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LetQ be the unit cube in R n and H a hyperplane thru the Origin. The intersection is called Cube slice and was investigated by Henesley, Vaaler , Ball and others. We give an example of a cube slice in R 4 that is not a zonoid. This contrasts with a result in R 3 that follows from a Theorem due to Herz and Lindenstrauss where every cube slice is a zonoid. The volume of this slice is computed and used to determine the likely known result, the value of the sinc integral I 4

Given the close relationship between protein structure and function, protein structure searches have long played an established role in bioinformatics. Despite their maturity, existing protein structure searches either use simplifying assumptions or compromise between fast response times and quality of results. These limitations can prevent the easy and efficient exploration of relationships between protein structures, which is the norm in other areas of inquiry. To address these limitations we have developed RUPEE, a fast and accurate purely geometric structure search combining techniques from information retrieval and big data with a novel approach to encoding sequences of torsion angles. Comparing our results to the output of mTM, SSM, and the CATHEDRAL structural scan, it is clear that RUPEE has set a new bar for purely geometric big data approaches to protein structure searches. RUPEE in top-aligned mode produces equal or better results than the best available protein structure searches, and RUPEE in fast mode demonstrates the fastest response times coupled with high quality results. The RUPEE protein structure search is available at https://ayoubresearch.com. Code and data are available at https://github.com/rayoub/rupee.

The objective of this study was to optimize the physicodynamic conditions of polymeric system as a coating substrate for drug eluting stents against restenosis. As Nitric Oxide (NO) has multifunctional activities, such as regulating blood flow and pressure, and influencing thrombus formation, a continuous and spatiotemporal delivery of NO loaded in the polymer based nanoparticles could be a viable option to reduce and prevent restenosis. To identify the most suitable carrier for S-Nitrosoglutathione (GSNO), a NO prodrug, stents were coated with various polymers, such as poly (lactic-co-glycolic acid) (PLGA), polyethylene glycol (PEG) and polycaprolactone (PCL), using solvent evaporation technique. Full factorial design was used to evaluate the effects of the formulation variables in polymer-based stent coatings on the GSNO release rate and weight loss rate. The least square regression model was used for data analysis in the optimization process. The polymer-coated stents were further assessed with Differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy analysis (FTIR), Scanning electron microscopy (SEM) images and platelet adhesion studies. Stents coated with PCL matrix displayed more sustained and controlled drug release profiles than those coated with PLGA and PEG. Stents coated with PCL matrix showed the least platelet adhesion rate. Subsequently, stents coated with PCL matrix were subjected to the further optimization processes for improvement of surface morphology and enhancement of the drug release duration. The results of this study demonstrated that PCL matrix containing GSNO is a promising system for stent surface coating against restenosis.