Discrete Sturm comparison theorems on finite and infinite intervals

The Sturm comparison theorem for second-order Sturm–Liouville difference equations on infinite intervals is established and discussed.     

Target-Decoy Approach and False Discovery Rate: When Things May Go Wrong

The target-decoy approach (TDA) has done the field of proteomics a great service by filling in the need to estimate the false discovery rates (FDR) of peptide identifications. While TDA is often viewed as a universal solution to the problem of FDR evaluation, we argue that the time has come to critically re-examine TDA and to acknowledge not only its merits but also its demerits. We demonstrate that some popular MS/MS search tools are not TDA-compliant and that it is easy to develop a non-TDA compliant tool that outperforms all TDA-compliant tools. Since the distinction between TDA-compliant and non-TDA compliant tools remains elusive, we are concerned about a possible proliferation of non-TDA-compliant tools in the future (developed with the best intentions). We are also concerned that estimation of the FDR by TDA awkwardly depends on a virtual coin toss and argue that it is important to take the coin toss factor out of our estimation of the FDR. Since computing FDR via TDA suffers from various restrictions, we argue that TDA is not needed when accurate p-values of individual Peptide-Spectrum Matches are available.     

Multiple-instrument analyses of single micron-size particles.

Physical, chemical, and isotopic analyses of individual radioactive and other particles in the micron-size range, key tools in environmental research and in nuclear forensics, require the ability to precisely relocate particles of interest (POIs) in the secondary ion mass spectrometer (SIMS) or in another instrument, after having been located, identified, and characterized in the scanning electron microscope (SEM). This article describes the implementation, testing, and evaluation of the triangulation POIs re-location method, based on microscopic reference marks imprinted on or attached to the sample holder, serving as an inherent coordinate system. In SEM-to-SEM and SEM-to-SIMS experiments re-location precision better than 10 microm and 20 microm, respectively, is readily attainable for instruments using standard specimen stages. The method is fast, easy to apply, and facilitates repeated analyses of individual particles in different instruments and laboratories.     

Transition from zero-dimensional to one-dimensional behavior in InAs and CdSe nanorods

Tunneling and optical spectroscopy performed on InAs nanorods 7–25 nm long, reveal a clear dependence of the band gap on length. This (zero-dimension like) behavior is different from that of CdSe rods, where the band gap is nearly independent of length, a signature of quasi-one-dimensionality. The transition between these two regimes is governed by the ratio between the Bohr radius and the nanorods length. The gaps measured by tunneling spectroscopy are larger than the optical gaps by a factor that depends on the tunneling configuration. This is attributed to a combination of the Coulomb interaction and the voltage division between the two tunnel junctions in the STM experiment. However, the tunneling gaps were found to reduce in dense aggregates of rods.     

Enoxacin trihydrate

The structure of the title compound, 1‐ethyl‐6‐fluoro‐1,4‐di­hydro‐4‐oxo‐7‐(piperazin‐4‐ium‐1‐yl)‐1,8‐naphthyridine‐3‐carb­oxylate trihydrate, C₁₅H₁₇FN₄O₃·3H₂O, has a zwitterion of enoxacin and three water mol­ecules in the asymmetric unit. The zwitterions form sheets lying parallel to each other and are hydrogen bonded in a head‐to‐tail manner. The crystal structure is stabilized by the involvement of O and H atoms from all the water mol­ecules in strong hydrogen bonds. The naphthyridine ring system is essentially planar, with the carboxyl­ate group lying out of this plane at an angle of 26.13 (6)° and the ethyl group oriented at approximately right angles to this plane. The piperazinium ring adopts a chair conformation.     

Integral means and Pólya factorizations

Integral means of functions and their derivatives are studied. We find a relation between integral means and the Pólya factorization of ordinary linear differential operators.

     

The rheologic properties of erythrocytes: a study using an automated rheoscope

Red blood cells (RBCs) suspended in a high-viscosity medium were filmed while flowing through a microchannel using an automated rheoscope. Under these conditions, erythrocytes take different orientations and undergo varying deformation according to their location in the velocity profile. Measurements of the mean deformation at several distances from the center of the microchannel at a constant flow rate were acquired for normal and thalassemia erythrocytes. The measurements demonstrate how diagnosis can be made based on a single flow rate in contrast to conventional methods where shear is mechanically controlled. The spatial distribution and velocity of RBCs and rigid microspheres (1 μm) were measured. The maximum slip velocity was found to be linearly correlated to the flow rate for both cells and microspheres. RBCs showed enhanced inward lateral migration compared to the rigid spheres, which is attributed to RBC deformation. The results demonstrate the coupling between RBC mechanical properties and their motion in microvessels. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27-29, 2006.     

Analysis of customers’ impatience in queues with server vacations

Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival. In this paper we consider systems with servers vacations where customers’ impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation discipline. This work was supported by the Euro-Ngi network of excellence.