Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large scale structure of the Universe. In papers I & II of this series we saw that the Spherical Collapse (SC) model provides with the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next to leading orders), indicating negligible tida...

Abstract Mesokurtic projections are linear with null fourth cumulants. They might be useful data pre-processing tools when nonnormality, as measured by the cumulants, is either an opportunity or a challenge. Nonnull cumulants opportunities extreme kurtosis used to identify interesting nonnormal features, for example clusters and outliers. Unfortunately, this approach suffers from curse of dimen...

We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys–Murphy elements—or equivalently—of the transition measure associated with a Young diagram. We express these cumulants in terms of normalized characters of the appropriate representation of the symmetric group Sq. Our analysis considers the case when the Young diagrams rescaled...

This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a suitable polynomial representation of Abel polynomials. The algorithm relies on the classical umbral calculus, a symbolic language introduced by Rota and Taylor...

We analyze in detail the interaction correction to full counting statistics FCS of electron transfer in a quantum contact originating from the electromagnetic environment surrounding the contact. The correction can be presented as a sum of two terms, corresponding to elastic-inelastic electron transfer. Here we primarily focus on the inelastic correction. For our analysis, it is important to un...

In statistical control, the cost function is viewed as a random variable and one optimizes the distribution of the cost function through the cost cumulants. We consider a statistical control problem for a control-affine nonlinear system with a nonquadratic cost function. Using the Dynkin formula, the Hamilton–Jacobi–Bellman equation for the nth cost moment case is derived as a necessary conditi...

An algebraic principle for blind source separation is presented in this paper. This separation principle identi"es a (smaller) set of equations whose solutions can blindly extract non-Gaussian signals. The concept of `Mth-order uncorrelatednessa is introduced and it is proven that for Mth-order uncorrelated source signals, signals with nonzero kth-order cumulant (2(k)M) can always be extracted ...

Fig. 1. Absolute value of the crosstalk with respect to the number of samples (NS) used to estimate the cross cumulants. Each point is the average of 10 experiments. to estimate the cross-cumulants. Each point in Fig. 1 corresponds to the average over 10 experiments, in which the mixing matrix is randomly chosen: The matrix entries mC3 (i # j) are random numbers in the range [-1, +1]. With 500 ...

We introduce a new analysis technique for fluorescence fluctuation data. Time-integrated fluorescence cumulant analysis (TIFCA) extracts information from the cumulants of the integrated fluorescence intensity. TIFCA builds on our earlier FCA theory, but in contrast to FCA or photon counting histogram (PCH) analysis is valid for arbitrary sampling times. The motivation for long sampling times li...