标题： 宇宙微波背景地图的闵可夫斯基泛函和聚类分析 显示英文标题

标题： Minkowski Functionals and Cluster Analysis for CMB Maps

摘要： 我们提出了针对宇宙微波背景（CMB）地图的新统计方法，这些方法对非高斯特征敏感。 这些统计方法是已经用于宇宙学中的几何和拓扑方法的自然推广，例如累积分布函数和基因型。 我们计算了超出或低于恒定温度阈值的超越集部分闵可夫斯基泛函的分布函数。 闵可夫斯基泛函是可加的，并且平移和旋转不变。 因此，它们可以用于斑块状和/或不完整的覆盖区域。 该技术在计算上非常高效（它只需要O(N)操作，其中N是一个阈值级别的像素数）。 此外，它允许将大数据集分割为较小的子集。 只有在非常大的数据集上才能充分发挥这些统计方法的优势。 我们将其应用于经过银河系污染校正的COBE DMR 4年数据，以说明该技术的应用。 显示英文摘要

摘要： We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, it allows to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.