<p> The closed graph and open mapping theorems are two of the deeper results in the theory of locally convex spaces. They are very rich in their applications in functional analysis. This thesis contains some extensions of these theorems in locally convex spaces. We begin with a study of α-spaces, and γ-spaces, which leads us naturally to a study of δ-spaces. On these spaces, we prove closed graph and open mapping theorems. Similar theorems are also proved for certain classes of Br ('&)-spaces. In particular, a closed graph theorem for B(m)-spaces enables us to characterise certain classes of B( &. y)-spaces. A consideration of countability conditions in locally convex spaces enables us to prove open mapping theorems in Br (J )-spaces. These theorems are then used to relate boundedness of linear mappings and their graphs. </p> / Thesis / Doctor of Philosophy (PhD)

The Message Passing Interface (MPI) standard defines virtual topologies that can be applied to systems of cooperating processes. Among issues regarding a more convenient namespace this may be used to optimize the placement of MPI processes in order to reduce communication time. That means, the processes with their main communication paths represent a graph that has to be cost efficiently mapped onto the graph representing the actual communication network. In this context, this work analyses and compares state-of-the-art task mapping strategies with respect to running time and their quality of solutions to the MPI mapping problem. In particular, the focus is on generic strategies that can be used for arbitrary process/network topologies although, here, the topologies of interest are regular ones, where the number of processes is greater than the number of processors in the underlying physical network. Additionally, different measures of mapping quality are discussed and a close correspondence between the most appropriate, the weighted edge cut, and program execution time is shown. In order to investigate how mapping quality affects MPI program execution time, some mapping strategies have been incorporated into Open MPI. Finally, benchmark results prove that optimized process-to-processor mappings can improve program execution time by up to 60%, compared to the default mapping in many MPI implementations (linear mapping). The findings in this work can serve as reference not only for MPI implementors, but also for researchers investigating static process-to-processor mappings, in general.

Master of Science / Department of Computing and Information Sciences / Gurdip Singh / Severe energy constraints and limited computing abilities of the nodes in a network present a major challenge in the design and deployment of a wireless sensor network. This thesis aims to present energy efficient algorithms for data fusion and information aggregation in a sensor network. The various methodologies of data fusion presented in this thesis intend to reduce the data traffic within a network by mapping the sensor network application task graph onto a sensor network topology. Partitioning of an application into sub-tasks that can be mapped onto the nodes of a sensor network offers opportunities to reduce the overall energy consumption of a sensor network. The first approach proposes a grid based coordinated incremental data fusion and routing with heterogeneous nodes of varied computational abilities. In this approach high performance nodes arranged in a mesh like structure spanning the network topology, are present amongst the resource constrained nodes. The sensor network protocol performance, measured in terms of hop-count is analysed for various grid sizes of the high performance nodes. To reduce network traffic and increase the energy efficiency in a randomly deployed sensor network, distributed clustering strategies which consider network density and structure similarity are applied on the network topology. The clustering methods aim to improve the energy efficiency of the sensor network by dividing the network into logical clusters and mapping the fusion points onto the clusters. Routing of network information is performed by inter-cluster and intra-cluster routing.

The Message Passing Interface (MPI) standard defines virtual topologies that can be applied to systems of cooperating processes. Among issues regarding a more convenient namespace this may be used to optimize the placement of MPI processes in order to reduce communication time. That means, the processes with their main communication paths represent a graph that has to be cost efficiently mapped onto the graph representing the actual communication network. In this context, this work analyses and compares state-of-the-art task mapping strategies with respect to running time and their quality of solutions to the MPI mapping problem. In particular, the focus is on generic strategies that can be used for arbitrary process/network topologies although, here, the topologies of interest are regular ones, where the number of processes is greater than the number of processors in the underlying physical network. Additionally, different measures of mapping quality are discussed and a close correspondence between the most appropriate, the weighted edge cut, and program execution time is shown. In order to investigate how mapping quality affects MPI program execution time, some mapping strategies have been incorporated into Open MPI. Finally, benchmark results prove that optimized process-to-processor mappings can improve program execution time by up to 60%, compared to the default mapping in many MPI implementations (linear mapping). The findings in this work can serve as reference not only for MPI implementors, but also for researchers investigating static process-to-processor mappings, in general.

Computer hardware and algorithm design have seen significant progress over the years. It is also seen that there are several domains in which humans are more efficient than computers. For example in image recognition, image tagging, natural language understanding and processing, humans often find complicated algorithms quite easy to grasp. This thesis presents the different case studies to learn human mapping strategy to solve the mapping problem in the area of coarse-grained reconfigurable architectures (CGRAs). To achieve optimum level performance and consume less energy in CGRAs, place and route problem has always been a major concern. Making use of human characteristics can be helpful in problems as such, through pattern recognition and experience. Therefore to conduct the case studies a computer mapping game called UNTANGLED was analyzed as a medium to convey insights of human mapping strategies in a variety of architectures. The purpose of this research was to learn from humans so that we can come up with better algorithms to outperform the existing algorithms. We observed how human strategies vary as we present them with different architectures, different architectures with constraints, different visualization as well as how the quality of solution changes with experience. In this work all the case studies obtained from exploiting human strategies provide useful feedback that can improve upon existing algorithms. These insights can be adapted to find the best architectural solution for a particular domain and for future research directions for mapping onto mesh-and- stripe based CGRAs.