5 resultados para exponential function

em Aston University Research Archive


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Various hypotheses could explain the relationship between beta-amyloid (Abeta) deposition and the vasculature in Alzheimer's disease (AD). Amyloid deposition may reduce capillary density, affect endothelial cells of blood vessels, result in diffusion from blood vessels, or interfere with the perivascular clearance mechanism. Hence, the spatial pattern of the classic ('cored') type of Abeta deposit was studied in the upper laminae (I,II/III) of the superior frontal gyrus in nine cases of sporadic AD (SAD). Sections were immunostained with antibodies against Abeta and with collagen IV to study the relationships between the spatial distribution of the classic deposits and the blood vessel profiles. Both the classic deposits and blood vessel profiles were distributed in clusters. In all cases, there was a positive spatial correlation between the clusters of the classic deposits and the larger diameter (>10 microm) blood vessel profiles and especially the vertically penetrating arterioles. In only 1 case, was there a significant spatial correlation between the clusters of the classic deposits and the smaller diameter (<10 microm) capillaries. There were no negative correlations between the density of Abeta deposits and the smaller diameter capillaries. In 9/11 cases, the clusters of the classic deposits were significantly larger than those of the clusters of the larger blood vessel profiles. In addition, the density of the classic deposits declined as a negative exponential function with distance from a vertically penetrating arteriole. These results suggest that the classic Abeta deposits cluster around the larger blood vessels in the upper laminae of the frontal cortex. This aggregation could result from diffusion of proteins from blood vessels or from overloading the system of perivascular clearance from the brain.

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The spatial pattern of the classic (‘cored’) type of beta-amyloid (Abeta) deposit was studied in the upper laminae of the superior temporal gyrus in 9 cases of sporadic Alzheimer’s disease (SAD). Abeta stained tissue was counterstained with collagen IV to study the relationships between the spatial distribution of the classic deposits and the blood vessel profiles. Both the classic deposits and blood vessel profiles were distributed in clusters. In all cases, there was a spatial correlation between the clusters of the classic deposits and the larger diameter (>10 micron) blood vessel profiles and especially the vertically penetrating arterioles. In only 1 case, was there a significant spatial correlation between the clusters of the classic deposits and the smaller diameter (<10 micron) capillaries. In 9/11 cases, the clusters of the classic deposits were significantly larger than those of the clusters of the larger blood vessels. In addition, the density of the classic deposits declined as a negative exponential function with distance from the vertically penetrating arterioles. These results suggest that the classic Abeta deposits cluster around the larger blood vessels in the frontal cortex and that diffusion of proteins from these blood vessels could be involved in the pathogenesis of the classic deposits in SAD.

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In variant Creutzfeldt-Jakob disease (vCJD), a disease linked to bovine spongiform encephalopathy (BSE), florid-type prion protein (PrP(sc)) deposits are aggregated around the larger diameter (> 10 µm) cerebral microvessels. Clustering of PrP(sc) deposits around blood vessels may result from blood-borne prions or be a consequence of the cerebral vasculature influencing the development of the florid deposits. To clarify the factors involved, the dispersion of the florid PrP(sc) deposits was studied around the larger diameter microvessels in the neocortex, hippocampus, and cerebellum of ten cases of vCJD. In the majority of brain regions, florid deposits were clustered around the larger diameter vessels with a mean cluster size of between 50 µm and 628 µm. With the exception of the molecular layer of the dentate gyrus, the density of the florid deposits declined as a negative exponential function of distance from a blood vessel profile suggesting that diffusion of molecules from blood vessels is a factor in the formation of the florid deposits. Diffusion of PrP(sc) directly into the brain via the microvasculature has been demonstrated in vCJD in a small number of cases. However, the distribution of the prion deposits in vCJD is more likely to reflect molecular 'chaperones' diffusing from vessels and promoting the aggregation of pre-existing PrP(sc) in the vicinity of the vessels to form florid deposits.

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An ultra high vacuum system capable of attaining pressures of 10-12 mm Hg was used for thermal desorption experiments. The metal chosen for these experiments was tantalum because of its suitability for thermal desorption experiments and because relatively little work has been done using this metal. The gases investigated were carbon monoxide, hydrogen and ethylene. The kinetic and thermodynamic parameters relating to the desorption reaction were calculated and the values obtained related to the reaction on the surface. The thermal desorption reaction was not capable of supplying all the information necessary to form a complete picture of the desorption reaction. Further information was obtained by using a quadrupole mass spectrometer to analyse the desorbed species. The identification of the desorbed species combined with the value of the desorption parameters meant that possible adatom structures could be postulated. A combination of these two techniques proved to be a very powerful tool when investigating gas-metal surface reactions and gave realistic values for the measured parameters such as the surface coverage, order of reaction, the activation energy and pre-exponential function for desorption. Electron microscopy and X-ray diffraction were also used to investigate the effect of the gases on the metal surface.

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This thesis is concerned with the inventory control of items that can be considered independent of one another. The decisions when to order and in what quantity, are the controllable or independent variables in cost expressions which are minimised. The four systems considered are referred to as (Q, R), (nQ,R,T), (M,T) and (M,R,T). Wiith ((Q,R) a fixed quantity Q is ordered each time the order cover (i.e. stock in hand plus on order ) equals or falls below R, the re-order level. With the other three systems reviews are made only at intervals of T. With (nQ,R,T) an order for nQ is placed if on review the inventory cover is less than or equal to R, where n, which is an integer, is chosen at the time so that the new order cover just exceeds R. In (M, T) each order increases the order cover to M. Fnally in (M, R, T) when on review, order cover does not exceed R, enough is ordered to increase it to M. The (Q, R) system is examined at several levels of complexity, so that the theoretical savings in inventory costs obtained with more exact models could be compared with the increases in computational costs. Since the exact model was preferable for the (Q,R) system only exact models were derived for theoretical systems for the other three. Several methods of optimization were tried, but most were found inappropriate for the exact models because of non-convergence. However one method did work for each of the exact models. Demand is considered continuous, and with one exception, the distribution assumed is the normal distribution truncated so that demand is never less than zero. Shortages are assumed to result in backorders, not lost sales. However, the shortage cost is a function of three items, one of which, the backorder cost, may be either a linear, quadratic or an exponential function of the length of time of a backorder, with or without period of grace. Lead times are assumed constant or gamma distributed. Lastly, the actual supply quantity is allowed to be distributed. All the sets of equations were programmed for a KDF 9 computer and the computed performances of the four inventory control procedures are compared under each assurnption.