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The test of independence of two groups of variables is addressed in the case where the sample size N is considered randomly distributed. This assumption may lead to a more realist testing procedure since in many situations the sample size is not known in advance. Three sample schemes are considered where N may have a Poisson, Binomial or Hypergeometric distribution. For the case of two groups with p1 and p2 variables, it is shown that when either p1 or p2 (or both) are even the exact distribution corresponds to a finite or an infinite mixture of Exponentiated Generalized Integer Gamma distributions. In these cases a computational module is made available for the cumulative distribution function of the test statistic. When both p1 and p2 are odd, the exact distribution of the test statistic may be represented as a finite or an infinite mixture of products of independent Beta random variables whose density and cumulative distribution functions do not have a manageable closed form. Therefore, a computational approach for the evaluation of the cumulative distribution function is provided based on a numerical inversion formula originally developed for Laplace transforms. When the exact distribution is represented through infinite mixtures, an upper bound for the error of truncation of the cumulative distribution function is provided. Numerical studies are developed in order to analyze the precision of the results and the accuracy of the upper bounds proposed. A simulation study is provided in order to assess the power of the test when the sample size N is considered randomly distributed. The results are compared with the ones obtained for the fixed sample size case.

Protein crystallization still remains mostly an empirical science, as the production of crystals with the required quality for X-ray analysis is dependent on the intensive screening of the best protein crystallization and crystal’s derivatization conditions. Herein, this demanding step was addressed by the development of a high-throughput and low-budget microfluidic platform consisting of an ion exchange membrane (117 Nafion® membrane) sandwiched between a channel layer (stripping phase compartment) and a wells layer (feed phase compartment) forming 75 independent micro-contactors. This microfluidic device allows for a simultaneous and independent screening of multiple protein crystallization and crystal derivatization conditions, using Hen Egg White Lysozyme (HEWL) as the model protein and Hg2+ as the derivatizing agent. This microdevice offers well-regulated crystallization and subsequent crystal derivatization processes based on the controlled transport of water and ions provided by the 117 Nafion® membrane. Diffusion coefficients of water and the derivatizing agent (Hg2+) were evaluated, showing the positive influence of the protein drop volume on the number of crystals and crystal size. This microfluidic system allowed for crystals with good structural stability and high X-ray diffraction quality and, thus, it is regarded as an efficient tool that may contribute to the enhancement of the proteins’ crystals structural resolution.

Abstract Fiber reinforced polymer (FRP) composites can be efficient for flexural strengthening of flat slabs if debonding of the FRP is postponed. However, with the increase of the flexural capacity, the flat slab becomes more susceptible to punching shear failure. In this context, four flexural or simultaneous flexural and punching shear retrofitting systems are investigated in this study to strengthen a flexure-deficient flat slab. Externally Bonded Reinforcement on Grooves (EBROG) and externally bonded reinforcement (EBR) methods are used for flexural strengthening in two cases: slabs without punching shear reinforcement and with post-installed shear bolts as shear reinforcement. According to the results, flexural strengthening of the slab using the EBR and EBROG techniques increased its load capacity by 12% and 21%, respectively. Simultaneous flexural and shear strengthening of the slab using the EBROG technique was the most effective, leading to a 57% enhancement of the load capacity. For specimens whose failure was governed by punching, comparing the results with code predictions showed that Eurocode and ACI (and the respective guide documents fib bulletin 90 and ACI 440.2R) overestimated the capacity of these specimens. In cases where failure was governed by flexure, a simple application of the yield line theory predicted reasonably well the load capacity of the specimens.

Microstructured transparent conductive oxides (TCOs) have shown great potential as photonic electrodes in photovoltaic (PV) applications, providing both optical and electrical improvements in the solar cells’ performance due to: (1) strong light trapping effects that enhance broadband light absorption in PV material and (2) the reduced sheet resistance of the front illuminated contact. This work developed a method for the fabrication and optimization of wavelength-sized indium zinc oxide (IZO) microstructures, which were soft-patterned on flexible indium tin oxide (ITO)-coated poly(ethylene terephthalate) (PET) substrates via a simple, low-cost, versatile, and highly scalable colloidal lithography process. Using this method, the ITO-coated PET substrates patterned with IZO micro-meshes provided improved transparent electrodes endowed with strong light interaction effects—namely, a pronounced light scattering performance (diffuse transmittance up to  50%). In addition, the photonic-structured IZO mesh allowed a higher volume of TCO material in the electrode while maintaining the desired transparency, which led to a sheet resistance reduction (by  30%), thereby providing further electrical benefits due to the improvement of the contact conductance. The results reported herein pave the way for a new class of photonic transparent electrodes endowed with mechanical flexibility that offer strong potential not only as advanced front contacts for thin-film bendable solar cells but also for a much broader range of optoelectronic applications.