Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 93).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Finite fields; implementation. Includes bibliographical references (leaves 59-62).

Traditional data integration offers high quality services for managing and querying interrelated but heterogeneous data sources but at a high cost. This is because a significant amount of manual effort is required to help specify precise relationships between the data sources in order to set up a data integration system. The recent proposed vision of dataspaces aims to reduce the upfront effort required to set up the system. A possible solution to approaching this aim is to infer schematic correspondences between the data sources, thus enabling the development of automated means for bootstrapping dataspaces. In this thesis, we discuss a two-step research programme to automatically infer schematic correspondences between data sources. In the first step, we investigate the effectiveness of existing schema matching approaches for inferring schematic correspondences and contribute a benchmark, called MatchBench, to achieve this aim. In the second step, we contribute an evolutionary search method to identify the set of entity-level relationships (ELRs) between data sources that qualify as entity-level schematic correspondences. Specifically, we model the requirements using a vector space model. For each resulting ELR we further identify a set of attribute-level relationships (ALRs) that qualify as attribute-level schematic correspondences. We demonstrate the effectiveness of the contributed inference technique using both MatchBench scenarios and real world scenarios.

We define morphism (E, M)-structures in an abstract category, develop their basic properties and present some examples. We also consider the existence of such factorization structures, and find conditions under which they can be extended to factorization structures for certain classes of sources. There is a Galois correspondence between the collection of all subclasses of X-morphisms and the collection of all subclasses of X-objects. A-epimorphisms diagonalize over A-regular morphisms. Given an (E, M)-factorization structure on a finitely complete category, E-separated objects are those for which diagonal morphisms lie in M. Other characterizations of E-separated objects are given. We give a bijective correspondence between the class of all (E, M)factorization structures with M contained in the class of all X-embeddings and the class of all strong limit operators. We study M-preserving morphisms, M-perfect morphisms and M-compact objects in a morphism (E, M)-hereditary construct, and prove some of their properties which are analogous to the topological ones. / Mathematical Sciences / M. Sc. (Mathematics)

This thesis focuses on a class of Galois field used to achieve fast finite field arithmetic which we call Optimal Extension Fields (OEFs), first introduced in cite{baileypaar98}. We extend this work by presenting an adaptation of Itoh and Tsujii's algorithm for finite field inversion applied to OEFs. In particular, we use the facts that the action of the Frobenius map in $GF(p^m)$ can be computed with only $m-1$ subfield multiplications and that inverses in $GF(p)$ may be computed cheaply using known techniques. As a result, we show that one extension field inversion can be computed with a logarithmic number of extension field multiplications. In addition, we provide new variants of the Karatsuba-Ofman algorithm for extension field multiplication which give a performance increase. Further, we provide an OEF construction algorithm together with tables of Type I and Type II OEFs along with statistics on the number of pseudo-Mersenne primes and OEFs. We apply this new work to provide implementation results for elliptic curve cryptosystems on both DEC Alpha workstations and Pentium-class PCs. These results show that OEFs when used with our new inversion and multiplication algorithms provide a substantial performance increase over other reported methods.

Our senses take in a large amount of information, information that sometimes is congruent across sensory modalities. Crossmodal correspondences are the study of how this information across modalities is integrated by the brain, across which dimensions the correspondences exists, and how it affect us. In the present paper four experiments were conducted, in which potential crossmodal correspondences between audition, vision and olfaction were investigated. It was hypothesized that crossmodal correspondences between olfaction, vision and audition exist along different dimensions. The results showed significant correlations between olfaction and audition when volume varies, i.e., a high volume is associated to a high concentration of an odor, and a low volume is associated to a low concentration of an odor, and vice versa. Furthermore, existing correspondences between vision and audition is reconfirmed. In conclusion, the results provide support to the notion that crossmodal correspondences exists between all sensory modalities, although along different dimensions.

Thesis--Bonn, 1978. / "Als Manuskript gedruckt." Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 118-120).

We define morphism (E, M)-structures in an abstract category, develop their basic properties and present some examples. We also consider the existence of such factorization structures, and find conditions under which they can be extended to factorization structures for certain classes of sources. There is a Galois correspondence between the collection of all subclasses of X-morphisms and the collection of all subclasses of X-objects. A-epimorphisms diagonalize over A-regular morphisms. Given an (E, M)-factorization structure on a finitely complete category, E-separated objects are those for which diagonal morphisms lie in M. Other characterizations of E-separated objects are given. We give a bijective correspondence between the class of all (E, M)factorization structures with M contained in the class of all X-embeddings and the class of all strong limit operators. We study M-preserving morphisms, M-perfect morphisms and M-compact objects in a morphism (E, M)-hereditary construct, and prove some of their properties which are analogous to the topological ones. / Mathematical Sciences / M. Sc. (Mathematics)

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Holomorphic correspondences are multivalued functions from the Riemann sphere to itself. This thesis is concerned with a certain type of holomorphic correspondence known as a covering correspondence. In particular we are concerned with a one complexdimensional family of correspondences constructed by post-composing a covering correspondence with a conformal involution. Correspondences constructed in this manner have varied and intricate dynamics. We introduce and analyze two subfamilies of this parameter space. The first family consists of correspondences for which the limit set is a Cantor set, the second family consists of correspondences for which the limit set is connected and for which the action of the correspondence on the complement of this limit set exhibits certain group like behaviour.