NONUNIQUENESS AND SINGULAR RADIAL SOLUTIONS OF SYSTEMS OF CONSERVATION LAWS Dedicated to Professor Constantine M. Dafcrmos on the occasion of his 70th birthday

The case of a radial initial state for a family of hyperbolic systems of conservation laws with several spatial dimensions is considered.It will be shown that the singularity at the origin introduces multiple solutions outside of the traditional admissible classes.     

Identification of a set of genes showing regionally enriched expression in the mouse brain

Background

We have recorded responses from single neurons in murine visual cortex to determine the effectiveness of the input from the two murine cone photoreceptor mechanisms and whether there is any unique selectivity for cone inputs at this higher region of the visual system that would support the possibility of colour vision in mice. Each eye was stimulated by diffuse light, either 370 (strong stimulus for the ultra-violet (UV) cone opsin) or 505 nm (exclusively stimulating the middle wavelength sensitive (M) cone opsin), obtained from light emitting diodes (LEDs) in the presence of a strong adapting light that suppressed the responses of rods.

Results

Single cells responded to these diffuse stimuli in all areas of striate cortex. Two types of responsive cells were encountered. One type (135/323 – 42%) had little to no spontaneous activity and responded at either the on and/or the off phase of the light stimulus with a few impulses often of relatively large amplitude. A second type (166/323 – 51%) had spontaneous activity and responded tonically to light stimuli with impulses often of small amplitude. Most of the cells responded similarly to both spectral stimuli. A few (18/323 – 6%) responded strongly or exclusively to one or the other spectral stimulus and rarely in a spectrally opponent manner.

Conclusion

Most cells in murine striate cortex receive excitatory inputs from both UV- and M-cones. A small fraction shows either strong selectivity for one or the other cone mechanism and occasionally cone opponent responses. Cells that could underlie chromatic contrast detection are present but extremely rare in murine striate cortex.     

Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.     

Energy-minimizing deformations of elastic sheets with bending stiffness

Necessary conditions for energy-minimizing deformations are derived for a theory of sheets in which the strain energy function depends on the second derivatives of the deformation as well as its first derivatives. All of these conditions are extensions of well-known necessary conditions in classical calculus of variations. The interpretation of some of these conditions as material stability conditions is explained.     

Pickering emulsions: wetting and colloidal stability of hairy particles--a self-consistent field theory

The assembly of sterically stabilized colloids at liquid-liquid interfaces is studied with the self-consistent field (SCF) theory using the discretization scheme that was developed by Scheutjens, Fleer, and co-workers. The model is based on a poly(methyl methacrylate) (pMMA) particle with poly(isobutylene) (pIB) grafted to the surface. The stabilizing groups on the particle surface have a significant effect on the interfacial assembly and, therefore, also on the formation and properties of Pickering emulsions. The wetting behavior of the particle is altered by the presence of the stabilizing groups, which affects the equilibrium position of the particles at the interface. The stabilizing groups can also lead to an activation barrier before interfacial adsorption, analogous to the steric repulsion between two particles. These effects are numerically solved with the SCF theory. It is commonly known that flocculating conditions enhance the interfacial adsorption and yield stable Pickering emulsions, which is confirmed in this work. Additionally, it is concluded that those conditions are not an absolute requirement. There is a window of stabilizer concentrations Γ(pIB), 2.2-3.3 mg/m(2) pIB, that shows both partial wetting and colloidal stability. The activation barrier for interfacial assembly is 140-550 k(B)T and is an order of magnitude higher than the colloidal stability. The difference can be attributed to the unfavorable interaction of pIB with water and a difference in geometry (plate-sphere vs sphere-sphere). This study demonstrates the interplay and provides a quantitative comparison between the wetting behavior and the colloidal stability, and it gives a better understanding of the colloidal assembly at soft interfaces and formation of Pickering emulsions in general.     

Influence of natural organic matter on the screening of pharmaceuticals in water by using liquid chromatography with full scan mass spectrometry

The influence of natural organic matter on the screening of pharmaceuticals in water was determined by using high resolution liquid chromatography (HRLC) combined with full scan mass spectrometry (MS) techniques like time of flight (ToF) or Orbitrap MS. Water samples containing different amount of natural organic matter (NOM) and residues of a set of 11 pharmaceuticals were analyzed by using Exactive Orbitrap? LC-MS. The samples were screened for residues of pharmaceuticals belonging to different classes like benzimidazoles, macrolides, penicillins, quinolones, sulfonamides, tetracyclines, tranquillizers, non-steroidal anti-inflammatory drugs (NSAIDs), anti-epileptics and lipid regulators. The method characteristics were established over a concentration range of 0.1-500 μg L(-1). The 11 pharmaceuticals were added to two effluent and two influent water samples. The NOM concentration within the samples ranged from 2 to 8 mg L(-1) of dissolved organic carbon. The HRLC-Exactive Orbitrap? LC-MS system was set at a resolution of 50,000 (FWHM) and this selection was found sufficient for the detection of the list of pharmaceuticals. With this resolution setting, accurate mass measurements with errors below 2 ppm were found, despite of the NOM concentration of the different types of water samples. The linearities were acceptable with correlation coefficients greater than 0.95 for 30 of the 51 measured linearities. The limit of detection varies between 0.1 μg L(-1)and 100 μg L(-1). It was demonstrated that sensitivity could be affected by matrix constituents in both directions of signal reduction or enhancement. Finally it was concluded that with direct shoot method used (no sample pretreatment) all compounds, were detected but LODs depend on matrix-analyte-concentration combination. No direct relation was observed between NOM concentration and method characteristics. For accurate quantification the use of internal standards and/or sample clean-up is necessary. The direct shoot method is only applicable for qualitative screening purposes. The use of full scan MS makes it possible to search for unknown contaminants. With the use of adequate software and a database containing more than 50,000 entries a tool is available to search for unknowns.     

A fast, comprehensive screening method for doping agents in urine by gas chromatography-triple quadrupole mass spectrometry

The use of performance enhancing drugs in sports is prohibited. For the detection of misuse of such substances gas chromatography or liquid chromatography coupled to mass spectrometry are the most frequently used detection techniques. In this work the development and validation of a fast gas chromatography tandem mass spectrometric method for the detection of a wide range of doping agents is described. The method can determine 13 endogenous steroids (the steroid profile), 19-norandrosterone, salbutamol and 11-nor-Δ9-tetrahydrocannabinol.9carboxylic acid in the applicable ranges and to detect qualitatively over 140 substances in accordance with the minimum required performance levels of the World Anti-Doping Agency in 1ml of urine. The classes of substances included in the method are anabolic steroids, β2-agonists, stimulants, narcotics, hormone antagonists and modulators and beta-blockers. Moreover, using a short capillary column and hydrogen as a carrier gas the run time of the method is less than 8min.