This work aims at extracting the cosmological information content of the several cosmic web environments. While we know that the matter power spectrum is not containing all the information about hte underlying cosmological model, we can wonder wether the environments are enclosing different types of information that one can use to break some of the degeneracies among parameters of the model. In particular, we show that a simple two-point correlator becomes sensitive to higher-order features when we have a look at the environments instead of the full matter distribution.

The extraction of patterns from spatially structured point-cloud datasets is ubiquitous in many fields of science. In this work, we address the case of extracting one-dimensional structure from such data by formulating the problems in terms of a regularised version of a mixture model.

The task of clustering point-cloud data is nowadays believed to be either easy to carry or uninformative because the lack of knowledge (number of clusters, sizes, etc.) on the underlying pattern. This work proposes to use a statistical physics formulation of the clustering performed by means of a Gaussian Mixture Model to alleviate some of the drawbacks of the clustering task. In particular, it shows that we can explore the dataset to obtain several key information on the number of clusters, their size and how they are embedded in space, even in high dimensions.