This dissertation seeks to describe advancements made in computational methods for multi-messenger astrophysics (MMA) using gravitational waves GW and neutrinos during Advanced LIGO (aLIGO)’s first through third observing runs (O1-O3) and, looking forward, to describe novel computational techniques suited to the challenges of both the burgeoning MMA field and high-performance computing as a whole. The first two chapters provide an overview of MMA as it pertains to gravitational wave/high energy neutrino (GWHEN) searches, including a summary of expected astrophysical sources as well as GW, neutrino, and gamma-ray detectors used in their detection. These are followed in the third chapter by an in-depth discussion of LIGO’s timing system, particularly the diagnostic subsystem, describing both its role in MMA searches and the author’s contributions to the system itself. The fourth chapter provides a detailed description of the Low-Latency Algorithm for Multi-messenger Astrophysics (LLAMA), the GWHEN pipeline developed by the author and used in O2 and O3. Relevant past multi-messenger searches are described first, followed by the O2 and O3 analysis methods, the pipeline’s performance, scientific results, and finally, an in-depth account of the library’s structure and functionality. In particular, the author’s high-performance multi-order coordinates (MOC) HEALPix image analysis library, HPMOC, is described. HPMOC increases performance of HEALPix image manipulations by several orders of magnitude vs. naive single-resolution approaches while presenting a simple high-level interface and should prove useful for diverse future MMA searches. The performance improvements it provides for LLAMA are also covered. The final chapter of this dissertation builds on the approaches taken in developing HPMOC, presenting several novel methods for efficiently storing and analyzing large data sets, with applications to MMA and other data-intensive fields. A family of depth-first multi-resolution ordering of HEALPix images — DEPTH9, DEPTH19, and DEPTH40 — is defined, along with algorithms and use cases where it can improve on current approaches, including high-speed streaming calculations suitable for serverless compute or FPGAs. For performance-constrained analyses on HEALPix data (e.g. image analysis in multi-messenger search pipelines) using SIMD processors, breadth-first data structures can provide short-circuiting calculations in a data-parallel way on compressed data; a simple compression method is described with application to further improving LLAMA performance. A new storage scheme and associated algorithms for efficiently compressing and contracting tensors of varying sparsity is presented; these demuxed tensors (D-Tensors) have equivalent asymptotic time and space complexity to optimal representations of both dense and sparse matrices, and could be used as a universal drop-in replacement to reduce code complexity and developer effort while improving performance of existing non-optimized numerical code. Finally, the big bucket hash table (B-Table), a novel type of hash table making guarantees on data layout (vs. load factor), is described, along with optimizations it allows for (like hardware acceleration, online rebuilds, and hard realtime applications) that are not possible with existing hash table approaches. These innovations are presented in the hope that some will prove useful for improving future MMA searches and other data-intensive applications.

Orientador: Diego Sebastian Ledesma / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:36:25Z (GMT). No. of bitstreams: 1 Paula_PedroManfrimMagalhaesde_M.pdf: 1130226 bytes, checksum: bbd8d375ddf7846ed2eafe024103e682 (MD5) Previous issue date: 2015 / Resumo: Este trabalho apresenta um estudo sobre variedades Riemannianas que possuem um tensor de Bakry-Émery-Ricci com limitações. Inicialmente abordamos tanto aspectos da geometria Riemanniana tradicional como métricas e geodésicas, quanto aspectos mais avançados como as fórmulas de Bochner, Weitzenböck e o teorema de Hodge. Em seguida discutimos a convergência de Gromov-Hausdorff e suas propriedades, além de serem apresentados alguns teoremas como os de Kasue e Fukaya. Por fim estudamos as propriedades topológicas e geométricas de variedades com limitação no tensor de Bakry-Émery-Ricci e o comportamento de tais limitações com respeito à submersões e à convergência de Gromov-Hausdorff / Abstract: This work presents a study about Riemannian manifolds having a Bakry-Émery-Ricci tensor with bounds. Initially we approached both the traditional aspects of Riemannian geometry like metrics and geodesics, as more advanced aspects like the Bochner, Weitzenböck formulas and the Hodge's theorem. Then we discussed the Gromov-Hausdorff convergence and its properties, in addition to showing some theorems as those from Kasue and Fukaya. Lastly we studied the topological and geometric properties of manifolds with bounds on the Bakry-Émery-Ricci tensor and the behavior of these bounds with respect to submersions and the Gromov-Hausdorff convergence / Mestrado / Matematica / Mestre em Matemática

Supervised learning tasks like building a classifier, estimating the error rate of the predictors, are typically performed with labeled data. In most cases, obtaining labeled data is costly as it requires manual labeling. On the other hand, unlabeled data is available in abundance. In this thesis, we discuss methods to perform supervised learning tasks with no labeled data. We prove consistency of the proposed methods and demonstrate its applicability with synthetic and real world experiments. In some cases, small quantities of labeled data maybe easily available and supplemented with large quantities of unlabeled data (semi-supervised learning). We derive the asymptotic efficiency of generative models for semi-supervised learning and quantify the effect of labeled and unlabeled data on the quality of the estimate. Another independent track of the thesis is efficient computational methods for nonnegative tensor factorization (NTF). NTF provides the user with rich modeling capabilities but it comes with an added computational cost. We provide a fast algorithm for performing NTF using a modified active set method called block principle pivoting method and demonstrate its applicability to social network analysis and text mining.