A Fourier-cumulant analysis for multiharmonic flow fluctuation

The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on $$_\mathtt{R}$$ R ++. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.

Cumulative features for determining the type of signal manipulation

This paper describes the apparatus of cumulant analysis in relation to the problem of recognizing the types of signal modulation. The article presents the results of using artificial neural networks in the task of automating the detection of intra-pulse modulation signs for the identification (classification) of signals. A mathematical model of a phase-shift keyed signal is developed, the main properties of this type of signals are described and a method is proposed that allows one to determine the type of signal manipulation based on the calculation of informative (cumulative) features. Simulation was carried out in Matlab/Simulink.

ANALYSIS OF RESIDUES AS METHOD FOR THE FORMALIZATION OF CHANGES IN COMPOSITION WINTER DIESEL FUEL AFTER CAVITATIONAL IMPACT

An example of the cumulant analysis of the work and the quadratic transformation centered and non-centered random variables