Some transformation techniques with applications in global optimization

In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, often not all variables need to be transformed. A method for minimizing the number of original variables involved in the transformations is, therefore, presented. In order to illustrate how the given method can be integrated into the transformation framework, some mixed integer optimization problems including signomial functions are finally solved to global optimality using the given techniques.     

Measurement and modeling of diffraction from an edge of a thin panel

The diffraction of sound from an edge of a thin chipboard panel was measured in an anechoic chamber, and compared to simulations based on the diffraction formulation developed by Svensson et al. [Svensson UP, Fred RI, Vanderkooy J. An analytic secondary source model of edge diffraction impulse responses. J Acoust Soc Am 1999;106(5):2331-44]. The measurements and simulations were performed for a line of receiver positions below the panel to include cases for which the direct sound had an unobstructed propagation path to the receivers, as well as cases for which the direct sound was occluded by the panel. Comparison of the measured and simulated responses is provided in both the time and frequency-domains, and shows that the differences between them are small over the entire audible frequency range. This case study verifies that the applied diffraction-modeling method gives accurate results, and that the assumptions of ideal source and wedge characteristics inherent in the method do not preclude its use in simulations of realistic scenarios.     

Antibacterial activity of N-quaternary chitosan derivatives: Synthesis, characterization and structure activity relationship (SAR) investigations

Quaternary N-(2-(N,N,N-tri-alkyl ammoniumyl and 2-pyridiniumyl) acetyl) derivatives of chitosan polymer, chitooligomer, and glucosamine (monomer) were synthesized for the purpose of investigating the structure activity relationship (SAR) for the antibacterial effect. Novel methods were used in the synthesis. The final chitosan and chitooligomer derivatives could thus be obtained in two steps without prior protection of the hydroxyl groups. However, in order to obtain chitosan derivatives with the bulky N,N-dimethyl-N-dodecyl- and N,N-dimethyl-N-butyl side chains three steps were needed, starting from 3,6-O-di-tert-butyldimethylsilyl chitosan (3,6-O-di-TBDMS chitosan) as the key intermediate. The quaternary ammoniumyl acetyl derivatives of glucosamine were synthesized from glucosamine or tetra-O-acetylglucosamine. N,N,N-trimethyl chitosan (TMC) was used as reference compound for investigation of antibacterial activity. Clinical Laboratory Standard Institute (CLSI) protocols were used to determine MIC and MLC for activity against clinically important Gram-positive strains Staphylococcus aureus (ATCC 25923), and S. aureus (MRSA) (ATCC 43300), and Gram-negative strains of Escherichia coli (ATCC 25922), P. aeriginosa (ATCC 27853) and Enterococcus facialis (ATCC 29212). The MIC values for the compounds ranged from 8 to ?8192 mg/L. In general the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitooligomer and glucosamine monomer were more active against bacteria than derivatives with shorter alkyl chains. In contrast the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitosan were less active than derivatives with N-(2-N,N,N-trimetylammoniumyl) acetyl or N-(2-(N-pyridiniumyl) acetyl) quaternary moiety. N,N,N-trimethyl chitosan (TMC) was the most active compound in this study.     

Lateral reflections are favorable in concert halls due to binaural loudness

A recent study on perceptual difference in simulated concert halls showed that a concert hall renders stronger sound with more bass when the temporal envelope of a signal is preserved in the reflections [Lokki et al., J. Acoust. Soc. Am. 129, EL223-EL228 (2011)]. In the same study the lateral reflections were shown to contribute to the perceived envelopment and openness. Moreover, the listening test results suggest that lateral reflections contribute to perception of sound source distance. Here, it is shown that lateral reflections are beneficial due to their increasing effect on binaural loudness-the phenomenon known well in psychoacoustics, but not in architectural acoustics. The reflections from the side are amplified more than median plane reflections, in particular at high frequencies, due to the shape of the human head.     

Investigations on the balloon as an impulse source

Measurements of impulses produced by bursting balloons are presented. Various sizes of balloons were popped with a mechanical device in an anechoic chamber and recorded with a spherical microphone array. The power responses and directivity of the balloons are analyzed. Results indicate that power responses have two emphasized frequencies which depend on balloon size and inflation level. Larger balloons radiated more energy and higher inflation levels resulted in stronger high frequency content. Balloon directivity patterns are stable over repetitions. However, balloons do not radiate omnidirectionally. The degree of omnidirectionality improves with balloon size and for midrange frequencies.     

Focusing effect of a graded index photonic crystal lens

We present a new graded-index photonic crystal (GRIN PhC) structure which can be made by laser interference lithography (LIL). It can be applied as miniaturized focusing lens. Numerical simulations are carried out on the structures with different widths, lengths, and modulations. In the qualitative analysis of the focal length, focusing of a GRIN PhC was proved to originate from both the graded sizes of the rods and multimode interference. Multimode interference dominates the focusing effect when a GRIN PhC has a small length or a small difference in the rod sizes. Intensity distributions in different cases were given to support the conclusion.     

Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces

We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics, and we apply the latter to prove suitable generalizations of Brenier’s theorem of existence of optimal maps.     

New methods for calculating \alpha BB-type underestimators

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another.     

Non-branching geodesics and optimal maps in strong CD(K,\infty )-spaces

We prove that in metric measure spaces where the entropy functional is \(K\) -convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant.