Related papers: Cumulant mapping as the basis of multi-dimensional…
Cumulant mapping has been recently suggested [Frasinski, Phys. Chem. Chem. Phys. 24, 207767 (2022)] as an efficient approach to observing multi-particle fragmentation pathways, while bypassing the restrictions of the usual…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…
The quantum statistics of damped optical solitons is studied using cumulant-expansion techniques. The effect of absorption is described in terms of ordinary Markovian relaxation theory, by coupling the optical field to a continuum of…
We describe here an iterative method for jointly estimating the noise power spectrum from a scanning experiment's time-ordered data, together with the maximum-likelihood map. We test the robustness of this method on simulated datasets with…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
We present a new method for analyzing multi--detector maps containing contributions from several components. Our method, based on matching the data to a model in the spectral domain, permits to estimate jointly the spatial power spectra of…
Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant.…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
Extended derivations regarding the cumulant-based formulation of higher-order fluorescence correlation spectroscopy (FCS) are presented. First, we review multivariate cumulants and their relation to photon counting distributions in single…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
We reconcile for the first time the strict mathematical formalism of multivariate cumulants with the usage of cumulants in anisotropic flow analyses in high-energy nuclear collisions. This reconciliation yields to the next generation of…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…