Cumulant mapping as the basis of multi-dimensional spectrometry

TL;DR

This paper develops a comprehensive theoretical framework for cumulant mapping in multi-dimensional spectrometry, enabling improved statistical reconstruction of molecular fragmentation data and assessing experimental feasibility.

Contribution

It formalizes and extends covariance mapping methods, deriving explicit formulas for cumulants up to the 6th order and their variances, including considerations for detection efficiency and background noise.

Findings

Derived formulas for cumulants up to 6th order

Provided methods to estimate sample size for noise suppression

Assessed feasibility for femtosecond and x-ray laser experiments

Abstract

Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae have been derived for the expected values of up to the 6th cumulant and the variance has been calculated for up to the 4th cumulant. A method of extending these formulae to higher cumulants has been described. The formulae take into account reduced fragment detection efficiency and a background from uncorrelated events. Number of samples needed for suppressing the statistical noise to a required level can be estimated using Matlab code included in Supplemental Material. The theory can be used to assess the experimental feasibility of studying molecular fragmentations induced by femtosecond or x-ray free-electron lasers. It is also relevant for extending the conventional mass spectrometry of biomolecules to multiple dimensions.