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Th. : Droit : Toulouse : 1905.

Thesis (Ph.D.)--Columbia University, 2008. / Adviser: Virginia Page Fortna. Includes bibliographical references.

Thesis (doctoral)--Universität Zürich. / Includes bibliographical references.

Würzburg, Univ., Diss., 2001. / Erscheinungsjahr an der Haupttitelstelle: 2000. Computerdatei im Fernzugriff.

Würzburg, Univ., Diss., 2001. / Erscheinungsjahr an der Haupttitelstelle: 2000. Computerdatei im Fernzugriff.

Würzburg, University, Diss., 2001. / Erscheinungsjahr an der Haupttitelstelle: 2000.

A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non-dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating) sets is a non-dominating (non-total dominating) set partition. We show that the minimum number of sets in a non-dominating set partition of a graph G equals the total domination number of its complement Ḡ and the minimum number of sets in a non-total dominating set partition of G equals the domination number of Ḡ. This perspective yields new upper bounds on the domination and total domination numbers. We motivate the study of these concepts with a social network application.

In this thesis, we solve for (equivariant) Gromov-Witten theories of some important classes of surfaces and threefolds, and study their relationships to other brances of mathematics. The first object is the class of P2-bundles over a smooth curve C of genus g. Our bundles are of the form P(L0 + L1 +L2) for arbitrary line bundles L0, L1 and L2 over C. We compute the partition functions of these invariants for all classes of the form s + nf, where s is a section, f is a fiber and n is an integer. In the case where the class is Calabi-Yau, i.e., K • (s + nf) = 0,the partition function is given by 3g (2sin u/2) 2g-2 As an application, one can obtain a series of full predictions for the equivariant Donaldson Thomas invariants for this family of non-toric threefolds. Secondly, we compute the C-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C2 /G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root lattice of any root system. Using the Crepant Resolution Conjecture, we obtain a prediction for the orbifold Grornov-Witten potential of [C2 /G]. Thirdly, for a polyhedral group G, that is a finite subgroup of S0(3), we completely determine the Gromov-Witten theory of Nakamura's G- Hilbert scheme, which is a preferred Calabi-Yau resolution of the polyhedral singularity C3/G. The classical McKay correspondence determines the (classical) cohomology of this resolution in terms of the representation theory of G. We express the Cromov-Witten potential in terms of an ADE root system associated to G. As an application, we use the Crepant Resolution Conjecture to provide a full prediction for the orbifold Grornov-Witten invariants of [C3/G]. Finally, in the case that G is the group A4 or Z2 x Z2, we compute the integral of Ag on the Hurwitz locus HG C Mg of curves admitting a degree 4 cover of P1 having monodromy group G. We compute the generating functions for these integrals and write them as a trigonometric expression summed over the positive roots of the E6 and D4 root systems respectively. As an application, we prove the Crepaut Resolution Conjecture for the orbifolds [C3/A4] and [C3/(Z2 x Z2)].

How to manage a dynamic environment and how to provide task partitioning are two key concerns when developing distributed computing applications. The emergence of Grid computing environments extends these problems. Conventional resource management systems are based on a relatively static resource model and a centralized scheduler that assigns computing resources to users. Distributed management introduces resource heterogeneity: not only the set of available resources, but even the set of resource types is constantly changing. Obviously this is unsuitable for the present Grid. In addition, the Grid provides users with the physical infrastructure to run parallel programs. Because of this increasing availability, there are more requirements for parallelization technologies. Therefore, based on problems outlined above, this thesis provides a novel scheduler which not only enables dynamic management but also provides skeleton library to support the task partition. Dynamic management is derived from the concept of reflectiveness, which allows the Grid to perform like an efficient market with some limited government controls. To supplement the reflective mechanism, this thesis integrates a statistical forecasting approach to predict the environment of the Grid in the next period. The task partitioning support is extended from the skeleton library in the parallel computing and cluster computing areas. The thesis shows how this idea can be applied in the Grid environment to simplify the user’s programming works. Later in this PhD thesis, a Petri-net based simulation methodology is introduced to examine the performance of the reflective scheduler. Moreover, a real testing environment is set up by using a reflective scheduler to run a geometry optimization application. In summary, by combining knowledge from economics, statistics, mathematics and computer science, this newly invented scheduler not only provides a convenient and efficient way to parallelize users’ tasks, but also significantly improves the performance of the Grid.