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 impedance of the alkaline zinc-mercuric oxide cell. I. Cell behaviour and interpretation of impedance spectra

The impedances of small (2400 mA h) alkaline Zn-HgO cells have been measured in the range 10 kHz-0.001 Hz at various states of charge from fully charged to fully discharged. The behaviour of the cell conforms to that expected for rate control by charge transfer at the zinc electrode and diffusion in solution. At low frequencies there is a relaxation in the diffusive circuit elements which ultimately results in a complete suppression of the capacitative component of the impedance at zero frequency. The low-frequency behaviour is analogous to convective diffusion and is due to the effective distance between the electrodes being small compared with the characteristic length (D/)^1/2. The magnitude of the charge transfer resistance is the best measure of the state of charge.Nomenclature a effective electrode separation - C _DL double-layer capacitance of cell - C _R capacitative component of cell impedance - C concentration difference - D percentage discharge in Equation 12 - D _i diffusion coefficient of speciesi - R ohmic resistance of cell - R _R resistive component of cell Faradaic impedance - Ui constant defined by Equation 10 - Z total cell impedance - Z _F cell Faradaic impedance - Z _F cell impedance modified for porosity effect - Z _x cell impedance of Faradaic component plus double layer - cell Warburg coefficient (slope ofR _R and 1/C _Rversus su}-1/2) - _C Warburg coefficient calculated fromC _r values - _i cell Warburg coefficient for speciesi - Warburg coefficient calculated fromR _R values - dihedral angle of tail of Sluyters plot (after coming-off high-frequency semicircle) - angular frequency     

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.     

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.     

Rheology of poly(n‐butyl methacrylate) and its composites with calcium carbonate

Poly(n‐butyl methacrylate) (PBMA) composites with calcium carbonate (CaCO₃) were prepared by in situ radical copolymerization of butyl methacrylate (BMA) and methacrylic acid (MA) with precipitated calcium carbonate. To compare the different rheological behaviors of the monomer mixtures with CaCO₃ and the composites, the steady and dynamic viscosities of BMA/MA/CaCO₃ and poly(BMA/MA/CaCO₃) were measured by means of steady and oscillatory shear flows. The viscosity of the mixture BMA/MA/CaCO₃ was found to increase evidently with the increasing of CaCO₃%. The influence of MA% on viscosity of BMA/MA/CaCO₃ was slight. During the in situ polymerization, the viscosity of the reacting system was measured to be enhanced by a factor of about 10⁴ from the monomer/CaCO₃ mixture to composites. The dependency of zero‐shear viscosity on molar mass of PBMA was also investigated. The relation between the zero‐shear viscosity and molar mass is η₀ = 10^?15 M_w^3.5. The evolution of the viscosity with the temperature for both PBMA and its composites was obtained and time–temperature superposition was used to build master curves for the dynamic moduli. The flow activation energies were found to be 115.0, 148.6, and 178.7 kJ/mol for PBMA, composite PBMA/CaCO₃ (90/10), and PBMA/MA/CaCO₃ (89/1/10), respectively. The viscosity of the composites containing less than 10% CaCO₃ was lower than that of pure PBMA with the same molar mass. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1376–1383, 2003     

Engineering microfluidic papers: effect of fiber source and paper sheet properties on capillary-driven fluid flow

In the present study, we introduce a novel approach to control and modulate fluid transport inside microfluidic papers using lab-engineered paper sheets. Lab-sheets consisting of different fiber sources (eucalyptus sulfate and cotton linters pulp) and varying porosities were designed and further modified with small millimeter-scaled channels using hydrophobic barriers consisting of fiber-attached, hydrophobic polymers. The capillary-driven transport of an aqueous solution was monitored visually, and the influence of parameters such as fiber source, paper grammage, and channel width on the flow rates through the channel was investigated. The experimental results were compared with those obtained with commercially available filter papers. Our findings suggest that accurate control of fluid transport processes with standard filter papers is complex. Additionally, if the channel width is smaller than the mean fiber length, flow rates become dependent on the geometric parameters of the channel because of the formation of dead-end pores at the hydrophobic barriers. Finally, control of the paper sheets porosity, by varying the fiber density of the lab-made paper, affords the fabrication of chemically identical sheets whereby capillary flow is largely influenced and can be modulated accordingly by simple papermaking processes.