An efficient method for pattern discovery from discrete time series is introduced in this paper. The method utilizes two parallel streams of data, a discrete unit time-series and a set of labeled events, From these inputs it builds associative models between systematically co-occurring structures existing in both streams. The models are based on transitional probabilities of events at several d...

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire inte...

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

Discrete Wavelet Transform is a data transformation method that represents in the time domain and frequency domain. This appears to overcome weakness of Fourier transform which only able provide one information limited certain windowing . The type wavelet used Haar Wavelet. Identification periodicity using Periodogram analysis with Fisher's Test statistics. transformed decomposed into two compo...

Let G be a reductive algebraic group over Q, and suppose that Γ ⊂ G(R) is an arithmetic subgroup defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in L2(Γ\G(R)), and in general to determine the traces of Hecke operators on these spaces. In this paper we give a conjectural formula for the traces of Hecke operator...