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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Order 4 (1987), S. 165-189 
    ISSN: 1572-9273
    Schlagwort(e): 08A02 ; 08A35 ; Archimedean ; automorphism ; measurement ; ordered relational structure ; translation group
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The paper focuses on three problems of generalizing properties of concatenation structures (ordered structures with a monotonic operation) to ordered structures lacking any operation. (1) What is the natural generalization of the idea of Archimedeaness, of commensurability between large and small? (2) What is the natural generalization of the concept of a unit concatenation structure in which the translations (automorphisms with no fixed point) can be represented by multiplication by a constant? (3) What is the natural generalization of a ratio scale concatenation structure being distributive in a conjoint one, which has been shown to force a multiplicative representation of the latter and the product-of-powers representation of units found in physics? It is established (Theorems 5.1 and 5.2) that for homogeneous structures, the latter two questions are equivalent to it having the property that the set of all translations forms a homogeneous Archimedean ordered group. A sufficient condition for Archimedeaness of the translations is that they form a group, which is equivalent to their being 1-point unique, and the structure be Dedekind complete and order dense (Theorems 2.1 and 2.2). It is suggested that Archimedean order of the translations is, indeed, also the answer to the first question. As a lead into that conclusion, a number of results are reported in Section 3 on Archimedeaness in concatenation structures, including for positive structures sufficient conditions for several different notions of Archimedeaness to be equivalent. The results about idempotent structures are fragmentary.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Psychometrika 42 (1977), S. 461-489 
    ISSN: 1860-0980
    Schlagwort(e): Thurstonian scaling model ; discriminal process ; neural schema for auditory psychophysics ; attention bands ; attention as sampling ; absolute identification ; magnitude estimation ; frequency discrimination
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract Four issues are discussed concerning Thurstone's discriminal processes: the distributions governing the representation, the nature of the response decision rules, the relation of the mean representation to physical characteristics of the stimulus, and factors affecting the variance of the representation. A neural schema underlying the representation is proposed which involves samples in time of pulse trains on individual neural fibers, estimators of parameters of the several pulse trains, samples of neural fibers, and an aggregation of the estimates over the sample. The resulting aggregated estimate is the Thurstonian representation. Two estimators of pulse rate, which is monotonic with signal intensity, are timing and counting ratios and two methods of aggregation are averaging and maximizing. These lead to very different predictions in a speed-accuracy experiment; data indicate that both estimators are available and the aggregation is by averaging. Magnitude estimation data are then used both to illustrate an unusual response rule and to study the psychophysical law. In addition, the pattern of variability and correlation of magnitude estimates on successive trials is interpreted in terms of the sample size over which the aggregation takes place. Neural sample size is equated with selective attention, and is an important factor affecting the variability of the representation. It accounts for the magical number seven phenomenon in absolute identification and predicts the impact of nonuniform distributions of intensities on the absolute identification of two frequencies.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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