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  • 1
    Electronic Resource
    Electronic Resource
    Relative error in floating-point multiplication (1985)
    Springer
    Computing 35 (1985), S. 127-139 
    Details
    ISSN: 1436-5057
    Keywords: 65G05 ; 65G10 ; Relative error ; computer arithmetic ; floating point multiplication ; normalization options ; guard digits ; floating point numbers ; floating point precision and significance ; round-off error ; fraction error ; mean and standard deviation of errors ; logarithmically distributed numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein Modell für den relativen Fehler bei der Gleitkomma-Multiplikation entwickelt unf für verschiedene Kombinationen der Arithmetikparameter stochastisch analysiert. Die Parameter sind die Basis, die Rundungsart, die Anzahl der Schutzstellen, und ob die Normalisierung vor oder nach dem Runden erfolgt. Bei einer angenommenen logarithmischen Verteilung für die Mantisse kommt man zu folgenden Schlüssen: 1. Der durchschnittliche relative Fehler bei der Multiplikation wächst mit der Basis. 2. Dieser Fehler wird minimal für die Basis 2 (am besten mit verborgenem ersten Bit) und recht groß für die Basis 16. 3. Die klassischen Schranken für den relativen Fehler sind pessimistisch. Ihre durchschnittliche Überschätzung wächst mit der Basis.
    Notes: Abstract A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of computer design parameters. These parameters include the base, the type of rounding rule, the number of guard digits, and whether the post-arithmetic normalization shift (if needed) is done before or after rounding. Under the assumption of logarithmic distribution for the fraction (mantissa), the major stochastic conclusions are: 1. The average relative error in multiplication increases as the base increases. 2. This error is minimized by selecting the machine base to be binary (better yet, binary with a hidden bit) and is rather large for machines with base 16. 3. The classical relative error bounds are pessimistic. The average overestimation by those bounds increases as the base increases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02260500
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  • 2
    Electronic Resource
    Electronic Resource
    Somatostatin-containing D cells exhibit immunoreactivity for rat somatostatin cryptic peptide in six mammalian species (1986)
    Springer
    Cell & tissue research 246 (1986), S. 197-204 
    Details
    ISSN: 1432-0878
    Keywords: Electron immunocytochemistry ; Gastro-entero-pancreatic endocrine system ; Gut ; Pancreas ; Prosomatostatin ; Rat somatostatin cryptic peptide (RSCP) ; Rat somatostatin-28
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary Antisera raised against rat somatostatin cryptic peptide (RSCP; corresponding to amino acids 63–77 of rat pro-somatostatin), somatostatin-28-(1–12) and somatostatin-28-(17–28) were used to compare the morphological distribution of these pro-somatostatin-derived sequences within the gastroenteropancreatic system of six mammalian species, including man. Using the immunogold staining procedure, RSCP, SS28-(1–12) and SS28-(17–28) immunoreactivity was found to be present in all the D cells of the tissues investigated. Extra-islet RSCP and SS28-(1–12) immunoreactive cells were also identified in some species. RSCP, SS28-(1–12) and SS28-(17–28) immunoreactivities were also present in a single case of human duodenal somatostatinoma. Immunostaining of serial ultrathin sections from all specimens in this study revealed that RSCP and both somatostatin immunoreactivities were co-localised in a majority of the reactive cells. Corroborative evidence was obtained by double immunogold staining which further showed that RSCP, SS28-(1–12) and SS28-(17–28) immunoreactivities were co-localised to individual secretory granules in D type cells, both normal and tumour. RSCP and SS28-(17–28) immunoreactivities were invariably co-localised, whereas SS28-(1–12) immunoreactivity was restricted to a sub-population of secretory granules. Our findings suggest that RSCP immunoreactivity is conserved in a number of mammalian species and is stored in each secretory granule type. Consequently, detection of the RSCP sequence may serve as a useful marker for somatostatin-producing systems throughout the diffuse neuroendocrine system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00219018
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