Optimal dispatching in a tandem queue

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant.     

A feedback fluid queue with two congestion control thresholds

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B ₁ is used to signal the beginning of congestion while the lower threshold B ₂ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B ₁ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B ₂ (smaller than B ₁) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.     

A minimization version of a directed subgraph homeomorphism problem

We consider a special case of the directed subgraph homeomorphism or topological minor problem, where the host graph has a specific regular structure. Given an acyclic directed pattern graph, we are looking for a host graph of minimal height which still allows for an embedding. This problem has applications in compiler design for certain coarse-grain reconfigurable architectures. In this application domain, the task is to simultaneously schedule, bind and route a so-called data-flow graph, where vertices represent operations and arcs stand for data dependencies between the operations, given an orthogonal grid structure of reconfigurable processing elements (PEs) that have restricted communication abilities. We show that the problem of simultaneously scheduling, binding and routing is NP-complete by describing a logic engine reduction from NAE-3-SAT. This result holds even when the input graph is a directed tree with maximum indegree two. We also give a |V|^3/2-approximation algorithm. J. A. Brenner’s research supported by the DFG Research Center Matheon “Mathematics for key technologies”. J. C. van der Veen’s research supported by DFG Focus Program 1148, “Reconfigurable Architectures”, Grants FE 407/8-1 and FE 407/8-2.     

Hydrogen interaction with EUVL-relevant optical materials

Mo/Si multilayer mirrors were exposed to deuterium ions with well-defined energies in order to gain insight into the effects of Extreme UV light driven plasma generation on reflective elements in commercial lithography equipment. Post-irradiation analysis by Rutherford Backscattering Spectrometry showed erosion of both Mo and Si layers for the highest energy 50 eV/D and exposure time 5.4 × 10⁴ s. Nuclear Reaction Analysis revealed detectable deuterium retention for energies ⩾25 eV/D. Surface analysis by X-ray Photoelectron Spectroscopy showed erosion of the first Si layer for energies ⩾5 eV/D. Inferences on the spatial distribution of trapped deuterium are made on the basis of available data regarding deuterium retention in the materials in question.     

DFT study on H2O activation by stepped and planar Rh surfaces

In this research the effect of steps (lower coordinated surface atoms) and the presence of pre-adsorbed oxygen on the activation energy of water are studied with DFT. Without oxygen water activation is found to be structure insensitive. When oxygen is adsorbed on the surface and acts as the acceptor for the hydrogen at the step edge, the barrier will decrease significantly.     

One-dimensional photonic crystal design

In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piecewise constant refractive indices we develop an algorithm to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and the scattering matrix containing the information on the localized modes.     

Quantification of midazolam,morphine and metabolites in plasma using 96‐well solid‐phase extraction and ultra‐performance liquid chromatography–tandem mass spectrometry

Currently, pharmacokinetic–pharmacodynamic studies of sedatives and analgesics are performed in neonates and children to find suitable dose regimens. As a result, sensitive assays using only small volumes of blood are necessary to determine drug and metabolite concentrations. We developed an ultra‐performance liquid chromatographic method with tandem mass spectrometry detection for quantification of midazolam, 1‐hydroxymidazolam, hydroxymidazolamglucuronide, morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide in 100 μL of plasma. Cleanup consisted of 96 wells micro‐solid phase extraction, before reversed‐phase chromatographic separation (ultra‐performance liquid chromatography) and selective detection using electrospray ionization tandem mass spectrometry. Separate solid‐phase extraction methods were necessary to quantify morphine, midazolam and their metabolites because of each group's physicochemical properties. Standard curves were linear over a large dynamic range with adequate limits of quantitation. Intra‐ and interrun accuracy and precision were within 85–115% (of nominal concentration using a fresh calibration curve) and 15% (coefficient of variation, CV) respectively. Recoveries were >80% for all analytes, with interbatch CVs (as a measure of matrix effects) of less than 15% over six batches of plasma. Stability in plasma and extracts was sufficient, allowing large autosampler loads. Runtime was 3.00 min per sample for each method. The combination of 96‐well micro‐SPE and UPLC‐MS/MS allows reliable quantification of morphine, midazolam and their major metabolites in 100 μL of plasma. Copyright © 2010 John Wiley & Sons, Ltd.     

An efficient and versatile synthesis of GlcNAcstatins-potent and selective O-GlcNAcase inhibitors built on the tetrahydroimidazo[1,2-a]pyridine scaffold

We report a novel approach to the synthesis of GlcNAcstatins-members of an emerging family of potent and selective inhibitors of peptidyl O-GlcNAc hydrolase build upon tetrahydroimidazo[1,2-a]pyridine scaffold. Making use of a streamlined synthetic sequence featuring de novo synthesis of imidazoles from glyoxal, ammonia and aldehydes, a properly functionalised linear GlcNAcstatin precursor has been efficiently prepared starting from methyl 3,4-O-(2',3'-dimethoxybutane-2',3'-diyl)-α-d-mannopyranoside. Subsequent ring closure of the linear precursor in an intramolecular S(N)2 process furnished the key fused d-mannose-imidazole GlcNAcstatin precursor in excellent yield. Finally, a sequence of transformations of this key intermediate granted expeditious access to a variety of the target compounds bearing a C(2)-phenethyl group and a range of N(8) acyl substituents. The versatility of the new approach stems from an appropriate choice of a set of acid labile permanent protecting groups on the monosaccharide starting material. Application was demonstrated by the synthesis of GlcNAcstatins containing polyunsaturated and thiol-containing amido substituents.     

Towards the synthesis of sulfonamide-based RNA mimetics

The scalable, divergent synthesis of all four monomers required for the preparation of sulfonamide-based RNA mimetics is described. Such mimetics may combine excellent mimicry of the parent RNA with enhanced (bio)chemical robustness and convenient oligomerization. As a proof of principle, a dimer resulting from the monomers is described.