20 research outputs found

    Euclidean distance geometry and applications

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    Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

    Exact semidefinite programming bounds for packing problems

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    In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are unique up to rotations. In particular, we show that the configuration coming from the E8\mathsf{E}_8 root lattice is the unique optimal code with minimal angular distance π/3\pi/3 on the hemisphere in R8\mathbb R^8, and we prove that the three-point bound for the (3,8,ϑ)(3, 8, \vartheta)-spherical code, where ϑ\vartheta is such that cosϑ=(221)/7\cos \vartheta = (2\sqrt{2}-1)/7, is sharp by rounding to Q[2]\mathbb Q[\sqrt{2}]. We also use our machinery to compute sharp upper bounds on the number of spheres that can be packed into a larger sphere.Comment: 24 page

    Moldable Items Packing Optimization

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    This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

    Solución del problema de empaquetamiento óptimo usando técnicas metaheurísticas de optimización simultáneas a través de procesamiento paralelo

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    El problema de la mochila irrestricta bidimensional no guillotinada (U2DNGSKP) del inglés unconstrained two-dimensional non-guillotine single knapsack problem, es un problema de corte que se presenta cuando el material a ser utilizado es una pieza rectangular (hoja de material) donde se deben ubicar piezas rectangulares más pequeñas de las que se conoce el tamaño y un costo (bien sea su propia área o un valor establecido). El objetivo es maximizar el beneficio asociado a cada una de las piezas cortadas, sin sobreponer las piezas y sin sobrepasar los límites de la hoja de material

    Evidence of protein adsorption in pegylated liposomes: Influence of liposomal decoration

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    In order to contribute to a better knowledge of the events involved in the formation of the protein corona when nanoparticles (NPs) come in contact with proteins, we report a study about the changes on the physicochemical properties of pristine, PEGylated and Cyclic Arginine-Glycine-Aspartate peptide (RGD)-functionalized large unilamelar liposomes (LUVs) or magnetoliposomes (MLs) upon incubation with Bovine Serum Albumin (BSA). The main phospholipid component of both LUVs and MLs was L-α-phosphatydylcholine (PC) or 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) with 20% of cholesterol. The most obvious indication of the interaction of BSA-nanosystems is given by changes in the hydrodynamic diameter of the particles but other evidence is needed to corroborate the process. Our findings indicate that size modification is a process that is accomplished in few hours and that is strongly dependent not only on the surface decoration but also of the lipid composition of both LUVs and MLs. Fluorescence quenching experiments as well as cryogenic transmission electron microscopy (Cryo-TEM) images assessed these changes and confirmed that although each system has to be studied in a particular way, we can establish three distinctive features that turn into more reactive systems: (a) compositions containing PC compared with their DMPC counterparts; (b) the presence of PEG and/or RGD compared to the pristine counterparts; and (c) the presence of SPIONs: MLs show higher interaction than LUVs of the same lipid composition. Consequently, PEGylation (that is supposed to make stealth NPs) actually fails in preventing complete protein binding
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