An alternative parametric description for discrete random variables, called muculants, is proposed. Contrary to cumulants, muculants are based on the Fourier series expansion rather than on the Taylor series expansion of the logarithm of the characteristic function. Utilizing results from cepstral theory, elementary properties of muculants are derived. A connection between muculants and cumulan...

In this paper, we propose an automatic modulation classification scheme for digitally modulated signals, such as MSK, GMSK, BPSK, QPSK, 8-PSK, 16-QAM, 32-QAM, and 64-QAM. As features which characterize the modulation type, higher order cyclic cumulants up to eighth order of the signal are used. For feature classification, a Gaussian mixture model based algorithm is used. Simulation results are ...

We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results are supported by extensive numerical simulations. It is found that the order parameter equations are completely equivalent to those of the Generating Functional Method, which means that crosstalk noise follows normal distribution even in th...

We show that the values of first three cumulants baryon number distribution can be used to calculate isothermal speed sound and its logarithmic derivative with respect density. discuss applications this result heavy-ion collision experiments address possible challenges, including effects due conservation, differences between proton cumulants, influence finite statistics on fluctuation observabl...

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerati...

We introduce the notion of cumulants as applied to linear maps between associative (or commutative) algebras that are not compatible with algebraic product structure. These have a close relationship $$A_{\infty }$$ and $$C_{\infty morphisms, which classical homotopical tools for analyzing deformations algebraically maps. look at these two different perspectives understand how infinity-morphisms...