Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equations

We study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation $u_{yy}=\bigl(u_{xxx}+uu_x+u_t\bigr)_x$ with holomorphic initial data possessing nonnegative Taylor coefficients around the origin. For the KdV equation with initial value $u(0,x)=u_0(x)$, we show that there is no solution holomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\mathbb C}^2$ unless $u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of $y$-independent solutions of the KP equation. We extend this to $y$-dependent cases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$, $u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around $t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic solution around the origin in ${\mathbb C}^3$ unless $u_0$ and $u_1$ are polynomials of degree 2 or lower.Comment: 17 pages in LaTeX2e, to appear in Stud. Appl. Mat

The peppermint breath test benchmark for PTR-MS and SIFT-MS

18openInternationalInternational coauthor/editorA major challenge for breath research is the lack of standardization in sampling and analysis. To address this, a test that utilizes a standardized intervention and a defined study protocol has been proposed to explore disparities in breath research across different analytical platforms and to provide benchmark values for comparison. Specifically, the Peppermint Experiment involves the targeted analysis in exhaled breath of volatile constituents of peppermint oil after ingestion of the encapsulated oil. Data from the Peppermint Experiment performed by proton transfer reaction mass spectrometry (PTR-MS) and selected ion flow tube mass spectrometry (SIFT-MS) are presented and discussed herein, including the product ions associated with the key peppermint volatiles, namely limonene, α- and β-pinene, 1,8-cineole, menthol, menthone and menthofuran. The breath washout profiles of these compounds from 65 individuals were collected, comprising datasets from five PTR-MS and two SIFT-MS instruments. The washout profiles of these volatiles were evaluated by comparing the log-fold change over time of the product ion intensities associated with each volatile. Benchmark values were calculated from the lower 95% confidence interval of the linear time-to-washout regression analysis for all datasets combined. Benchmark washout values from PTR-MS analysis were 353 min for the sum of monoterpenes and 1,8-cineole (identical product ions), 173 min for menthol, 330 min for menthofuran, and 218 min for menthone; from SIFT-MS analysis values were 228 min for the sum of monoterpenes, 281 min for the sum of monoterpenes and 1,8-cineole, and 370 min for menthone plus 1,8-cineole. Large inter- and intra-dataset variations were observed, whereby the latter suggests that biological variability plays a key role in how the compounds are absorbed, metabolized and excreted from the body via breath. This variability seems large compared to the influence of sampling and analytical procedures, but further investigations are recommended to clarify the effects of these factors.openHenderson, Ben; Slingers, Gitte; Pedrotti, Michele; Pugliese, Giovanni; Malásková, Michaela; Bryant, Luke; Lomonaco, Tommaso; Ghimenti, Silvia; Moreno, Sergi; Cordell, Rebecca; Harren, Frans J M; Schubert, Jochen; Mayhew, Chris A; Wilde, Michael; Di Francesco, Fabio; Koppen, Gudrun; Beauchamp, Jonathan D; Cristescu, Simona MHenderson, B.; Slingers, G.; Pedrotti, M.; Pugliese, G.; Malásková, M.; Bryant, L.; Lomonaco, T.; Ghimenti, S.; Moreno, S.; Cordell, R.; Harren, F.J.M.; Schubert, J.; Mayhew, C.A.; Wilde, M.; Di Francesco, F.; Koppen, G.; Beauchamp, J.D.; Cristescu, S.M

Astroparticle Physics with a Customized Low-Background Broad Energy Germanium Detector

The MAJORANA Collaboration is building the MAJORANA DEMONSTRATOR, a 60 kg array of high purity germanium detectors housed in an ultra-low background shield at the Sanford Underground Laboratory in Lead, SD. The MAJORANA DEMONSTRATOR will search for neutrinoless double-beta decay of 76Ge while demonstrating the feasibility of a tonne-scale experiment. It may also carry out a dark matter search in the 1-10 GeV/c^2 mass range. We have found that customized Broad Energy Germanium (BEGe) detectors produced by Canberra have several desirable features for a neutrinoless double-beta decay experiment, including low electronic noise, excellent pulse shape analysis capabilities, and simple fabrication. We have deployed a customized BEGe, the MAJORANA Low-Background BEGe at Kimballton (MALBEK), in a low-background cryostat and shield at the Kimballton Underground Research Facility in Virginia. This paper will focus on the detector characteristics and measurements that can be performed with such a radiation detector in a low-background environment.Comment: Submitted to NIMA Proceedings, SORMA XII. 9 pages, 4 figure

The Majorana Project

Building a \BBz experiment with the ability to probe neutrino mass in the inverted hierarchy region requires the combination of a large detector mass sensitive to \BBz, on the order of 1-tonne, and unprecedented background levels, on the order of or less than 1 count per year in the \BBz signal region. The MAJORANA Collaboration proposes a design based on using high-purity enriched Ge-76 crystals deployed in ultra-low background electroformed Cu cryostats and using modern analysis techniques that should be capable of reaching the required sensitivity while also being scalable to a 1-tonne size. To demonstrate feasibility, the collaboration plans to construct a prototype system, the MAJORANA DEMONSTRATOR, consisting of 30 kg of 86% enriched \Ge-76 detectors and 30 kg of natural or isotope-76-depleted Ge detectors. We plan to deploy and evaluate two different Ge detector technologies, one based on a p-type configuration and the other on n-type.Comment: paper submitted for the 2008 Carolina International Symposium on Neutrino Physic

Setting things straight: a comparison of measures of saccade trajectory deviation

In eye movements, saccade trajectory deviation has often been used as a physiological operationalization of visual attention, distraction, or the visual system’s prioritization of different sources of information. However, there are many ways to measure saccade trajectories and to quantify their deviation. This may lead to noncomparable results and poses the problem of choosing a method that will maximize statistical power. Using data from existing studies and from our own experiments, we used principal components analysis to carry out a systematic quantification of the relationships among eight different measures of saccade trajectory deviation and their power to detect the effects of experimental manipulations, as measured by standardized effect size. We concluded that (1) the saccade deviation measure is a good default measure of saccade trajectory deviation, because it is somewhat correlated with all other measures and shows relatively high effect sizes for two well-known experimental effects; (2) more generally, measures made relative to the position of the saccade target are more powerful; and (3) measures of deviation based on the early part of the saccade are made more stable when they are based on data from an eyetracker with a high sampling rate. Our recommendations may be of use to future eye movement researchers seeking to optimize the designs of their studies

Selective area epitaxy of ultra-high density InGaN quantum dots by diblock copolymer lithography

Highly uniform InGaN-based quantum dots (QDs) grown on a nanopatterned dielectric layer defined by self-assembled diblock copolymer were performed by metal-organic chemical vapor deposition. The cylindrical-shaped nanopatterns were created on SiNx layers deposited on a GaN template, which provided the nanopatterning for the epitaxy of ultra-high density QD with uniform size and distribution. Scanning electron microscopy and atomic force microscopy measurements were conducted to investigate the QDs morphology. The InGaN/GaN QDs with density up to 8 × 1010 cm-2 are realized, which represents ultra-high dot density for highly uniform and well-controlled, nitride-based QDs, with QD diameter of approximately 22-25 nm. The photoluminescence (PL) studies indicated the importance of NH3 annealing and GaN spacer layer growth for improving the PL intensity of the SiNx-treated GaN surface, to achieve high optical-quality QDs applicable for photonics devices

TThe {\sc Majorana} Project

The {\sc Majorana} Project, a neutrinoless double-beta decay experiment is described with an emphasis on the choice of Ge-detector configuration.Comment: 3 pages, contributed to TAUP 200

Copper binding to the Alzheimer’s disease amyloid precursor protein

Alzheimer’s disease is the fourth biggest killer in developed countries. Amyloid precursor protein (APP) plays a central role in the development of the disease, through the generation of a peptide called Aβ by proteolysis of the precursor protein. APP can function as a metalloprotein and modulate copper transport via its extracellular copper binding domain (CuBD). Copper binding to this domain has been shown to reduce Aβ levels and hence a molecular understanding of the interaction between metal and protein could lead to the development of novel therapeutics to treat the disease. We have recently determined the three-dimensional structures of apo and copper bound forms of CuBD. The structures provide a mechanism by which CuBD could readily transfer copper ions to other proteins. Importantly, the lack of significant conformational changes to CuBD on copper binding suggests a model in which copper binding affects the dimerisation state of APP leading to reduction in Aβ production. We thus predict that disruption of APP dimers may be a novel therapeutic approach to treat Alzheimer’s disease