Mathematical Arguments in Context

Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of explicit and implicit, formal and informal background knowledge.     

Contributions to the life history of Sacramento perch, Archoplites interruptus, in Pyramid Lake, Nevada

During a two-year period (1976&ndash;1977), 180 Sacramento perch ( Archoplites interruptus ) were sampled from Pyramid Lake, Nevada, on a monthly basis using several capture methods in all lake areas. Age and growth determinations of these fish were inconsistent with previous research on this species. Sacramento perch are entirely carnivorous, adults feeding primarily on tui chub ( Gila bicolor ). Fish accounted for 6 percent of the diet (by volume) of Sacramento perch less than 300 mm fork length, and 98 percent for those exceeding 300 mm. Amphipods, Odonata, and Chironomidae composed 6.3, 5.7, and 1.8 percent, respectively, of the stomach contents by volume for all sizes combined. Females spawned from June to August when water temperatures approached 20 C, and their gonad weight was about 6 percent of the total body weight. A sample of 20 female perch had a mean fecundity of 84,203 eggs. The mean diameter of mature eggs was 0.88 mm. Sacramento perch almost exclusively inhabit the littoral zone of Pyramid Lake. Activity, as indicated by net catches, was greatest during the warm months of May to October. Monthly catches were significantly correlated with temperature (r = 0.577, P < 0.01). No short-term changes in population abundances were observed during 1976&ndash;1977.     

Mechanical and biochemical characterization of the contraction elicited by a calcium-independent myosin light chain kinase in chemically skinned smooth muscle

Summary The contraction induced by a Ca²⁺-independent myosin light chain kinase (MLCK-) was characterized in terms of isometric force (F_o), immediate elastic recoil (SE), unloaded shortening velocity (V_us), shortening under a constant load and ATPase activity of chemically skinned smooth muscle preparations. These parameters were compared to those measured in a Ca²⁺-induced contraction to assess the nature of cross bridge interaction in the MLCK-induced contraction. F_o developed in chicken gizzard fibers as well as SE were similar in contractions elicited by either agent. V_us in the contraction induced by MLCK-(0.36 mg/ml) was similar though averaged 39.3±8.9% less than V_us induced by Ca²⁺ (1.6x10^–6M) in the control fibers. Addition of Ca²⁺ (1.6x10^–6M) to a contraction induced by MLCK-resulted in small increases in both F_o and V_us. Shortening under a constant load was similar for both types of contractions. The contraction induced by MLCK-was accompanied by an increased rate of ATP hydrolysis. The MLCK-induced contraction is thus kinetically similar though not identical to a contraction induced by Ca²⁺. We conclude that with respect to actin-myosin interaction, MLCK- and Ca²⁺-induced contractions are similar.     

Combining var estimation and state space model reduction for simple good predictions

A combination of VAR estimation and state space model reduction techniques are examined by Monte Carlo methods in order to find good, simple to use, procedures for determining models which have reasonable prediction properties. The presentation is largely graphical. This helps focus attention on the aspects of the model determination problem which are relatively important for forecasting. One surprising result is that, for prediction purposes, knowledge of the true structure of the model generating the data is not particularly useful unless parameter values are also known. This is because the difficulty in estimating parameters of the true model causes more prediction error than results from a more parsimonious approximate model.     

The minimal rank correlation,subject to order restrictions,with application to the weighted linear choice model

The weighted linear choice model is one of the most popular models in the social sciences. In this model the utility of a choice object is represented as a weighted sum of attribute-level desirabilities, where the weights are attribute importances. In many empirical contexts the choice objects are such that individuals are highly correlated in terms of their desirability ordering of levels within attribute (e.g., price levels, durability levels, etc.) but may differ appreciably in terms of their evaluations of each attribute's importance.In this paper we address the problem of how dissimilar two individuals may be, in a rank correlation sense, given that they agree completely on the desirability ordering of levels within attributes, but may disagree considerably regarding the importance they attach to the attributes themselves. The problem has interesting implications regarding the potential value of clustering individuals' utility functions for market segmentation or other such purposes.The authors would like to thank the editor and three anonymous reviewers for their excellent comments on an earlier draft of the paper.     

Peroxidase activity and thiocyanate accumulation in salivary glands

Summary Salivary glands with high, low, or no peroxidase activity do not differ in [S¹⁴CN^–] after the i.v. injection of KS¹⁴CN, nor do the glands differ from blood and muscle in [S¹⁴CN^–]. The content of SCN^– in a salivary gland does not mirror the gland's participation in the peroxidase-mediated antimicrobial mechanism.     

The estimative functions of physical theory

Attention is drawn to two closely related functions served by scientific theory (called here ‘mensurative’ and ‘reconstructive estimation’) which are of fundamental importance in physical science but as yet little discussed in philosophy. As indicated by their names, they constitute the theoretical basis of physical measurements.After analysing some historically important examples and sketching the historical development of these ideas, this paper examines the similarities and differences between the estimate functions of theory and such well-known functions as prediction and explanation. The pervasiveness of the estimative functions even when theory is but poorly developed is noted; and some of the problems raised by the physical equivalence of the measuring instrument to the object measured are discussed. The relations of estimation to ‘reductive logic’ are also considered.We then apply this understanding of estimative functioning to distinguishing experimental errors from those genuine anomalies which result in discovery. It is also shown that there can be no facts established nor any verification of predictions except on the basis of valid estimates derived, in turn, from antecedently accepted theories.