A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.     

Multiplicative maps preserving the higher rank numerical ranges and radii

Let M_n be the semigroup of n×n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in M_n including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λ_k(A) is the rank-k numerical range and r_k(A) is the rank-k numerical radius of A∈M_n. Multiplicative maps ?:S→M_n satisfying r_k(?(A))=r_k(A) are characterized. From these results, one can deduce the structure of multiplicative preservers of Λ_k(A).     

Ionic‐liquid‐based dispersive liquid–liquid microextraction for high‐throughput multiple food contaminant screening

This paper describes an innovation of dispersive liquid–liquid microextraction enabling multiple‐component analysis of eight high‐priority food contaminants in two chemically distinctive families: Sudan dyes and phthalate plasticizers. To provide convenient sample handling for solid and solid‐containing matrices, a modified dispersive liquid–liquid microextraction procedure used an extractant precoated frit to perform simultaneous filtration, solvent mixing, and phase dispersion in one simple step. A binary ionic liquid extractant system was carefully tuned to deliver high quality analysis based only on affordable LC with diode array detector instrumentation. The method is comprehensively validated for robust quantification with good precision (6.9–9.8% RSD) in a linear 2–1000 μg/L range. Having accomplished enrichment factors up to 451, the treatment enables sensitive detection at 0.09–1.01 μg/L levels. Analysis of six high‐risk solid condiments and sauces further verified its practical applicability within a 70–120% recovery range. Compared to other approaches, the current dispersive liquid–liquid microextraction treatment offers major advantages in terms of minimal solvent (1.5 mL) and sample (0.1 g) consumption, ultra‐high analytical throughput (6 min), and the ability to handle complex solid matrices. The idea of performing simultaneous analysis for multiple contaminants presented here fosters a more effective mode of operation in food control routines.     

Evaluating protein attraction and adhesion to biomaterials with the atomic force microscope

Failure of implanted biomaterials is commonly due to nonspecific protein adsorption, which in turn causes adverse reactions such as the formation of fibrous capsules, blood clots, or bacterial biofilm infections. Current research efforts have focused on modifying the biomaterial interface to control protein reactions. Designing biomaterial interfaces at the molecular level, however, requires an experimental technique that provides detailed, dynamic information on the forces involved in protein adhesion. The goal of this study was to develop an atomic force microscope (AFM)-based technique to evaluate protein adhesion on biomaterial surfaces. In this study, the AFM was used to evaluate (i) protein-protein, (ii) protein-substrate, and (iii) protein-dextran interactions. The AFM was first used to measure the pull-off forces between bovine serum albumin (BSA) tips/BSA surfaces and BSA tips/anti-BSA surfaces. Results from these protein-protein studies were consistent with the literature. More importantly, the successful measurement of antibody-antigen binding interactions demonstrates that both the BSA and anti-BSA proteins retain their folded conformation and remain functional following our immobilization protocol. The AFM was also used to quantify the physiochemical interactions of proteins during adhesion to various self-assembled monolayers (SAMs) and dextran-coated substrates representative of potential biomaterial interface modifications. Dextran, which renders surfaces very hydrophilic, was the only surface coating that BSA protein did not adhere to. Hydrophobic interactions were not found to play a significant role in BSA adhesion. Therefore, the dextran molecules may resist protein adhesion by repulsive steric effects or hydration pressure. Moreover, the AFM-based methodology provides dynamic, quantitative information about protein adhesion at the nanoscale level.     

Rhenium(I) polypyridine biotin isothiocyanate complexes as the first luminescent biotinylation reagents: synthesis, photophysical properties, biological labeling, cytotoxicity, and imaging studies

We report here the design of the first class of luminescent biotinylation reagents derived from rhenium(I) polypyridine complexes. These complexes [Re(N-N)(CO)(3)(py-biotin-NCS)](PF(6)) (py-biotin-NCS = 3-isothiocyanato-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = 1,10-phenanthroline (phen) (1a), 3,4,7,8-tetramethyl-1,10-phenanthroline (Me(4)-phen) (2a), 4,7-diphenyl-1,10-phenanthroline (Ph(2)-phen) (3a)), containing a biotin unit and an isothiocyanate moiety, have been synthesized from the precursor amine complexes [Re(N-N)(CO)(3)(py-biotin-NH(2))](PF(6)) (py-biotin-NH(2) = 3-amino-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = phen (1c), Me(4)-phen (2c), Ph(2)-phen (3c)). To investigate the amine-specific reactivity of the isothiocyanate complexes 1a-3a, they have been reacted with a model substrate ethylamine, resulting in the formation of the thiourea complexes [Re(N-N)(CO)(3)(py-biotin-TU-Et)](PF(6)) (py-biotin-TU-Et = 3-ethylthioureidyl-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = phen (1b), Me(4)-phen (2b), Ph(2)-phen (3b)). All the rhenium(I) complexes have been characterized, and their photophysical properties have been studied. The avidin-binding properties of the thiourea complexes 1b-3b have been examined by the 4'-hydroxyazobenzene-2-carboxylic acid (HABA) assay. Titration results indicated that the complexes exhibited emission enhancement by ca. 1.4-1.5-fold upon binding to avidin, and the lifetimes were elongated to ca. 0.8-2.0 micros. Additionally, we have biotinylated bovine serum albumin (BSA) with the isothiocyanate complexes. All the resultant rhenium-BSA bioconjugates displayed intense and long-lived orange-yellow to greenish-yellow emission upon irradiation in aqueous buffer under ambient conditions. The avidin-binding properties of the bioconjugates have been investigated using the HABA assay. Furthermore, the cytotoxicity of the thiourea complexes 1b-3b toward the HeLa cells has been examined by the 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyltetrazolium bromide (MTT) assay. The IC50 values were determined to be ca. 17.5-28.5 microM, which are comparable to that of cisplatin (26.7 microM) under the same conditions. The cellular uptake of complex 3b has been investigated by fluorescence microscopy, and the results showed that the complex was localized in the perinuclear region after interiorization.     

Maps preserving the nilpotency of products of operators

Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:

(a)

There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S^-1.

(b)

The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S⁻¹.

If X has dimension n with 3 ? n < ∞, and B(X) is identified with the algebra M_n of n × n complex matrices, then there exist a map f:M_n→C?{0}, a field automorphism ξ:C→C, and an invertible S ∈ M_n such that ? has one of the following forms:

     

Domain wall nucleation and propagation in spin-transfer torque switching with thermal effects

We conduct micro-magnetic simulations to study spin-transfer torque induced magnetization switching in perpendicular magnetic tunneling junctions. The effects of current densities and temperatures on the switching processes are studied in details. We then proposed an approach to compute the deterministic switching time by taking thermal-effect into account. The switching time is less temperature-dependent under higher current density; however, as the current density decreases, the effect of temperature on the switching time becomes more and more significant. The switching process with micro-magnetic simulations is shown to be via domain wall nucleation and propagation. The phenomena are consistent with the recent experimental found-out. We further propose a method to compute the switching time based on domain wall nucleation and propagation theory, and compare the switching time with those from macro-spin approximation. It is found the switching times from the micro-magnetic simulations are much shorter than that from the macro-spin approximations. Macro-spin approximation over-estimates the switching times due to its coherent rotation assumptions.     

Reaction pathways of Sc+ (3D, 1D) and Fe+ (6D, 4F) with acetone in the gas phase: metal ion oxidation and acetone deethanization

The reactions of Sc⁺ (³D, ¹D) and Fe⁺ (⁶D, ⁴ F) with acetone have been investigated in both high‐ and low‐spin states using density functional theory. Our calculations have indicated that oxidation of Sc⁺ by acetone can take place by (1) metal‐mediated H migration, (2) direct methyl‐H shift and/or (3) C = O insertion. The most energetically favorable pathway is metal‐mediated H migration followed by intramolecular ScO⁺ rotation and dissociation. For the deethanization of acetone mediated by Fe⁺, the reaction occurs on either the quartet or sextet surfaces through five elementary steps, i.e. encounter complexation, C–C bond activation, methyl migration, C–C coupling and non‐reactive dissociation. The rate‐determining step along the quartet‐state potential‐energy surface (PES) is similar to that in the case of Ni⁺ (² F, 3d⁹), namely the methyl‐migration step. For the sextet‐state PES, however, the energy barrier for methyl migration is lower than that for C–C bond activation, and the rate‐determining step is C–C coupling. In general, the low‐spin‐state pathways are lower in energy than the high‐spin‐state pathways; therefore, the reaction pathways for the oxidation of Sc⁺ and the Fe⁺‐mediated deethanization of acetone mostly involve the low‐spin states. Copyright © 2012 John Wiley & Sons, Ltd.