Branch-and-Cut-and-Price for Capacitated Connected Facility Location

We consider a generalization of the Connected Facility Location Problem (ConFL), suitable to model real world network extension scenarios such as fiber-to-the-curb. In addition to choosing a set of facilities and connecting them by a Steiner tree as in ConFL, we aim to maximize the resulting profit by potentially supplying only a subset of all customers. Furthermore, capacity constraints on potential facilities need to be considered. We present two mixed integer programming based approaches which are solved using branch-and-cut and branch-and-cut-and-price, respectively. By studying the corresponding polyhedra we analyze both approaches theoretically and show their advantages over previously presented models. Furthermore, using a computational study we are able to additionally show significant advantages of our models over previously presented ones from a practical point of view.     

Direct multielement determination of trace elements in boron carbide powders by direct current arc atomic emission spectrometry using a CCD spectrometer

The use of direct current arc atomic emission spectrometry (DC-arc-AES) with a CCD spectrometer for the direct determination of the trace impurities Al, Ca, Cr, Cu, Fe, Mg, Mn, Na, Ni, Si, Ti, and Zr in three well characterized boron carbide powders is described. The detection limits obtained by the procedure were found to be between 0.2 (Mg) and 25 (Na) ??g?g^?1 for the above elements. Three boron carbide powder samples with trace element concentrations between 0.9 (Cu) and 934 (Si) ??g?g^?1 for Al, Ca, Cr, Cu, Fe, Mg, Mn, Na, Ni, Si, Ti, and Zr ?? including the standard reference material ERM?-ED102 ?? were analyzed by DC-arc-AES. The relative standard deviations for 9 measurements when using 5.0?±?0.3?mg of the respective samples were found to vary from 6.2 to 27% for Al and Cu, respectively. The trace elements Al, Ca, Cr, Cu, Fe, Mn, Ni, Si, Ti and Zr could be determined in the standard reference material and their concentrations determined by DC-arc AES were found to be between 89 and 116% of the accepted values. Fe and Ti were determined by DC-arc AES in the three boron carbide samples as well as in Al₂O₃, BN, SiC, coal fly ash, graphite and obsidian rock. The correlation coefficients of the plots of the net intensities versus the accepted values over the concentration ranges from 18 to 1750 and from 6 to 8000???g?g^?1 are 0.999 and 0.990 for Fe and Ti, respectively.

On the chromatic number of random geometric graphs

Given independent random points X ₁,...,X _n ∈ℝ ^d with common probability distribution ν, and a positive distance r=r(n)>0, we construct a random geometric graph G _n with vertex set {1,..., n} where distinct i and j are adjacent when ‖X _i −X _j ‖≤r. Here ‖·‖ may be any norm on ℝ ^d , and ν may be any probability distribution on ℝ ^d with a bounded density function. We consider the chromatic number χ(G _n ) of G _n and its relation to the clique number ω(G _n ) as n→∞. Both McDiarmid [11] and Penrose [15] considered the range of r when $r \ll \left( {\tfrac{{\ln n}} {n}} \right)^{1/d}$r \ll \left( {\tfrac{{\ln n}} {n}} \right)^{1/d} and the range when $r \gg \left( {\tfrac{{\ln n}} {n}} \right)^{1/d}$r \gg \left( {\tfrac{{\ln n}} {n}} \right)^{1/d}, and their results showed a dramatic difference between these two cases. Here we sharpen and extend the earlier results, and in particular we consider the ‘phase change’ range when $r \sim \left( {\tfrac{{t\ln n}} {n}} \right)^{1/d}$r \sim \left( {\tfrac{{t\ln n}} {n}} \right)^{1/d} with t>0 a fixed constant. Both [11] and [15] asked for the behaviour of the chromatic number in this range. We determine constants c(t) such that $\tfrac{{\chi (G_n )}} {{nr^d }} \to c(t)$\tfrac{{\chi (G_n )}} {{nr^d }} \to c(t) almost surely. Further, we find a “sharp threshold” (except for less interesting choices of the norm when the unit ball tiles d-space): there is a constant t ₀>0 such that if t≤t ₀ then $\tfrac{{\chi (G_n )}} {{\omega (G_n )}}$\tfrac{{\chi (G_n )}} {{\omega (G_n )}} tends to 1 almost surely, but if t>t ₀ then $\tfrac{{\chi (G_n )}} {{\omega (G_n )}}$\tfrac{{\chi (G_n )}} {{\omega (G_n )}} tends to a limit >1 almost surely.     

Maximum distance separable codes over {\mathbb{Z}_4} and {\mathbb{Z}_2 \times \mathbb{Z}_4}

Known upper bounds on the minimum distance of codes over rings are applied to the case of ${\mathbb Z_{2}\mathbb Z_{4}}$ -additive codes, that is subgroups of ${\mathbb Z_{2}^{\alpha}\mathbb Z_{4}^{\beta}}$ . Two kinds of maximum distance separable codes are studied. We determine all possible parameters of these codes and characterize the codes in certain cases. The main results are also valid when ?? = 0, namely for quaternary linear codes.     

Ultra-trace analysis of 36Cl by accelerator mass spectrometry: an interlaboratory study

A first international (36)Cl interlaboratory comparison has been initiated. Evaluation of the final results of the eight participating accelerator mass spectrometry (AMS) laboratories on three synthetic AgCl samples with (36)Cl/Cl ratios at the 10(-11), 10(-12), and 10(-13) level shows no difference in the sense of simple statistical significance. However, more detailed statistical analyses demonstrate certain interlaboratory bias and underestimation of uncertainties by some laboratories. Following subsequent remeasurement and reanalysis of the data from some AMS facilities, the round-robin data indicate that (36)Cl/Cl data from two individual AMS laboratories can differ by up to 17%. Thus, the demand for further work on harmonising the (36)Cl-system on a worldwide scale and enlarging the improvement of measurements is obvious.     

Toxicity of amorphous silica nanoparticles on eukaryotic cell model is determined by particle agglomeration and serum protein adsorption effects

Cell cultures form the basis of most biological assays conducted to assess the cytotoxicity of nanomaterials. Since the molecular environment of nanoparticles exerts influence on their physicochemical properties, it can have an impact on nanotoxicity. Here, toxicity of silica nanoparticles upon delivery by fluid-phase uptake is studied in a 3T3 fibroblast cell line. Based on XTT viability assay, cytotoxicity is shown to be a function of (1) particle concentration and (2) of fetal calf serum (FCS) content in the cell culture medium. Application of dynamic light scattering shows that both parameters affect particle agglomeration. The DLS experiments verify the stability of the nanoparticles in culture medium without FCS over a wide range of particle concentrations. The related toxicity can be mainly accounted for by single silica nanoparticles and small agglomerates. In contrast, agglomeration of silica nanoparticles in all FCS-containing media is observed, resulting in a decrease of the associated toxicity. This result has implications for the evaluation of the cytotoxic potential of silica nanoparticles and possibly also other nanomaterials in standard cell culture.     

Porous polymer monoliths for small molecule separations: advancements and limitations

Porous polymer monoliths are considered to be one of the major breakthroughs in separation science. These materials are well known to be best suited for the separation of large molecules, specifically proteins, an observation most often explained by convective mass transfer and the absence of small pores in the polymer scaffold. However, this conception is not sufficient to explain the performance of small molecules. This review focuses in particular on the preparation of (macro)porous polymer monoliths by simple free-radical processes and the key events in their formation. There is special focus on the fluid transport properties in the heterogeneous macropore space (flow dispersion) and on the transport of small molecules in the swollen, and sometimes permanently porous, globule-scale polymer matrix. For small molecule applications in liquid chromatography, it is consistently found in the literature that the major limit for the application of macroporous polymer monoliths lies not in the optimization of surface area and/or modification of the material and microscopic morphological properties only, but in the improvement of mass transfer properties. In this review we discuss the effect of resistance to mass transfer arising from the nanoscale gel porosity. Gel porosity induces stagnant mass transfer zones in chromatographic processes, which hamper mass transfer efficiency and have a detrimental effect on macroscopic chromatographic dispersion under equilibrium (isocratic) elution conditions. The inherent inhomogeneity of polymer networks derived from free-radical cross-linking polymerization, and hence the absence of a rigid (meso)porous pore space, represents a major challenge for the preparation of efficient polymeric materials for the separation of small molecules.     

Development and practical application of a library of CID accurate mass spectra of more than 2,500 toxic compounds for systematic toxicological analysis by LC�CQTOF-MS with data-dependent acquisition

A library of collision-induced dissociation (CID) accurate mass spectra has been developed for efficient use of liquid chromatography in combination with hybrid quadrupole time-of-flight mass spectrometry (LC-QTOF-MS) as a tool in systematic toxicological analysis. The mass spectra (Δm < 3 ppm) of more than 2,500 illegal and therapeutic drugs, pesticides, alkaloids, other toxic chemicals and metabolites were measured, by use of an Agilent 6530 instrument, by flow-injection of 1 ng of the pure substances in aqueous ammonium formate-formic acid-methanol, with positive and negative electrospray-ionization (ESI), selection of the protonated or deprotonated molecules [M+H](+) or [M-H](-) by the quadrupole, and collision induced dissociation (CID) with nitrogen as collision gas at CID energies of 10, 20, and 40 eV. The fragment mass spectra were controlled for structural plausibility, corrected by recalculation to the theoretical fragment masses and added to a database of accurate mass data and molecular formulas of more than 7,500 toxicologically relevant substances to form the "database and library of toxic compounds". For practical evaluation, blood and urine samples were spiked with a mixture of 33 drugs at seven concentrations between 0.5 and 500 ng mL(-1), prepared by dichloromethane extraction or protein precipitation, and analyzed by LC-QTOF-MS in data-dependent acquisition mode. Unambiguous identification by library search was possible for typical basic drugs down to 0.5-2 ng mL(-1) and for benzodiazepines down to 2-20 ng mL(-1). The efficiency of the method was also demonstrated by re-analysis of venous blood samples from 50 death cases and comparison with previous results. In conclusion, LC-QTOF-MS in data-dependent acquisition mode combined with an accurate mass database and CID spectra library seemed to be one of the most efficient tools for systematic toxicological analysis.