We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the...

There are two major approaches for blind separation: Maximum Entropy (ME) and Minimum Mutual Information (MMI). Both can be implemented by the stochastic gradient descent method for obtaining the de-mixing matrix. The MI is the contrast function for blind separation while the entropy is not. To justify the ME, the relation between ME and MMI is rstly elucidated by calculating the rst derivative...

We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship o...

We use a concrete shelling order of chessboard complexes ∆n,m for m > 2n − 1 to describe the type of each facet of ∆n,m in this order. Further, we find some recursive relations for h-vector, describe the generating facets of shellable ∆n,m and show that the number of generating facets of ∆n,m is the value of a special Poisson-Charlier polynomial pn(m). Some of these results can be extended to c...

Independent component analysis (ICA) is the decomposition of a random vector in linear components which are “as independent as possible.” Here, “independence” should be understood in its strong statistical sense: it goes beyond (second-order) decorrelation and thus involves the nonGaussianity of the data. The ideal measure of independence is the “mutual information” and is known to be related t...

An analytical technique based on Gram–Charlier series expansion is presented for the computation of the error probability of equal-gain combiner (EGC) with partially coherent fading signals. Imperfect carrier recovery is attributed to the random noise present in the carrier recovery loops. The resulting noisy phase references are assumed to satisfy Tikhonov distribution. The fades on the divers...

X-ray diffraction data in heavy-atom compounds may be sensitive to anharmonic atomic displacements, since the large core electron densities result in appreciable scattering amplitudes at large reciprocal distances. Since bonding electron densities may also exhibit sharp features affecting high-order reflections, they may be difficult to distinguish from anharmonic effects. We have analyzed an a...

It is common to characterize the spatial distribution of plant patterns as random, aggregate, or uniform. In this context, a major challenge for researcher choice method identify pattern correctly well factors related it. The vast literature on subject not recent, especially regarding dispersion indices. aim review was conduct critical and temporal analysis these indices test their effectivenes...

Viviane Chenal-Francisque, Caroline Charlier, Saleem Mehvish, Hélène Dieye, Alexandre Leclercq, Patrice Courvalin, Marc Lecuit Institut Pasteur, French National Reference Center and WHO Collaborating Center for Listeria, Paris, France; Institut Pasteur, Biology of Infection Unit, Paris, France; Inserm U1117, Paris, France; Paris Descartes University, Sorbonne Paris Cité, Division of Infectious ...