A Computational Comparison of Optimization Methods for the Golomb Ruler Problem

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features

Microdevices for extensional rheometry of low viscosity elastic liquids : a review

Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations

Effects of composition and phase relations on mechanical properties and crystallisation of silicate glasses

Crystallization, mechanical properties and workability are all important for commercialization and optimization of silicate glass compositions. However, the inter-relations of these properties as a function of glass composition have received little investigation. Soda-lime-silica glasses with Na2O-MgO-CaO-Al2O3-SiO2 compositions relevant to commercial glass manufacture were experimentally studied and multiple liquidus temperature and viscosity models were used to complement the experimental results. Liquidus temperatures of the fabricated glasses were measured by the temperature gradient technique, and Rietveld refinements were applied to X-Ray powder diffraction (XRD) data for devitrified glasses, enabling quantitative determination of the crystalline and amorphous fractions and the nature of the crystals. Structural properties were investigated by Raman spectroscopy. Acoustic echography, micro-Vicker’s indentation and single-edge notched bend testing methods were used to measure Young’s moduli, hardness and fracture toughness, respectively. It is shown that it is possible to design lower-melting soda-lime-silica glass compositions without compromising their mechanical and crystallization properties. Unlike Young’s modulus, brittleness is highly responsive to the composition in soda-lime-silica glasses, and notably low brittleness values can be obtained in glasses with compositions in the wollastonite primary phase field: an effect that is more pronounced in the silica primary phase field. The measured bulk crystal fractions of the glasses subjected to devitrification at the lowest possible industrial conditioning temperatures, indicate that soda-lime-silica glass melts can be conditioned close to their liquidus temperatures within the compositional ranges of the primary phase fields of cristobalite, wollastonite or their combinations

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201

CD4+ T Cell-Derived IL-2 Signals during Early Priming Advances Primary CD8+ T Cell Responses

Stimulating naïve CD8+ T cells with specific antigens and costimulatory signals is insufficient to induce optimal clonal expansion and effector functions. In this study, we show that the activation and differentiation of CD8+ T cells require IL-2 provided by activated CD4+ T cells at the initial priming stage within 0–2.5 hours after stimulation. This critical IL-2 signal from CD4+ cells is mediated through the IL-2Rβγ of CD8+ cells, which is independent of IL-2Rα. The activation of IL-2 signaling advances the restriction point of the cell cycle, and thereby expedites the entry of antigen-stimulated CD8+ T-cell into the S phase. Besides promoting cell proliferation, IL-2 stimulation increases the amount of IFNγ and granzyme B produced by CD8+ T cells. Furthermore, IL-2 at priming enhances the ability of P14 effector cells generated by antigen activation to eradicate B16.gp33 tumors in vivo. Therefore, our studies demonstrate that a full CD8+ T-cell response is elicited by a critical temporal function of IL-2 released from CD4+ T cells, providing mechanistic insights into the regulation of CD8+ T cell activation and differentiation