Proof of the Labastida-Marino-Ooguri-Vafa Conjecture

Based on large N Chern-Simons/topological string duality, in a series of papers, J.M.F. Labastida, M. Marino, H. Ooguri and C. Vafa conjectured certain remarkable new algebraic structure of link invariants and the existence of infinite series of new integer invariants. In this paper, we provide a proof of this conjecture. Moreover, we also show these new integer invariants vanish at large genera.Comment: 57pages, typos corrected, add some detail

Relying on Safe Distance to Achieve Strong Partitionable Group Membership in Ad Hoc Networks

The design of ad hoc mobile applications often requires the availability of a consistent view of the application state among the participating hosts. Such views are important because they simplify both the programming and verification tasks. We argue that preventing the occurrence of unannounced disconnection is essential to constructing and maintaining a consistent view in the ad hoc mobile environment. In this light, we provide the specification for a partitionable group membership service supporting ad hoc mobile applications and propose a protocol for implementing the service. A unique property of this partitionable group membership is that messages sent between group members are guaranteed to be delivered successfully, given appropriate system assumptions. This property is preserved over time despite movement and frequent disconnections. The protocol splits and merges groups and maintains a logical connectivity graph based on a notion of safe-distance. An implementation of the protocol in Java is available for testing. The implementation is used to implement Lime 1, a middleware for mobility that supports transparent sharing of data in both wired and ad hoc wireless environments

Spatiotemporal Multicast and Partitionable Group Membership Service

The recent advent of wireless mobile ad hoc networks and sensor networks creates many opportunities and challenges. This thesis explores some of them. In light of new application requirements in such environments, it proposes a new multicast paradigm called spatiotemporal multicast for supporting ad hoc network applications which require both spatial and temporal coordination. With a focus on a special case of spatiotemporal multicast, called mobicast, this work proposes several novel protocols and analyzes their performances. This dissertation also investigates implications of mobility on the classical group membership problem in distributed computing, proposes a new specification for a partitionable group membership service catering to applications on wireless mobile ad hoc networks, and provides a mobility-aware algorithm and middleware for this service. The results of this work bring new insights into the design and analysis of spatiotemporal communication protocols and fault-tolerant computing in wireless mobile ad hoc networks

OLTP on Hardware Islands

Modern hardware is abundantly parallel and increasingly heterogeneous. The numerous processing cores have non-uniform access latencies to the main memory and to the processor caches, which causes variability in the communication costs. Unfortunately, database systems mostly assume that all processing cores are the same and that microarchitecture differences are not significant enough to appear in critical database execution paths. As we demonstrate in this paper, however, hardware heterogeneity does appear in the critical path and conventional database architectures achieve suboptimal and even worse, unpredictable performance. We perform a detailed performance analysis of OLTP deployments in servers with multiple cores per CPU (multicore) and multiple CPUs per server (multisocket). We compare different database deployment strategies where we vary the number and size of independent database instances running on a single server, from a single shared-everything instance to fine-grained shared-nothing configurations. We quantify the impact of non-uniform hardware on various deployments by (a) examining how efficiently each deployment uses the available hardware resources and (b) measuring the impact of distributed transactions and skewed requests on different workloads. Finally, we argue in favor of shared-nothing deployments that are topology- and workload-aware and take advantage of fast on-chip communication between islands of cores on the same socket.Comment: VLDB201

On Seifert fibered spaces embedding in 4-space, bounding definite manifolds and quasi-alternating Montesinos links

This dissertation is concerned with the question of which Seifert fibered spaces smoothly embed in the 4-sphere and the related question of which Seifert fibered spaces bound both a positive definite and a negative definite smooth 4-manifold. Using Donaldson’s diagonalization theorem we derive strong obstructions in both of these settings. We construct new embeddings of Seifert fibered spaces in S⁴ out of old ones, giving many new examples of Seifert fibered spaces which embed in S⁴ . Our results allow us to classify precisely when a Seifert fibered space over an orientable base surface smoothly embeds in S⁴ provided e > k/2, where e is the normalized central weight and k is the number of singular fibers. Based on these results and an analysis of the Neumann-Siebenmann invariant [mu with macron], we make some conjectures concerning Seifert fibered spaces which embed in S⁴. Finally, we classify the quasi-alternating Montesinos links, showing that a Montesinos link L is quasialternating if and only if its double branched cover is an L-space which bounds definite manifolds of both signs with torsion-free first homologyMathematic

Heterogeneous computing with an algorithmic skeleton framework

The Graphics Processing Unit (GPU) is present in almost every modern day personal computer. Despite its specific purpose design, they have been increasingly used for general computations with very good results. Hence, there is a growing effort from the community to seamlessly integrate this kind of devices in everyday computing. However, to fully exploit the potential of a system comprising GPUs and CPUs, these devices should be presented to the programmer as a single platform. The efficient combination of the power of CPU and GPU devices is highly dependent on each device’s characteristics, resulting in platform specific applications that cannot be ported to different systems. Also, the most efficient work balance among devices is highly dependable on the computations to be performed and respective data sizes. In this work, we propose a solution for heterogeneous environments based on the abstraction level provided by algorithmic skeletons. Our goal is to take full advantage of the power of all CPU and GPU devices present in a system, without the need for different kernel implementations nor explicit work-distribution.To that end, we extended Marrow, an algorithmic skeleton framework for multi-GPUs, to support CPU computations and efficiently balance the work-load between devices. Our approach is based on an offline training execution that identifies the ideal work balance and platform configurations for a given application and input data size. The evaluation of this work shows that the combination of CPU and GPU devices can significantly boost the performance of our benchmarks in the tested environments, when compared to GPU-only executions

Communities of Minima in Local Optima Networks of Combinatorial Spaces

In this work we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we shortly discuss the consequences of the findings for heuristically searching the corresponding problem spaces