Fast Algorithms and Efficient Statistics: N-Point Correlation Functions

Moore, Andrew W.; Connolly, A. J.; Genovese, Christopher R.; Gray, Alexander; Grone, Larry; Kanidoris, Nick; Nichol, R. C.; Schneider, Jeff; Szalay, Alexander S.; Szapudi, István; Wasserman, Larry

doi:10.1007/10849171_5

Cited by 74 publications

(63 citation statements)

References 7 publications

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“…Increasing λ makes N cell larger and for too large λ, the method is slow again. Another scheme relies on a double walk in a quad-tree or a oct-tree according to the dimension of the survey (a hierarchical decomposition of space in cubes/squares and subcubes/subsquares, [461]). This approach is potentially powerful, since it scales as O(N 3/2 g ) according to its authors [461].…”

Section: Estimatorsmentioning

confidence: 99%

“…Another scheme relies on a double walk in a quad-tree or a oct-tree according to the dimension of the survey (a hierarchical decomposition of space in cubes/squares and subcubes/subsquares, [461]). This approach is potentially powerful, since it scales as O(N 3/2 g ) according to its authors [461]. It is also possible to rely on FFT's or fast harmonic transforms at large scales [636], but it requires appropriate treatment of the Fourier coefficients to make sure that the quantity finally measured corresponds to the estimator of interest, e.g.…”

Section: Estimatorsmentioning

confidence: 99%

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Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

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Section: Estimatorsmentioning

confidence: 99%

Section: Estimatorsmentioning

confidence: 99%

Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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“…The algorithm for N = 2 is described next; higher orders are exactly analogous, although more tedious to describe. For details see [21] The spatial configuration of the two-point function is characterized by the distance r between the two points: this should lie within a bin, i.e. b 1 < r ≤ b 2 .…”

Section: N -Point Correlation Functionsmentioning

confidence: 99%

Introduction to Higher Order Spatial Statistics in Cosmology

Szapudi

2008

Data Analysis in Cosmology

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“…Point Correlation (PC) is a data mining algorithm that computes the 2-point correlation statistic by traversing a kd-tree to find, for each point in a data set, how many other points are in a given radius [20]. PC is an unguided algorithm.…”

Section: Benchmarksmentioning

confidence: 99%

General transformations for GPU execution of tree traversals

Goldfarb

Kulkarni

2013

Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

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With the advent of programmer-friendly GPU computing environments, there has been much interest in offloading workloads that can exploit the high degree of parallelism available on modern GPUs. Exploiting this parallelism and optimizing for the GPU memory hierarchy is well-understood for regular applications that operate on dense data structures such as arrays and matrices. However, there has been significantly less work in the area of irregular algorithms and even less so when pointer-based dynamic data structures are involved. Recently, irregular algorithms such as Barnes-Hut and kd-tree traversals have been implemented on GPUs, yielding significant performance gains over CPU implementations. However, the implementations often rely on exploiting application-specific semantics to get acceptable performance. We argue that there are general-purpose techniques for implementing irregular algorithms on GPUs that exploit similarities in algorithmic structure rather than application-specific knowledge. We demonstrate these techniques on several tree traversal algorithms, achieving speedups of up to 38× over 32-thread CPU versions.

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Fast Algorithms and Efficient Statistics: N-Point Correlation Functions

Cited by 74 publications

References 7 publications

Large-scale structure of the Universe and cosmological perturbation theory

Large-scale structure of the Universe and cosmological perturbation theory

Introduction to Higher Order Spatial Statistics in Cosmology

General transformations for GPU execution of tree traversals

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