vorgelegt von

theta series and modular formsMichael Hentschel ⋆ On Hermitian theta series and modular forms„On Hermitian theta series and modular forms

Type-Inference Based Deforestation of Functional Programs

In lazy functional programming modularity is often achieved by using intermediate data structures to combine separate parts of a program. Each intermediate data structure is produced by one part and consumed by another one. Deforestation optimises a functional program by transformation into a program which does not produce such intermediate data structures. In this thesis we present a new method for deforestation, which combines a known method,short cut deforestation, with a new analysis that is based on type inference. Short cut deforestation eliminates an intermediate list by a single, local transformation. In return, short cut deforestation expects both producer and consumer of the intermediate list in a certain form. Whereas the required form of the consumer is generally considered desirable in a well-structured program anyway, the required form of the producer is only a crutch to enable deforestation. Hence only the list-producing functions of the standard libraries were defined in the desired form and short cut deforestation has been confined to compositions of these functions. Here, we present an algorithm which transforms an arbitrary producer into the required form. Starting from the observation that short cut deforestation is based on a parametricity theorem of the second-order typed lambda-calculus, we show how the construction of the required form can be reduced to a type inference problem. Typability for the second-order typed lambda-calculus is undecidable, but we only need to solve a partial type inference problem. For this problem we develop an algorithm based on the well-known Hindley-Milner type inference algorithm. The transformation of a producer often requires inlining of some function definitions. Type inference even indicates which function definitions need to be inlined. However, only limited inlining across module boundaries is practically feasible. Therefore, we extend the previously developed algorithm to split a function definition into a worker definition and a wrapper definition. We only need to inline the small wrapper definition, which transfers all information required for deforestation. The flexibility of type inference allows us to remove intermediate lists which original short cut deforestation cannot remove, even with hand-crafted producers. In contrast to most previous work on deforestation, we give a detailed proof of completeness and semantic correctness of our transformation

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Super-specific DNA methylation by a DNA methyltransferase coupled with a triple helix-forming oligonucleotide Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades eine

vorgelegt von Diplom-Physiker

This thesis describes the behavior of cracks and pores under the influence of elastic and curvature effects. In a continuum theory approach, these structure deformations are treated as free moving boundaries. Our investigation start with well established sharp interface equations for which no fully dynamical solutions exist so far. The equations include only linear dynamical elasticity, surface energy and non-equilibrium transport theory. By proper use of the phase-field concept, we are now able to tackle the fully time-dependent free moving boundary problem to describe crack propagation in a fully self-consistent way. We concentrate on two material transport processes, namely surface diffusion and phase transition dynamics. We show analytically that the intuitive and widely used approach for constructing a phase-field model for surface diffusion fails, since it does not reduce to the desired sharp interface equations, providing an uncontrolled approximation to the dynamics. We then develop two completely new models that ensure the correct asymptotic behavior and support our analytical findings by numerical simulations, which are are computationally very demanding due to the high order equations that have to be solved