Related papers: New Interpretable Statistics for Large Scale Struc…
This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via…
In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PDE systems can be reformulated as WHFs. We use parameterized…
It is important to properly correct for measurement error when estimating density functions associated with biomedical variables. These estimators that adjust for measurement error are broadly referred to as density deconvolution…
We study signatures of primordial non-Gaussianity (PNG) in the redshift-space halo field on non-linear scales, using a combination of three summary statistics, namely the halo mass function (HMF), power spectrum, and bispectrum. The choice…
Good statistics for measuring large-scale structure in the Universe must be able to distinguish between different models of structure formation. In this paper, two and three dimensional ``counts in cell" statistics and a new ``discrete…
The thermal state of the intergalactic medium (IGM) contains vital information about the epoch of reionization, one of the most transformative yet poorly understood periods in the young universe. This thermal state is encoded in the…
Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many…
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point…
Upcoming surveys such as \LSST{} and \Euclid{} will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics…
Relativistic ultracompact objects without an event horizon may be able to form in nature and merge as binary systems, mimicking the coalescence of ordinary black holes. The postmerger phase of such processes presents characteristic…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
We undertake a careful analysis of stochastic gravitational wave production from cosmological phase transitions in an expanding universe, studying both a standard radiation as well as a matter dominated history. We analyze in detail the…
Beyond the linear regime, Fourier modes of cosmological random fields become correlated, and the power spectrum of density fluctuations contains only a fraction of the available cosmological information. To unveil this formerly hidden…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…