Data Management and Mining in Astrophysical Databases

We analyse the issues involved in the management and mining of astrophysical data. The traditional approach to data management in the astrophysical field is not able to keep up with the increasing size of the data gathered by modern detectors. An essential role in the astrophysical research will be assumed by automatic tools for information extraction from large datasets, i.e. data mining techniques, such as clustering and classification algorithms. This asks for an approach to data management based on data warehousing, emphasizing the efficiency and simplicity of data access; efficiency is obtained using multidimensional access methods and simplicity is achieved by properly handling metadata. Clustering and classification techniques, on large datasets, pose additional requirements: computational and memory scalability with respect to the data size, interpretability and objectivity of clustering or classification results. In this study we address some possible solutions.Comment: 10 pages, Late

The Sunyaev Zel'dovich effect: simulation and observation

The Sunyaev Zel'dovich effect (SZ effect) is a complete probe of ionized baryons, the majority of which are likely hiding in the intergalactic medium. We ran a $512^3$ $\Lambda$CDM simulation using a moving mesh hydro code to compute the statistics of the thermal and kinetic SZ effect such as the power spectra and measures of non-Gaussianity. The thermal SZ power spectrum has a very broad peak at multipole $l\sim 2000-10^4$ with temperature fluctuations $\Delta T \sim 15\mu$K. The power spectrum is consistent with available observations and suggests a high $\sigma_8\simeq 1.0$ and a possible role of non-gravitational heating. The non-Gaussianity is significant and increases the cosmic variance of the power spectrum by a factor of $\sim 5$ for $l<6000$. We explore optimal driftscan survey strategies for the AMIBA CMB interferometer and their dependence on cosmology. For SZ power spectrum estimation, we find that the optimal sky coverage for a 1000 hours of integration time is several hundred square degrees. One achieves an accuracy better than 40% in the SZ measurement of power spectrum and an accuracy better than 20% in the cross correlation with Sloan galaxies for $2000<l<5000$. For cluster searches, the optimal scan rate is around 280 hours per square degree with a cluster detection rate 1 every 7 hours, allowing for a false positive rate of 20% and better than 30% accuracy in the cluster SZ distribution function measurement.Comment: 34 pages, 20 figures. Submitted to ApJ. Simulation maps have been replaced by high resolution images. For higher resolution color images, please download from http://www.cita.utoronto.ca/~zhangpj/research/SZ/ We corrected a bug in our analysis. the SZ power spectrum decreases 50% and y parameter decrease 25

Geometric modeling and optimization over regular domains for graphics and visual computing

The effective construction of parametric representation of complicated geometric objects can facilitate many design, analysis, and simulation tasks in Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM), and Computer-Aided Engineering (CAE). Given a 3D shape, the procedure of finding such a parametric representation upon a canonical domain is called geometric parameterization. Regular geometric regions, such as polycubes and spheres, are desirable domains for parameterization. Parametric representations defined upon regular geometric domains have many desirable mathematical properties and can facilitate or simplify various surface/solid modeling and processing computation. This dissertation studies the construction of parameterization on regular geometric domains and explores their applications in shape modeling and computer-aided design. Specifically, we studies (1) the surface parameterization on the spherical domain for closed genus-zero surfaces; (2) the surface parameterization on the polycube domain for general closed surfaces; and (3) the volumetric parameterization for 3D-manifolds embedded in 3D Euclidean space. We propose novel computational models to solve these geometric problems. Our computational models reduce to nonlinear optimizations with various geometric constraints. Hence, we also need to explore effective optimization algorithms. The main contributions of this dissertation are three-folded. (1) We developed an effective progressive spherical parameterization algorithm, with an efficient nonlinear optimization scheme subject to the spherical constraint. Compared with the state-of-the-art spherical mapping algorithms, our algorithm demonstrates the advantages of great efficiency, lower distortion, and guaranteed bijectiveness, and we show its applications in spherical harmonic decomposition and shape analysis. (2) We propose a first topology-preserving polycube domain optimization algorithm that simultaneously optimizes polycube domain together with the parameterization to balance the mapping distortion and domain simplicity. We develop effective nonlinear geometric optimization algorithms dealing with variables with and without derivatives. This polycube parameterization algorithm can benefit the regular quadrilateral mesh generation and cross-surface parameterization. (3) We develop a novel quaternion-based optimization framework for 3D frame field construction and volumetric parameterization computation. We demonstrate our constructed 3D frame field has better smoothness, compared with state-of-the-art algorithms, and is effective in guiding low-distortion volumetric parameterization and high-quality hexahedral mesh generation

Solid reconstruction using recognition of quadric surfaces from orthographic views

International audienceThe reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided