Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

Dopamine-D1 and δ-opioid receptors co-exist in rat striatal neurons

Cocaine’s enhancement of dopaminergic neurotransmission in the mesolimbic pathway plays a critical role in the initial reinforcing properties of this drug. However, other neurotransmitter systems are also integral to the addiction process. A large body of data indicates that opioids and dopamine together mediate emotional and reinforced behaviors. In support of this, cocaine-mediated increases in activation of dopamine D1 receptors (D1R) results in a desensitization of δ-opioid receptor (DOR) signaling through adenylyl cyclase (AC) in striatal neurons. To further define cellular mechanisms underlying this effect, the subcellular distribution of DOR and D1R was examined in the rat dorsolateral striatum. Dual immunoperoxidase/gold-silver detection combined with electron microscopy was used to identify DOR and D1R immunoreactivities in the same section of tissue. Semi-quantitative analysis revealed that a subset of dendritic cellular profiles exhibited both DOR and D1R immunoreactivities. Of 165 randomly sampled D1R immunoreactive profiles, 43% contained DOR. Similarly of 198 DOR-labeled cellular profiles, 52% contained D1R. The present data provide ultrastructural evidence for co-existence between DOR and D1R in striatal neurons, suggesting a possible mechanism whereby D1R modulation may alter DOR function

Dispersion vs. anti-diffusion: well-posedness in variable coefficient and quasilinear equations of KdV-type

We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition between the dispersive effects which stem from the leading-order term, and anti-diffusion which stems from the lower-order terms with two spatial derivatives. We show that the dispersive effects can dominate the backwards diffusion: we find a condition which guarantees well-posedness of the initial value problem for linear, variable coefficient equations of this kind, even when such anti-diffusion is present. In fact, we show that even in the presence of localized backwards diffusion, the dispersion will in some cases lead to an overall effect of parabolic smoothing. By contrast, we also show that when our condition is violated, the backwards diffusion can dominate the dispersive effects, leading to an ill-posed initial value problem. We use these results on linear evolution equations as a guide when proving well-posedness of the initial value problem for some quasilinear equations which also exhibit this competition between dispersion and anti-diffusion: a Rosenau-Hyman compacton equation, the Harry Dym equation, and equations which arise in the numerical analysis of finite difference schemes for dispersive equations. For these quasilinear equations, the well-posedness theorem requires that the initial data be uniformly bounded away from zero

Serfati solutions to the 2D Euler equations on exterior domains

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This work completes and extends the ideas outlined by P. Serfati for the same problem in the whole-plane case. With non-decaying vorticity, the Biot-Savart integral does not converge, and thus velocity cannot be reconstructed from vorticity in a straightforward way. The key to circumventing this difficulty is the use of the Serfati identity, which is based on the Biot-Savart integral, but holds in more general settings.Comment: 50 page

A large conjugative Acinetobacter baumannii plasmid carrying the sul2 sulphonamide and strAB streptomycin resistance genes

Acinetobacter baumannii is an important nosocomial pathogen that often complicates treatment because of its high level of resistance to antibiotics. Though plasmids can potentially introduce various genes into bacterial strains, compared to other Gram-negative bacteria, information about the unique A. baumannii plasmid repertoire is limited. Here, whole genome sequence data was used to determine the plasmid content of strain A297 (RUH875), the reference strain for the globally disseminated multiply resistant A. baumannii clone, global clone 1(GC1). A297 contains three plasmids. Two known plasmids were present; one, pA297-1 (pRAY*), carries the aadB gentamicin, kanamycin and tobramycin resistance gene and another is an 8.7kb cryptic plasmid often found in GC1 isolates. The third plasmid, pA297-3, is 200kb and carries the sul2 sulphonamide resistance gene and strAB streptomycin resistance gene within Tn6172 and a mer mercuric ion resistance module elsewhere. pA297-3 transferred sulphonamide, streptomycin and mercuric ion resistance at high frequency to a susceptible A. baumannii recipient, and contains several genes potentially involved in conjugative transfer. However, a relaxase gene was not found. It also includes several genes encoding proteins involved in DNA metabolism such as partitioning. However, a gene encoding a replication initiation protein could not be found. pA297-3 includes two copies of a Miniature Inverted-Repeat Transposable Element (MITE), named MITE-297, bracketing a 77.5kb fragment, which contains several IS and the mer module. Several plasmids related to but smaller than pA297-3 were found in the GenBank nucleotide database. They were found in different A. baumannii clones and are wide spread. They all contain either Tn6172 or a variant in the same position in the backbone as Tn6172 in pA297-3. Some related plasmids have lost the segment between the MITE-297 copies and retain only one MITE-297. Others have segments of various lengths between two MITE-297 copies, and these can be derived from the region in pA297-3 via a deletion adjacent to IS related to IS26 such as IS1007 or IS1007-like. pA297-3 and its relatives represent a third type of conjugative Acinetobacter plasmid that contributes to the dissemination of antibiotic resistance in this species.NHMR

Field quantification of foliar chlorophyll content in Pisum germplasm

Variation in the chlorophyll content of the foliage of peas has been long documented. Traditional quantification of chlorophyll levels in leaves is by acetone extraction and spectrophotometer analysis (1) which takes time and requires laboratory equipment and facilities. In the classification of cultivated germplasm, the variation in the colour of foliage is graded based on morphological descriptor states. The UPOV guidelines for distinctness, uniformity and stability for Pisum (2) recognises three descriptor states, yellow green (J), green (2) and blue green (3). State 2 (green) is further broken down into light (3), medium (5) and dark (7). Three descriptor states are used in recording on the John Innes Pisum Collection namely, 1. yellow green, 2. green, 3. dark green. While these scales are clearly discernable by eye, a quick and reliable objective method of quantifying this variation could be useful in quantifying this character. The portable Minolta SPAD 502 chlorophyll meter determines the relative chlorophyll in leaf tissue by measuring absorbance at two wavelengths, namely in the regions of 400-500nm and 600-700nm which are characteristics of chlorophyll absorption peaks. Initially developed for monitoring the nitrogen status of wheat crops, the meter has subsequently been deployed on a range of monocot crop and woody species where good linear relationships between SPAD readings and leaf chlorophyll content were obtained (3). The method has also been used in crop nitrogen studies in pea (4, 5, 6) and in studies in chickpea (7, 8). This is the first deployment of the meter on pea germplasm in order to establish whether its utility could be extended to studies of pea germplasm and mutation stocks