The local circular law III: general case

In the first part (Bourgade et al., Local circular law for random matrices, preprint, arXiv:1206.1449, 2012) of this article series, Bourgade, Yau and the author of this paper proved a local version of the circular law up to the finest scale \(N^{-1/2+ {\varepsilon }}\) for non-Hermitian random matrices at any point \(z \in \mathbb {C}\) with \(||z| - 1| > c \) for any constant \(c>0\) independent of the size of the matrix. In the second part (Bourgade et al., The local circular law II: the edge case, preprint, arXiv:1206.3187, 2012), they extended this result to include the edge case \( |z|-1={{\mathrm{o}}}(1)\) , under the main assumption that the third moments of the matrix elements vanish. (Without the vanishing third moment assumption, they proved that the circular law is valid near the spectral edge \( |z|-1={{\mathrm{o}}}(1)\) up to scale \(N^{-1/4+ {\varepsilon }}\) .) In this paper, we will remove this assumption, i.e. we prove a local version of the circular law up to the finest scale \(N^{-1/2+ {\varepsilon }}\) for non-Hermitian random matrices at any point \(z \in \mathbb {C}\) .     

Modelling variations in hospital service delivery based on real time locating information

Variations in service delivery have been identified as a major challenge to the success of process improvement studies in service departments of hospital such as radiology. Largely, these variations are due to inherent system level factors, i.e., system variations such as unavailability of resources (nurse, bed, doctors, and equipment). These system variations are largely unnecessary/unwarranted and mostly lead to longer waiting times, delays, and lowered productivity of the service units. There is limited research on identifying system variations and modelling them for service improvements within hospital. Therefore, this paper proposes a modelling methodology to model system variations in radiology based on real time locating system (RTLS) tracking data. The methodology employs concepts from graph theory to identify and represent system variations. In particular, edge coloured directed multi-graphs (ECDMs) are used to model system variations which are reflected in paths adopted by staff, i.e., sequence of rooms/areas traversed while delivering services. The main steps of the methodology are: (i) identifying the most standard path followed by staff for service delivery; (ii) filtering the redundant events in RTLS tracking database for analysis; (iii) identifying rooms/areas of hospital site involved in the service delivery; (iv) determining patterns of paths adopted by staff from filtered tracking database; and, (v) representation of patterns in graph based model called as edge coloured directed multigraphs (ECDMs) of a role. A case study of MR scanning process is utilized to illustrate the implementation of the proposed methodology for modelling system variations reflected in the paths adopted by staff.     

Combining capillary electrophoresis matrix-assisted laser desorption/ionization mass spectrometry and stable isotopic labeling techniques for comparative crustacean peptidomics

Herein we describe a sensitive and straightforward off-line capillary electrophoresis (CE) matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) interface in conjunction with stable isotopic labeling (SIL) technique for comparative neuropeptidomic analysis in crustacean model organisms. Two SIL schemes, including a binary H/D formaldehyde labeling technique and novel, laboratory-developed multiplexed dimethylated leucine-based isobaric tagging reagents, have been evaluated in these proof-of-concept experiments. We employ these isotopic labeling techniques in conjunction with CE-MALDI-MS for quantitative peptidomic analyses of the pericardial organs isolated from two crustacean species, the European green crab Carcinus maenas and the blue crab Callinectes sapidus. Isotopically labeled peptide pairs are found to co-migrate in CE fractions and quantitative changes in relative abundances of peptide pairs are obtained by comparing peak intensities of respective peptide pairs. Several neuropeptide families exhibit changes in response to salinity stress, suggesting potential physiological functions of these signaling peptides.     

Push-pull alkenes from cyclic ketene-N,N′-acetals: a wide span of double bond lengths and twist angles

Push-pull alkenes can be quickly accessed by cyclic ketene-N,N′-acetal chemistry. A number of push-pull structures with a wide span of double bond lengths and twist angles were synthesized from the reactions of (1) N,N′-dimethyl cyclic ketene-N,N′-acetals with isocyanates, (2) the products from (1) with isocyanates, (3) 2-methylimidazoline and 2-methyl-1,4,5,6-tetrahydropyrimidine with diacid chlorides, (4) 2-methylimidazoline, and 1,2-dimethyl-1,4,5,6-tetrahydropyrimidine with benzoyl chlorides, and (5) 1,2-dimethylimidazoline and 1,2-dimethyl-1,4,5,6-tetrahydropyrimidine with aryl isocyanates. These reactions proceed under very mild conditions and give moderate to excellent yields. X-ray crystallographic analysis of eight pxush-pull alkenes indicates that the central double bond lengths and twists are sensitive to the ring sizes (5 or 6), ring structures (fused or non-fused), electron donating and withdrawing strengths of pushing and pulling portions, respectively, number of electron pushing or pulling groups and substituent steric effects.     

Mass spectral imaging and profiling of neuropeptides at the organ and cellular domains

Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (MS) is a rapid and sensitive analytical method that is well suited for determining molecular weights of peptides and proteins from complex samples. MALDI-MS can be used to profile the peptides and proteins from single-cell and small tissue samples without the need for extensive sample preparation. Furthermore, the recently developed MALDI imaging technique enables mapping of the spatial distribution of signaling molecules in tissue samples. Several examples of signaling molecule analysis at the single-cell and single-organ levels using MALDI-MS technology are highlighted followed by an outlook of future directions.     

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (?, S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures.     

Microfluidic sensing devices employing in situ-formed liquid crystal thin film for detection of biochemical interactions

Although biochemical sensing using liquid crystals (LC) has been demonstrated, relatively little attention has been paid towards the fabrication of in situ-formed LC sensing devices. Herein, we demonstrate a highly reproducible method to create uniform LC thin film on treated substrates, as needed, for LC sensing. We use shear forces generated by the laminar flow of aqueous liquid within a microfluidic channel to create LC thin films stabilized within microfabricated structures. The orientational response of the LC thin films to targeted analytes in aqueous phases was transduced and amplified by the optical birefringence of the LC thin films. The biochemical sensing capability of our sensing devices was demonstrated through experiments employing two chemical systems: dodecyl trimethylammonium bromide (DTAB) dissolved in an aqueous solution, and the hydrolysis of phospholipids by the enzyme phospholipase A(2) (PLA(2)).     

X-ray absorption spectroscopic, crystallographic, theoretical (DFT) and chemical evidence for a chalcogen-chalcogen two-center/three-electron half bond in an unprecedented "subselenide" Se2(3-) ligand

Doing things by halves: The dimeric compound (Cp'Ni)(2)(μ(2)-Se(2)) (Cp' = 1,2,3,4-tetraisopropylcyclopentadienyl), shown in the scheme, was investigated by using low temperature X-ray crystallography and X-ray absorption spectroscopy. The Se K-edge energy strongly indicates a Se physical oxidation state of -1.5, consistent with an unprecedented two-center/three-electron half-bonded Se(2)(3-) or "subselenide" ion.