The problem of estimating the log-spectrum of a stationary Gaussian time series by Bayesianly induced shrinkage of empirical wavelet coefficients is studied. A model in the wavelet domain that accounts for distributional properties of the log-periodogram at levels of fine detail and approximate normality at coarse levels in the wavelet decomposition, is proposed. The smoothing procedure, called...

The nature and extent of microbial biodiversity remain controversial with persistent debates over patterns of distributions (i.e. cosmopolitanism versus endemism) and the processes that structure these patterns (neutrality versus selection). We used culture-independent approaches to address these issues focusing on two groups of ciliates, the Oligotrichia (Spirotrichea) and Choreotrichia (Spiro...

A sequence of complex numbers is holonomic if it satisfies a linear recurrence with polynomial coefficients. A power series is holonomic if it satisfies a linear differential equation with polynomial coefficients, which is equivalent to its coefficient sequence being holonomic. It is well known that all algebraic power series are holonomic. We show that the analogous statement for sequences is ...

(To the memory of S. Minakshisundaram) 1. In the second paper of this series we proved the following two theorems. Let Sn stand for the symmetric group with n letters, P a generic element of it and O(P) its order. Then we have THEOREM A. For almost all P's in Sn , i .e. with the exception of o(n!) P's at most, 0(P) is divisible by all prime powers not exceeding log n 1 + 3 log log log n w(n) lo...

The author continues to study series transformations for the Euler-Mascheroni constant γ . Here, we discuss in detail recently published results of A. I. Aptekarev and T. Rivoal who found rational approximations to γ and γ log q q ∈ Q>0 defined by linear recurrence formulae. The main purpose of this paper is to adapt the concept of linear series transformations with integral coefficients such t...

This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis for factorizations other than the well-known binary and ternary basis. We show that is possible to reduce the overall complexity for the usual binary decompos...

The tails of the Taylor series for many standard functions such as arctan and log can be expressed as continued fractions in a variety of ways. A surprising side effect is that some of these continued fractions provide a dramatic acceleration for the underlying power series. These investigations were motivated by a surprising observation about Gregory’s series. Gregory’s series for π, truncated...

Detecting stratigraphic discontinuities using well log data is a fundamental task in petroleum geosciences projects. Wavelet transforms (WT) and S-transform (ST) of well log data can provide objective identification of lithological interfaces to aid in this effort. The continuous wavelet transform (CWT) of a time series gives the wavelet correlation coefficients (i.e. similarity) between the gi...