. Understanding the biogeochemical cycle of silicon in surface environments and the DSi export from soils into rivers is crucial given that the marine primary bio-productivity depends on the availability of H4SiO4 for phytoplankton that requires Si. Continental fluxes of DSi seem to be deeply influenced by climate (temperature and runoff) as well as soil-vegetation systems. Therefore, continental areas can be characterized by various abilities to transfer DSi from soil-plant systems towards rivers. Here we pay special attention to those processes taking place in soil-plant systems and controlling the Si transfer towards rivers. We aim at identifying relevant geochemical tracers of Si pathways within the soil-plant system to obtain a better understanding of the origin of DSi exported towards rivers. In this review, we compare different soil-plant systems (weathering-unlimited and weathering-limited environments) and the variations of the geochemical tracers (Ge/Si ratios and d30Si) in DSi outputs. We recommend the use of biogeochemical tracers in combination with Si mass-balances and detailed physico-chemical characterization of soil-plant systems to allow better insight in the sources and fate of Si in these biogeochemical systems

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

Determinants of institutional delivery among young married women in Nepal: Evidence from the Nepal Demographic and Health Survey, 2011

OBJECTIVES: To identify the determinants of institutional delivery among young married women in Nepal. DESIGN: Nepal Demographic and Health Survey (NDHS) data sets 2011 were analysed. Bivariate and multivariate logistic regression analyses were performed using a subset of 1662 ever-married young women (aged 15-24 years). OUTCOME MEASURE: Place of delivery. RESULTS: The rate of institutional delivery among young married women was 46%, which is higher than the national average (35%) among all women of reproductive age. Young women who had more than four antenatal care (ANC) visits were three times more likely to deliver in a health institution compared with women who had no antenatal care visit (OR: 3.05; 95% CI: 2.40 to 3.87). The probability of delivering in an institution was 69% higher among young urban women than among young women who lived in rural areas. Young women who had secondary or above secondary level education were 1.63 times more likely to choose institutional delivery than young women who had no formal education (OR: 1.626; 95% CI: 1.171 to 2.258). Lower use of a health institution for delivery was also observed among poor young women. Results showed that wealthy young women were 2.12 times more likely to deliver their child in an institution compared with poor young women (OR: 2.107; 95% CI: 1.53 to 2.898). Other factors such as the age of the young woman, religion, ethnicity, and ecological zone were also associated with institutional delivery. CONCLUSIONS: Maternal health programs should be designed to encourage young women to receive adequate ANC (at least four visits). Moreover, health programs should target poor, less educated, rural, young women who live in mountain regions, are of Janajati ethnicity and have at least one child as such women are less likely to choose institutional delivery in Nepal

What Influences Adolescent Girls' Decision-Making Regarding Contraceptive Methods Use and Childbearing? A Qualitative Exploratory Study in Rangpur District, Bangladesh

BACKGROUND: Bangladesh has the highest rate of adolescent pregnancy in South Asia. Child marriage is one of the leading causes of pregnancies among adolescent girls. Although the country's contraceptive prevalence rate is quite satisfactory, only 52% of married adolescent girls use contraceptive methods. This qualitative study is aimed at exploring the factors that influence adolescent girls' decision-making process in relation to contraceptive methods use and childbearing. METHODS AND RESULTS: We collected qualitative data from study participants living in Rangpur district, Bangladesh. We conducted 35 in-depth interviews with married adolescent girls, 4 key informant interviews, and one focus group discussion with community health workers. Adolescent girls showed very low decision-making autonomy towards contraceptive methods use and childbearing. Decisions were mainly made by either their husbands or mothers-in-law. When husbands were unemployed and financially dependent on their parents, then the mothers-in-law played most important role for contraceptive use and childbearing decisions. Lack of reproductive health knowledge, lack of negotiation and communication ability with husbands and family members, and mistrust towards contraceptive methods also appeared as influential factors against using contraception resulting in early childbearing among married adolescent girls. CONCLUSIONS: Husbands and mothers-in-law of newly married adolescent girls need to be actively involved in health interventions so that they make more informed decisions regarding contraceptive use to delay pregnancies until 20 years of age. Misunderstanding and distrust regarding contraceptives can be diminished by engaging the wider societal actors in health intervention including neighbours, and other family members

Non-intersecting squared Bessel paths: critical time and double scaling limit

We consider the double scaling limit for a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t=0$ at the same positive value $x=a$, remain positive, and are conditioned to end at time $t=1$ at $x=0$. After appropriate rescaling, the paths fill a region in the $tx$--plane as $n\to \infty$ that intersects the hard edge at $x=0$ at a critical time $t=t^{*}$. In a previous paper (arXiv:0712.1333), the scaling limits for the positions of the paths at time $t\neq t^{*}$ were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as $n\to \infty$ of the correlation kernel at critical time $t^{*}$ and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections with the Pearcey kernel. The analysis is based on the study of a $3\times 3$ matrix valued Riemann-Hilbert problem by the Deift-Zhou steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions of a particular third-order linear differential equation, and its matching with a global parametrix.Comment: 53 pages, 15 figure

Transfer of Communication Skills to the Workplace during Clinical Rounds : Impact of a Program for Residents

peer reviewe

The “invisible cholecystectomy”: A transumbilical laparoscopic operation without a scar

Background Looking to further reduce the operative trauma of laparoscopic cholecystectomy, we developed, in patients with no history of cholecystitis and a normal BMI, a scarless operation through the umbilicus. The operative technique, along with the results of the first 10 patients operated in this way, are fully described. Methods 10 female patients underwent transumbilical scarless laparoscopic cholecystectomy. Through the umbilicus, two trocars of 5 mm were introduced parallel to another with a bridge of fascia between them (one for the 5-mm laparoscope and the other for the grasper). With the help of one 1-mm Kirschner wire, introduced at the subcostal line and bent with a special designed device, the gallbladder was pulled up and the triangle of Callot was dissected free, clipped, cut, and the gallbladder was subsequently resected. Finally the gallbladder was taken out through the umbilicus and the umbilicus reconstructed. Results 10 female patients, mean age 36 years (range: 31–49), mean body mass index (BMI) 23 (range: 20–26), after one attack (six patients) or a second attack (four patients) and cholelithiasis confirmed by ultrasonography with no suspicion of inflammation were included in this preliminary study. Mean operative time was 70 minutes (range: 65–85) with no conversions; hospital stay was less than 24 hours with no complications. Conclusion Looking to reduce operative trauma and improve the cosmetic result following laparoscopic cholecystectomy, a transumbilical operative technique has been developed. Results of the operative procedure in a selected group of patients are encouraging with no signs of inflammation and normal BMI. The umbilicus can be developed as a natural port for performing various operative procedures with the help of the traction produced by thin Kirschner wires