A Distributed O(1)-Approximation Algorithm for the Uniform Facility Location Problem

We investigate a metric facility location problem in a distributed setting. In this problem, we assume that each point is a client as well as a potential location for a facility and that the opening costs for the facilities and the demands of the clients are uniform. The goal is to open a subset of the input points as facilities such that the accumulated cost for the whole point set, consisting of the opening costs for the facilities and the connection costs for the clients, is minimized. We present a randomized distributed algorithm that computes in expectation an ${\mathcal {O}}(1)$ -approximate solution to the metric facility location problem described above. Our algorithm works in a synchronous message passing model, where each point is an autonomous computational entity that has its own local memory and that communicates with the other entities by message passing. We assume that each entity knows the distance to all the other entities, but does not know any of the other pairwise distances. Our algorithm uses three rounds of all-to-all communication with message sizes bounded to $\mathcal{O}(\log(n))$ bits, where n is the number of input points. We extend our distributed algorithm to constant powers of metric spaces. For a metric exponent ?≥1, we obtain a randomized ${\mathcal {O}}(1)$ -approximation algorithm that uses three rounds of all-to-all communication with message sizes bounded to $\mathcal{O}(\log(n))$ bits.     

Unmanned Ground Vehicle Navigation in Coordinate-Free and Localization-Free Wireless Sensor and Actuator Networks

We present a set of algorithms for the navigation of Unmanned Ground Vehicles (UGVs) towards a set of pre-identified target nodes in coordinate-free and localization-free wireless sensor and actuator networks. The UGVs are equipped with a set of wireless listeners that provide sensing information about the potential field generated by the network of actuators. Two main navigation scenarios are considered: single-UGV, single-destination navigation and multi-UGV, multi-destination navigation. For the single-UGV, single-destination case, we present both centralized and distributed navigation algorithms. Both algorithms share a similar two-phase concept. In the first phase, the system assigns level numbers to individual nodes based on their hop distance from the target nodes. In the second phase, the UGV uses the potential field created by the network of actuators to move towards the target nodes, requiring cooperation between triplets of actuator nodes and the UGV. The hop distance to the target nodes is used to control the main moving direction while the potential field, which can be measured by listeners on the UGV, is used to determine the UGV’s movement. For the multi-UGV, multi-destination case, we present a decentralized allocation algorithm such that multiple UGVs avoid converging to the same destination. After each UGV determines its destination, the proposed navigation scheme is applied. The presented algorithms do not attempt to localize UGVs or sensor nodes and are therefore suitable for operating in GPS-free/denied environments. We also present a study of the communication complexity of the algorithms as well as simulation examples that verify the proposed algorithms and compare their performances.     

Ordering Partial Partitions for Image Segmentation and Filtering: Merging,Creating and Inflating Blocks

The refinement order on partitions corresponds to the operation of merging blocks in a partition, which is relevant to image segmentation and filtering methods. Its mathematical extension to partial partitions, that we call standard order, involves several operations, not only merging, but also creating new blocks or inflating existing ones, which are equally relevant to image segmentation and filtering techniques. These three operations correspond to three basic partial orders on partial partitions, the merging, inclusion and inflating orders. There are three possible combinations of these three basic orders, one of them is the standard order, the other two are the merging-inflating and inclusion-inflating orders. We study these orders in detail, giving in particular their minimal and maximal elements, covering relations and height functions. We interpret hierarchies of partitions and partial partitions in terms of an adjunction between (partial) partitions (possibly with connected blocks) and scalars. This gives a lattice-theoretical interpretation of edge saliency, hence a typology for the edges in partial partitions. The use of hierarchies in image filtering, in particular with component trees, is also discussed. Finally, we briefly mention further orders on partial partitions that can be useful for image segmentation.     

Characterization of Maximum Likelihood Solutions to Image Reconstruction in Photon Emission Tomography

For photon emission tomography, the maximum likelihood (ML) estimator for image reconstruction is generally solution to a nonlinear equation involving the vector of measured data. No explicit closed-form solution is known in general for such a nonlinear ML equation, and numerical resolution is usually implemented, with a very popular iterative method formed by the expectation-maximization algorithm. The numerical character of such resolutions usually makes it difficult to obtain a general characterization of the performance of the ML solution. We show that the nonlinear ML equation can be replaced by an equivalent system of two dual linear equations nonlinearly coupled. This formulation allows us to exhibit explicit (to some extent) forms for the solutions to the ML equation, in general conditions corresponding to the various possible configurations of the imaging system, and to characterize their performance with expressions for the mean-squared error, bias and Cramér-Rao bound. The approach especially applies to characterize the ML solutions obtained numerically, and offers a theoretical framework to contribute to better appreciation of the capabilities of ML reconstruction in photon emission tomography.     

The cholesterol-lowering effect of guar gum is not the result of a simple diversion of bile acids toward fecal excretion

The effects of partially hydrolyzed, nonviscous, guar gum (PHGG) on cholesterol metabolism and digestive balance have been compared with those of native guar gum (GUAR) in rats adapted to 0.4% cholesterol diets. Both types of guar gum elicited acidic fermentations in the large intestine, but only GUAR effectively lowered plasma cholesterol (P<0.001), chiefly in the triglyceride-rich lipoprotein fraction. The biliary bile acid excretion was significantly enhanced in rats fed GUAR (P<0.05), as well as the intestinal and cecal bile acid pool (P<0.001). In rats fed GUAR and to a lesser extent in those fed PHGG, the fecal excretion of bile acids and neutral sterol was higher than in controls (P<0.01). The digestive balance (cholesterol intake-steroid excretion) was positive in control rats (+47 μmol/d), whereas it was negative in rats fed GUAR (−20 μmol/d), which could involve a higher rate of endogenous cholesterol synthesis. In rats fed PHGG, the steroid balance remained slightly positive. Liver 3-hydroxy-3-methylglutaryl-CoA (HMG-CoA) reductase activity was very low (22 pmol/min/mg protein), owing to cholesterol supplementation, in control rats or in rats fed PHGG, whereas it was markedly higher (+463%) in rats fed GUAR. In conclusion, even if PHGG does alter some parameters of the enterohepatic cycle of cholesterol and bile acids, its effects are not sufficient to elicit a significant cholesterol-lowering effect. The intestinal (ileal or cecal) reabsorption of bile acids was not reduced, but rather increased, by GUAR; nevertheless the intestinal capacities of reabsorption were overwhelmed by the enlargement of the digestive pool of bile acids. In the present model, induction of HMG-CoA reductase probably takes place in the presence of elevated portal bile acid concentrations.     

Modification of margarine fats by enzymatic interesterification: Evaluation of a solid-fat-content-based exponential model with two groups of oil blends

Lipozyme TL IM-catalyzed interesterification for the modification of margarine fats was carried out in a batch reactor at 70°C with a lipase dosage of 4%. Solid fat content (SFC) was used to monitor the reaction progress. Lipase-catalyzed interesterification, which led to changes in the SFC, was assumed to be a first-order reversible reaction. Accordingly, the change in SFC vs. reaction time was described by an exponential model. The model contained three parameters, each with a particular physical or chemical meaning: (i) the initial SFC (SFC₀), (ii) the change in SFC (ΔSFC) from the initial to the equilibrium state, and (iii) the reaction rate constant value (k). SFC_o and ΔSFC were related to only the types of blends and the blend ratios. The rate constant k was related to lipase activity on a given oil blend. Evaluation of the model was carried out with two groups of oil blends, i.e., palm stearin/coconut oil in weight ratios of 90∶10, 80∶20, and 70∶30, and soybean oil/fully hydrogenated soybean oil in weight ratios of 80∶20, 65∶35, and 50∶50. Correlation coefficients higher than 0.99 between the experimental and predicted values were observed for SFC at temperatures above 30°C. The model is useful for predicting changes in the SFC during lipase-catalyzed interesterification with a selected group of oil blends. It also can be used to control the process when particular SFC values are targeted.     

Microstructures and mechanical properties of polypropylene/polyamide 6/polyethelene-octene elastomer blends

A series of polymer blends were designed and manufactured. They are composed of three phases: polypropylene (PP), polyamide-6 (PA6) and polyethylene-octene elastomer (POE) grafted with maleic anhydride. The weight fraction of PA6 was adjusted from 0 to 40% by increments of 10%, and the weight fraction of POE was systematically half that of PA6. The morphology, essentially made of PA6 particles dispersed in the PP matrix, was characterised by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). In the extruded plates prepared with the blends, the shape of the dispersed PA6 particles showed an elongated ellipsoidal shape, whose aspect ratio increased somehow with alloying content. The POE modifier was observed both as a thin interlayer (less than 100 nm thickness) at the PP/PA6 interface, and as a few isolated particles. The elastic modulus and yield stress in tension are nearly constant for PP and blends. By contrast, the notched Izod impact strength increases very much with alloying content. This remarkable effect is interpreted in terms of POE interphase cavitation, enhanced plastic shear deformation and resistance of PA6 particles to crack propagation.     

Synthesis and characterization of soluble (porphyrinato)iron(II) polymers

The use of (tetrakis(4-hexylphenyl)porphyrinato)Fe(II) in polymerization reactions with bidentate ligands such as 9,10-diisocyanoanthracene and 1,4-diisocyanobenzene led to well-defined stacked polymers1 and2 which are still soluble in common organic solvents such as chloroform, dichloromethane, and tetrahydrofurane. They have been completely characterized by¹H-NMR and UV/vis spectropscopy in solution, even allowing end-group analysis for determination of the average degree of polymerization, yieldingn=10 andn=5 for1 and2, respectively. Mößbauer and IR spectroscopy further established the strong Fe-CN bonding reflected by very small isomer shifts and quadrupole splittings (E _Q0.2 mm s^–1) and a large decrease in the IR stretching frequency (v _CN60 cm^–1). The axially stacked polymers exhibit semiconducting properties only upon doping.Presented at the 5th International Symposium on Macromolecule-Metal Complexes (MMV), Summer 1993 in Bremen, Germany.