Bolzano,Cauchy and the “new analysis” of the early nineteenth century

Summary In this paper I discuss the development of mathematical analysis during the second and third decades of the nineteenth century; and in particular I assert that the well-known correspondence of new ideas to be found in the writings of Bolzano and Cauchy is not a coincidence, but that Cauchy had read one particular paper of Bolzano and drew on its results without acknowledgement. The reasons for this conjecture involve not only the texts in question but also the state of development of mathematical analysis itself, Cauchy both as personality and as mathematician, and the rivalries which were prevalent in Paris at that time.     

A deficiency of the homeotic complex of the beetle Tribolium

In Drosophila, the establishment of regional commitments along most of the anterior/posterior axis of the developing embryo depends on two clusters of homeotic genes: the Antennapedia complex (ANT-C) and the bithorax complex (BX-C). The red flour beetle has a single complex (HOM-C) representing the homologues of the ANT-C and BX-C in juxtaposition. Beetles trans-heterozygous for two particular HOM-C mutations spontaneously generate a large deficiency, presumably by an exchange within the common region of two overlapping inversions. Genetic and molecular results indicate that this deficiency spans at least the interval between the Deformed and abdominal-A homologues. In deficiency homozygous embryos, all gnathal, thoracic and abdominal segments develop antennal appendages, suggesting that a gene(s) has been deleted that acts to distinguish trunk from head. There is no evidence that beetles have a homologue of the segmentation gene fushi tarazu of similar genomic location and function. On the basis of the genetic tractability, convenient genome size and organization of Tribolium, and its relatively long phylogenetic divergence from Drosophila (>300 million years), we have integrated developmental genetic and molecular analyses of the HOM-C. We isolated about 70 mutations in the complex representing at least six complementation groups. The homeotic phenotypes of adults and lethal embryos lead us to believe that these beetle genes are homologous with the Drosophila genes indicated in Fig. 1 (see text).     

Evolutionary distinctiveness of the endangered Kemp's ridley sea turtle

The endangered Kemp's ridley sea turtle (Lepidochelys kempi) nests almost exclusively at a single locality in the western Gulf of Mexico, whereas the olive ridley (L. olivacea) nests globally in warm oceans. Morphological similarities between kempi and olivacea, and a geographical distribution that "...makes no sense at all under modern conditions of climate and geography", raise questions about the degree of evolutionary divergence between these taxa. Analysis of mitochondrial (mt) DNA restriction sites shows that Kemp's ridley is distinct from the olive ridley in matriarchal phylogeny, and that the two are sister taxa with respect to other marine turtles. Separation of olive and the Kemp's ridley lineages may date to formation of the Isthmus of Panama, whereas the global spread of the olive ridley lineage occurred recently. In contrast to recent examples in which molecular genetic assessments challenged systematic assignments underlying conservation programmes, our mtDNA data corroborate the taxonomy of an endangered form.     

Genetic factors in neurotoxicology and neuropharmacology: A critical evaluation of the use of genetics as a research tool

Animals have evolved a detoxication system to enable them to survive in a hostile chemical environment in which foods contain many non-nutrient chemicals. Detoxication depends on enzymes which are often genetically polymorphic. As a result, inter-individual variation is common, and in humans several Mendelian loci have been identified. However, most variation in response is probably due to the action of several genes. Genetic variation in response to the neurotoxin MPTP and to chemically and physically-induced seizures is reviewed. In the former case, differences between pigmented and white mouse strains have been noted which are consistent with the hypothesis that humans are more sensitive than mice or rats because of the presence of melanin in human brains. However, variation in sensitivity probably also depends on other genes. In the case of audiogenic seizures, a single locus has been identified and mapped, but its relationship with seizures induced by other agents is not clear. Genetic variation in response to alcohol is also discussed. The failure of most toxicologists to consider genetic variation as a potentially confounding variable, and as a powerful research tool, is discussed critically in relation to non-repeatability of research on the neurotoxic effects of lead, and in relation to the genetic variation in MPTP, seizures, and alcohol response already noted. It seems clear that genetic methods provide a powerful research tool which is largely being ignored by toxicologists.     

MD Method in Solving Multiple Criteria Decision Problems Arising from Investment Systems

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A user designer-based systems methodology

This paper develops the argument that in organizational redesign it is desirable to utilize user-designers as the architects for the redesign. A methodology is developed which emphasizes the use of ideal systems models by user-designers to plan for the organization's future. The methodology involves the creation of an ideal system model, then an analysis of the present system through the creation of root definitions and process models of the existing system. Then root definitions and process models for the idealized system are created. Finally, the two are compared and desirable changes are generated which bring the existing system toward the idealized.     

Error rates in quadratic discrimination with constraints on the covariance matrices

In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions. We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following four models: (i) arbitrary covariance matrices, (ii) common principal components, (iii) proportional covariance matrices, and (iv) identical covariance matrices. Using Monte Carlo simulation to estimate expected error rates, we study the performance of the four discrimination procedures for five different parameter setups corresponding to standard situations that have been used in the literature. The procedures are examined for sample sizes ranging from 10 to 60, and for two to four groups. Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.The authors wish to thank the editor and three referees for their helpful comments on the first draft of this article. M. J. Schmid supported by grants no. 2.724-0.85 and 2.038-0.86 of the Swiss National Science Foundation.