Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis

A method of counts-in-cells analysis of galaxy distribution is investigated with arbitrary smoothing functions in obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, considering a series of $m$-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second moments of counts-in-cells as a first step. We analytically derive the covariance matrix among different smoothing scales of cells, taking into account possible overlaps between cells. We find that the Epanechnikov kernel of $m=1$ is better than top-hat and Gaussian smoothing functions in estimating cosmological parameters. As an example, we estimate expected parameter bounds which comes only from the analysis of second moments of galaxy distributions in a survey which is similar to the Sloan Digital Sky Survey.Comment: 33 pages, 10 figures, accepted for publication in PASJ (Vol.59, No.1 in press

Uncovering Causality from Multivariate Hawkes Integrated Cumulants

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database

An improved cosmological parameter inference scheme motivated by deep learning

Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have measured the effect, and there are currently running, and planned efforts to provide even larger, and higher resolution weak lensing maps. Due to nonlinearities on small scales, the traditional analysis with two-point statistics does not fully capture all the underlying information. Multiple inference methods were proposed to extract more details based on higher order statistics, peak statistics, Minkowski functionals and recently convolutional neural networks (CNN). Here we present an improved convolutional neural network that gives significantly better estimates of $\Omega_m$ and $\sigma_8$ cosmological parameters from simulated convergence maps than the state of art methods and also is free of systematic bias. We show that the network exploits information in the gradients around peaks, and with this insight, we construct a new, easy-to-understand, and robust peak counting algorithm based on the 'steepness' of peaks, instead of their heights. The proposed scheme is even more accurate than the neural network on high-resolution noiseless maps. With shape noise and lower resolution its relative advantage deteriorates, but it remains more accurate than peak counting