We produce explicit geometric representatives of non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live off of the vanishing line of a homology spectral sequence due to Sinha. We use con figuration space integrals to show our classes pair non-trivially with cohomology classes due to Longoni. We then give an alternate formula for the first differential in the homology spectral sequence due to Sinha. This differential connects the geometry of the cycles we define to the combinatorics of the spectral sequence. The new formula for the differential also simplifies calculations in the spectral sequence.

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No / We describe the work of the European project QUASI (Quantum Simulation in Industry, project EP25047) which has sought to develop a flexible QM/MM scheme and to apply it to a range of industrial problems. A number of QM/MMapproaches were implemented within the computational chemistry scripting system, ChemShell, which provides the framework for deploying a variety of independent program packages. This software was applied in several large-scale QM/MM studies which addressed the catalytic decomposition of N2O by Cu-containing zeolites, the methanol synthesis reaction catalysed by Cu clusters supported on ZnO surfaces, and the modelling of enzyme structure and reactivity.

No description available.

A point-set embedding of a planar graph G with n vertices on a set S of n points is a planar straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. We prove that the point-set embeddability problem is NP-complete for 3-connected planar graphs, answering a question of Cabello [20]. We give an O(nlog^3n)-time algorithm for testing point-set embeddability of plane 3-trees, improving the algorithm of Moosa and Rahman [60]. We prove that no set of 24 points can support all planar 3-trees with 24 vertices, partially answering a question of Kobourov [55]. We compute 2-bend point-set embeddings of plane 3-trees in O(W^2) area, where W is the length of longest edge of the bounding box of S. Finally, we design algorithms for testing convex point-set embeddability of klee graphs and arbitrary planar graphs.

A point-set embedding of a planar graph G with n vertices on a set S of n points is a planar straight-line drawing of G, where each vertex of G is mapped to a distinct point of S. We prove that the point-set embeddability problem is NP-complete for 3-connected planar graphs, answering a question of Cabello [20]. We give an O(nlog^3n)-time algorithm for testing point-set embeddability of plane 3-trees, improving the algorithm of Moosa and Rahman [60]. We prove that no set of 24 points can support all planar 3-trees with 24 vertices, partially answering a question of Kobourov [55]. We compute 2-bend point-set embeddings of plane 3-trees in O(W^2) area, where W is the length of longest edge of the bounding box of S. Finally, we design algorithms for testing convex point-set embeddability of klee graphs and arbitrary planar graphs.

As businesses are increasingly relying on the cloud to host their services, cloud providers are striving to offer guaranteed and highly-available resources. To achieve this goal, recent proposals have advocated to offer both computing and networking resources in the form of Virtual Data Centers (VDCs). However, to offer VDCs, cloud providers have to overcome several technical challenges. In this thesis, we focus on two key challenges: (1) the VDC embedding problem: how to efficiently allocate resources to VDCs such that energy costs and bandwidth consumption are minimized, and (2) the availability-aware VDC embedding and backup provisioning problem which aims at allocating resources to VDCs with hard guarantees on their availability. The first part of this thesis is primarily concerned with the first challenge. The goal of the VDC embedding problem is to allocate resources to VDCs while minimizing the bandwidth usage in the data center and maximizing the cloud provider's revenue. Existing proposals have focused only on the placement of VMs and ignored mapping of other types of resources like switches. Hence, we propose a new VDC embedding solution that explicitly considers the embedding of virtual switches in addition to virtual machines and communication links. Simulations show that our solution results in high acceptance rate of VDC requests, less bandwidth consumption in the data center network, and increased revenue for the cloud provider. In the second part of this thesis, we study the availability-aware VDC embedding and backup provisioning problem. The goal is to provision virtual backup nodes and links in order to achieve the desired availability for each VDC. Existing solutions addressing this challenge have overlooked the heterogeneity of the data center equipment in terms of failure rates and availability. To address this limitation, we propose a High-availability Virtual Infrastructure (Hi-VI) management framework that jointly allocates resources for VDCs and their backups while minimizing total energy costs. Hi-VI uses a novel technique to compute the availability of a VDC that considers both (1) the heterogeneity of the data center networking and computing equipment, and (2) the number of redundant virtual nodes and links provisioned as backups. Simulations demonstrate the effectiveness of our framework compared to heterogeneity-oblivious solutions in terms of revenue and the number of physical servers used to embed VDCs.

Embedding of virtual network (VN) requests on top of a shared physical network poses an intriguing combination of theoretical and practical challenges. Two major problems with the state-of-the-art VN embedding algorithms are their indifference to the underlying substrate topology and their lack of re-optimization mechanisms for already embedded VN requests. We argue that topology-aware embedding together with re-optimization mechanisms can improve the performance of the previous VN embedding algorithms in terms of acceptance ratio and load balancing. The major contributions of this thesis are twofold: (1) we present a mechanism to differentiate among resources based on their importance in the substrate topology, and (2) we propose a set of algorithms for re-optimizing and re-embedding initially-rejected VN requests after fixing their bottleneck requirements. Through extensive simulations, we show that not only our techniques improve the acceptance ratio, but they also provide the added benefit of balancing load better than previous proposals. The metrics we use to validate our techniques are improvement in acceptance ratio, revenue-cost ratio, incurred cost, and distribution of utilization.

Embedding of virtual network (VN) requests on top of a shared physical network poses an intriguing combination of theoretical and practical challenges. Two major problems with the state-of-the-art VN embedding algorithms are their indifference to the underlying substrate topology and their lack of re-optimization mechanisms for already embedded VN requests. We argue that topology-aware embedding together with re-optimization mechanisms can improve the performance of the previous VN embedding algorithms in terms of acceptance ratio and load balancing. The major contributions of this thesis are twofold: (1) we present a mechanism to differentiate among resources based on their importance in the substrate topology, and (2) we propose a set of algorithms for re-optimizing and re-embedding initially-rejected VN requests after fixing their bottleneck requirements. Through extensive simulations, we show that not only our techniques improve the acceptance ratio, but they also provide the added benefit of balancing load better than previous proposals. The metrics we use to validate our techniques are improvement in acceptance ratio, revenue-cost ratio, incurred cost, and distribution of utilization.

With smaller electronic devices and higher transmission speeds, a digital circuit will cause potential electromagnetic interference (EMI) and signal integrity (SI) problems. Nowadays, the flexible printed circuit board (FPC) is widely used in electronic systems, especially in the video circuit. In this thesis, we used transmission line model to explain effect of the structure of the flexible printed circuit board transmission lines. Eye-diagram is a fast and convenient tool to analyze the quality of the high speed transmission, and we can use the equivalent model to substitute for the electromagnetic (EM) model to simulate the performance. We used differential circuit and the reflection gain to increase the height and width parameters of Eye-diagram, and make the quality of signal transmission higher. For video driver circuit, since the terminal resistance is different depending on whether the IC is on or off, the standard probe cannot measure mixed-mode S-parameter directly due to the connectors. Thus, we provided a de-embedding method to remove the effects of high speed interconnect line on the test board. Finally, we use a simple structure to verify the method, and it can be used to measure mixed-mode S-parameter on the standard of Mobile Industry Processor Interface (MIPI) for D-PHY, v0.90.00.